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2 shows the mosaic continuum map of sgr b2(n ) and sgr b2(m ) at 1.3 mm . the brightest components of sgr b2(n ) ( i@[email protected] jy beam@xmath4 ) and sgr b2(m ) ( i@[email protected] jy beam@xmath4 ) , are associated with the massive star forming cores k1 - 3 and f1 - 4 ( gaume & claussen 1990 ) , respectively . in addition to the emission from these cores , a few nearby continuum clumps were detected , including the components k4 ( i@[email protected] jy beam@xmath4 ) , ne ( i@[email protected] jy beam@xmath4 ) , nw ( i@[email protected] jy beam@xmath4 ) , me ( i@[email protected] jy beam@xmath4 ) and mw ( i@[email protected] jy beam@xmath4 ) . gaussian fitting to the individual continuum components was carried out . the individual emission clumps near the compact cores or the k1 - 3 and f1 - 4 clusters were modeled as simple gaussian components . the two compact cores , k1 - 3 and f1 - 4 , appeared to be too complicated to be fitted with single gaussian components . a model consisting of a gaussian and two unresolved compact components was used to fit to the data of the core ( k1 - 3 ) . the peaks of the gaussian component and one of the point components are consistent with k3 and k2 positions , respectively . another point component agrees ( within @xmath6 1@xmath33 ) with the 3.5 mm continuum source that is located south of k3 ( see fig.1(b ) of liu & snyder 1999 ) . sgr b2(m ) core ( f1 - 4 ) is fitted well with a gaussian component and a point component ( close to f3 within @xmath6 0@xmath215 ) . the peak positions , deconvolved angular sizes , peak intensities and total flux densities of the continuum components are summarized in table 1 . the components k4 , mw and z10.24 have been detected at radio and millimeter wavelengths ( lis et al . 1993 ; kuan & snyder 1994 ; gaume et al . 1995 ; liu & snyder 1999 ) . z10.24 located in the middle between sgr b2(n ) and sgr b2(m ) ( see fig . 2 ) shows a unique filamentary structure at 1.3 mm continuum . the designation of z10.24 follows that used by gaume et al . ( 1995 ) and de pree et al . ( 1996 ) who detected the h66@xmath34 line towards it . z10.24 was marginally detected at 1.3 mm by lis et al . ( 1993 ) with higher angular resolution ( 4@xmath35 ) and poorer sensitivity . the sma observations show an elongated structure in z10.24 with a peak intensity of 2.02 @xmath3 0.16 jy beam@xmath4 ( 12 @xmath28 ) . the core of z10.24 is unresolved in the sub - arcsec resolution images at both 1.3 cm and 3.5 mm ( gaume et al . 1995 ; liu & snyder 1999 ) . the 1.3 mm continuum image and the detected vibrational hc@xmath26n emission ( de vicente et al . 2000 ) suggest that the 1.3 mm continuum of z10.24 is dominated by the dust emission and z10.24 is likely to be a younger massive star formation region . there have been no detections of the components nw , ne and me in the previous observations at longer wavelengths . these three components are possibly the dust emission from sub - cores at a relatively early stage of star formation . the detections need to be verified with further observations at shorter wavelengths and at higher angular resolutions . the continuum - free channel maps in both h@xmath7co ( 3@xmath23 ) and h@xmath7co ( 3@xmath25 ) lines were constructed in the velocity range from 8 to 151 km s@xmath4 at intervals of 1 km s@xmath4 . the channel maps of the h@xmath7co transitions are complicated , containing several kinematical features in either emission or absorption . those emission and absorption components are separated well in our higher spectral resolution maps but some of them ( in the continuum core regions ) are overlapped . in the moment analysis , the negative intensity value from the absorption and the positive value from the emission may cancel each other in the overlapping regions and thus the resultant moment maps might not reflect the true gas distribution . hence , the emission and absorption need to be handled separately . fig . 3 is the integrated line emission images constructed from the channel maps for the two transitions , h@xmath7co ( @xmath2 ) and ( @xmath1 ) , respectively . the moment 0 images were made with a 4 @xmath28 cutoff in each channel maps . the less significant emission and the absorption are excluded in the moment analysis . most of emission is distributed around the two cores of sgr b2(n ) and sgr b2(m ) . clearly , the distribution of the h@xmath7co emission is not spherically symmetric with respect to each of these cores . in the sgr b2(n ) region , in addition to the gas concentration at the core , gas clumps located north - east and south - west of the core are observed in both h@xmath7co transitions . we note that in sgr b2(n ) , the morphology of h@xmath7co ( @xmath2 ) emission , the higher transition gas , is similar to that of the emission from the lower transition gas h@xmath7co ( @xmath1 ) . hereafter we refer h@xmath7co ( @xmath2 ) as the higher transition and h@xmath7co ( @xmath1 ) as the lower transition . in the sgr b2(m ) region , a strong emission component elongated in northwest - southeast direction is observed in both h@xmath7co transitions . an arch structure ( m1 30@xmath33 long and 10@xmath33 wide ) , 8@xmath33 northwest of the sgr b2(m ) core appears in both h@xmath7co transitions . the major difference in the emission distribution from the two transitions occurs in the outflow ( lis et al . 1993 ) region located south - east of the sgr b2(m ) core . a significant emission `` tongue '' ( m5 ) ( 15@xmath36 ) was detected from the higher h@xmath7co transition gas while no significant detection was made of the lower h@xmath7co transition gas . based on a line survey at 340 ghz from single dish observations , sutton et al . ( 1991 ) obtained mean systematic velocities 65 and 61 km s@xmath4 of sgr b2(n ) and sgr b2(m ) . their observations showed significant velocity variations among the different species . the differences are mostly caused by the chemical differences of the molecules . the different species sample different physical environments . the high angular resolution observations of h66@xmath34 ( de pree et al . 1995 ; 1996 ) showed that the mean systematic velocities are 69.8 and 65.3 km s@xmath4 for the sgr b2(m)-f and sgr b2(n)-k clusters , respectively . the relatively higher mean velocity of 69.8 km s@xmath4 in sgr b2(m ) is likely caused by the high velocity motion of the ionized gas of the uchii regions with respect to the centroid of the system . in section 4 , we will show that the systematic velocity determined from the terminal velocity of the outflow in sgr b2(m ) is 58 km s@xmath4 ( see also appendix a ) . in the rest of the paper , we adopt systematic velocities of 58 km s@xmath4 and 65 km s@xmath4 for sgr b2(m ) and sgr b2(n ) , respectively . the strong continuum cores are excellent probes of absorption by the cold gas that resides in front of them . absorption is observed towards both sgr b2(n ) and sgr b2(m ) continuum cores ( see the top - left and bottom - left panels of fig . multiple gaussian line components were fitted to the spectra for each of the two transitions in both cores . the parameters of these fits are listed in table 2 . the systematic velocities are marked with the vertical lines in fig . the majority of the absorbing gas in sgr b2(n ) and sgr b2(m ) is red - shifted with respect to the systematic velocities 58 and 65 km s@xmath4 , respectively . the red - shifted absorption gas provides evidence for the existence of gas accreting onto the two cores . if the absorbing gas covers the continuum source completely and the emission from the gas is insignificant , the line intensity is @xmath37 . the optical depth ( @xmath38 ) can be derived from the formula @xmath39 where @xmath40 is the observed line intensity and the @xmath41 is the observed continuum intensity . the errors in @xmath42 based on the fractional errors @xmath43 of each line channel and @xmath44 if the line is optically thin ( @xmath45 ) are given by @xmath46 in the optically thick case , the channels in the line center are saturated and the line - to - continuum ratio only gives a lower limit to the optical depth of the line . for example if @xmath47 spectral channels are saturated by the absorption gas component at a velocity , we have @xmath48 in 3 @xmath49 . substituting this formula into the equation ( 1 ) , the lower limit of the optical depth is @xmath50 with the rayleigh - jeans approximation , the value of 1 jy beam@xmath4 in our sma observations is equivalent to 1.5 k. the observed peak continuum intensities of the sgr b2(n ) and sgr b2(m ) cores are 29.2 and 20.2 jy beam@xmath4 , which correspond to brightness temperature of 44 and 30 k in our observations , respectively . the solution of radiation transfer function in terms of the observed brightness temperature of the line ( @xmath51 ) is given by @xmath52 where @xmath53 is the excitation temperature of the molecular line and @xmath54 is the observed brightness temperature of the continuum emission with the true brightness temperature of @xmath55 ; @xmath56 is the optical depth of the molecular cloud ; for given solid angles of the molecular cloud ( @xmath57 ) , continuum source ( @xmath58 ) and the telescope beam ( @xmath59 ) , @xmath60 and @xmath61 are the beam filling factors of the line and continuum , respectively , if both the source and the telescope beam are in gaussian shape ; @xmath62 denotes the fraction of the continuum source covered by the molecular cloud . if the molecular cloud is in front of the larger continuum source ( @xmath63 ) , the observed brightness temperature of the line ( @xmath64 ) becomes : @xmath65 if the molecular clouds cover the continuum cores with the same beam filling factor ( @xmath66 ) , the upper limits of the excitation temperatures h@xmath7co absorbing gas ( @xmath67 ) are imposed by the observed continuum brightness temperatures of the continuum cores , i.e. 44/@xmath68 and 31/@xmath68 k , for the sgr b2(n ) and sgr b2(m ) cores . for a given filling factor @xmath69 , the excitation temperatures of h@xmath7co would be less than 150 and 103 k for sgr b2(n ) and sgr b2(m ) , respectively . fig . 4 shows the spectra of the h@xmath7co lines ( averaged over one beam ) made from the image cube for the rest of components . each of spectral panels includes both the lower ( 3@xmath23 , the green profile ) and the higher ( 3@xmath25 , the red profile ) transition lines . gaussian fits to the h@xmath7co spectra were carried out for both absorption and emission components . the emission and absorption probably come from the different regions along the line of sight . the angular resolution of our observations appears to be inadequate to distinguish the discrete components in the cores . however , our high spectral resolution is adequate to separate the emission from the absorption in the gaussian fits . the parameters derived from the gaussian fits to the two h@xmath7co transitions are summarized in table 2 including the central line velocity ( v@xmath70 ) , the full width of half maximum ( @xmath71v ) and peak intensity ( i@xmath32 ) . the m1 , m4 and m5 are located along the major axis of the bipolar outflow originated from the f - cluster ( lis et al . m1 is on the blue - shifted side of the outflow . both the high- and low - transition spectra can be fitted with two gaussian components at 52 km s@xmath4 in emission and 64 km s@xmath4 in absorption . the weak red - shifted absorption with respect to the systematic velocity suggests that a relatively cold gas component in front of the continuum source are moving towards it . the strong blue - shifted emission with respect to the systematic velocity is the highly - excited gas emission in the outflow ( in front of the continuum source ) likely mixed with the infall gas emission ( behind the continuum source ) . sgr b2(m)-m4 is located close to the hii regions , _ i.e. _ , the f1 - 4 cluster . the higher transition spectrum can be fitted with two gaussian components in emission at 66 and 70 km s@xmath4 , both of which are red - shifted with respect to the systematic velocity 58 km s@xmath4 . the lower transition spectrum can be fitted with five gaussian components at velocity 51 , 65 , 70 , 75 km s@xmath4 in absorption and 100 km s@xmath4 in emission . the morphology of this region is a complex . a possible model to interpret the spectral characteristics of m4 is considered here . if we assume a non - lte condition for the gas and that both higher and lower transition gas comes from the same gas clump located in front of the continuum core , the excitation temperature of the higher transition gas is larger than the brightness temperature of the continuum , while the excitation temperature of the lower transition gas is less than the brightness temperature of the continuum . the red - shifted absorption suggests that the gas flows towards the continuum core . the nature of absorption and emission at m4 suggests that the process of excitation of the infall molecular cloud is complicated . the radiative excitation by the strong fir radiation field might play an important role in the region near the core since the collision alone can not produce the observed line ratio or the inverse population between the higher transition in k@xmath5=2 and the lower transition in k@xmath5=0 based on the lvg fitting ( see appendix b ) . the inversion in population between the two lowest k ladders is observed best in the red - shifted outflow component . at m5 , the spectrum of the higher transition gas shows a very significant line emission ( 7 - 8 @xmath28 ) , fitted to a gaussian at 66 km s@xmath4 with a line width of 16 km s@xmath4 , while less significant emission ( 1 - 2 @xmath28 ) of the lower transition gas is shown at the same position . the highly reversed line ratio @xmath72 suggests that local thermodynamic equilibrium ( lte ) is not valid at this location and a weak maser process is active in the outflow region . the gas components m2 and m3 and mw show significant line emission ( @xmath73 @xmath28 ) from the lower transition gas while the higher transition emission is relatively weak . the line ratio @xmath74 in those isolated component varies in the range between 1.5 to 5.2 . maser at 6 cm ( mehringer , goss & palmer 1994 ) was detected in the z10.24 region . the sma spectrum of the lower transition at z10.24 shows that a significant amount of gas is in absorption while the emission is present but red - shifted with respect to the absorption feature , a typical p - cygni profile suggesting an outflow in this region . the spectrum of the higher h@xmath7co transition can be fitted with two emission gaussian components at 50 and 84 km s@xmath4 with an absorbing gaussian at 75 km s@xmath4 , which is consistent with the h66@xmath34 transition ( de pree , et al . 1996 ) . excluding the possibility of the expanding shell model , de pree et al . argued that an ionized outflow is likely centered at z10.24 . our h@xmath7co observations appear to favor their argument of a bipolar outflow from the uchii region . towards the ne continuum source , both the higher and lower h@xmath7co transitions show that the majority of the gas in absorption is red - shifted with respect to the mean systematic velocity 65 km s@xmath4 . towards nw , a broad ( @xmath75 km s@xmath4 ) absorption ( @xmath76 jy beam@xmath4 ) from the lower transition line is detected at 71 km s@xmath4 . the spectrum of the higher transition shows no significant lines in either emission or absorption . 5 and 6 show the images of intensity weighted velocity ( or moment 1 ) of the h@xmath7co emission gas from both transitions . the moment 1 maps were constructed with a cutoff of 8 @xmath28 from each of the channel images in the velocity range of 8 - 151 km s@xmath4 . in the sgr b2(m ) region , the kinematical structure observed from the lower transition ( see fig . 5 ) consists of the highly red - shifted components 5@xmath33 south - east of the compact core and a northeast - southwest arch structure . the component m4 appears to be a fast moving compact component ( v@xmath77 km s@xmath4 ) ejected from the core . the morphology of the northeast - southwest arch in sgr b2(m ) from the velocity field in the higher transition gas ( see fig . 6 ) appears to be consistent with that observed in the lower transitions . a velocity gradient is present south - east of m4 ( shown in fig . 6 ) , which appears to indicate a decelerating outflow . in the case of sgr b2(m ) , the higher h@xmath7co transition appears to trace outflow well , which is consistent with the interpretation of the larger scale mass outflow based on the lower angular - resolution observations of nh@xmath26 and so ( vogel , genzel & palmer 1987 ) . the higher angular - resolution observations of nh@xmath26 ( guame & claussen 1990 ) showed that the red - shifted emission is located south of the f3 hii region , and the blue - shifted absorption is located north of the red - shifted emission , showing a velocity gradient in north - south direction . based on their higher angular - resolution observations of oh maser and nh@xmath26 , guame & claussen ( 1990 ) suggested that the north - south velocity gradient can be explained by a rotating disk or a torus of material with an extent of 2@xmath215 surrounding the sgr b2(m)-f cluster . although the angular resolution in our observations is not adequate to verify the kinematical model proposed by guame & claussen ( 1990 ) , our observed arch - liked morphology of the h@xmath0co gas shown in blue - shifted emission from northeast to southwest in the larger scale also indicates that the gas is undergoing a complicated infall process interacting with the outflow while the gas is spiraling onto the core rather than being in simple free fall . in the sgr b2(n ) region , the lower transition map ( see fig . 5 ) shows the red - shifted velocity located north of k2 and blue - shifted velocity located south of k2 with a north - south velocity gradient across k2 . a similar velocity gradient has been observed in the hc@xmath26n line ( lis et al . these authors argued that the north - south velocity gradient in sgr b2(n ) traces rotation . the kinematics of the lower h@xmath7co transition in emission gas of sgr b2(n ) is likely dominated by the gas rotating around the core . in addition to the north - south velocity gradient from the higher transition h@xmath7co ( @xmath2 ) map as observed in the lower transition gas , an east - west velocity gradient is also observed in sgr b2(n ) ( see fig . the outflow in sgr b2(n ) was observed in east - west direction ( lis et al . 1993 ) . the higher angular - resolution observations of nh@xmath26 ( gaume & claussen 1990 ) appeared to show a southeast - northwest velocity gradient across k2 . the southeast - northwest velocity gradient in the larger scale from our observations appears to be consistent with the kinematical structure observed in nh@xmath26 . based on the higher angular - resolution observations of nh@xmath26 , ruling out a simple outflow / rotation model , gaume & claussen ( 1990 ) suggested that several kinematic components in outflow , infall and rotation might be involved in the sgr b2(n ) core . the southeast - northwest velocity gradient observed from the h@xmath7co emission gas in sgr b2(n ) appears to be caused by a combination of rotation , infall and outflow . the angular resolution of our observations is not adequate to discern the details of these motions .

observations of two hco ( and ) lines and continuum emission at 1.3 mm towards sgr b2(n ) and sgr b2(m ) have been carried out with the sma . the mosaic maps of sgr b2(n ) and sgr b2(m ) in both continuum and lines show a complex distribution of dust and molecular gas in both clumps and filaments surrounding the compact star formation cores . we have observed a decelerating outflow originated from the sgr b2(m ) core , showing that both the red - shifted and blue - shifted outflow components have a common terminal velocity . this terminal velocity is 58 km s . the sma observations have also shown that a large fraction of absorption against the two continuum cores is red - shifted with respect to the systematic velocities of sgr b2(n ) and sgr b2(m ) , respectively , suggesting that the majority of the dense molecular gas is flowing into the two major cores where massive stars have been formed . the observed hco line intensities and their ratios can be adequately fitted with this model for the most of the gas components . however , the line intensities between the higher energy level transition hco ( ) and the lower energy level transition hco ( ) is reversed in the red - shifted outflow region of sgr b2(m ) , suggesting the presence of inversion in population between the ground levels in the two k ladders ( k= 0 and 2 ) . the possibility of weak maser processes for the hco emission in sgr b2(m ) is discussed .

observations of two hco ( and ) lines and continuum emission at 1.3 mm towards sgr b2(n ) and sgr b2(m ) have been carried out with the sma . the mosaic maps of sgr b2(n ) and sgr b2(m ) in both continuum and lines show a complex distribution of dust and molecular gas in both clumps and filaments surrounding the compact star formation cores . we have observed a decelerating outflow originated from the sgr b2(m ) core , showing that both the red - shifted and blue - shifted outflow components have a common terminal velocity . this terminal velocity is 58 km s . it provides an excellent method in determination of the systematic velocity of the molecular cloud . the sma observations have also shown that a large fraction of absorption against the two continuum cores is red - shifted with respect to the systematic velocities of sgr b2(n ) and sgr b2(m ) , respectively , suggesting that the majority of the dense molecular gas is flowing into the two major cores where massive stars have been formed . we have solved the radiative transfer in a multi - level system with lvg approximation . the observed hco line intensities and their ratios can be adequately fitted with this model for the most of the gas components . however , the line intensities between the higher energy level transition hco ( ) and the lower energy level transition hco ( ) is reversed in the red - shifted outflow region of sgr b2(m ) , suggesting the presence of inversion in population between the ground levels in the two k ladders ( k= 0 and 2 ) . the possibility of weak maser processes for the hco emission in sgr b2(m ) is discussed .

1502.06738

i

throughout the rest of this paper , let @xmath2 denote the sequence of positive integers which have an even sum - of - digits function in base @xmath9 , sorted in increasing order . in other words , @xmath2 is the sequence of thue morse integers @xmath10 . furthermore , we write @xmath11 for the sequences of those numbers which are _ not _ contained in @xmath2 , sorted in increasing order ; thus @xmath12 . the numbers @xmath2 are frequently called _ evil numbers _ , while the numbers @xmath11 are called _ odious numbers_. + the thue morse integers are characterized by the thue morse sequence @xmath13 which has been discovered several times in the literature . for an extensive survey , see @xcite . in our notation we have @xmath14 if and only if @xmath15 + in this paper we analyze exponential sums of the form @xmath16 for reals @xmath17 , and what is intimately connected products of the form @xmath18 , as well as distribution properties of the sequence @xmath19 . to quantify the regularity of the distribution of a finite set of real numbers in @xmath20 $ ] we use the notion of the _ star - discrepancy _ @xmath21 . for given numbers @xmath22 , their star - discrepancy is defined by @xmath23 } \left| \frac{1}{n } \sum_{n=1}^n \mathbf{1}_{[0,a ] } ( x_n ) - a \right|.\ ] ] an infinite sequence @xmath24 whose discrepancy @xmath21 tends to zero as @xmath25 is called _ uniformly distributed modulo one _ ( u.d . mod 1 ) . informally speaking , the star - discrepancy is a measure for the deviation between uniform distribution on @xmath20 $ ] and the empirical distribution of a given point set ; in probabilistic terminology this corresponds to the kolmogorov smirnov statistic . discrepancy theory is a rich subject , which has close links to number theory , probability theory , ergodic theory and numerical analysis . for more information on discrepancy theory , we refer to the standard monographs @xcite . + sequences of the form @xmath26 are called _ kronecker sequences_. one of the fundamental results of discrepancy theory states that such a sequence is u.d . mod 1 if and only if @xmath1 is irrational . it is also well - known that the discrepancy of such a sequence depends on diophantine approximation properties of @xmath1 . more precisely , we have @xmath27 as @xmath25 , where @xmath28 are the continued fraction coefficients of @xmath1 and where @xmath29 is defined by @xmath30 with @xmath31 denoting the best approximation denominators of @xmath1 ( see for example ( * ? ? ? * corollary 1.64 ) ) . hence @xmath32 if @xmath1 has bounded continued fraction coefficients , and , as a consequence of metric results of khintchine @xcite , for every @xmath33 we have @xmath34 for almost all @xmath35 . + + it is known ( and it will be re - proved implicitly in this paper ; see section 6 ) that the sequence @xmath36 ( which we will call _ thue morse kronecker sequence _ ) is also uniformly distributed in the unit interval if and only if @xmath1 is irrational . however , it turns out to be a very difficult task to give sharp estimates for the discrepancy of this sequence for concrete values of @xmath1 . as we will see , the discrepancy of a thue morse kronecker sequence @xmath37 depends on diophantine approximation properties _ and _ properties of the digit representation of @xmath1 in base 2 . until now there are only few ( non - trivial ) cases of @xmath1 where we have enough information about both of these aspects . + exponential sums and discrepancy theory are intimately connected . one such connection is weyl s criterion , two others are the erds turn inequality and koksma s inequality . the erds turn inequality ( see for example @xcite ) states that for points @xmath38 $ ] we have @xmath39 where @xmath40 is an arbitrary positive integer . koksma s inequality says that @xmath41 } f ) d_n^*(x_1 , \dots , x_n),\ ] ] for any function @xmath42 having bounded variation on @xmath20 $ ] . when combined , the erds turn inequality and koksma s inequality show that exponential sums can be used to obtain both upper and lower bounds for the discrepancy . + as an explicit lower bound from we get ( compare for example @xcite ) : @xmath43 where @xmath40 is an arbitrary positive integer . koksma s inequality and its multi - dimensional generalization are also the cornerstone of the application of low - discrepancy point sets in numerical integration ( so - called _ quasi - monte carlo integration _ ; see for example @xcite ) . + consequently , in this paper we will mainly be concerned with the problem of investigating exponential sums of the form @xmath16 . it turns out that this investigation relies on studying lacunary products of the form @xmath18 . furthermore we study the discrepancy of @xmath36 . for all three topics we obtain sharp metric results . the investigation of the lower bound for the discrepancy leads to a challenging open problem in diophantine approximation . finally , we consider two concrete non - trivial special examples for @xmath1 . + the main results of this paper are the following . ( throughout the rest of this paper , we write @xmath44 for @xmath45 . ) + [ th_thue ] let @xmath2 be the sequence of thue morse integers , and let @xmath46 be an integer . let @xmath47 be arbitrary . then for almost all @xmath48 we have @xmath49 for all @xmath50 , and @xmath51 for infinitely many @xmath52 . + note that the exponential function in grows more slowly than any ( fixed ) power of @xmath52 ; but faster than any ( fixed ) power of @xmath53 . in other words , as a consequence of theorem [ th_thue ] for every @xmath47 and every @xmath54 we have @xmath55 for almost all @xmath1 . + it will turn out that theorem [ th_thue ] is an almost immediate consequence of the following result on lacunary trigonometric products . + [ th_theorem2 ] let @xmath56 be arbitrary . then for almost all @xmath57 we have @xmath58 for all @xmath59 , and @xmath60 for infinitely many @xmath61 . + this result is a consequence of a more general result , theorem [ lac_co1 ] , which will be formulated later in section [ sect_lac ] since it needs some technical prerequisites . + from the lower bound in theorem [ th_thue ] and formula we immediately obtain a metric lower bound for the discrepancy @xmath62 of the thue kronecker sequence . however in theorem [ th_thue2 ] it turns out that the true metric order of the discrepancy @xmath62 is much larger . + [ th_thue2 ] let @xmath63 be the sequence of thue morse integers . let @xmath47 be arbitrary . then for almost all @xmath57 we have @xmath64 and @xmath65 for infinitely many @xmath52 . here @xmath66 is a real constant defined below for which it is known that @xmath67 + the number @xmath66 in theorem [ th_thue2 ] appears in a result of fouvry and mauduit @xcite , which states that @xmath68 for @xmath69 , with constants @xmath70 and @xmath66 with @xmath71 in lemma [ lem7 ] , which is contained in section [ sect_proof_th2 ] , we will improve the estimate for @xmath66 to . note that as a consequence of and we have @xmath72 for almost all @xmath1 . this should be compared with the general metric discrepancy bound @xmath73 for almost all @xmath1 , which holds for every strictly increasing sequence of positive integers @xmath74 ( see @xcite ) . it is known that in the general setting the upper bound given by is optimal ( up to powers of logarithms ; see @xcite ) . thus the upper bound given in theorem [ th_thue2 ] is significantly stronger than the general metric discrepancy bound given by . furthermore we want to emphasize the fact that the precision of theorem [ th_thue2 ] is quite remarkable , in view of the fact that good bounds for the typical order of the discrepancy are only known for a very small number of classes of parametric sequences . + one of the main objectives of theorems [ th_thue ] and [ th_thue2 ] is to examine the degree of pseudorandomness of the parametric sequences @xmath75 , and consequently also of the thue morse sequence @xmath2 of integers itself . by classical probability theory , for a sequence @xmath76 of independent , identically distributed ( i.i.d . ) random variables having uniform distribution on @xmath20 $ ] we have the law of the iterated logarithm ( lil ) @xmath77 and the chung smirnov lil for the kolmogorov smirnov statistic ( that is , for the discrepancy ) @xmath78 in other words , for a random sequence of points exponential sums are typically of asymptotic order roughly @xmath79 , and the discrepancy is typically also of the corresponding asymptotic order . furthermore , similar results usually hold for exponential sums of @xmath80 and for the discrepancy of @xmath81 when @xmath82 is a `` random '' increasing sequence of integers . in the simplest model , when for every number @xmath83 we decide independently and with fair probability whether it should be contained in @xmath82 or not , then holds almost surely ( with respect to the probability space over which the @xmath84 s are defined ) for almost all @xmath1 . in a similar fashion both results and essentially remain valid when the random sequence @xmath82 is constructed in a more complicated fashion ( see for example @xcite ) . + thus theorem [ th_thue ] and theorem [ th_thue2 ] show that the typical we mean a result which is valid for a set of full lebesgue measure . ] asymptotic order of exponential sums and of the discrepancy of @xmath75 for the thue morse integers @xmath2 does _ not _ match with the corresponding order in the random case , by this means showing an interesting deviation from `` pseudorandom '' behavior of the sequence @xmath2 itself . on the other hand , the behavior of @xmath75 also does _ not _ match with the behavior of @xmath85-sequences for typical values of @xmath1 . more precisely , as already mentioned above , as a consequence of metric results of khintchine @xcite and due to the fact that the discrepancy of @xmath86 can be expressed in terms of the continued fractions expansion of @xmath1 , we have @xmath87 for almost all @xmath1 . consequently , by theorem [ th_thue2 ] , the typical asymptotic order of the discrepancy of parametric sequences @xmath75 is significantly larger than that of typical @xmath85-sequences , and by theorem [ th_thue ] this is also true for exponential sums . thus , with respect to exponential sums as well as with respect to the discrepancy , parametric sequences @xmath3 generated by the thue morse integers @xmath2 occupy a position somewhere between @xmath85-sequences and truly random sequences . we also want to comment on the fact that there is a huge difference between the order of the exponential sums in theorem [ th_thue ] and the order of the discrepancy in theorem [ th_thue2 ] . this is a very surprising phenomenon , which is related to problems from metric diophantine approximation ( which are implicit in the proof of theorem [ th_thue2 ] , and are briefly discussed in the concluding section [ sec_conc ] ) . + as already mentioned earlier , it is rather difficult to give the right order for the exponential sums in theorem [ th_thue ] , the trigonometric products in theorem [ th_theorem2 ] , and the discrepancy of @xmath19 for concrete non - trivial examples of @xmath1 . what do we mean by a `` non - trivial '' example ? in the first part of section [ sect_proof_th4 ] we will point out the following facts : * the order of the discrepancy of the pure kronecker sequence @xmath88 never is significantly larger than the order of the discrepancy of the thue kronecker sequence @xmath19 . * if the order of the discrepancy @xmath89 of the pure kronecker sequence satisfies @xmath90 then the discrepancy @xmath91 of the thue kronecker sequence is essentially of the same order as the discrepancy of the pure kronecker sequence . * if the order of the discrepancy @xmath89 of the pure kronecker sequence satisfies @xmath92 then @xmath91 satisfies @xmath93 . + thus an `` interesting non - trivial '' example means for us an example where @xmath1 is a `` natural '' real number such as @xmath94 ( it seems to us that there is no chance to handle these numbers since we do not have enough information on their digit representation ) , or where @xmath1 is such that @xmath91 and hence @xmath89 is small ( say @xmath95 however we can not give such examples ) or where the quality of the distribution of the sequences @xmath26 and @xmath19 differ strongly . two such examples are given in theorem [ th_thue4 ] . especially in the first example the difference between @xmath89 and @xmath91 is of the maximal possible form . + [ th_thue4 ] 1 . let @xmath96 . then for the star - discrepancy @xmath97 of the pure kronecker sequence @xmath26 we have @xmath98 whereas for the star - discrepancy @xmath91 of the thue kronecker sequence @xmath19 we have @xmath99 @xmath100 for every @xmath101 2 . let @xmath102 the thue morse real in base 2 . then for the star - discrepancy @xmath97 of the pure kronecker sequence @xmath103 we have @xmath104 whereas for the star - discrepancy @xmath91 of the thue kronecker sequence @xmath105 we have @xmath106 + we would like to point out here that there is an intimate connection between distribution properties of @xmath19 and of certain types of hybrid sequences . for some information on the analysis of hybrid sequences see for example @xcite , @xcite and @xcite . + as already mentioned , the proofs of theorems [ th_thue ] and [ th_thue2 ] are based on a connection between exponential sums of @xmath3 and the lacunary trigonometric products studied in theorem [ th_theorem2 ] . we will establish this connection in the following lines , and exploit it in section [ sect_lac ] in more detail . for the time being , we assume that @xmath52 is of the form @xmath107 for some positive integer @xmath61 . + to analyze the exponential sums appearing in theorem [ th_thue ] and on the right - hand side of , we define @xmath108 by the assumption that @xmath109 we have @xmath110 which yields @xmath111 and @xmath112 a similar analysis for the sequence @xmath11 shows that @xmath113 where again we assume that @xmath109 . + by taking logarithms , we can convert the trigonometric products appearing in and into so - called _ lacunary sums _ ; these sums have been intensively investigated in fourier analysis , and a wide range of mathematical methods is available for studying them ( see the following section [ sect_lac ] ) . thus the theory of lacunary sums allows us to obtain an estimate for the size of the exponential sums @xmath114 in the case when @xmath52 is a power of 2 ; however , it will turn out that we may also drop the condition that @xmath52 is an integral power of @xmath9 by applying a dyadic decomposition method . + note that by and by the fact that the thue morse integers have asymptotic density 1/2 it is easy to show that all the conclusions of theorem [ th_thue ] and theorem [ th_thue2 ] remain valid if we replace the sequence @xmath2 by the sequence @xmath11 ( of those numbers which are _ not _ thue morse integers ) . + the outline of the remaining part of this paper is as follows . in section [ sect_lac ] we explain the main principles of the theory of lacunary ( trigonometric ) sums , and state several lemmas as well as theorem [ lac_co1 ] , which we require for the proofs of theorem [ th_thue ] and theorem [ th_theorem2 ] . in section [ sect_lac2 ] we give the proofs for the results stated in section [ sect_lac ] , and in section [ sect_proof ] we give the proofs of theorem [ th_thue ] and theorem [ th_theorem2 ] . in section [ sect_proof_th2 ] , we prove theorem [ th_thue2 ] , and in section [ sect_proof_th4 ] we prove theorem [ th_thue4 ] . finally , in section [ sec_conc ] , we briefly mention a problem from metric diophantine approximation , which was posed by leveque in @xcite and is related to the proof of theorem [ th_thue2 ] .

one of the fundamental theorems of uniform distribution theory states that the fractional parts of the sequence are uniformly distributed modulo one ( u.d . mod 1 ) for every irrational number . another important result of weyl states that for every sequence of distinct positive integers the sequence of fractional parts of is u.d . we investigate this problem in the case when is the thue morse sequence of integers , which means the sequence of positive integers having an even sum of digits in base 2 . in particular we utilize a connection with lacunary trigonometric products , and by giving sharp metric estimates for such products we derive sharp metric estimates for exponential sums of and for the discrepancy of furthermore , we comment on the connection between our results and an open problem in the metric theory of diophantine approximation , and we provide some explicit examples of numbers for which we can give estimates for the discrepancy of .

one of the fundamental theorems of uniform distribution theory states that the fractional parts of the sequence are uniformly distributed modulo one ( u.d . mod 1 ) for every irrational number . another important result of weyl states that for every sequence of distinct positive integers the sequence of fractional parts of is u.d . mod 1 for almost all . however , in this general case it is usually extremely difficult to classify those for which uniform distribution occurs , and to measure the speed of convergence of the empirical distribution of towards the uniform distribution . in the present paper we investigate this problem in the case when is the thue morse sequence of integers , which means the sequence of positive integers having an even sum of digits in base 2 . in particular we utilize a connection with lacunary trigonometric products , and by giving sharp metric estimates for such products we derive sharp metric estimates for exponential sums of and for the discrepancy of furthermore , we comment on the connection between our results and an open problem in the metric theory of diophantine approximation , and we provide some explicit examples of numbers for which we can give estimates for the discrepancy of .

1409.1447

i

our knowledge on how the solar corona is heated and maintained at a million degrees kelvin , when the photosphere below is at 5800 kelvin , is still far from being comprehensive . active regions ( ars ) are ideal observing targets to probe the underlying heating mechanisms as they are the locations of profound heating processes . in addition , they show a wide distribution of physical parameters . accurate measurements of such parameters are critical in the formulation and constraint of coronal heating theories . for extended discussions on coronal heating , refer to , e.g. , @xcite and @xcite . topologically , ars possess different structures like the core loops primarily seen at @xmath1 3 - 5 mk rooted in moss regions which are seen primarily at around 1 - 2 mk ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , warm loops at @xmath1 1 mk @xcite , the cool fan structures at the edges of the ars at @xmath2 1 mk @xcite . in addition to the visible loop structures , there is a substantial amount of diffuse emission in and around the active regions @xcite . diffuse emission regions may be defined as regions with no resolvable structures . they may , however , appear to be loop - like structures at higher resolution . in fact , the emissions from confined loops structures are just about 20 - 30% higher than the background / foreground diffuse emission @xcite . @xcite investigated the density and temperature structure of a limb ar . the authors reported that ar plasmas are multi - thermal and the electron densities fall off as a function of distance from the core , as was also obtained using the white light observations of the corona . ar heating has often been debated between effectively steady heating ( high frequency nanoflares ) and impulsive heating ( low frequency nanoflares ) . in the former scenario , the delay between heating events is smaller than the cooling / draining timescale of the plasma , leading to conditions that are similar to constant heating . impulsive heating , however , suggests that the delay between heating events is longer than the cooling / draining timescale of the plasma , i.e. the plasma gets some time to cool down before another heating event takes place . the properties of 1 mk warm loops seem to favor impulsive heating @xcite . however , the heating of core loops is a matter of strong debate @xcite . recent analysis suggest that active regions during the early part of their evolution seem to show an em distribution ( emd ) that is consistent with impulsive heating , while during the latter part of their evolution , the variability of the core becomes more gentle and the em distribution is more consistent with high - frequency nanoflare heating @xcite . the study of diffuse emission has not been explored in great detail . the main aim of this paper is to study and probe the heating mechanism in the diffuse part of active regions . direct observations of heating processes are not possible yet , as these events happen on scales much smaller than the resolvable limits with the available present day instrumentation @xcite . emission measure ( em ) diagnostics have been advocated ( see e.g. , * ? ? ? * ) to be one of the possible indirect modes of studying the heating mechanisms among others such as doppler shifts @xcite and the recently developed time lag analysis @xcite . here , we have employed the technique of em to study the diffuse emission in active regions . in addition , we estimate the em(t ) distribution of topologically different regions in off limb _ ar 10939 _ and _ ar 10961 _ , i.e. , warm and core loop structures and compare with the em(t ) of the diffuse emission regions with the aim to probe the thermal structure in diffuse regions and thereby their heating mechanisms . @xcite presented a revised radiometric calibration , due to the degradation of detector s response of the eis instrument over time , since the launch date of the hinode mission . the revised calibration has been accepted by the eis team and has been provided in the solarsoftware package . in the present work , we have applied the revised calibration on intensities to obtain the em and compared with that obtained using the unrevised intensities . the rest of the paper is organised as follows : in section [ obs ] , we describe the data used in this study and the reduction procedures applied ; in section [ db ] , we discuss about an instrumental effect , the diffraction bands that are observed in our datasets ; we describe our data analysis method and present our results in section [ analysis ] followed by a summary and discussion in section [ conc ] .

we investigate two off - limb active regions , namely ar10939 and ar10961 , to probe the underlying heating mechanisms . for this purpose we have used spectral observations from hinode / eis and employed the emission measure ( em ) technique to obtain the thermal structure of these diffuse regions .

our knowledge of the diffuse emission that encompasses active regions is very limited . in the present paper we investigate two off - limb active regions , namely ar10939 and ar10961 , to probe the underlying heating mechanisms . for this purpose we have used spectral observations from hinode / eis and employed the emission measure ( em ) technique to obtain the thermal structure of these diffuse regions . our results show that the characteristic em distributions of the diffuse emission regions peak at and the cool - ward slopes are in the range 1.4 - 3.3 . this suggests that both low as well as high frequency nanoflare heating events are at work . our results provide additional constraints on the properties of these diffuse emission regions and their contribution to the background / foreground when active region cores are observed on - disk .

0807.2525

i

we have developed a method of extracting statistical information on the icm inhomogeneity from x - ray observations of galaxy clusters . with a lognormal model for the fluctuations motivated by cosmological hydrodynamic simulations , we have created synthetic clusters , and have found that their x - ray surface brightness fluctuations retain the lognormal nature . in addition , the result that @xmath108 and @xmath45 are linearly related implies that one can , in principle , estimate the statistical properties of the three dimensional density inhomogeneity ( @xmath45 ) from x - ray observations of galaxy clusters ( @xmath108 and @xmath117 ) . we have compared the predictions of our model to _ chandra _ x - ray observations of the galaxy cluster a3667 . for the first time in a real galaxy cluster we were able to detect the lognormal signature of x - ray surface brightness fluctuations , which was originally motivated by simulations . based on the synthetic cluster results , this enabled an estimate of the statistical properties of the inhomogeneity of the icm of a3667 . in the context of lognormally distributed inhomogeneity , we obtain @xmath266 for the gas density fluctuations of a3667 . it is encouraging that the value of the fluctuation amplitude for abell 3667 is in reasonable agreement with typical values from the simulated clusters . finally we check the validity and limitation of our method using several clusters from cosmological hydrodynamic simulations . unlike the fairly idealized synthetic clusters , simulated clusters exhibit complex structure more akin to real galaxy clusters . as a result , the empirical relation between the two- and three - dimensional fluctuation properties calibrated with synthetic clusters when applied to simulated clusters shows large scatter . nevertheless we are able to reproduce the true value of the fluctuation amplitude of simulated clusters within a factor of two from their two - dimensional x - ray surface brightness alone . our current methodology combined with existing observational data is useful in describing and inferring the statistical properties of the three dimensional inhomogeneity in galaxy clusters . the fluctuations in the icm have several implications in properly interpreting galaxy cluster data . in particular , our current model may be useful in interpreting data from current and future galaxy cluster surveys using the sunyaev - zeldovich effect , which have the potential to provide tight constraints on cosmology . we thank naomi ota , noriko y. yamasaki , and kazuhisa mitsuda for useful discussions and klaus dolag for providing a set of simulated clusters . hk is supported by a jsps ( japan society for promotion of science ) grant - in - aid for science fellows . edr gratefully acknowledges support from a jsps postdoctoral fellowship for foreign researchers ( p07030 ) . this work is also supported by grant - in - aid for scientific research from jsps and from the japanese ministry of education , culture , sports , science and technology ( nos . 20@xmath26710466 , 19@xmath26707030 , 16340053 , 1874012 , 20340041 , and 20540235 ) , and by the jsps core - to - core program `` international research network for dark energy '' .

the empirical relation between the two- and three - dimensional fluctuation properties calibrated with synthetic clusters when applied to simulated clusters shows large scatter . nevertheless we are able to reproduce the true value of the fluctuation amplitude of simulated clusters within a factor of two from their two - dimensional x - ray surface brightness alone . our current methodology combined with existing observational data is useful in describing and inferring the statistical properties of the three dimensional inhomogeneity in galaxy clusters .

our previous analysis indicates that small - scale fluctuations in the intracluster medium ( icm ) from cosmological hydrodynamic simulations follow the lognormal probability density function . in order to test the lognormal nature of the icm directly against x - ray observations of galaxy clusters , we develop a method of extracting statistical information about the three - dimensional properties of the fluctuations from the two - dimensional x - ray surface brightness . we first create a set of synthetic clusters with lognormal fluctuations around their mean profile given by spherical isothermal models , later considering polytropic temperature profiles as well . performing mock observations of these synthetic clusters , we find that the resulting x - ray surface brightness fluctuations also follow the lognormal distribution fairly well . systematic analysis of the synthetic clusters provides an empirical relation between the three - dimensional density fluctuations and the two - dimensional x - ray surface brightness . we analyze _ chandra _ observations of the galaxy cluster abell 3667 , and find that its x - ray surface brightness fluctuations follow the lognormal distribution . while the lognormal model was originally motivated by cosmological hydrodynamic simulations , this is the first observational confirmation of the lognormal signature in a real cluster . finally we check the synthetic cluster results against clusters from cosmological hydrodynamic simulations . as a result of the complex structure exhibited by simulated clusters , the empirical relation between the two- and three - dimensional fluctuation properties calibrated with synthetic clusters when applied to simulated clusters shows large scatter . nevertheless we are able to reproduce the true value of the fluctuation amplitude of simulated clusters within a factor of two from their two - dimensional x - ray surface brightness alone . our current methodology combined with existing observational data is useful in describing and inferring the statistical properties of the three dimensional inhomogeneity in galaxy clusters .

nucl-th0306051

i

except for a few nuclei lying in the vicinity of shell closures , most of the heavy nuclei are difficult to describe in a spherical shell model framework because of the unavoidable problem of dimension explosion . therefore , the study of nuclear structure in heavy nuclei has relied mainly on the mean - field approximations , in which the concept of spontaneous symmetry breaking is applied @xcite . however , there has been an increasing number of compelling evidences indicating that the nuclear many - body correlations are important . thus , the necessity of a proper quantum mechanical treatment for nuclear states has been growing , and we are facing the challenge of understanding the nuclear structure by going beyond the mean - field approximations . demand for a proper shell model treatment arises also from the nuclear astrophysics . since heavy elements are made in stellar evolution and explosions , nuclear physics , and in particular nuclear structure far from stability , enters into the stellar modeling in a crucial way . the nucleosynthesis and the correlated energy generation is not completely understood , and the origin of elements in the cosmos remains one of the biggest unsolved physics puzzles . nuclear shell models can generate well - defined wave functions in the laboratory frame , allowing us to compute , without further approximations as often assumed in the mean - field approaches , the quantities such as transition probabilities , spectroscopic factors , and @xmath0-decay rates . these quantities provide valuable structure information to nuclear astrophysics . in fact , the nuclear shell model calculations could strongly modify the results of nuclear astrophysics , as the recent work of langanke and martinez - pinedo has demonstrated ( see , for example , ref . @xcite ) . tremendous efforts have been devoted to extending the shell model capacity from its traditional territory of the @xmath1-shell to heavier shells . over the years , one has looked for possible solutions in the following two major directions . in the first direction , one employs rapidly growing computer power and sophisticated diagonalization algorithms to improve the traditional shell model code . the shell model code antoine @xcite is a representative example of the recent developments along this line . using this code the deformed @xmath2 nuclei up to mass @xmath3 can be well explained . the recent record example performed by this code is the full @xmath4 shell calculation of @xmath5 nuclei @xcite , with the basis dimensions in excess of 100 million . while in principle , it does not matter how to prepare a shell model basis , it is crucial in practice to use the most efficient one . moreover , feasibility in computation is not our only concern . the other important aspect of using an efficient basis is that it may have a good classification scheme , such that a simple configuration in that basis corresponds approximately to a real mode of excitation . this not only can simplify the calculations , but also make the physical interpretations of results more easy and transparent . in the second direction , which is defined in a much wider scope , one employs various methods in seeking judicious truncation schemes . such schemes should contain the most significant configurations , each of which can be a complicated combination in terms of the original shell model basis states . in this way , the basis dimension can be significantly reduced and the final diagonalization is performed in a much smaller space , thus making a shell model calculation for heavy nuclei possible . the early monster - vampire approach @xcite and the recent monte carlo shell model @xcite are examples along this line . nevertheless , numerical calculations required by these models are still quite heavy , which may make a systematical application difficult . there are two other existing models that belong to the second category : the project shell model ( psm ) @xcite , and the fermion dynamical symmetry model ( fdsm ) @xcite . in the psm , the shell model basis is constructed by choosing a few quasi - particle ( qp ) orbitals near the fermi surfaces and performing angular - momentum and particle - number projection on the chosen configurations . by taking multi - qp states as the building blocks , the psm has been designed to describe the rotational bands built upon qp excitations @xcite . the psm has been rather successful in calculating the high - spin states of well - deformed and superdeformed nuclei . for lighter nuclei where the large - scale shell model calculation is feasible @xcite , studies for the deformed @xmath6cr @xcite and the superdeformed @xmath7ar @xcite have demonstrated that the psm calculation can achieve a similar accuracy in describing the data . in the fdsm , the truncated basis is built by the symmetry detected @xmath8- and @xmath9-pairs , assuming that these are the relevant degrees of freedom for the low - lying collective motions . having these pairs as the building blocks , the fdsm can provide a unified description for the low - spin collective excitations from the spherical to the well - deformed region @xcite . it is clear that the psm and the fdsm follow the shell model philosophy and both have their own shell model truncation scheme . however , the truncations emphasize different excitation modes , which are contained in one model but are absent in the other . an idea emerges naturally that one may combine the advantages of the two models to construct a new shell model for heavy nuclei . the question is how . the psm is a microscopic approach employing the deformed intrinsic states and the projection method , while the fdsm is a fermionic model based on the group theory . the crucial step that leads us to connect these two different approaches is made through the recent recognition @xcite that the numerical results obtained by the psm exhibit , up to high angular momenta and excitations , a remarkable one - to - one correspondence with the analytical @xmath10 spectrum of the fdsm . this suggests that the projected deformed - bcs vacuum has at the microscopic level @xmath10-like structures which are very close to the representations of the @xmath10 dynamical symmetry of an @xmath8-@xmath9 fermion - pair system . this recognition has motivated us to propose a multi - shell shell model for heavy nuclei . hereafter , we shall call it heavy shell model , or hsm for short . in the following section , the psm and the fdsm will be briefly reviewed . the emphasis will be given on the discussion of the advantages and deficiencies of each model . in section 3 , the connection between the two models will be explored . in section 4 , we will discuss in detail how the two models are integrated to form the hsm . we will give the basis states and the basis truncations for the well - deformed , transitional , and spherical regions . the effective interactions and the general method for evaluating the projected matrix elements will also be discussed in this section . finally , the paper will be summarized in section 5 .

performing a shell model calculation for heavy nuclei has been a long - standing problem in nuclear physics . here we propose one possible solution . the central idea of this proposal is to take the advantages of two existing models , the projected shell model ( psm ) and the fermion dynamical symmetry model ( fdsm ) , to construct a multi - shell shell model .

performing a shell model calculation for heavy nuclei has been a long - standing problem in nuclear physics . here we propose one possible solution . the central idea of this proposal is to take the advantages of two existing models , the projected shell model ( psm ) and the fermion dynamical symmetry model ( fdsm ) , to construct a multi - shell shell model . the psm is an efficient method of coupling quasi - particle excitations to the high - spin rotational motion , whereas the fdsm contains a successful truncation scheme for the low - spin collective modes from the spherical to the well - deformed region . the new shell model is expected to describe simultaneously the single - particle and the low - lying collective excitations of all known types , yet keeping the model space tractable even for the heaviest nuclear systems .

nucl-th0306051

i

in this paper , a multi - shell shell model for heavy nuclei is proposed . for performing a shell model diagonalization involving several major shells in the model space , we seek an efficient truncation scheme . the new heavy shell model can be viewed as an integration of two existing models : the project shell model and the fermion dynamical symmetry model . the psm is an efficient method for the high - spin description of rotational states built upon qp - excitations , but it is not a practical method for the low - spin collective vibrations . in contrast , the fdsm provides a well - defined truncation scheme for all known types of low - lying collective vibrations , workable from the spherical to the well - deformed region , but it is lack of the necessary degrees of freedom of single particle excitations . the idea proposed in the present paper is to combine the advantages of both models . to construct the shell model basis , we follow the fdsm discovery that the intrinsic collective states can be built by applying @xmath9-pairs onto the bcs vacuum state , and employ the psm qp truncation scheme combined with the projection techniques . in this sense the model goes beyond the traditional one - major - shell shell model , yet the calculation is tractable for heavy , and even for superheavy nuclei . given the past success of the psm and the fdsm in their own applicable regimes , which has been documented in the literature , we expect that the new model can work reasonably well for heavy nuclear systems where traditional shell - model calculations are not feasible . this model should be capable of describing the low - excitation collective vibrations of all known types , including fragmentations due to the quasi - particle mixing . it should be capable of applying to the high - spin regions where quasi - particle alignments play an important role . it should also be capable of treating weakly - deformed nuclei across the transitional to the spherical region . we conclude that the development of the heavy shell model may open possibilities of shell model calculations for heavy nuclei to a much wider range of nuclear structure problems .

the psm is an efficient method of coupling quasi - particle excitations to the high - spin rotational motion , whereas the fdsm contains a successful truncation scheme for the low - spin collective modes from the spherical to the well - deformed region . the new shell model is expected to describe simultaneously the single - particle and the low - lying collective excitations of all known types , yet keeping the model space tractable even for the heaviest nuclear systems .

performing a shell model calculation for heavy nuclei has been a long - standing problem in nuclear physics . here we propose one possible solution . the central idea of this proposal is to take the advantages of two existing models , the projected shell model ( psm ) and the fermion dynamical symmetry model ( fdsm ) , to construct a multi - shell shell model . the psm is an efficient method of coupling quasi - particle excitations to the high - spin rotational motion , whereas the fdsm contains a successful truncation scheme for the low - spin collective modes from the spherical to the well - deformed region . the new shell model is expected to describe simultaneously the single - particle and the low - lying collective excitations of all known types , yet keeping the model space tractable even for the heaviest nuclear systems .

1407.0406

i

polynomial interpretations are a simple yet useful technique for proving termination of term rewrite systems ( trss , for short ) . while originally conceived in the late seventies by lankford @xcite as a means for establishing direct termination proofs , polynomial interpretations are nowadays often used in the context of the dependency pair ( dp ) framework @xcite . in the classical approach of lankford , one considers polynomials with integer coefficients inducing polynomial algebras over the well - founded domain of the natural numbers . to be precise , every @xmath0-ary function symbol @xmath1 is interpreted by a polynomial @xmath2 in @xmath0 indeterminates with integer coefficients , which induces a mapping or _ interpretation _ from terms to integer numbers in the obvious way . in order to conclude termination of a given trs , three conditions have to be satisfied . first , every polynomial must be _ well - defined _ , i.e. , it must induce a well - defined polynomial function @xmath3 over the natural numbers . in addition , the interpretation functions @xmath4 are required to be _ strictly monotone _ in all arguments . finally , one has to show _ compatibility _ of the interpretation with the given trs . more precisely , for every rewrite rule @xmath5 , the polynomial @xmath6 associated with the left - hand side must be greater than @xmath7 , the corresponding polynomial of the right - hand side , i.e. , @xmath8 for all values of the indeterminates . already back in the seventies , an alternative approach using polynomials with real coefficients instead of integers was proposed by dershowitz @xcite . however , as the real numbers @xmath9 equipped with the standard order @xmath10 are not well - founded , a subterm property is explicitly required to ensure well - foundedness . it was not until 2005 that this limitation was overcome , when lucas @xcite presented a framework for proving polynomial termination over the real numbers , where well - foundedness is basically achieved by replacing @xmath10 with a new ordering @xmath11 requiring comparisons between terms to not be below a given positive real number @xmath12 . moreover , this framework also facilitates polynomial interpretations over the rational numbers . thus , one can distinguish three variants of polynomial interpretations , polynomial interpretations with real , rational and integer coefficients , and the obvious question is : what is their relationship with regard to termination proving power ? for knuth - bendix orders it is known @xcite that extending the range of the underlying weight function from natural numbers to non - negative reals does not result in an increase in termination proving power . in 2006 lucas @xcite proved that there are trss that can be shown polynomially terminating by polynomial interpretations with rational coefficients , but can not be shown polynomially terminating using polynomials with integer coefficients only . likewise , he proved that there are trss that can be handled by polynomial interpretations with real ( algebraic ) coefficients , but can not be handled by polynomial interpretations with rational coefficients . in this article we extend these results and give a complete comparison between the various notions of polynomial termination .. ] in general , the situation turns out to be as depicted in figure [ fig : summary ] , which illustrates both our results and the earlier results of lucas @xcite . ( 0,0 ) node[anchor = south west ] terminating trss rectangle ( 13cm,4 cm ) ; ( 7cm,20 mm ) ellipse ( 36 mm and 13 mm ) ; ( 86mm,25 mm ) ellipse ( 9 mm and 9 mm ) ; ( 75mm,20 mm ) ellipse ( 2 cm and 10 mm ) ; ( 7cm,20 mm ) ellipse ( 36 mm and 13 mm ) ; ( 32mm,12 mm ) rectangle + + ( 7mm,14 mm ) ; ( 36.5mm,20 mm ) node @xmath13 ; ( 52mm,17.5 mm ) rectangle + + ( 5mm,5 mm ) ; ( 54.5mm,20 mm ) node @xmath14 ; ( 92mm,27 mm ) ellipse ( 11 mm and 11 mm ) ; ( 79mm,22 mm ) rectangle + + ( 5mm,5 mm ) ; ( 81.5mm,24.5 mm ) node @xmath15 ; ( 45mm,20 mm ) node @xmath16 ; ( 70mm,20 mm ) node @xmath17 ; ( 98mm,24 mm ) node @xmath18 ; ( 95mm,34 mm ) node @xmath19 ; in particular , we prove that polynomial interpretations with real coefficients subsume polynomial interpretations with rational coefficients . moreover , we show that polynomial interpretations with real or rational coefficients do not subsume polynomial interpretations with integer coefficients by exhibiting the trs @xmath20 in section [ sect : nvsr ] . likewise , we prove that there are trss that can be shown terminating by polynomial interpretations with real coefficients as well as by polynomial interpretations with integer coefficients , but can not be shown terminating using polynomials with rational coefficients only , by exhibiting the trs @xmath21 in section [ sect : nrvsq ] . the trss @xmath22 and @xmath23 can be found in section [ sect : incrementality ] . the remainder of this article is organized as follows . in section [ sect : prelim ] , we introduce some preliminary definitions and terminology concerning polynomials and polynomial interpretations . in section [ sect : qvsr ] , we show that polynomial interpretations with real coefficients subsume polynomial interpretations with rational coefficients . we further show that for polynomial interpretations over the reals , it suffices to consider real algebraic numbers as interpretation domain . section [ sect : nvsr ] is dedicated to showing that polynomial interpretations with real or rational coefficients do not subsume polynomial interpretations with integer coefficients . then , in section [ sect : nrvsq ] , we present a trs that can be handled by a polynomial interpretation with real coefficients as well as by a polynomial interpretation with integer coefficients , but can not be handled using polynomials with rational coefficients . in section [ sect : incrementality ] , we show that the relationships in figure [ fig : summary ] remain true if incremental termination proofs with polynomial interpretations are considered . we conclude in section [ sect : conclusion ] . this paper is an extended version of @xcite , which contained the result of section [ sect : nvsr ] . the results in sections [ sect : qvsr ] , [ sect : nrvsq ] and [ sect : incrementality ] are new .

polynomial interpretations are a useful technique for proving termination of term rewrite systems . they come in various flavors : polynomial interpretations with real , rational and integer coefficients . as to their relationship with respect to termination proving power , lucas managed to prove in 2006 that there are rewrite systems that can be shown polynomially terminating by polynomial interpretations with real ( algebraic ) coefficients , but can not be shown polynomially terminating using polynomials with rational coefficients only . he also proved the corresponding statement regarding the use of rational coefficients versus integer coefficients . in this article we extend these results , thereby giving the full picture of the relationship between the aforementioned variants of polynomial interpretations . in particular , we show that polynomial interpretations with real or rational coefficients do not subsume polynomial interpretations with integer coefficients . our results hold also for incremental termination proofs with polynomial interpretations .

polynomial interpretations are a useful technique for proving termination of term rewrite systems . they come in various flavors : polynomial interpretations with real , rational and integer coefficients . as to their relationship with respect to termination proving power , lucas managed to prove in 2006 that there are rewrite systems that can be shown polynomially terminating by polynomial interpretations with real ( algebraic ) coefficients , but can not be shown polynomially terminating using polynomials with rational coefficients only . he also proved the corresponding statement regarding the use of rational coefficients versus integer coefficients . in this article we extend these results , thereby giving the full picture of the relationship between the aforementioned variants of polynomial interpretations . in particular , we show that polynomial interpretations with real or rational coefficients do not subsume polynomial interpretations with integer coefficients . our results hold also for incremental termination proofs with polynomial interpretations .

1401.7387

c

in this paper we have developed a predictive model for the spatial distribution of bidisperse granular materials in bounded heap flow using a classical transport formalism . the theoretical predictions match well with experimental and simulation results . the model includes the effects of three different mechanisms advection due to mean flow , segregation due to percolation , and diffusion due to random particle collisions . compared with previous predictive models @xcite , the model presented here is based on an understanding of the kinematics of bounded heap flow and has no arbitrarily adjustable fitting parameters . instead , particle configurations are controlled by two dimensionless parameters : @xmath265 and @xmath119 . both parameters are functions of physical control parameters ( e.g. feed rate , @xmath25 , and flowing layer length , @xmath21 ) and kinematic parameters that can be measured from experiments or simulations ( e.g. diffusion coefficient , @xmath5 , percolation length scale , @xmath107 , and flowing layer thickness , @xmath20 ) . particle configurations can be controlled by @xmath1 and/or @xmath0 through the physical control parameters such as @xmath107 ( by changing size ratio ) , @xmath21 , or @xmath25 . furthermore , these two dimensionless parameters reveal the physical mechanisms observed in previous experiments @xcite . @xmath1 describes the interplay between segregation and advection ( essentially the same as the dimensionless time scale @xmath266 in @xcite ) , and @xmath0 represents the interplay between advection and diffusion . a parametric study of @xmath1 and @xmath0 and a dimensional analysis of the timescale of the three different driving mechanisms show how particle configurations in bounded heap flow depend on the interplay of advection , segregation , and diffusion . the kinematic parameters ( @xmath5 , @xmath107 , and @xmath20 ) can be measured from simulations and experiments , but their relationship with the physical control parameters ( @xmath25 , @xmath21 , and the particle sizes , @xmath267 and @xmath268 ) is not yet clear . we are currently investigating whether and , if so , how @xmath1 and @xmath0 can be determined solely from the physical control parameters . the theoretical framework for modeling segregation and mixing of granular flows described here is not limited to quasi-2d bounded heap flow , but can be adapted for other flow geometries ( including three - dimensional systems ) as long as the flow kinematics are accurately determined . this is particularly useful for flows with complicated kinematics such as rotating tumbler flow , where rich segregation - driven patterns have been observed @xcite . new challenges arise , though . in a thin rotating cylindrical tumbler , there are gradients of the shear rate in both the streamwise and normal directions @xcite . moreover , unlike bounded heap flow , the flowing layer thickness in rotating tumbler flow changes significantly along the length of the flowing layer . in addition , the flowing layer length changes in non - circular rotating tumblers , which can result in different particle configurations ( such as radially segregated core patterns or striped patterns @xcite ) . in these cases , @xmath1 and @xmath0 change in both space and time . we thank karl jacob and ben freireich for helpful discussions . we also gratefully acknowledge financial support from the dow chemical company . c. p. s. was supported by nsf grant no .

predicting segregation of granular materials composed of different - sized particles is a challenging problem . in this paper , we develop and implement a theoretical model that captures the interplay between advection , segregation , and diffusion in size bidisperse granular materials . the fluxes associated with these three driving factors depend on the underlying kinematics , whose characteristics play key roles in determining particle segregation configurations . unlike previous models for segregation , our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters , and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi - two - dimensional bounded heaps . the pclet number , , captures the interplay of advection and diffusion , and the second dimensionless parameter , , describes the interplay between segregation and advection . a parametric study of and demonstrates how the particle segregation configuration depends on the interplay of advection , segregation , and diffusion . the model can be readily adapted to other flow geometries . authors should not enter keywords on the manuscript , as these must be chosen by the author during the online submission process and will then be added during the typesetting process ( see http://journals.cambridge.org/data/relatedlink/jfm-keywords.pdf for the full list )

predicting segregation of granular materials composed of different - sized particles is a challenging problem . in this paper , we develop and implement a theoretical model that captures the interplay between advection , segregation , and diffusion in size bidisperse granular materials . the fluxes associated with these three driving factors depend on the underlying kinematics , whose characteristics play key roles in determining particle segregation configurations . unlike previous models for segregation , our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters , and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi - two - dimensional bounded heaps . the model yields two dimensionless control parameters , both of which are only functions of physically control parameters ( feed rate , particle sizes , and system size ) and kinematic parameters ( diffusion coefficient , flowing layer depth , and percolation velocity ) . the pclet number , , captures the interplay of advection and diffusion , and the second dimensionless parameter , , describes the interplay between segregation and advection . a parametric study of and demonstrates how the particle segregation configuration depends on the interplay of advection , segregation , and diffusion . the model can be readily adapted to other flow geometries . authors should not enter keywords on the manuscript , as these must be chosen by the author during the online submission process and will then be added during the typesetting process ( see http://journals.cambridge.org/data/relatedlink/jfm-keywords.pdf for the full list )

1105.4286

c

in this paper we have studied the theory of preheating in the framework of a nonsingular bouncing cosmology with a matter - dominated contracting phase . important in our analysis is that the contracting phase is dominated by an oscillating scalar mater field condensate . we have seen that preheating is driven by a period of stochastic parametric resonance and can in principle explain the origin of the post - bounce entropy . our analysis does not depend much on the precise mechanism which realizes the non - singular bounce since the preheating takes place before the terms yielding the non - singular bounce become very important . the epoch of preheating takes place near the bouncing phase after the amplitude of the condensate has had time to grow to a sufficiently large value for the parametric resonance parameter @xmath73 to become larger than @xmath141 . depending on the magnitude of the coupling coefficient between the condensate and the entropy field @xmath6 , preheating will proceed either throughout the whole pre- and post - bounce intervals during which @xmath61 , or it will end before the bounce . when the coupling is weak , the process of stochastic resonance is similar to that in inflation , but the oscillation number is doubled . therefore , compared with inflationary cosmology , there will be more particles of the entropy field excited in a bouncing cosmology . in the case of strong coupling , the back - reaction of the entropy field can not be neglected and leads to an earlier cutoff for the time interval of stochastic resonance . for a typical parameter values of our model , it is found that parametric resonance terminates before the universe arrives at the bounce point . we also have studied an extended picture of preheating in which the entropy field couples to the background scalar field mainly gravitationally . explicitly , the entropy field couples to the ricci scalar non - minimally and thus can also give rise to parametric resonance . in this approach , we are able to accommodate the entropy generation studied here with the matter bounce curvaton scenario @xcite . according to our qualitative estimates , the condition for the entropy field to preheat geometrically in a matter bounce scenario is slightly easier than in the case of inflation . note that we have not addressed the interesting question of how thermalization after preheating takes place in the context of a nonsingular bouncing universe . this thermalization process involves a lot of non - perturbative effects , and thus calls for corresponding non - perturbative analyses . some numerical studies in the framework of inflationary cosmology were performed in recent years @xcite , and it was found that the evolution of the entropy field enters a regime of turbulent scaling@xcite . we expect that a similar phase could also occur in the matter bounce model . however , the most distinctive difference between preheating in inflation and matter bounce is the initial state . we expect that this could yield new results for thermalization of a bouncing universe . to conclude , we would like to highlight the importance of our analysis . the study of preheating has a lot of applications to other topics , e.g. to topological defect production @xcite , primordial magnetic fields @xcite , induced non - gaussianities @xcite , preheating with non - standard kinetic terms @xcite , and so on . the mechanism of preheating in bounce cosmology , since the initial condition is modified when compared to inflationary preheating , could provide a new window to explore early universe phenomenology combined with particle physics . this process is rather robust and ought to be considered in all bounce models . yc is supported by funds of department of physics at arizona state university . the research of rb is supported in part by a nserc discovery grant at mcgill and by funds from the canada research chairs program . the research of xz is supported in part by the national science foundation of china under grants no . 10533010 and 10675136 , by the 973 program no . 2007cb815401 , by nsfc no . 10821063 , and by the chinese academy of sciences under grant no . kjcx3-syw - 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gaussianity from instant preheating , '' jcap * 0901 * , 011 ( 2009 ) [ arxiv:0810.3913 [ astro - ph ] ] . j. lachapelle and r. h. brandenberger , `` preheating with non - standard kinetic term , '' jcap * 0904 * , 020 ( 2009 ) [ arxiv:0808.0936 [ hep - th ] ] .

preheating describes the stage of rapidly depositing the energy of cosmological scalar field into excitations of other light fields . our results show that the preheating process in bouncing cosmology is even more efficient than that in inflationary cosmology . in the limit of weak coupling , the period of preheating is doubled . for the case of normal coupling , the back - reaction of light fields can lead to thermalization before the bouncing point .

preheating describes the stage of rapidly depositing the energy of cosmological scalar field into excitations of other light fields . this stage is characterized by exponential particle production due to the parametric resonance . we study this process in the frame of matter bounce cosmology . our results show that the preheating process in bouncing cosmology is even more efficient than that in inflationary cosmology . in the limit of weak coupling , the period of preheating is doubled . for the case of normal coupling , the back - reaction of light fields can lead to thermalization before the bouncing point . the scenario of matter bounce curvaton could be tightly constrained due to a large coupling coefficient if the curvaton field is expected to preheat the universe directly . however , this concern can be greatly relaxed through the process of geometric preheating .

1509.00917

r

the strategy for the proof of instability was largely prompted by numerical observations described below . the numerical implementation presented here treats the case @xmath568 of : @xmath569 with @xmath570 and given initial data @xmath571 solution was discretized in space via a ritz - galerkin method . the dynamic problem could be analyzed explicitly using a discretization in time and a runge - kutta scheme , though , rigorous justification of convergence becomes more delicate . another approach is to approximate the successive approximations of theorem [ thm : local ] which , when exact , are guaranteed to converge , at least over small time intervals . the iterates correspond to _ linear _ inhomogeneous pde problems that are resolved using a hybrid scheme : a. for relatively short times find solutions using an approximation of semi - discrete ritz - galerkin method by discretizing time - integrals in the variation of parameter formula . if the error in numerical integration is small , then this approach enjoys an explicit convergence estimate ( for smooth solutions and over finite time intervals ) essentially proportional to the space discretization parameter @xmath572 . b. for larger times , collect the last @xmath93-points of the semi - discrete approximation and resolve the rest of the iteration using a multi - step method ( adams - bashforth ) . thus , we begin with some initial guess @xmath573 } , \dot{u}_{[0]})$ ] and proceed to solve inhomogeneous linear problems @xmath574 } - { \partial}_{xx } u_{[k ] } = f_{[k-1]}\ ] ] on the space @xmath575 with the forcing term from the preceding iteration @xmath576 } = - u_{[k-1]}^2 \dot{u}_{[k-1]}\,.\ ] ] the constants in the estimates and could potentially be determined explicitly in this case ( by following the proof with specific @xmath577 and @xmath578 in the definition of @xmath41 ) which would yield an explicit bound on the lipschitz constant @xmath579 " of the contraction mapping in terms of @xmath380 . in turn , given this constant @xmath580 if @xmath581}-u_{[k-1]}\|_{c_t { \mathscr{h}}^0 } < { \varepsilon}\ ] ] then the absolute error between @xmath93-th iteration and the true solution is no more than @xmath582 . if we use a ritz - galerkin scheme with element size @xmath572 to find an approximate solution @xmath583}$ ] to linear inhomogeneous problem , then for @xmath572 small , e.g. see ( * ? ? ? 13.1 , p. 202 ) , and for simplicity taking the initial conditions to be the more accurate ritz projections of the initial data , we get @xmath581 } - u_{[k , h ] } \|_{c_t{\mathscr{h}}^0 } \leq c h { \int_0^t}|\ddot{u}_{[k]}(s)|_2 ds\,.\ ] ] this estimate of course requires sufficiently regular solutions . as theorem [ thm : well - posed ] and example [ ex : square ] show , in order to have the @xmath584 regularity on @xmath585}$ ] it suffices to have initial data in the space @xmath586 for example , the demonstrated numerical results below use displacement and velocity proportional to the eigenfunctions of @xmath6 , which are smooth . consider an equipartitioned mesh of subintervals of length @xmath572 and the standard piecewise linear nodal basis @xmath587 , with @xmath588 . let @xmath589 denote the restriction of the linear evolution generator @xmath590 to the subspace @xmath591 of @xmath592 spanned by @xmath593 . by @xmath594 denote the elliptic ritz projection on the subspace of @xmath56 and let @xmath595 stand for the corresponding @xmath94 projection . given a candidate approximation @xmath596 } = { \begin{bmatrix } u_{[k-1,h]}\\ \dot{u}_{[k-1,h ] } \end{bmatrix}}\ ] ] we compute the forcing @xmath597}(t , x ) = u_{[k-1,h]}^2(t , x)\dot{u}_{[k-1,h]}(t , x)\ ] ] the coefficient vector @xmath598}$ ] of the projection of @xmath599}$ ] is obtained in terms of the coefficients @xmath600 ( which for this choice of basis functions @xmath601 form a very sparse tensor with only 3 distinct values ) . the initial guess used to calculate @xmath602}$ ] is the constant solution : @xmath603}(t , x ) = ( { \mathcal{r}}_h^{1 } u_0(x))^2({\mathcal{r}}_h^{0 } u_1(x ) ) { \quad\text{for all}\quad}t\geq 0.\ ] ] let @xmath604 denote the projection of the initial data @xmath605 . we obtain a semi - discrete approximation of the original system for unknown coefficient vector @xmath606}$ ] : @xmath607 } ' = -{\mathbb{a}}_h { \mathbf{y}}_{[k , h ] } + { \mathbf{f}}_{[k-1,h]},\qquad { \mathbf{y}}(0 ) = { \mathbf{y}}_0\,.\ ] ] for relatively short times we can invoke @xmath608}(s)ds\ ] ] which is in turn discretized over time scale @xmath609 with @xmath610 . according to @xmath611}(s)ds\,.\ ] ] at each step only the integral over @xmath612 $ ] needs to be computed . for this purpose only several values of the matrix exponentials @xmath613 are needed in order to apply the newton - cotes rule on sub - interval @xmath614 $ ] , specifically : @xmath615 where @xmath578 is number of points used for newton - cotes formula ( e.g. , boole s or simpson s @xmath616th ) . these @xmath617 matrices need to be computed just once and only depend on the time - step , but not the total number of these steps . in turn , the vectors @xmath618 have to be found for each @xmath619 . but since @xmath604 is fixed , these can be more accurately determined using scaling and truncated taylor series approximation @xcite . for simulations over larger time - scales we can use the last few values : @xmath620 to initialize a linear @xmath70-step method , e.g. , @xmath136-step adams - bashforth to efficiently obtain solution on the interval @xmath621 $ ] . as before , let @xmath95 be the eigenfunction @xmath622 for @xmath6 with eigenvalue @xmath623 . then for initial data @xmath624 for constants @xmath625 , @xmath626 , the solution of can be reduced to a dissipative ode using the ansatz @xmath627 plugging it into equation yields @xmath628 this identity would be implied if for each @xmath629 function @xmath378 solves the 2nd - order nonlinear ode @xmath630 @xmath631 it corresponds to a first - order nonlinear system : @xmath632 function @xmath633 is smooth with respect to the components of @xmath634 and to variable @xmath635 , which now acts as a parameter . this ode system has global differentiable solutions , moreover since @xmath636 is smooth , in fact , analytic in @xmath635 then local solutions are differentiable with respect to @xmath635 ( * ? ? ? 3.1 , p. 95 ) . because the initial data is smooth then by theorem [ thm : well - posed ] the unique solution @xmath114 is , among other things , in @xmath637 . consequently @xmath114 must coincide with the solution to the ansatz . in turn , is a dissipative @xmath638 system of odes and can be approximated by a runge - kutta scheme . to get some quantitative estimate on the absolute error of solutions found in section [ particulars ] , at least for initial data of the form , one can consider a piecewise linear interpolation of and then calculate the energy - norm difference from the finite - element solution . the accompanying figures and data demonstrate some of the numerical results . the initial data is considered of the form @xmath639 which permits to compare the finite element solutions to the pointwise runge - kutta solutions described in section [ sec : pointwise - rk ] . figure [ fig:1 ] shows the point - value of displacement @xmath640 next to the displacement value at the same @xmath641 for the corresponding initial boundary value problem _ with linear damping_. figure [ fig:2 ] presents numerical estimates of the energy for solutions obtained by ritz - galerkin finite element scheme and successive approximations . the graphs indicate that the energy decay deteriorates as the frequency of the initial data goes up while the initial finite - energy remains fixed ( @xmath642 independently of @xmath93 ) , thus illustrating the lack of uniform which was rigorously confirmed by theorem [ thm : unstable ] . the initial data are of the form with zero initial velocity . the indicated errors are obtained by comparing each finite - element solution to a piecewise - linear interpolant of the corresponding piecewise rk solution . figure [ fig:3 ] uses multi - step extensions of the same solutions shown in figure [ fig:2 ] to a larger time - scale using ( 5-step ) adams - bashforth method . it also includes the decay of the @xmath50-norm @xmath501 for these solutions .

these theoretical findings were motivated by numerical simulations of this model using a finite element scheme and successive approximations . a description of the numerical approach and sample plots of energy decay are supplied . in addition , for certain initial data the solution can be determined in closed form up to a dissipative nonlinear ordinary differential equation . such solutions can be used to assess the accuracy of the numerical examples . [ pageinit ] department of computing & mathematical sciences , california institute of technology , ca 91125 + department of mathematics , university of nebraska - lincoln , ne 68588 + carroll college , mt 59625 + school of public health , university of michigan , mi 48104 + department of mathematics & statistics , texas tech university , tx 79409 + _ corresponding author : _ [email protected]

presented here is a study of well - posedness and asymptotic stability of a degenerately damped " pde modeling a vibrating elastic string . the coefficient of the damping may vanish at small amplitudes thus weakening the effect of the dissipation . it is shown that the resulting dynamical system has strictly monotonically decreasing energy and uniformly decaying lower - order norms , however , is _ not uniformly stable _ on the associated finite - energy space . these theoretical findings were motivated by numerical simulations of this model using a finite element scheme and successive approximations . a description of the numerical approach and sample plots of energy decay are supplied . in addition , for certain initial data the solution can be determined in closed form up to a dissipative nonlinear ordinary differential equation . such solutions can be used to assess the accuracy of the numerical examples . [ pageinit ] department of computing & mathematical sciences , california institute of technology , ca 91125 + department of mathematics , university of nebraska - lincoln , ne 68588 + carroll college , mt 59625 + school of public health , university of michigan , mi 48104 + department of mathematics & statistics , texas tech university , tx 79409 + _ corresponding author : _ [email protected]

1610.09412

i

the taurus complex of dark clouds is one of the nearest star - forming regions ( @xmath3 pc , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and is relatively well - populated with @xmath4 known members . many of its members reside in loose aggregates near the dark clouds while others are scattered more widely across the @xmath5 deg@xmath1 extent of the cloud complex . even in the aggregates , the stellar densities are only @xmath6 pc@xmath7 , which is 1001000 times lower than the densities of the most compact clusters in other nearby star - forming regions . because the stars and cloud cores in taurus are so sparsely distributed , they have served as some of the best available targets for studying the formation of stars in relative isolation . the close proximity and low density of taurus also made it amenable to observations with early telescopes at x - ray , infrared ( ir ) , and radio wavelengths that had low sensitivity and resolution . as a result , much of the foundational observational work in the field of star formation has been performed in taurus @xcite . stars and brown dwarfs within taurus have been sought with a variety of diagnostics of youth and membership , consisting of photometric variability @xcite , emission lines @xcite , proper motions @xcite , uv emission @xcite , optical and near - infrared ( ir ) photometry @xcite , x - ray emission @xcite , and mid - ir emission @xcite . each survey has been capable of finding members that have specific ranges of mass , extinction , location , and evolutionary stage . the current census of members has the highest level of completeness in @xmath0 deg@xmath1 fields surrounding the richest stellar aggregates . the initial mass function ( imf ) constructed from the known members within those fields @xcite exhibits a large surplus of solar - mass stars relative to the mass functions of clusters like the orion nebula cluster , ic 348 , and chamaeleon i @xcite . given that more massive stars are often found preferentially near the centers of star - forming clusters ( e.g. , * ? ? ? * ; * ? ? ? * ) , it is plausible that the anomalous nature of the imfs measured in the taurus aggregates is at least partially due to mass segregation . to better determine the degree to which the imf in taurus differs from mass functions in other nearby star - forming regions , we have performed a survey for new members of taurus across a large area of the region ( @xmath8 deg@xmath1 ) using optical images from the sloan digital sky survey ( sdss ; * ? ? ? * ; * ? ? ? * ) in conjunction with near - ir data from the two micron all sky survey ( 2mass , * ? ? ? * ) . in our presentation of this survey , we begin by compiling a list of all known members of taurus from previous studies ( section [ sec : previous ] ) . we then select candidate members based on their positions in color - magnitude diagrams constructed from sdss and 2mass data and several other diagnostics of membership ( section [ sec : select ] ) and use optical and near - ir spectra to measure their spectral types and assess their membership ( section [ sec : spectra ] ) . we conclude by using our updated census of members to check for imf variations between the sdss fields , the smaller regions surrounding the stellar aggregates in taurus , and denser clusters like ic 348 ( section [ sec : imf ] ) .

previous studies have found that deg fields surrounding the stellar aggregates in the taurus star - forming region exhibit a surplus of solar - mass stars relative to denser clusters like ic 348 and the orion nebula cluster . to test whether this difference reflects mass segregation in taurus or a variation in the imf , we have performed a survey for members of taurus across a large field ( deg ) that was imaged by the sloan digital sky survey ( sdss ) .

previous studies have found that deg fields surrounding the stellar aggregates in the taurus star - forming region exhibit a surplus of solar - mass stars relative to denser clusters like ic 348 and the orion nebula cluster . to test whether this difference reflects mass segregation in taurus or a variation in the imf , we have performed a survey for members of taurus across a large field ( deg ) that was imaged by the sloan digital sky survey ( sdss ) . we obtained optical and near - infrared spectra of candidate members identified with those images and the two micron all sky survey , as well as miscellaneous candidates that were selected with several other diagnostics of membership . we have classified 22 of the candidates as new members of taurus , which includes one of the coolest known members ( m9.75 ) . our updated census of members within the sdss field shows a surplus of solar - mass stars relative to clusters , although it is less pronounced than in the smaller fields towards the stellar aggregates that were surveyed for previously measured mass functions in taurus . in addition to spectra of our new members , we include in our study near - ir spectra of roughly half of the known members of taurus , which are used to refine their spectral types and extinctions . we also present an updated set of near - ir standard spectra for classifying young stars and brown dwarfs at m and l types .

1610.09412

c

we have attempted to measure the imf across a larger fraction of taurus than considered in previous imf studies of this region to better determine whether it exhibits an anomalous imf relative to denser nearby clusters like ic 348 . to do this , we have performed a thorough survey for new members within a @xmath240 deg@xmath1 field that was imaged by sdss . we have obtained spectra of candidate members appearing in cmds for that field , as well as a miscellaneous sample of candidates across all of taurus that were selected with a variety of diagnostics of membership . through our spectroscopy , we have classified 22 candidates as new members , which includes one of the coolest known members ( m9.75 ) . the update census of taurus now contains 413 members that are resolved by 2mass or _ spitzer_. for the sdss field , we have constructed an extinction - limited sample of members that should be nearly complete down to masses of @xmath60 @xmath55 . that sample exhibits a surplus of solar - mass stars relative to clusters like ic 348 , although it is less pronounced than in previously reported imfs in taurus that have been measured for smaller fields . _ gaia _ @xcite and pan - starrs1 @xcite will soon provide photometry and astrometry that can be used to search the entire extent of the taurus cloud complex for new members down to substellar masses and at low - to - moderate extinctions , which will further improve the statistical accuracy of the measurement of the imf . k. l. acknowledges support from nsf grant ast-1208239 and e. m. acknowledges support from nsf grant ast-1313029 and the nasa nexss program . we thank jackie faherty for providing her spex data and david schlegel and doug finkbeiner for information regarding the sdss data . the gemini data were obtained through program gn-2009b - q-91 . gemini observatory is operated by aura under a cooperative agreement with the nsf on behalf of the gemini partnership : the nsf ( united states ) , the nrc ( canada ) , conicyt ( chile ) , the arc ( australia ) , ministrio da cincia , tecnologia e inovao ( brazil ) and ministerio de ciencia , tecnologa e innovacin productiva ( argentina ) . the irtf is operated by the university of hawaii under contract nnh14ck55b with nasa . 2mass is a joint project of the university of massachusetts and ipac at caltech , funded by nasa and the nsf . funding for sdss has been provided by the alfred p. sloan foundation , the participating institutions , the nsf , the u.s . department of energy , nasa , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , the university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences , los alamos national laboratory , the max - planck - institute for astronomy , the max - planck - institute for astrophysics , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . the het is a joint project of the university of texas at austin , the pennsylvania state university , stanford university , ludwig - maximillians - universitt mnchen , and georg - august - universitt gttingen . the het is named in honor of its principal benefactors , william p. hobby and robert e. eberly . the marcario low - resolution spectrograph at het is named for mike marcario of high lonesome optics , who fabricated several optics for the instrument but died before its completion ; it is a joint project of the het partnership and the instituto de astronoma de la universidad nacional autnoma de mxico . wircam is a joint project of cfht , taiwan , korea , canada , and france . cfht is operated by the nrc of canada , the institute national des sciences de lunivers of the centre national de la recherche scientifique of france , and the university of hawaii . this work used data from the spex prism spectral libraries ( maintained by adam burgasser at http://www.browndwarfs.org/spexprism ) , the nasa / ipac infrared science archive ( operated by jpl under contract with nasa ) , and simbad database , operated at cds , strasbourg , france . the center for exoplanets and habitable worlds is supported by the pennsylvania state university , the eberly college of science , and the pennsylvania space grant consortium .

we obtained optical and near - infrared spectra of candidate members identified with those images and the two micron all sky survey , as well as miscellaneous candidates that were selected with several other diagnostics of membership . we have classified 22 of the candidates as new members of taurus , which includes one of the coolest known members ( m9.75 ) .

previous studies have found that deg fields surrounding the stellar aggregates in the taurus star - forming region exhibit a surplus of solar - mass stars relative to denser clusters like ic 348 and the orion nebula cluster . to test whether this difference reflects mass segregation in taurus or a variation in the imf , we have performed a survey for members of taurus across a large field ( deg ) that was imaged by the sloan digital sky survey ( sdss ) . we obtained optical and near - infrared spectra of candidate members identified with those images and the two micron all sky survey , as well as miscellaneous candidates that were selected with several other diagnostics of membership . we have classified 22 of the candidates as new members of taurus , which includes one of the coolest known members ( m9.75 ) . our updated census of members within the sdss field shows a surplus of solar - mass stars relative to clusters , although it is less pronounced than in the smaller fields towards the stellar aggregates that were surveyed for previously measured mass functions in taurus . in addition to spectra of our new members , we include in our study near - ir spectra of roughly half of the known members of taurus , which are used to refine their spectral types and extinctions . we also present an updated set of near - ir standard spectra for classifying young stars and brown dwarfs at m and l types .

1308.0978

i

in our current understanding of pulsar magnetospheres and radiation mechanisms , strongly magnetized rotating neutron stars play a central role . the underlying plasma processes like particle acceleration , pair creation and pulsed emission profiles throughout the whole electromagnetic spectrum strongly depend on the peculiar magnetic field geometry and strength adopted or extracted from numerical simulations of the magnetosphere . for instance radio emission is believed to emanate from the polar caps , therefore in regions of strong gravity where curvature and frame - dragging effects are considerable due to the high compacity of neutron stars @xmath4 for typical models with its mass @xmath5 , its radius @xmath6 and the schwarzschild radius given by @xmath1 , @xmath7 being the gravitational constant and @xmath8 the speed of light . detailed quantitative analysis of radio pulse polarization and pair cascade dynamics could greatly benefit from a better quantitative description of the electromagnetic field around the polar caps . although there exists an extensive literature about flat space - time electrodynamics , only little work has been done to include general - relativistic effects . the first general solution for an oblique rotator in flat vacuum space - time was found by @xcite with closed analytical formulas . this solution is often quoted to explain the magnetic dipole radiation losses . to be truly exact , we emphasize that the poynting flux @xmath9 derived from his solution does not strictly coincide with the point dipole losses @xmath10 but depends on the ratio @xmath11 , where @xmath12 is the light cylinder radius and @xmath3 the rotation rate of the neutron star . it is only equal to the textbook equation for dipole losses in the limit of vanishing radius @xmath13 . the distinction is meaningful at least for checking results emanating from numerical computations . indeed , because of limited computer resources , we are often forced to take ratios @xmath14 not completely negligible compared to unity . therefore the computed spin - down luminosity can significantly deviate from the point dipole losses . moreover , @xcite showed in the case of an aligned rotator that the electric field induced by frame - dragging effects could be as high as the one induced by the stellar rotation itself . these results were extended to an oblique rotator a few years later by thanks to a formalism developed earlier by @xcite . it is therefore crucial to treat maxwell equations in the general - relativistic framework in order to analyse quantitatively acceleration and radiation in the vicinity of the neutron star . this led @xcite to seek for an approximate solution of maxwell equations in a curved space - time either described by the schwarzschild metric or by the kerr metric , using a linearised approach employing the newman - penrose formalism . he computed the structure of the electromagnetic waves propagating in vacuum and launched by a rotating dipole . he also gave an expression for the poynting flux @xmath15 depending on the ratio @xmath11 . the exact analytical solution for the static magnetic dipole in schwarzschild space - time was given by @xcite and extended to multipoles by . @xcite also studied the influence of space - time curvature and frame dragging effects on the electric field around the polar caps of a pulsar and confirmed the earlier claims of an increase in its strength . @xcite computed the electric field for an aligned rotator in vacuum in the schwarzschild metric . the aligned rotator has also been investigated by @xcite with special emphasize to particle acceleration in vacuum . @xcite and @xcite took a similar approach to study the acceleration of particles around polar caps . @xcite computed the electromagnetic field in the exterior of a slowly rotating neutron star in the slow rotation metric as well as inside the star and investigated the impact of oscillations . they gave approximate analytical expressions for the external electromagnetic field close to the neutron star . @xcite extended the previous work by solving numerically the equations for the oblique rotator in vacuum in general relativity . they retrieve @xcite results close to the surface and the deutsch solution for distances larger than the light cylinder @xmath16 . it is the purpose of this paper to elucidate quantitatively and accurately some aspects of general - relativistic effects on the electrodynamics close to the neutron star . our goal is to derive a general formalism to compute the solution of maxwell equations in curved space - time for any multipole component of the magnetic field . consequently , we use a 3 + 1 formalism of electrodynamics in curved space - time as presented in [ sec : modele ] . next we show how to solve for the electromagnetic field for an aligned rotator in [ sec : aligne ] . this method is easily extended to a perpendicular rotator as explained in [ sec : orthogonal ] . because maxwell equations in vacuum are linear , the most general solution for an oblique rotator will be a linear superposition of the weighted aligned and perpendicular rotator . conclusions and future possible work are drawn in [ sec : conclusion ] .

being highly compact objects with compactness close to , where is the schwarzschild radius and the mass and radius of the neutron star , general - relativistic effects become important close to their surface . this is especially true for the polar caps where radio emission is supposed to emanate from , leading to well defined signatures such as linear and circular polarization . in this paper , we derive a general formalism to extend to general relativity the deutsch field solution valid in vacuum space .

pulsars are thought to be highly magnetized rotating neutron stars accelerating charged particles along magnetic field lines in their magnetosphere and visible as pulsed emission from the radio wavelength up to high energy x - rays and gamma - rays . being highly compact objects with compactness close to , where is the schwarzschild radius and the mass and radius of the neutron star , general - relativistic effects become important close to their surface . this is especially true for the polar caps where radio emission is supposed to emanate from , leading to well defined signatures such as linear and circular polarization . in this paper , we derive a general formalism to extend to general relativity the deutsch field solution valid in vacuum space . thanks to a vector spherical harmonic expansion of the electromagnetic field , we are able to express the solution to any order in the spin parameter of the compact object . we hope this analysis to serve as a benchmark to test numerical codes used to compute black hole and neutron star magnetospheres . [ firstpage ] stars : neutron - stars : magnetic fields - general relativity - methods : analytical - methods : numerical

1407.1535

i

when building devices for quantum information processing one has to take changing environment conditions and device imperfections into account . it is therefore necessary to include adaptive mechanisms that characterize and calibrate the device from within . furthermore , it is desirable for these devices to obtain a certain degree of autonomy in maintaining their functional state despite detrimental environment influences , in particular , when they are assembled to a larger quantum information processing infrastructure . in the attempt to miniaturize current implementations of quantum devices , we will reach the point where these devices will be of microscopic scale and require short reaction times . for such microscopic systems we can no longer assume that their internal controllers are full - fledged universal computers that can carry out arbitrary programs . instead , controllers will be small physical systems that are specialized for their respective purpose with a program that emerges from the controller s analog dynamics . in this paper we explore the applicability of a controller in form of an intelligent learning agent that has access to a _ projective simulator _ @xcite . within this agent framework , the aim is to demonstrate adaptive calibration and compensation strategies against stray external fields when carrying out quantum information tasks . the agent shall thereby implement a simple form of adaptive error avoidance and implicit parameter estimation . algorithms from machine learning have been used to find strategies for parameter estimation , and optimal strategies for parameter estimation are known for specific cases , see e.g. @xcite . here , however , we focus on strategies that arise naturally from the adaptive dynamics of the underlying physical system , for which we choose a projective simulator . the projective simulator is a platform that has been proposed as a physical model for reinforcement learning @xcite , and it effectively reproduces input output reward correlations from an internal adaptive stochastic process . with the restriction to this particular system , one can not hope for the best possible strategy to emerge while keeping the rules governing the dynamics reasonably simple and computational overhead low . both requirements are necessary to allow for an actual physical realization . as an additional feature , the projective simulator offers a natural route to quantization as indicated in @xcite and thereby a way to intelligent agents that benefit from internal quantum dynamics , as demonstrated in the reflective quantum projective simulator @xcite . agent quantization is not explored further in the present work as we focus on the application of a classical agent to quantum information processing first . for recent comprehensive reviews in the domain of quantum physics and artificial intelligence or machine learning see @xcite and @xcite . as illustration of our method of adaptive quantum information processing we study grover s quantum search algorithm @xcite in the paradigm of measurement - based quantum computation . grover s algorithm provides a fast way to find a marked item in an unsorted database with @xmath0 elements . in particular , it provides a quadratic speed - up with @xmath1 database look - ups over a search by means of a classical computer with @xmath2 look - ups . first proof - of - principle implementations of grover s algorithm with nuclear magnetic resonance techniques @xcite and entangled photons @xcite employed the circuit model of quantum computation , where individual unitary quantum logic gates are applied to a register of qubits to process information . measurement - based quantum computation ( mbqc ) @xcite is a different paradigm of quantum computation , where the computation is carried out by measuring single qubits of an initially highly entangled resource state @xcite . the first experimental demonstration of mbqc in a system of entangled photons @xcite ( and with trapped ions @xcite ) also demonstrated the grover algorithm in its smallest realization with a database of 4 entries ( 2-qubits ) by using a 4-qubit cluster state as computation resource . as preparation for the full measurement - based algorithm we first study a basic setting . we situate a quantum system , a single qubit , in an unknown external magnetic field . an artificial agent , the controller , is endowed with a projective simulator and the ability to measure the quantum system and thereby prepare quantum states . we hardwire the learning process , i.e. , the update rule in the reinforcement learning process of the projective simulator , such that the agent effectively carries out the following tasks : ( i ) adapt measurement directions to changes of the external magnetic field , and dynamically improve the sensing resolution . ( ii ) learn to adapt simultaneously for multiple measurement directions needed for general mbqc - algorithms in a feedback scheme . ( iii ) carry out a quantum information task , the grover algorithm @xcite in the setting of measurement - based quantum computation , with unknown stray magnetic fields . this provides a completely worked - out example , starting from the physical system that generates the actions of an adaptive `` intelligent '' agent , here a projective simulator , to a controller tailored to a specific quantum information task , e.g. measurement - based grover s search algorithm .

quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation . in a setting of measurement - based quantum computation , we assess the agent s learning behavior in static and time - varying fields and explore composition strategies in the projective simulator to improve the agent s performance . thereby , we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks .

quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation . in a setting of measurement - based quantum computation , we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction . we assess the agent s learning behavior in static and time - varying fields and explore composition strategies in the projective simulator to improve the agent s performance . we demonstrate the applicability by correcting for stray fields in a measurement - based algorithm for grover s search . thereby , we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks .

1407.1535

r

first , we describe an approach that allows the projective simulator to effectively obtain a notion of the strength of an external magnetic field and hence carry out a primitive form of parameter estimation . however , there is a conceptual difference between our approach and parameter estimation . after the agent has learned , the information on the strength of the magnetic field will _ not _ be available as a number that the agent gives as an output . instead , this information is only indirectly incorporated into the dynamics and decision patterns of the agent , and it can be exploited to _ do _ certain things that are adapted to the external field . therefore , we will analyze the learning process of the agent from two different perspectives : from an _ operational _ perspective we characterize how well the agent adapts its actions to the external field , and from an _ informational _ perspective we quantify how much of the information about the external field is really contained in the parameters that define the dynamics of the agent . we start with a detailed description of the setting , that is , of the agent and its interaction with the measurement apparatus , the dynamics of the projective simulator , and an analysis of the learning process . in the present setting the magnetic field direction is promised to be fixed along the @xmath3-axis , and the agent needs to estimate its strength @xmath4 . the following steps are visualized in figure [ fig : agentsetup ] . the agent starts by preparing a single qubit in the state @xmath5 , which in the presence of the field evolves according to the hamiltonian @xmath6 , where the frequency @xmath7 is proportional to the magnetic field strength @xmath4 . after some fixed time interval @xmath8 , the initial state has evolved into @xmath9 up to a global phase , with @xmath10 . estimating the field strength @xmath4 amounts to estimating @xmath11 and obtaining information about the angle @xmath12 between this state and the initial state in the equatorial plane of the bloch sphere . in a linear optics setup @xcite , the unknown angle @xmath12 would correspond to an unknown phase shifter in the beam line . the agent measures the qubit in the unknown state @xmath11 in various directions and incorporates the measurement outcomes to change its choice of measurement directions . the measurements applied by the agent are in general described by povms @xcite . for simplicity , we will restrict our analysis to projective measurements . we shall comment on the general case at the end of the paper . the challenge is to effectively realize a probability distribution for the unknown angle @xmath12 without explicitly performing computations and analyzing the measurement data . rather it should emerge dynamically as the result of a feedback loop by reinforcing certain actions on the quantum system . therefore , we choose an approach where the internals of the agent are wired such that it tries to optimize the direction of a measurement . in the optimal case @xmath11 is the @xmath13 eigenstate of this measurement . qubit observables whose eigenstates with eigenvalues @xmath14 lie in the equator of the bloch sphere are given by @xmath15 where @xmath16 is of the form with angle @xmath17 . both eigenstates lie on opposite sides of the equator . the probability to obtain the measurement outcome @xmath14 is @xmath18 that is , the closer the angles @xmath17 and @xmath12 the higher is the probability to obtain the @xmath13 measurement outcome . to simplify notation we often consider the projector onto the @xmath13 eigenstate @xmath19 instead of the observable @xmath20 , and measurements of the projector with outcomes 1 and 0 . for qubits , measuring @xmath21 gives the same statistics of measurement outcomes and resulting states as measuring the observable @xmath20 because there is a unique state orthogonal to @xmath16 . the projective simulator inside the agent employs an adaptive stochastic process that is modeled by a random walk of an excitation in a network of so - called `` clips '' @xcite . for now the clip network takes the form of a directed weighted graph depicted in figure [ fig : network_1to4 ] . the random walk starts at the only `` percept clip '' , which is excited by an internal trigger of the agent with a time interval @xmath8 after the qubit has been prepared ( cf . figure [ fig : agentsetup ] ) . the excitation propagates in the network according to the weights of the links that connect the percept clip to the action clips . once the excitation reaches an action clip , the corresponding action is performed and the process inside the projective simulator is finished . a single action is a measurement of a certain @xmath21 at the qubit . if the measurement outcome is @xmath13 it is fed back as reward to the agent to re - enforce and strengthen the link between the percept clip and the last action clip . the process is repeated for the next measurement . the probabilities to select certain measurements , however , change as a result of previous measurement outcomes . this makes measurements with angles @xmath17 closer to @xmath12 more likely . these probabilities in effect represent a coarse - grained , discrete probability distribution over angles @xmath12 . -clip , which then undergoes random walk dynamics according to the weights of the links . the action clip where the excitation arrives determines the measurement direction . ] in detail , each link in the clip network carries a weight @xmath22 . the probability to jump from the percept clip `` @xmath23 '' to the action clip corresponding to @xmath21 is given by the normalized weight of all edges from the percept clip , that is , @xmath24 at the beginning of the learning process all weights are initialized with @xmath25 . after the measurement of @xmath21 in the @xmath26-th round , the measurement outcome ( 0 or 1 ) is rescaled by a factor @xmath27 and fed back into the projective simulator as a reward @xmath28 to the transition with weight @xmath22 . regardless of whether or not a transition has been taken , all weights are damped by a small amount with rate @xmath29 . after the @xmath26-th round , in which @xmath17 was the measurement angle , all weights are changed according to the following update rule : @xmath30 as a result , the projective simulator converges to a state ( set of @xmath31-values ) that increases the chances of obtaining @xmath13 measurement outcomes and thereby increases the probability to measure in directions close to @xmath12 . from the perspective of the projective simulator only an outcome @xmath13 denotes success because the action that led to this outcome will be reinforced . this `` subjective '' success probability is @xmath32 an action that leads to a reward ( measurement result @xmath13 ) is also the correct action from an operational point of view . the transition probabilities @xmath33 provide an internal representation of a discretized probability distribution for the angle @xmath12 . the change of @xmath34 as a function of the number of rounds ( measurements on the quibt ) is depicted in figure [ fig : learning_single_phi ] for several examples of @xmath12 . the results in figure [ fig : learning_single_phi ] show that the agents learns to obtain rewards more often and thus obtains information about the state @xmath11 and thereby about @xmath4 . in our example we start with 4 projectors at angles every @xmath35 , which corresponds to the projectors onto the eigenstates of the observables that are given by the pauli matrices @xmath36 and @xmath37 . if @xmath38 , measurements of @xmath39 will always give outcome @xmath13 and hence be rewarded . the two adjacent projectors at @xmath40 and @xmath41 are rewarded in half of the measurements , and measurements in the direction @xmath42 are never rewarded . in this situation the projective simulator builds a strong link to @xmath39 , somewhat less strong links to @xmath43 and @xmath44 and leaves the link for @xmath45 at its initial value . the coarse - grained discrete probability distribution for @xmath12 is consequently peaked at @xmath38 and within statistical fluctuations symmetric around this direction ( figure [ fig : learning_single_phi ] top left inset ) . if @xmath12 is between two of the projectors , say @xmath46 , measurements of @xmath39 and @xmath43 will only be rewarded with only @xmath47 probability , and measurements of the opposite projectors with @xmath48 probability . the distribution of measurement probabilities will also be symmetric around the direction @xmath49 but less pronounced as shown by a broader distribution in figure [ fig : learning_single_phi ] ( bottom left inset ) . a broad distribution for measuring in the direction @xmath17 results in a lower success probability for angles that have a large distance to all projectors , e.g. , @xmath50 . at this point a smaller damping rate @xmath29 and a larger multiplier of the rewards @xmath27 both lead to a larger value of rewarded transitions in the steady - state and hence to a larger success probability and a probability distribution that is more peaked . at the same time increasing both @xmath27 and @xmath29 speeds - up the learning process leading to learning curves with a steeper initial rise . note , however , that extremal cases with too large rewards or too weak damping favor situations in which the agent prefers actions that just by luck led to a reward in the past although they are not highly rewarded on average . un - learning such an initial `` misunderstanding '' and building a probability distribution that reflects the actual probabilities of being rewarded may take a long time . this aspect leads to larger fluctuations in the success probability of an ensemble of agents and a slower final convergence . _ asymptotic success probability._for the asymptotes of the success probability we can find a first - order approximation by assuming a steady state of the transition probabilities @xmath51 and the respective @xmath31-values . the resulting steady - state success probability is @xmath52 . when coarse - graining over many measurements the time average of the reward for each action is given by @xmath53 , and the steady - state probability to measure in direction @xmath17 is @xmath54 . with these assumptions the update rule turns into a set of coupled equations for the steady - state values @xmath55 , @xmath56 in which the loss terms given by the damping @xmath29 and the gain terms given by the time - averaged reward are in equilibrium . this set of nonlinear equations can be solved numerically and yields a very good approximation for the ensemble average as seen in figure [ fig : learning_single_phi ] . the asymptotic value obtained in this approximation only depends on the ratio @xmath57 . : states are summarized as the position of the resulting vectors @xmath58 for each agent @xmath59 in the complex plane ( equatorial plane ) . the degeneracy with respect to the expected reward for @xmath60 provides a manifold of equally successful states , which is populated by the ensemble . blue dot on the unit circle gives the angle of the ensemble average , the black dot is the angle @xmath12 . ] ( left ) the action pair @xmath39 and @xmath43 is degenerate with respect to the expected reward . for @xmath61 ( middle ) , i.e. , not exactly between two projectors , the agent measures more often into the direction @xmath62 . fluctuations in the measurement probabilities do not necessarily show in the success probability . for comparison , the ensemble averages of 1000 agents after 1000 measurements are given as dashed lines . larger rewards @xmath27 and damping @xmath29 ( both rescaled by a factor 10 ) decrease the timescale of the fluctuations while maintaining approximately the same time average ( right ) . the agent jumps between different preferred action and stays for extended times . ] _ time average vs. ensemble average._the fluctuations of the probabilities to choose certain actions ( see insets in figure [ fig : learning_single_phi ] ) show that even after 1000 iterations of the update rule not all agents have converged to a single state ( figure [ fig : ensembleaverage ] ) . many steady states occur if there is a whole manifold that is rewarded equally , that is , when two or more actions have the same expected reward . for example , for @xmath60 both actions @xmath39 and @xmath43 have equal chances of being rewarded and thus the there is no preference of either action as long as one of them is carried out . actions that have the same expected reward span a subspace for which the sum of the probabilities for doing these actions is approximately constant in the steady state , however , their relative ratio is not . the states of the whole ensemble of agents fills this degenerate subspace of action probabilities . the ensemble average yields an approximation of @xmath12 . although the ensemble has learned , i.e. , the success probability has converged , the dynamics of each individual is not necessarily converged to a single state where it remains . in the course of time the state of a single agent explores the whole degenerate reward manifold while keeping the success probability constant as we numerically illustrate in figure [ fig : timeaverage ] . we find that the time average of a single agent for long times equals the ensemble average because the state of the single agent assumes all the different steady states that an ensemble produced after short time as in figure [ fig : ensembleaverage ] . hence , to obtain an ensemble average a snapshot after a relatively short time is sufficient . however , if there is a degenerate space in the reward scheme , the state of a single agent at a fixed time gives only an imprecise estimate of @xmath12 , and even its time average does when considered only for a short time . a larger damping parameter @xmath29 and higher rewards @xmath27 facilitate a faster exploration of the degenerate reward manifold and thus provide a better time average for a single agent for shorter times . for @xmath60 in figure [ fig : timeaverage](right ) , the agent selects either @xmath62 or @xmath35 for an extended time and then suddenly switches between these equally rewarded choices . this jumping behavior occurs for large reward and damping , whereas for smaller values ( left ) also equal probabilities occur for longer durations . the way that the agent uses the rewards to change its actions to do measurements more often along angles that are close to @xmath12 , is a way of representing information about @xmath12 . we regard this probability distribution of actions along the discrete set of angles as a probability distribution of @xmath12 @xcite , and compare it to standard computational analysis procedures employed in state and parameter estimation . by its actions and the returned rewards the agent effectively samples the reward distribution @xmath63 . the same data , namely the measurement direction and outcome , however , can also be used in a bayesian update rule to explicitly build a probability distribution @xmath64 , or the data can be used to reconstruct the state @xmath11 via state tomography . we compare the angular distribution of actions that the agent maintains to the angular distribution that a bayesian update would produce , and also to a simple state tomography by estimating expectation values from the same measurement data . a simple form of state tomography can be done by calculating the expectation values @xmath65 and @xmath66 from the measurement results of the four projective measurements . together with the initial assumption @xmath67 , these expectation values give an approximation of the state s bloch vector . our four measurement directions @xmath68 give the same measurements as the pauli matrices with expectation values @xmath69 where expectation values of the observables can be related to those of the projectors by @xmath70 for a total of @xmath71 measurements , of which @xmath72 are done in direction @xmath17 , with individual measurement outcomes @xmath73 for observable @xmath20 , the expectation values can be approximated with the mean @xmath74 the resulting bloch vector with coordinates @xmath75 provides an angle with the @xmath76-axis and thereby an estimate of @xmath12 . in a bayesian analysis , we update an initially flat prior distribution @xmath77 with the information obtained from each measurement . after each measurement , the distribution is updated with result @xmath78 for measurement in direction @xmath79 , e.g. , for the first update @xmath80 where we include the knowledge of quantum mechanics and the statistics of measurement outcomes for the underlying system with @xmath81 given by . after @xmath82 measurements the resulting probability distribution is @xmath83 with normalization @xmath84 . for an efficient update and a compact representation of the conditioned probability distribution we expand it in a fourier series , which has at most @xmath82 higher harmonics , and construct an recursive update rule for the expansion coefficients following the approach in @xcite for parameter estimation with a single fixed observable but variable time delays . for our choice of measurement directions , with @xmath17 being a multiple of @xmath35 , the fourier expansion generally contains @xmath85 and @xmath86 terms . the recursive update rules for the expansion coefficients are given in the appendix . . the data points represent the measurement data of 10 agents from 1500 measurements each , and they give an estimate of the angle @xmath12 as the mean of the 10 distributions . the 10 data points are supplemented by a black error bar , which indicates their circular mean and circular standard deviation . for the projective simulator , the blue error bar indicates the circular mean and circular standard deviation of the discrete probability distribution over the 4 actions , after averaging over all 10 agents . for most examples of @xmath12 the projective simulators generate a distribution of the mean angles that coincide with @xmath12 except for @xmath61 , where similar as in figure [ fig : ensembleaverage ] a bias towards the nearest available projector ( @xmath62 ) occurs . ] to compare the estimates of @xmath12 by these three approaches , we fix the angle @xmath12 , and let 10 agents with a projective simulator do 1500 measurements each and according to the dynamics arising from using the projective simulator . after these 1500 measurement each agent has built a probability distribution of actions @xmath33 , we take the mean of each distribution as the estimate of @xmath12 . figure [ fig : distributioncomparison ] shows these estimates as the blue data points . because the probability distributions for @xmath12 that we obtain from the @xmath33 have support only on 4 angles , which are uniformly and discretely spaced on the circle , each distribution has a large variance . we average the distributions of all 10 agents and give the mean and circular standard deviation of the resulting distribution as the blue error bar in figure [ fig : distributioncomparison ] for comparison . clearly , when @xmath12 is close to one of the possible choices of @xmath17 , the projective simulator captures @xmath12 accurately , but for values of @xmath61 or @xmath49 the estimates are biased towards one of the @xmath17 as in figure [ fig : ensembleaverage ] . for @xmath60 the angular means are widely spread , and their distribution has a large variance , which is reminiscent of the distributions given in the insets in figure [ fig : learning_single_phi ] and the distribution of means of a large ensemble in figure [ fig : ensembleaverage ] . the estimates for @xmath12 obtained from the expectation values of the pauli matrices , i.e. , the simple state tomography , are calculated from the same measurement record for each agent and are given by the orange data points in figure [ fig : distributioncomparison ] . for the bayesian update scheme , we construct the conditional probability distributions for @xmath12 , again from the same measurement record that the projective simulator generated . all of the resulting distributions assume an approximate gaussian shape with a narrow peak ( @xmath87 ) . the means are given as red data points in figure [ fig : distributioncomparison ] . both approaches can estimate @xmath12 correctly within the error bars . surprisingly , for @xmath12 along one of the @xmath17 , the estimates from the expectation values spread more than in the other two approaches . the reason is that in these cases the projective simulator samples most of measurements along a single direction and only few for the other observable , which causes a rather large uncertainty in one of the coordinates . although state tomography and bayesian estimation perform generally equally good or better than the projective simulator , the big conceptual difference between these approaches is that very little knowledge of quantum physics and measurement statistics is build into the projective simulator . the projective simulator does not assume that the rewards originate from measurement probabilities of a quantum state and , therefore , it is `` model free '' . the update rule causes a learning dynamics that drive the agent to measure more often into directions that give a + 1 measurement outcome and thereby implicitly align measurement directions with @xmath12 . even when no optimal measurement direction is available the agent learns how to deal with a system such that reward is most likely to occur . in principle , it could even adapt to artificial situations , where measurements along the @xmath76-axis always give a @xmath13 outcome and measurements along @xmath88 always give the outcome @xmath89 , something which can not be explained by measuring a qubit in a defined fixed state . therefore , it is not surprising that methods that make use of additional information , namely measurement probabilities predicted by quantum physics , can extract more information about @xmath12 from the measurement results . given that an agent with a projective simulator lacks this additional information it does comparably well , and , conceivably , it can be improved by changing the update rule to incorporate more knowledge about the underlying quantum physics . for example , a positive measurement result and reward in one direction can be combined with a negative reward into the opposite direction , or , for each measurement result the reward is distributed according to how close all potential actions are to the rewarded one . an important feature of the projective simulator is its ability to forget and thus to adapt to a changed situation . this ability distinguishes the present setting from schemes of parameter estimation , where the unknown parameter is assumed to be constant . for example , for a changing parameter standard bayesian updating can not be applied because past information needs to be disregarded and only recent information should be considered for estimating the current parameter . the projective simulator , in contrast , keeps track of an integrated average of past rewards for each action and is endowed with an element , the damping quantified by @xmath29 , to forget these rewards . the agent has the ability to completely change its behavior regardless of what has been rewarded earlier and irrespective of its earlier state . we shall consider two of such relearning scenarios in the following . we analyze the relearning by means of two quantities , the asymptotic success probability and the learning time it takes the agent to adapt . leading to a shift from @xmath12 to @xmath90 . an ensemble of 1000 agents first learns with @xmath12 for @xmath91 measurements , after which the angle changes to @xmath90 for another @xmath91 measurements , @xmath92 , @xmath93 . * top : * examples of learning curves for 4 different switches . @xmath12 and @xmath90 are given in the same color as the corresponding learning curve ( @xmath94 for blue and @xmath95 for the other examples ) . * middle : * the asymptotic success probability ( analytically obtained ) shifts due to the change in angles . * bottom : * the relearning time @xmath96 to reach 90% of the asymptotic success probability after the field has changed also gives rise to a periodically repeating pattern and shows a structure commensurate with the choice of projectors in intervals of @xmath35 . ] _ relearning after a switched field._ changes of @xmath4 result in a different @xmath12 and require the agent to adapt and relearn . for a single sudden change in @xmath4 the angle @xmath12 changes only once at a certain time to a new angle @xmath90 . depending on the values of @xmath12 and @xmath90 the agents shows a rich landscape of relearning patterns as illustrated in figure [ fig : relearning ] . after the switch the asymptotic success probability is always that of the new @xmath90 and may lie above or below the success probability of the old @xmath12 ( figure [ fig : relearning ] top ) . the change in @xmath97 is illustrated in figure [ fig : relearning ] ( middle ) . the sudden drop or increase in success right after the change of the angle and the time to reach a success probability depends strongly on the relation of the two angles and how much of the internal state ( @xmath31-values ) needs to be changed to reach the new state . these effects in the relearning time appear in addition to the known effects of changing the reward scaling @xmath27 and damping rate @xmath29 @xcite . a summary of the relearning times and change in asymptotic efficiencies is given in figure [ fig : relearning ] ( middle and bottom ) . _ time - dependent fields._an important feature for applications is the agent s ability to adapt its actions to slowly changing external fields . an agent s state is the result of a dynamical equilibrium between rewarded actions in the past and forgetting this information on a time scale given by @xmath29 . therefore , the speed at which an agent can adapt is limited by the speed with which it can modify its internal state . the agent can adapt to a change in the reward landscape caused by a changing field as long as it has enough time to sample the modified reward landscape and modify its internal state accordingly , which depends on @xmath27 and the timescale given by @xmath29 . figure [ fig : timedependentfields ] shows two examples . the first example ( left ) is a setting with a fast oscillating field , i.e. , one with @xmath98 as a function of the measurement round @xmath26 , where only the time average is learned because the agent effectively takes samples from the entire reward landscape . the state vector converges to angle @xmath38 and reaches almost unit length . the second example ( right ) shows a setting with a linearly increasing magnetic field , giving rise to @xmath99 . as @xmath12 moves anticlockwise on the unit circle as a function of the measurement round , the agent can keep up as quantified by @xmath100 with a state trajectory that also moves counterclockwise albeit with a slight delay and the length of the state vector is longer , i.e. , the field is learned better , for a slower rate of change . as averaged over an ensemble of 1000 agents . the state vector of the ensemble starts in the origin . * left : * for fast oscillating fields @xmath101 with @xmath102 ( red ) and @xmath103 ( blue ) the agents adapt to the average angle @xmath38 over 5000 measurements . data points are explicitly indicated for the first 20 measurements and joined by a line . * right : * linearly drifting fields @xmath104 can be learned by the agent the better the slower they change on the timescale of the learning time : @xmath105 ( blue ) shown for 10000 measurements , and @xmath106 ( red ) , @xmath107 ( orange ) shown for 4000 measurements each . the ensemble follows the field and the state trajectory converges to a limiting cycle . ] the choice of projectors that the agent can measure affects the agent s success in two ways : on one hand it fixes the available angles and thereby ability to measure the correct angle . a finer grained sample of measurement angles is beneficial because it will contain an angle that is closer to the actual angle and allow for almost perfect measurements . it also avoids efficiency minima due to the coarse - graining as they appear in figure [ fig : learning_single_phi ] ( top , right ) . a finer resolution of measurement angles , however , will introduce many angles that are almost equally successful and are hard to distinguish by their average reward . on the other hand , the choice of measurement angles fixes the discrete support on which the probability distribution for @xmath12 can be built , which contains the information on the angle @xmath12 . a drawback of a coarse - grained support is the arising large variance in the distribution . a fine - grained support , however , needs lots of sampling to evaluate each individual point in the distribution . measurement directions initially available to an agent ( blue ) , uniformly spaced on the circle , and with additional bisection compositions ( red ) . data points are angular averages , and the vertical region denotes the maximum and minimum of the success probability . these data summarize the angular dependence of @xmath97 as depicted for several examples in the inset . the reason for a decrease of @xmath97 with an increase in measurement directions is due to damping . ] as there are advantages and disadvantages to the number of measurement directions , we ask if there is an optimal number of fixed projectors . in order to distinguish directions on a circle , at least three directions are needed . ( for just two directions that are equally successful , it is not possible to decide which of the two angles between those two directions is the correct one . ) we have calculated the asymptotic success probability for an agent that has access to @xmath108 measurement angles that are equidistantly spaced on the unit circle , i.e. , it can measure @xmath109 observables of the form with two eigenstates each that are opposite on the equator of the bloch sphere . the angular dependence of the success probability in figure [ fig : initialprojectorscomposition ] ( inset ) shows maxima at angles that are measurement directions and minima between two neighboring angles . as more observables are added , the worst cases in between two neighboring projectors improve , but at the same time also the optimal cases decrease because the optimal angle is not chosen as frequently due to slightly better neighboring angles that are also rewarded more often . the success probability averaged over all angles first increases and then decreases as summarized in figure [ fig : initialprojectorscomposition ] . in the limit of large @xmath109 the success probability converges to 50% because of the constant damping @xmath29 . in the example case with @xmath92 and @xmath93 we can give these recommendations : for optimizing the best case , the number of 2 projectors is optimal , for the best worst case success probability , 8 projectors are best , and for the best average success probability 6 projectors are the best initial choice . a strategy to mitigate the decrease in overall efficiency for a more refined angular resolution is _ composition _ , which is one of the original features of projective simulation @xcite . with composition the projective simulator is endowed with the ability to generate new clips based on the composition of already existing ones . for parameter estimation the projective simulator can insert new clips with new measurement directions only where additional resolution is needed . the composition mechanism is an additional dynamical element in the projective simulator . based on the state of the projective simulator it is triggered and inserts a new clip based on existing ones . these new elements , i.e. , the trigger mechanism , constructing the new clip , and how the new clip is inserted into the network must be specified and leave room for arbitrarily complicated rules . we will restrict to the simplest mechanisms , which will also draw some intuition from actual conceivable physical dynamics . _ bisecting composition._the first composition mechanism simply operates by bisection and refining the resolution in the relevant regions . after the agent has learned with its initial set of projectors , the two actions clips with the largest @xmath31-values are selected and used to compose a new clip between the two . in situations with angles @xmath60 or @xmath110 the action clips with @xmath62 and @xmath35 will have the largest @xmath31-values and give rise to the creation of a new clip with @xmath50 , which improves the resolution of the discretization in the first quadrant . the success probability before and after one such composition is depicted in the inset in figure [ fig : initialprojectorscomposition ] as light blue and red curve , respectively . for the angle @xmath60 the success probability is increased from a minimum of 83.4% to a maximum with 96.2% without adding unnecessary projectors in the remaining quadrants , which would lower @xmath97 to 93.2% of the curve with 8 projectors . when always adding a single additional angle in the middle of the quadrant in which @xmath12 lies , worst case scenarios for @xmath97 appear only for angles like @xmath110 and @xmath111 with 93.32% , which still is a slight improvement over the coarse graining with only 4 projectors ( 93.26% ) . for @xmath61 the composition at @xmath50 is helpful but suboptimal . for angles at the projectors , e.g. @xmath38 , an additional composition is harmful and decreases @xmath97 from 97.1% to 96.1% . a single composition that doubles the angular resolution in one quadrant is qualitatively similar to 8 initial measurement angles , but with a higher success probability . a second composition step that adds another projector with an angle of odd multiples of @xmath110 , effectively reproduces the resolution of 16 initial angles but only in one octant of the unit circle . it improves the worst cases at the cost of a slightly reduced overall success probability . even more bisections will further increase the angular resolution but reduce the overall success to the point that they are counterproductive . although a bisecting composition is very simple approach , it provides the advantage of a larger number in initial projectors while avoiding a large penalty in overall efficiency due to a large action space with the same parameters . _ composition with the glow mechanism._the second mechanism departs from the strict bisection strategy of the first mechanism . the agent reaches an optimal success probability if it can measure along the direction @xmath112 . the bisection strategy only approximates @xmath12 and sometimes introduces unnecessarily many angles , e.g. , for @xmath61 the additional angle @xmath50 has to be built first . we overcome this disadvantage by a better use of the information provided by the measurement results to estimate which new projector angle should be inserted as addition action . we employ a variant of the `` edge glow mechanism '' @xcite to compose a single new action clip in the following way . we assign a second degree of freedom to each edge called `` glow '' and denote it by @xmath113 . instead of updating the @xmath31-values with the reward according to , we first accumulate rewards in the @xmath113 according to the following update rule : @xmath114 with initial values @xmath115 . the change in the update rule for @xmath31 effectively amounts to setting @xmath116 and @xmath117 . the behavior of the agent remains unchanged as the @xmath31-values remain at their initial values @xmath25 , i.e. , the agent measures equally often in all available directions . however , since there is no bias in the frequency of available measurement direction , the accumulated rewards in the respective @xmath113 provide a measure of the average reward for each direction . once the agent sampled enough measurement results , e.g. , when the first @xmath113 surpasses the threshold @xmath118 , a new action clip is composed and inserted into the projective simulator . the new measurement direction @xmath119 is composed from all @xmath17 and weighted by the @xmath113 : @xmath120 and we set the new @xmath121 . in order to prevent that a direction is inserted that is already present , the agent first checks that @xmath119 is sufficiently different from all already existing @xmath17 , e.g. , by inserting @xmath119 only if it differs from @xmath17 by more than @xmath122 circular standard deviations of the circular distribution given by the @xmath113 . if @xmath119 is too close to one @xmath17 , the @xmath22 of this @xmath17 is instead strengthened and set equal to the sum of all @xmath113 , and no new clip is inserted . after the composition , we continue with the usual update rule for the @xmath31-values . . the @xmath31-values are only updated with @xmath27 and @xmath29 after the composition . for @xmath12 coinciding with an existing @xmath17 only 4 agents compose a new angle @xmath119 , which is more than @xmath123 away from an existing @xmath17 , whereas all agents compose angles for the other examples of @xmath12 . the position of the step depends on the choice of the threshold for composition , here @xmath124 , which is chosen for large statistics but can be decreased without much penalty in the asymptotic efficiency albeit at the cost of slightly less accurate composed angles . ] the learning curves for the this form of glow composition are shown in figure [ fig : glow ] . starting with 4 angles and a @xmath118 , at least 2000 measurements have to be done on average before the first composition can occur . this threshold can be decreased leading to a faster composition , albeit at worse statistics , which result in inaccuracies of the composed angles . inaccurate compositions , however , impact the success probability only to a small extent because it decreases with the cosine of the angular difference between @xmath12 and the composed angle . in the direction of an existing angle , e.g. , @xmath38 or @xmath35 , the first amplifications of the respective @xmath17 occurs starting with 2000 measurements . for the direction @xmath60 , more measurement need to be done on average to reach @xmath125 or @xmath126 because these direction are not rewarded with certainty , and composition occurs on average later , with @xmath60 being one of the four latest instances . after the composition the success probability jumps from 50% to about 99% . since the newly set @xmath31-value for the best measurement direction is larger than the steady - state value for our choice of @xmath92 and @xmath93 , the success probability decreases slightly to approach @xmath97 from above . in an ensemble of 1000 agents only 4 compose an angle when @xmath38 or @xmath35 , whereas all do a composition for @xmath61 or @xmath49 . in our numerical experiment , the distribution of composed angles @xmath119 is sharply peaked around @xmath12 with a @xmath87 . by using the glow mechanism to obtain an effective average reward for each measurement direction , and then composing a mean angle from the reward distribution , the agent effectively creates a weighted sum of directions . it thereby embodies a method similar to the estimation of expectation values done in state tomography . so far we have demonstrated how an agent equipped with a suitable projective simulator can align a single measurement direction , e.g. , @xmath36 for the state @xmath127 , with an initially unknown state @xmath11 , which emerged from @xmath127 due to a magnetic field . since one of the aims is to employ the agent as a means to carry out measurement - based quantum computation ( mbqc ) @xcite in an unknown external field , all measurement directions that are required to run a specific algorithm in mbqc need to be adapted to this unknown stray field . we therefore need to extend the projective simulator to learn several measurement directions , which shall be given as the respective input . ultimately , the agent would translate the measurement directions necessary for the algorithm to the reference frame that rotates due to the magnetic field . we modify the inital agent setup depicted in figure [ fig : agentsetup ] in the following way . the step that prepares the defined initial state @xmath127 is removed and the qubit is simply left in the state that is prepared by the previous measurement . the projective simulator now receives as an input not just a trigger event , which activated the @xmath23-clip , but now it receives the previous measurement direction and the obtained measurement result as a percept . the initial state and percept can be chosen arbitrarily , e.g. , at random , as they do not matter in the subsequent feedback loop . and obtainable measurement outcome ( 0 or 1 ) . percepts that correspond to the same state prepared by the previous measurement are colored equally . ] for the new scheme , we also extend the clip network of the projective simulator to 8 percept clips , which represent all combinations of previous measurement direction and obtained reward , as depicted in figure [ fig : network_8to4 ] . effectively , the extended clip network consists of 8 copies of the previous simple clip network , which are activated according to the actions and results of the previous time step . the agent enters a feedback cycle , where measured directions and outcomes are fed back to the agent . the information about which state preparation method was used is available to the agent as percept , and thereby it indirectly receives a hint about which state has been prepared . given each prepared state , which then evolves to acquire an additional shift in the angle by @xmath12 , the agent learns which measurement direction most likely matches this rotated initial state . to give an example , consider the test qubit in the initial state @xmath128 , which evolves into @xmath11 . the agent measures this state , say along @xmath40 , and obtains result @xmath129 . it thereby prepares the test qubit in state @xmath130 , which again evolves for time @xmath8 into @xmath131 for the next measurement . this next measurement is chosen according to the @xmath31-values of edges originating from the percept clip `` @xmath132 '' to each of the four actions . . plotted are conditioned success probability , i.e. , given a percept , what is the probability of obtaining a + 1 measurement outcome , where each curve corresponds to one percept , solid lines represent outcome-@xmath129 preparation methods , dashed lines those for outcome @xmath133 . color codings are the same as for the clip network . curves are averages over 100 agents , with @xmath92 and @xmath93 . for the last time step the clip network with @xmath31-values encoded in the thickness of the edges are given in the inset . colors and clips match those of figure [ fig : network_8to4 ] . ] the clip network is now much larger than before and the agent needs more measurements to update all the connections until the @xmath31-values converge into those of the steady state . naively , we can expect an 8-fold increase , however , since the agent converges to a state in which measurements that give outcomes @xmath129 are preferred , learning the right measurements for a outcome-@xmath133 preparation is delayed . this learning behavior is shown in figure [ fig : completepslearning ] , where outcome-@xmath129 preparations converge early and outcome-@xmath133 preparations later , which in turn also delays the overall convergence . naturally , the training of the whole network is faster in situations where the @xmath133 outcomes occur more often , e.g. , for @xmath60 , or in situations that lead to different measurement directions , e.g. , for @xmath134 . as the agent encounters situations with different percepts , the number of time steps in between two successive activations of the same percept is now increased on average . this leads to a qualitative and quantitative change in the learning curves as compared to the previous simple agent with only one percept . the number of times that the damping reduces the @xmath31-value of each edge would increase and lead to a reduced efficiency , because the agent forgets too quickly in between rewards . to maintain high @xmath31-values for rewarded transitions we could adjust @xmath29 to a lower value , but we choose to simply restrict the application of the update rule , and the application of the damping in particular , to a subgraph of the clip network , namely , only those edges that are connected to the activated percept clip . thereby we maintain the quantitative behavior of the simple clip network used in the previous sections . percepts give the preparation procedure of the test qubit and thereby effectively encode information about which state has been prepared . a closer inspection reveals that each state is represented twice because is can be prepared in two ways , e.g. , @xmath127 can be prepared by a measurement of @xmath39 with outcome 1 or by @xmath45 with outcome 0 . preparation procedures that result in the same prepared states are highlighted with the same color of the percept clip in figures [ fig : network_8to4 ] and [ fig : completepslearning ] . this redundancy increases the learning times because the same behavior has to be learned twice . the clip network could be optimized with an additional intermediate layer that first maps preparation methods to states , which may be learned first without a stray field , and then the prepared states to best measurement directions in a stray field . once the agent has adapted its measurement directions to the unknown external field with a test qubit , it can be used as a translator between intended measurement directions and their corresponding directions in the rotated reference frame . this application of a trained agent works as follows . after a training period , we fix all the @xmath31-values . instead on the test qubit , the agent now acts on the qubit that needs to be measured along a certain direction according to a mbqc scheme , for example . we then excite a percept of the agent that corresponds to the direction of the intended measurement direction in zero field . the agent then chooses most likely the measurement direction that corresponds to this measurement in the rotated frame , i.e. , the measurement that takes the field into account . we first briefly repeat the mbqc variant of the grover search algorithm for a database with 4 elements @xcite and adapt it to our notation and use of projective measurements @xmath21 . the initial resource state is a cluster state of 4 qubits in ring form , i.e. , starting from the state @xmath135 we apply a controlled phase gate between the qubit pairs 12 , 23 , 34 , 41 , and obtain @xmath136 a database with 4 entries ( i.e. , with elements @xmath137 , @xmath138 , @xmath139 , and @xmath140 ) only requires a single grover step to find the marked element . the algorithm starts by doing this one necessary query to the database and thereby marks the database entry that is to be found . a measurement of the projectors @xmath39 or @xmath45 on qubits 1 and 4 realizes the specific database , where each pair of measurement directions @xmath137 , @xmath141 , @xmath142 , and @xmath143 corresponds to marking the database element @xmath137 , @xmath138 , @xmath139 , and @xmath140 , respectively . for each of the two measurements of @xmath39 or @xmath45 both measurement results @xmath144 or @xmath129 appear with probability @xmath145 . therefore , the results alone do not allow us to infer the measurement directions and thereby the marked element . in the problem setting of the algorithm the choice of measurement directions is hidden . only from the measurement results of qubits 1 and 4 , and from the measurements done on the remaining two qubits , we should infer the marked element . on the remaining qubits we therefore measure the observable @xmath39 , whose measurement outcome depends on the measurement directions on qubits 1 and 4 , and is correlated to the previous two outcomes . finally , the calculation of @xmath146 , i.e. , addition of the measurement outcomes modulo 2 , reveals the two bits of the marked element with certainty . although , at the present point the mbqc version of grover s algorithm appears to merely uncover ( anti-)correlations between measurement directions , there is an explicit mapping between the quantum circuit of gover s algorithm on one hand , and the circuit for creating and measuring the cluster state on the other @xcite . along the equator of the bloch sphere . data is obtained in independent runs with marked element @xmath137 for all fields giving rise to angles @xmath12 between 0 and @xmath147 in steps of @xmath148 . noisy data is the fraction of an ensemble of agents that identifies the marked element correctly when performing all four measurements in grover s algorithm . red ( analytical ) and orange ( numerical , 3000 agents ) curves give the success of the grover search ( all four measurements ) without taking into account the field in the measurement direction . the light blue curve gives the success for an ensemble of 1000 agents that each have a perfectly trained projective simulator with 4 measurement directions , which has learned the external magnetic field before doing the measurements for the grover search algorithm . the dark blue curve is an ensemble of 1000 agents that employs the glow mechanism to build a measurement direction that is adapted to the external magnetic field before using it to perform the grover search . ] if the initial state is placed in an unknown external field pointing along the @xmath3-direction , the state @xmath149 is transformed into @xmath150 with the local unitary rotations @xmath151 . if we recall that @xmath152 it is straightforward to see that the measurement protocol of the grover algorithm will no longer give the correct marked element because the external field effectively shifts the measurement directions by the angle @xmath153 with respect to the original measurement directions . as a result the probability to identify the correct marked element , i.e. , the success probability of the algorithm , is periodically modulated by @xmath12 and a straightforward calculation gives @xmath154 for @xmath12 being a multiple of @xmath155 the algorithm works perfectly because the local rotations align the qubits reference frames again with the @xmath76-axis . the grover algorithm is invariant under the inversion of all measurement directions ( i.e. , changing all directions @xmath133 to @xmath155 and vice versa ) . in the worst case , for @xmath12 being an odd multiple of @xmath35 , the chance of identifying the right element is 1/4 , as the measurements of the intended grover search actually reveal no useful information because they are unbiased with respect to the required measurement direction . in figure [ fig : grover ] , the analytic results for identifying the correct marked element @xmath137 in the rotated state match the trials with 1000 agents that simply measure all 4 qubits the direction @xmath62 and then try to identify the marked element from the obtained measurement results . for testing the agent with a projective simulator we restrict to a realization with a single marked element , namely @xmath137 , which can be implemented with measurements along the @xmath76-axis , all in the direction @xmath62 . the agent first learns with a test qubit exposed to the external field and adapts to the field strength . we then fix these obtained @xmath31-values and use the agent without update rule to carry out the four measurements on the cluster state , one after the other , according to its available measurement directions and internal probabilities . the first example is an agent that has only 4 fixed measurement directions available ( @xmath17 being a multiple of @xmath35 ) , which we first train to achieve optimal success probability with the test qubit . the optimal performance is reached in the limit @xmath156 , which amounts to @xmath157 for the single @xmath17 that is closest to @xmath12 and all others zero . the light blue curve in figure [ fig : grover ] shows the fraction of the agent ensemble that identifies the marked element with this projective simulator correctly . the grover search is recovered perfectly for fields with @xmath12 being a multiple of @xmath35 , which can be matched exactly by the available measurement directions . the second example is an agent that first learns with a test qubit in the external field with composition according to the glow mechanism . that is , after 2000 measurements on average , the agent composes a new measurement direction or strengthens an existing one that matches @xmath12 . the @xmath31-values after the composition remain fixed and the agent measures the cluster state according to the available measurement directions and probabilities . the dark blue curve in figure [ fig : grover ] illustrates that an ensemble of this kind of agent is highly successful in doing the grover search for all angles @xmath12 . the shortfall from a perfect performance ( the average success probability is 99.0% with a standard deviation of 0.3% ) originates in the slight deviations of the composed angle from @xmath12 and the non - zero probability to chose the remaining non - optimal measurement directions .

we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction . we demonstrate the applicability by correcting for stray fields in a measurement - based algorithm for grover s search .

quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation . in a setting of measurement - based quantum computation , we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction . we assess the agent s learning behavior in static and time - varying fields and explore composition strategies in the projective simulator to improve the agent s performance . we demonstrate the applicability by correcting for stray fields in a measurement - based algorithm for grover s search . thereby , we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks .

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recently , there has been an upsurge of research interests in radio frequency ( rf ) energy harvesting / scavenging technique ( see @xcite and references therein ) , or rf harvesting in short , which is the capability of converting the received rf signals into electricity . this technique becomes a promising solution to power energy - constrained wireless networks . conventionally , the energy - constrained wireless networks , such as wireless sensor networks , have a limited lifetime which largely confines the network performance . in contrast , an rf energy harvesting network ( rf - ehn ) has a sustainable power supply from a radio environment . therefore , the rf energy harvesting capability allows the wireless devices to harvest energy from rf signals for their information processing and transmission . consequently , rf - ehns have found their applications quickly in various forms , such as wireless sensor networks @xcite , wireless body networks @xcite , and wireless charging systems . with the increasingly emerging applications of rf energy harvesting / charging , the wireless power consortium is also making the efforts of establishing an international standard for the rf energy harvesting technique . in rf energy harvesting , radio signals with frequency range from 300ghz to as low as 3khz are used as a medium to carry energy in a form of electromagnetic radiation . rf energy transfer and harvesting is one of the wireless energy transfer techniques . the other techniques are inductive coupling and magnetic resonance coupling . inductive coupling @xcite is based on magnetic coupling that delivers electrical energy between two coils tuned to resonate at the same frequency . the electric power is carried through the magnetic field between two coils . magnetic resonance coupling @xcite utilizes evanescent - wave coupling to generate and transfer electrical energy between two resonators . the resonator is formed by adding a capacitance on an induction coil . both of the above two techniques are near - field wireless transmission featured with high power density and conversion efficiency . the power transmission efficiency depends on the coupling coefficient , which depends on the distance between two coils / resonators . the power strength is attenuated according to the cube of the reciprocal of the distance @xcite , specifically , 60 db per decade of the distance , which results in limited power transfer distance . besides , both inductive coupling and resonance coupling require calibration and alignment of coils / resonators at transmitters and receivers . therefore , they are not suitable for mobile and remote replenishment / charging . in contrast , rf energy transfer has no such limitation . as the radiative electromagnetic wave can not retroact upon the antenna that generated it ( by capacitive or inductive coupling ) at a distance of above @xmath0 @xcite , rf energy transfer can be regarded as a far - field energy transfer technique . thus , rf energy transfer is suitable for powering a larger number of devices distributed in a wide area . the signal strength of far - field rf transmission is attenuated according to the reciprocal of the distance between transmitter and receiver , specifically , 20 db per decade of the distance . table [ wet ] shows the comparison between the three major wireless energy transfer techniques . we can see that rf energy transfer technique has clear advantages in effective energy transfer distance . however , it has low rf - to - dc energy conversion efficiency especially when the harvested rf power is small . the readers can refer to @xcite for more detailed introduction of wireless energy transfer techniques . in this article , we focus on wireless networks with the rf energy harvesting technique . wireless power transfer has caught research attention since long ago , as a separate problem with wireless information transmission . traditionally , free - space beaming and antennas with large apertures were used to overcome propagation loss for large power transfer . for example , in 1960 s , the authors in @xcite demonstrate a small helicopter hovering at an height of 50-feet , powered by an rf source with a dc power supply of 270w operating on 2.45ghz on the ground . in @xcite , the authors demonstrate a space - to - earth power transfer system using gigantic transmit antenna arrays at a satellite and receive antenna arrays at a ground station . for transmit power of 2.7gw , the power transfer efficiency is estimated to be @xmath1 over a transfer distance of @xmath2 . during the past decade , with the development in rf energy harvesting circuit , low power transfer for powering mobile terminals in wireless communication systems began to attract increasing attention @xcite . the authors in @xcite propose a network architecture for rf charging stations , overlaying with an uplink cellular network . in @xcite , a harvest - then - transmit protocol is introduced for power transfer in wireless broadcast system . moreover , various modern beamforming techniques are employed to improve power transfer efficiency @xcite for mobile applications . [ cols="<,<,<,<,<,<",options="header " , ] table [ routing ] shows the comparison of the existing routing protocols for rf - ehns . it can be observed that all the protocols work in the systems with a dedicated rf charger , because of which the majority of them consider out - of - band charging to avoid interference . though in @xcite , the authors perform an experiment of the system where a sensor node and rf charger work on the same frequency , no interference management scheme is taken into account . therefore , this is a room for the investigation of routing protocols in the system adopting swipt . furthermore , given the routing metric , information exchange among the network devices through broadcasting is required during route selection . due to hardware limitation as aforementioned , network devices can not harvest rf energy from the same carrier for information decoding . as a result , the network devices working in rf harvesting mode may miss the broadcast information . thus , an efficient message broadcasting mechanism for the time - switching based receiver architecture is also required for routing protocols . besides , an rf - ehn operates on ism band ( e.g. , wifi , zigbee and bluetooth ) may overlap with the frequency band for wireless charging ( e.g. , the system in @xcite ) . in this context , an rf charger , if not well controlled , can cause severe interference to the network communication , as its power is usually much higher than that of network devices . thus , there is a need for efficient spectrum allocation mechanisms to coordinate communication and charging .

radio frequency ( rf ) energy transfer and harvesting techniques have recently become alternative methods to power the next generation wireless networks . , we present an extensive literature review on the research progresses in wireless networks with rf energy harvesting capability , referred to as rf energy harvesting networks ( rf - ehns ) .

radio frequency ( rf ) energy transfer and harvesting techniques have recently become alternative methods to power the next generation wireless networks . as this emerging technology enables proactive energy replenishment of wireless devices , it is advantageous in supporting applications with quality of service ( qos ) requirements . in this paper , we present an extensive literature review on the research progresses in wireless networks with rf energy harvesting capability , referred to as rf energy harvesting networks ( rf - ehns ) . first , we present an overview of the rf - ehns including system architecture , rf energy harvesting techniques and existing applications . then , we present the background in circuit design as well as the state - of - the - art circuitry implementations , and review the communication protocols specially designed for rf - ehns . we also explore various key design issues in the development of rf - ehns according to the network types , i.e. , single - hop networks , multi - antenna networks , relay networks , and cognitive radio networks . finally , we envision some open research directions . _ index terms- rf energy harvesting , simultaneous wireless information and power transfer ( swipt ) , receiver operation policy , beamforming , communication protocols , rf - powered cognitive radio network_.

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we have presented a comprehensive survey on rf energy harvesting networks ( rf - ehns ) . firstly , we have provided an overview of rf - ehns with the focus on architecture , enabling techniques and existing applications . then , we have reviewed the background in circuit design and state - of - the - art circuitry implementations . afterwards , we have surveyed various design issues related to resource allocation in rf - ehns , and the up - to - date solutions . finally , we have discussed on the future directions and practical challenges in rf energy harvesting techniques . h. j. visser and r. j. m. vullers , rf energy harvesting and transport for wireless sensor network applications : principles and requirements , " _ proceedings of the ieee _ , vol . 101 , no . 6 , 1410 - 1423 , june 2013 . x. zhang , h. jiang , l. zhang , c. zhang , z. wang , and x. chen , an energy - efficient asic for wireless body sensor networks in medical applications , " _ ieee transactions on biomedical circuits and systems _ , vol . 11 - 18 , feb . 2010 . a. kurs , a. karalis , r. moffatt , j. d. joannopoulos , p. fisher , and m. soljacic , `` wireless power transfer via strongly coupled magnetic resonances , '' _ science _ , vol . 5834 , pp . 83 - 86 , june 2007 . j. o. mur - miranda , w. franklin , g. fanti , y. feng , k. omanakuttan , r. ongie , a. setjoadi , and n. sharpe , wireless power transfer using weakly coupled magnetostatic resonators , " in _ proc . of ieee energy conversion congress and exposition ( ecce ) _ , atlanta , ga , sept . 2010 . n. shinohara , the wireless power transmission : inductive coupling , radio wave , and resonance coupling , " _ wiley interdisciplinary reviews : energy and environment _ , vol . 1 , no . 3 , pp . 337 - 346 , sept . 2012 . k. huang and v. k. n. lau , enabling wireless power transfer in cellular networks : architecture , modeling and deployment , " _ ieee transactions on wireless communications _ , vol 13 , no . 902 - 912 , feb . 2014 . x. chen , x. wang , and x. chen , energy - efficient optimization for wireless information and power transfer in large - scale mimo systems employing energy neamforming , " _ ieee wireless communications letters _ 2 , no . 6 , pp . 667 - 670 , dec . 2013 . grover and a. sahai , shannon meets tesla : wireless information and power transfer , " in _ proc . of ieee international symposium on information theory proceedings ( isit ) _ , pp . 2363 - 2367 , austin , tx , june 2010 . t. k. sarkar , j. zhong , k. kim , a. medouri , m. salazar - palma , a survey of various propagation models for mobile communication , " _ ieee antennas and propagation magazine _ , vol . 51 - 82 , june 2003 . m. erol - kantarci and h. t. mouftah , mission - aware placement of rf - based power transmitters in wireless sensor networks , " in _ proc . of ieee symposium on computers and communications ( iscc ) _ , pp . 12 - 17 , cappadocia , july 2012 . m. erol - kantarci and h.t . mouftah , drift : differentiated rf power transmission for wireless sensor network deployment in the smart grid , " in _ proc . of ieee globecom workshops _ 1491 - 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" _ ieee wireless communications letters _ , vol . 277 - 280 , june 2014 . s. timotheou , i. krikidis , g. zheng , and b. ottersten , beamforming for miso interference channels with qos and rf energy transfer , " _ ieee transactions on wireless communications _ , vol . 5 , pp . 2646 - 2658 , may 2014 . d. li , c. shen , and z. qiu , two - way relay beamforming for sum - rate maximization and energy harvesting , " in _ proc . of ieee international conference on communications ( icc ) _ , pp . 3115 - 3120 , budapest , hungary , june 2013 . d. li , c. shen , and z. qiu , sum rate maximization and energy harvesting for two - way af relay systems with imperfect csi , " in _ proc . of ieee international conference on acoustics , speech and signal processing ( icassp ) _ , pp . 4958 - 4962 , vancouver , bc , may 2013 . j. park , and b. clerckx , joint wireless information and energy transfer in a two - user mimo interference channel , " _ ieee transactions on wireless communications _ , vol 12 , no . 8 , pp . 4210 - 4221 , august 2013 . d. w. k. ng and r. schober , resource allocation for coordinated multipoint networks with wireless information and power transfer , " in _ proc . of ieee global communications conference ( globecom ) _ , austin , tx , usa , december 2014 . d. w. k. ng , e. s. lo , and r. schober , robust beamforming for secure communication in systems with wireless information and power transfer , " to appear in _ ieee transactions on wireless communications _ , 2014 . b. zhu , j. ge , y. huang , y. yang , and m. lin , rank - two beamformed secure multicasting for wireless information and power transfer , " _ ieee signal processing letters _ , 199 - 203 , feb . 2014 . d. w. k. ng , r. schober , and h. alnuweiri , secure layered transmission in multicast systems with wireless information and power transfer . " in _ proc . of ieee international conference on communications ( icc ) _ , sydney , australia , june 2014 . s. x. wu , a. m .- c . so , and w .- k . ma , rank - two transmit beamformed alamouti space - time coding for physical - layer multicasting , " in _ proc . ieee international conference on acoustics , speech and signal processing ( icassp ) _ , pp . 2793 - 2796 , kyoto , japan , mar . 2012 . d. w. k. ng , e. s. lo , and r. schober , multi - objective resource allocation for secure communication in cognitive radio networks with wireless information and power transfer . 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" _ ieee communications letters _ , vol . 11 , pp . 1772 - 1775 , november 2012 . i. krikidis , s. sasaki , s. timotheou , and z. ding , a low complexity antenna switching for joint wireless information and energy transfer in mimo relay channels , " _ ieee transactions on communications _ 5 , pp . 1577 - 1587 , april 2014 . a. a. nasir , x. zhou , s. durrani , and r. a. kennedy , relaying protocols for wireless energy harvesting and information processing , " _ ieee transactions on wireless communications _ 12 , no . 7 , pp . 3622 - 3636 , july 2013 . a. a. nasir , x. zhou , s. durrani , and r. a. kennedy , wireless energy harvesting and information relaying : adaptive time - switching protocols and throughput analysis . " ( available on - line at arxiv:1310.7648 ) d. s. michalopoulos , h. a. suraweera , and r. schober , relay selection for simultaneous information transmission and wireless energy transfer : a tradeoff perspective . 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" _ ieee transactions on wireless communications _ , vol . 846 - 860 , february 2014 . b. gurakan , o. ozel , j. yang , and s. ulukus , two - way and multiple - access energy harvesting systems with energy cooperation , " in _ proc . of ieee conference record of the forty sixth asilomar conference on signals , systems and computers ( asilomar ) 58 - 62 , pacific grove , ca , nov . 2012 . b. k. chalise , w .- k . ma , y. d. zhang , h. a. suraweera , and m. g. amin , optimum performance boundaries of ostbc based af - mimo relay system with energy harvesting receiver , " _ ieee transactions on signal processing _ , vol . 17 , sept . 2013 . g. l. moritz , j. l. rebelatto , r. d. souza , b. f. ucha - filho , and y. li , time - switching uplink network - coded cooperative communication with downlink energy transfer . " ( available on - line at arxiv:1312.2544 ) j. l. rebelatto , b. f. uchoa - filho , y. li , and b. vucetic , multiuser cooperative diversity through network coding based on classical coding theory , " _ ieee transactions on signal processing _ , vol . 60 , no . 916 - 926 , february 2012 . s. park , j. heo , b. kim , w. chung , h. wang , and d. hong , optimal mode selection for cognitive radio sensor networks with rf energy harvesting , " in _ proc . of ieee international symposium on personal indoor and mobile radio communications ( pimrc ) _ , pp . 2155 - 2159 , sydney , australia , sept . 2012 . n. barroca , j. m. ferro , l. m. borges , j. tavares , and f. j. velez , electromagnetic energy harvesting for wireless body area networks with cognitive radio capabilities . " ( available on - line at : http://www.anacom.pt/streaming/norbertobarroca@xmath7congressoursi2012 .pdf?contentid=1148324@xmath8field@xmath20attached@xmath7file ) j. kim and j .- w . lee , energy adaptive mac protocol for wireless sensor networks with rf energy transfer , " in _ proc . of ieee third international conference on ubiquitous and future networks ( icufn ) _ , pp . 89 - 94 , dalian , china , june 2011 . j. kim and j .- w . lee , performance analysis of the energy adaptive mac protocol for wireless sensor networks with rf energy transfer , " in _ proc . of ieee international conference on ict convergence ( ictc ) 14 - 19 , seoul , korea , sept . 2011 p. nintanavongsa , m. y. naderi , and k. r. chowdhury , medium access control protocol design for sensors powered by wireless energy transfer , " in _ proceedings of ieee infocom - mini conference _ , pp . 150 - 154 , turin , italy , april 2013 . r. doost , k. r. chowdhury , and m. di felice , routing and link layer protocol design for sensor networks with wireless energy transfer , " in _ proceedings of global telecommunications conference _ , miami , fl , december 2010 . l. zi , p. yang , w. zhang , and d. qiao , j - roc : a joint routing and charging scheme to prolong sensor network lifetime , " in _ proc . of ieee international conference on network protocols ( icnp ) 373 - 382 , vancouver , bc , oct . 2011 . b. tong , z. li , g. wang , and w. zhang , how wireless power charging technology affects sensor network deployment and routing , " in _ proc . of ieee international conference on distributed computing systems ( icdcs ) _ , pp . 438 - 447 , genoa , italy , june 2010 . a. h. coarasa , p. nintanavongsa , s. sanyal , and k. r. chowdhury , impact of mobile transmitter sources on radio frequency wireless energy harvesting , " in _ proc . of ieee international conference on computing , networking and communications ( icnc ) _ , pp . 573 - 577 , san diego , ca , jan . 2013 . p. v. mekikis , a. s. lalos , a. antonopoulos , l. alonso , and c. verikoukis , wireless energy harvesting in two - way network coded cooperative communications : a stochastic approach for large scale networks , " _ ieee communications letters _ , vol . 18 , no . 6 , pp . 1011 - 1014 , june 2014 . p. demestichas , a. georgakopoulos , d. karvounas , k. tsagkaris , v. stavroulaki , j. lu , c. xiong , and j. yao , 5 g on the horizon : key challenges for the radio - access network , " _ ieee vehicular technology magazine _ , vol . 47 - 53 , sept . 2013 . v. jungnickel , k. manolakis , w. zirwas , b. panzner , v. braun , m. lossow , m. sternad , r. apelfrojd , and t. svensson , the role of small cells , coordinated multipoint , and massive mimo in 5 g , " _ ieee communications magazine _ , vol . 44 - 51 , may 2014 . scientific committee on emerging and newly identified health risks ( scenihr ) : possible effects of electromagnetic fields on human health . docs/[email protected] ] . j. breckenkamp , e. m. g. berg - beckhoff , j. schuz , b. schlehofer , j. wahrendorft , and m. blettner , feasibility of a cohort study on health risks caused by occupational exposure to radiofrequency electromagnetic fields , " _ biomed central environmental health _ , vol . 8 , no . 23 , may 2009 . r. w. habash , j. m. elwood , d. krewski , w. g. lotz , j. p. mcnamee , and f. s. prato , recent advances in research on radiofrequency fields and health , " _ journal of toxicology and environmental health , part b _ , vol.12 , no . 4 , pp . 250288 , apr . 2009 .

first , we present an overview of the rf - ehns including system architecture , rf energy harvesting techniques and existing applications . then , we present the background in circuit design as well as the state - of - the - art circuitry implementations , and review the communication protocols specially designed for rf - ehns . we also explore various key design issues in the development of rf - ehns according to the network types , i.e. , single - hop networks , multi - antenna networks , relay networks , and cognitive radio networks . finally , we envision some open research directions . _ index terms- rf energy harvesting , simultaneous wireless information and power transfer ( swipt ) , receiver operation policy , beamforming , communication protocols , rf - powered cognitive radio network_.

radio frequency ( rf ) energy transfer and harvesting techniques have recently become alternative methods to power the next generation wireless networks . as this emerging technology enables proactive energy replenishment of wireless devices , it is advantageous in supporting applications with quality of service ( qos ) requirements . in this paper , we present an extensive literature review on the research progresses in wireless networks with rf energy harvesting capability , referred to as rf energy harvesting networks ( rf - ehns ) . first , we present an overview of the rf - ehns including system architecture , rf energy harvesting techniques and existing applications . then , we present the background in circuit design as well as the state - of - the - art circuitry implementations , and review the communication protocols specially designed for rf - ehns . we also explore various key design issues in the development of rf - ehns according to the network types , i.e. , single - hop networks , multi - antenna networks , relay networks , and cognitive radio networks . finally , we envision some open research directions . _ index terms- rf energy harvesting , simultaneous wireless information and power transfer ( swipt ) , receiver operation policy , beamforming , communication protocols , rf - powered cognitive radio network_.

astro-ph0103379

i

the radio source 3c 120 exhibits structure on all scales from under a parsec to hundreds of kiloparsecs @xcite . it is dominated by a variable core that is resolved with very long baseline interferometry ( vlbi ) . a prominent one - sided jet is seen extending from the core on subparsec scales to about a hundred kiloparsecs . on the largest scales there is a complex , two - sided lobe structure extending to about 14 , or about half a megaparsec for @xmath0 @xcite and @xmath1 km s@xmath2mpc@xmath2 , the value that will be used in this paper ( this gives a scale of 0.60 pc mas@xmath2 ) . superluminal motion is observed in the jet which , because of the low redshift , can be studied with greater linear resolution than most other extragalactic superluminal sources . this was one of the first 4 sources in which superluminal motions were found in the early 1970s and it has been studied with vlbi extensively ever since ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . the standard model for superluminal motion involves relativistic motions in a jet oriented nearly along the line - of - sight @xcite . the central region of the 3c 120 host galaxy is a strong and variable emitter of radiation at all observed frequencies . because of the presence of broad emission lines , the galaxy is usually classified as a seyfert 1 @xcite , although its properties are also consistent with those of a broad line radio galaxy and , to some extent , a low luminosity quasar . the galaxy is of order an arcminute in size , with extensive h ii regions that may be ionized by the nucleus @xcite . its morphology does not clearly match either a spiral or an elliptical , and may be the disturbed product of a merger @xcite . @xcite give broadband spectra from infrared to x - rays and report on monitoring observations over much of this range . there is a pronounced and variable uv excess which they model with a face - on accretion disk that feeds a @xmath3 black hole at a variable rate of somewhat under a solar mass per year . at optical wavelengths , variability is observed in both the continuum @xcite and the spectral lines @xcite . reverberation mapping techniques have been used to derive a mass for the central black hole of about @xmath4 @xcite . 3c 120 is a complex and variable x - ray source with the unusual property that the spectral index varies with the intensity @xcite . @xcite find x - ray properties similar to those of a radio quiet seyfert , including the presence of strong iron lines , indicating that beamed emission does not dominate at these frequencies . the radio jet is among the few that is seen at other wavelengths . an optical counterpart , extending out to 15 , was reported by @xcite . the radio - to - optical spectral index is 0.65 , about the same as the radio spectral index on the same scales . in addition , there is an x - ray emission knot that is coincident with the 20radio knot and is probably explained by synchrotron emission @xcite . recent high frequency vlbi observations at 86 , 43 and 22 ghz @xcite have produced high resolution images and a 16-month movie of the innermost features of the jet . the 86 ghz coordinated millimeter vlbi array observations put an upper limit on the core size of @xmath5 pc ; the core size lies below the resolution of the 86 ghz image which is @xmath6as . the 43 and 22 ghz observations , made with the national radio astronomy observatory s ( nrao ) very long baseline array ( vlba ) , show that the inner jet structure is complex and exhibits superluminal motions on very small scales . the movie shows evidence for interaction with a cloud of density and core distance intermediate between typical broad and narrow line clouds . the complexity of the structure at high resolution makes it clear that features in lower resolution observations , such as those presented in this paper , are likely to be blends of smaller scale components . the 43 and 22 ghz observations show that the linear polarization on small scales is variable with some features near the core having magnetic fields across the jet . polarization percentages of up to 10% are seen , increasing with core distance . farther from the core , and at much larger scales observed with the vla @xcite , the polarization indicates that the magnetic fields are parallel to the jet . vlba measurements made in 1996 showed upper limits to circular polarization of about 0.2% @xcite . recent studies have begun to apply physical models of jets to observations of 3c 120 . the jet shows a variety of knots and side - to - side structures , some reminiscent of helical structures . hydrodynamical jet theories incorporating shocks have been used to model the moving knots in superluminal sources ( * ? ? ? * and references therein ) . it has been suggested that the motion of the inner jet structure 3c 120 may be described in this way @xcite . both moving and stationary features can be accommodated in such models . helical patterns are expected for some types of jet instabilities ( * ? ? ? * ; * ? ? ? * and references therein ) . the superluminal motion along a curved trajectory seen in the radio source 3c 345 can be explained by helical jet models @xcite . according to the standard model , the observation of superluminal motions is good evidence that a jet is relativistic . the fact that a large proportion of bright , compact radio sources show superluminal motions suggests that many jets are relativistic on parsec scales , although there are selection effects due to relativistic beaming . it is not clear how far from the core the jets remain relativistic . at larger core distances , they become broader and features are larger , so measurement of small angular velocities is more difficult . because of its close proximity , 3c 120 has high angular rates of motion compared to other superluminal sources making it a prime candidate for attempts to find motions at large angular distances from the core . so far superluminal motion has been seen in the source to distances of tens of parsecs @xcite . on arc second scales , a radio knot in the jet 4 from the core has been shown to have an upper limit on its motions of significantly smaller than the speed of light @xcite . this might suggest that the jet has slowed , or moved out of the line - of - sight , by that distance . but the knot could be a stationary feature , perhaps a shock or bend , in a jet that is still relativistic . this possibility is supported by the fact that the large scale structure is two sided , but the jet is still very one sided on the scale of the knot , suggesting that the emission is still beamed on that scale . it is also supported by optical line observations of regions on both sides of the nucleus that show evidence of interaction with the jet @xcite . one of the goals of the 1.7 ghz observations presented here is to look for motions on scales intermediate between those usually probed with vlbi and the larger scale structures studied with linked interferometers . in this paper we present the results obtained from five epochs of 1.7 ghz ( @xmath7=18 cm ) vlbi observations spanning from 1982 to 1997 . we also present 5 ghz ( @xmath7=6 cm ) vlbi monitoring data which was taken approximately three times per year from 1977 through 1988 . a few of the early observations of this sequence were made at 10.7 ghz . with this long series of observations , we can attempt to discern how frequently new components appear , what sort of trajectory they follow , and whether the velocities are constant for a given feature and between features . at 1.7 ghz , the core is not as dominant as at higher frequencies and a wealth of jet structure is observable up to about half an arcsecond from the core .

the 5 ghz sequence includes a few early epochs at 10.7 ghz . some features that were observed leaving the core in the 5 ghz observations with 0.6 pc resolution are followed at 1.7 ghz , with 2.4 pc resolution , to projected distances in excess of 25 pc from the core . older features up to at least 150 pc in projection from the core are still moving at superluminal apparent speeds and are therefore presumed to be relativistic . beyond that , the data are inadequate for motion measurements .

results are presented from long term vlbi monitoring of the parsec - scale radio jet in 3c 120 at 5 and 1.7 ghz . the 5 ghz sequence includes a few early epochs at 10.7 ghz . superluminal features are seen leaving the core at intervals of less than a year , about as often as new features could be distinguished with the 0.6 parsec resolution of the observations . the underlying jet is continuous , but not smooth , and the measured features are simply the bright points in the convolution of the observing beam with brightness fluctuations that occur on many scales . the velocity of different features varies , but not by more than about a factor of 2 . clear variations in the velocity of an individual feature are not seen . some features that were observed leaving the core in the 5 ghz observations with 0.6 pc resolution are followed at 1.7 ghz , with 2.4 pc resolution , to projected distances in excess of 25 pc from the core . older features up to at least 150 pc in projection from the core are still moving at superluminal apparent speeds and are therefore presumed to be relativistic . beyond that , the data are inadequate for motion measurements . the region where the jet slows to non - relativistic speeds has not been found . there are suggestions of stationary features , or brightening and dimming regions , through which the moving features pass . these may be locations where there is interaction with the external medium , or they may simply be the result of variations in the jet angle to the line - of - sight . the observation of stationary features in an otherwise moving jet reinforces the idea that the lack of motion of the knot at 4 ( 2 kpc ) , that has been found not to be superluminal in other observations , might not actually imply that the jet has slowed by that position . the structure of the jet in the vicinity of the most likely stationary feature is suggestive of a helical pattern seen in projection . the deprojected wavelength of the pattern is very long relative to the jet radius , unlike the situation in sources such as m87 . if the 3c 120 jet does contain a slowly - moving , helical structure , then theory suggests that the jet resides in a relatively cool medium , not in a relativistically hot cocoon or lobe .

astro-ph0103379

c

the main conclusions of this study are : * the 3c 120 jet is a continuous structure with brightness variations . identifiable features in the brightness structure move down the jet at superluminal speeds . we are able to identify new features appearing at intervals of less than a year ( figure [ organ ] , table [ speeds ] ) , an interval that is set mainly by a combination of the jet speed and the angular resolution of the observations . finer scale structure is known to exist as shown by higher frequency observations by other groups ( c.f . gmez et al . 2000 ) * the two best 1.7 ghz images show structure with large variations of brightness along the jet , but a fairly smooth outer envelope of the emitting region ( figure [ big18 ] ) . * the speeds of the 5 ghz components in the region between 1 and 10 mas of the core appear to vary over a range that is well under a factor of two ( table [ speeds ] ) . the formal errors strongly exclude the possibility that the speeds are all the same . but because of the limited image reliability and the difficulty in identifying some of the features at larger core distances , that conclusion is not as firm as the formal statistics would suggest . * on the larger scales sampled by the 1.7 ghz images , most of the moving features have angular rates in the 2.5 to 3.1 mas yr@xmath2 range , and within the uncertainties , could all be the same ( figure [ small18 ] ) . this is within the range of speeds seen at higher resolution in our 5 ghz observations and in the 22 and 43 ghz observations of @xcite . the fact that the speeds show the same fairly narrow range between a few tenths of a parsec to about 120 parsecs in projection indicates that there are not large changes in either the underlying speed or angle to the line - of - sight of the jet in that range . the observed superluminal motions place an upper limit on the angle to the line - of - sight of about 20 so the 120 pc deprojects to at least 350 pc with much larger values more likely . * the outermost feature for which a speed could be determined is the bulge at around 200 mas ( figure [ medium18 ] ) . it is moving at a rate of 1.7 mas yr@xmath2 , which is slower than most of the features closer to the core , especially those with reliable speed measurements . this may be the leading edge of material ejected during a period of enhanced activity . it is now plowing into the older jet material plus expanding the jet , a situation similar to that seen in 3c 84 @xcite . such features in radio sources may constitute a fossil record of previous periods of enhanced activity , about 100 years ago in this case . * the 1.7 ghz data show evidence that there are both moving and stationary features in the same regions ( figure [ small18 ] ) . in fact , it appears that moving components can pass through a stationary feature , dimming or brightening as they do so . the stationary features could either be places of interaction with the external medium or could reflect changes in jet direction with corresponding changes in the intensity of the relativistic beaming . * the stationary brightening regions have structure reminiscent of the feature at 4 which also appears to be stationary to within the measurement errors @xcite . this enhances the suspicion that the 4 knot s lack of motion does not imply that the underlying jet is not relativistic . the knot may , like the stationary brightening regions in the 1.7 ghz images here , be regions of interaction with the external medium or a result of jet bending , perhaps as part of a helical pattern . the lack of a visible counterjet , despite the presence of a counter lobe on scales of several arcminutes , is further evidence that the jet remains relativistic to large scales . * some of the features seen in the 1.7 ghz images suggest that the jet has a helical structure . to match the observed structure , either the jet must be extremely close to the line - of - sight ( much closer than the maximum angle allowed by the superluminal motion alone ) or there must be an offset between the line traced by the peak brightness and the path of individual fluid elements . the fluid equations ( e.g. , hardee 2000 ) applied to helically twisted jets predict such an offset because the region of high pressure describes a helix of larger transverse amplitude than is followed by the fluid elements . additional theoretical constraints related to the low pattern speed suggest that the jet is closer to the line - of - sight than about @xmath40 . for any line - of - sight angle allowed by the superluminal motion , the wavelength of the helix is relatively long , in contrast to the situation in m87 where tightly wound helical patterns are seen . longer wavelengths are favored when the jet is surrounded by a relatively cool medium . the picture that emerges is one of a continuous , relativistic jet with much internal structure but a smooth outer envelope . the velocity is maintained from sub - parsec to hundreds of parsec scales . there is some slowing at the largest scale feature whose speed could be measured , but the jet appears to remain relativistic to kiloparsec and larger scales . the structure includes both features that move with the jet , perhaps density enhancements or shocks , and also features that do not move with the flow . the moving features can pass through the stationary features , suggesting that the stationary features do not significantly disrupt the flow . these could be places where there is some interaction with the external medium or they could be the result of variations in the jet path . individual features are followed for large fractional distances from the core , suggesting that they represent variations in fundamental and enduring parameters of the jet such as density . possible helical patterns of long wavelength are seen on several scales . theoretical arguments suggest such wavelengths when the jet is cool and/or of high lorentz factor and is moving through a cool and not relativistically hot medium . we would like to thank the staffs of all the observatories listed in the table [ antennas ] and the caltech , charlottesville , and socorro correlators , without whose efforts these observations would not have been possible . while we did not use their data directly in the above text , we often consulted the university of michigan radio astronomy observatory flux density history available on the internet for a consistent history of activity in 3c 120 . that project is supported by funds from the university of michigan . t. hunter and m. lystrup acknowledge support as summer students at nrao by the research experiences for undergraduates program of the national science foundation . p. hardee acknowledges support from the national science foundation through grant ast-9802955 to the university of alabama . p. hardee and c. walker acknowledge the aspen center for physics where some of this work was performed . lllr us vlbi network : + arecibo & a & puerto rico & 300 + haystack & k & massachusetts & 37 + green bank 140 & g & west virginia & 43 + north liberty & i & iowa & 18 + fort davis ( gras ) & f & texas & 26 + vla ( single antenna ) & y1 & new mexico & 25 + vla ( phased array ) & yp & new mexico & @xmath66 + owens valley & o & california & 40 + hat creek & h & california & 26 + maryland point ( nrl ) & n & maryland & 26 + european vlbi network : + jodrell mark i & j & united kingdom & 76 + jodrell mark ii & j2 & united kingdom & 38 by 25 + onsala & s & sweden & 26 + westerbork ( 1 or 12 antennas ) & w & the netherlands & ( @xmath67 ) 25 + effelsberg & b & germany & 100 + medicina & m & italy & 32 + torun 18 & t & poland & 18 + torun 32 & tr & poland & 32 + simeiz & r & ukraine & 22 + noto & nt & italy & 32 + vlba : + saint croix & sc & virgin islands & 25 + hancock & hn & new hampshire & 25 + north liberty & nl & iowa & 25 + fort davis & fd & texas & 25 + los alamos & la & new mexico & 25 + pie town & pt & new mexico & 25 + kitt peak & kp & arizona & 25 + owens valley & ov & california & 25 + brewster & br & washington & 25 + mauna kea & mk & hawaii & 25 + other : + defford & u & united kingdom & 25 + cambridge & e & united kingdom & 18 + dwingeloo & d & the netherlands & 25 + penticton & p & british columbia & 25 + pushkino & pu & russia & 25 + hartebeesthoek & x & south africa & 26 + 1978.91 & 10.7 & kgfo & 2.07 + 1979.25 & 5.0 & bgfoh & 1.30 + 1979.44 & 10.7 & bkgfo & 0.84 + 1979.92 & 5.0 & bkgfo & 0.85 + 1980.27 & 10.7 & bkgo & 1.18 + 1980.52 & 10.7 & bkgfo & 1.22 + 1980.72 & 5.0 & bkfo & 1.51 + 1981.10 & 10.7 & kgfo & 0.84 + 1981.63 & 5.0 & bkgypoh & 0.88 + 1981.93 & 5.0 & bskgfypoh & 1.14 + 1982.25 & 5.0 & bsagfy1oh & 1.21 + 1982.58 & 5.0 & bkgfypo & 0.92 + 1982.94 & 5.0 & bswjakngfypo & 0.83 + 1983.25 & 5.0 & bakgo & 0.45 + 1983.57 & 5.0 & bskngfypo & 0.64 + 1983.91 & 5.0 & bskgifypo & 0.62 + 1984.25 & 5.0 & bskgfy1oh & 0.53 + 1984.40 & 5.0 & smakgfypoh & 0.48 + 1984.78 & 5.0 & bskgfypok & 0.78 + 1985.12 & 5.0 & bsakgify1o & 1.65 + 1985.41 & 5.0 & sakngiy1oh & 2.31 + 1986.42 & 5.0 & bsakgfy1oh & 0.89 + 1986.90 & 5.0 & bskgy1o & 0.89 + 1987.41 & 5.0 & bswjmtxkgy1oh & 0.84 + 1987.73 & 5.0 & bsakngify1oh & 0.68 + 1988.19 & 5.0 & bswjakgify1o & 0.56 + 1988.45 & 5.0 & bswjmknpty1o & 0.50 + 1988.87 & 5.0 & bsjmkgifpto & 0.59 + cccc 1982.78 & s b d j k n g a i f ypo p h & 2.46 & 0.25 + 1984.26 & s b w j2 t e u r k n g a i f ypo p h & 0.61 & 0.17 + 1989.85 & s b w r pum x j a k g i ptkplay1 & 1.50 & 0.21 + 1994.44 & vlba & 0.58 & 0.12 + 1997.71 & b j m nttrw g y1 vlba & 1.05 & 0.05 + ccrrr a & 4 & @xmath68 & @xmath69 & 3.00 + b & 13 & @xmath70 & @xmath71 & 6.39 + c & 5 & @xmath72 & @xmath73 & 4.41 + d & 10 & @xmath74 & @xmath75 & 5.53 + e & 6 & @xmath76 & @xmath77 & 4.88 + f & 5 & @xmath78 & @xmath79 & 4.90 + g & 3 & @xmath80 & @xmath81 & 4.93 + h & 3 & @xmath82 & @xmath83 & 6.86 + i & 7 & @xmath84 & @xmath85 & 6.51 + j & 6 & @xmath86 & @xmath87 & 4.53 + k & 3 & @xmath88 & @xmath89 & 2.96 + gamma is significantly higher than the mimimum required for the observed superluminal motion . + physical theory focusing on the helix wavelength and the pressure distribution . & long helical wavelength implies cool external medium . apparent helix from the brightest emission can have a larger radius than the helical paths followed by the particles . + simple morphological model with the apparent helix wider than the particle path helix . & allows wider angles to line of sight without excessive brightness variations .

superluminal features are seen leaving the core at intervals of less than a year , about as often as new features could be distinguished with the 0.6 parsec resolution of the observations . the underlying jet is continuous , but not smooth , and the measured features are simply the bright points in the convolution of the observing beam with brightness fluctuations that occur on many scales . . these may be locations where there is interaction with the external medium , or they may simply be the result of variations in the jet angle to the line - of - sight . the deprojected wavelength of the pattern is very long relative to the jet radius , unlike the situation in sources such as m87 .

results are presented from long term vlbi monitoring of the parsec - scale radio jet in 3c 120 at 5 and 1.7 ghz . the 5 ghz sequence includes a few early epochs at 10.7 ghz . superluminal features are seen leaving the core at intervals of less than a year , about as often as new features could be distinguished with the 0.6 parsec resolution of the observations . the underlying jet is continuous , but not smooth , and the measured features are simply the bright points in the convolution of the observing beam with brightness fluctuations that occur on many scales . the velocity of different features varies , but not by more than about a factor of 2 . clear variations in the velocity of an individual feature are not seen . some features that were observed leaving the core in the 5 ghz observations with 0.6 pc resolution are followed at 1.7 ghz , with 2.4 pc resolution , to projected distances in excess of 25 pc from the core . older features up to at least 150 pc in projection from the core are still moving at superluminal apparent speeds and are therefore presumed to be relativistic . beyond that , the data are inadequate for motion measurements . the region where the jet slows to non - relativistic speeds has not been found . there are suggestions of stationary features , or brightening and dimming regions , through which the moving features pass . these may be locations where there is interaction with the external medium , or they may simply be the result of variations in the jet angle to the line - of - sight . the observation of stationary features in an otherwise moving jet reinforces the idea that the lack of motion of the knot at 4 ( 2 kpc ) , that has been found not to be superluminal in other observations , might not actually imply that the jet has slowed by that position . the structure of the jet in the vicinity of the most likely stationary feature is suggestive of a helical pattern seen in projection . the deprojected wavelength of the pattern is very long relative to the jet radius , unlike the situation in sources such as m87 . if the 3c 120 jet does contain a slowly - moving , helical structure , then theory suggests that the jet resides in a relatively cool medium , not in a relativistically hot cocoon or lobe .

1206.1643

i

dynamical systems theory plays an important role in many areas of mathematics and physics because it provides the building blocks that allow us to understand the changes many physical systems experience in their dynamics when parameters are varied . these building blocks are the generic bifurcations ( saddle - node , hopf , etc . ) that any arbitrary physical system experiences under parameter variation , regardless of the physical mechanisms underlying the dynamics . when one single parameter of the system under consideration is varied , codimension - one bifurcations are expected . if the system depends on more parameters , higher codimension bifurcations appear and they act as organizing centers of the dynamics . the presence of symmetries changes the nature and type of bifurcations that a dynamical system may undergo . symmetries play an important role in many idealized situations , where simplifying assumptions and the consideration of simple geometries result in dynamical systems equivariant under a certain symmetry group . bifurcations with symmetry have been widely studied @xcite . however , in any real system , the symmetries are only approximately fulfilled , and the breaking of the symmetries , due to the presence of noise , imperfections and/or other phenomena , is always present . there are numerous studies of how imperfect symmetries lead to dynamics that are unexpected in the symmetric problem , e.g. @xcite . however , a complete theory is currently unavailable . one observed consequence of imperfections in systems that support propagating waves is that the waves may become trapped by the imperfections ( e.g. , see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in these various examples , the propagation direction is typically biased . however , a more recent problem has considered a case where a rotating wave whose sense of precession changes sign is pinned by symmetry - breaking imperfections @xcite . we are unaware of any systematic analysis of the associated normal form dynamics for such a problem and this motivates the present study . when a system is invariant to rotations about an axis ( invariance under the @xmath0 symmetry group ) , @xmath0-symmetry - breaking hopf bifurcations result in rotating waves , consisting of a pattern that rotates about the symmetry axis at a given precession frequency without changing shape . this frequency is parameter dependent , and in many problems , when parameters are varied , the precession frequency changes sign along a curve in parameter space . what has been observed in different systems is that in the presence of imperfections , the curve of zero frequency becomes a band of finite width in parameter space . within this band , the rotating wave becomes a steady solution . this is the so - called pinning phenomenon . it can be understood as the attachment of the rotating pattern to some stationary imperfection of the system , so that the pattern becomes steady , as long as its frequency is small enough so that the imperfection is able to stop the rotation . this pinning phenomenon bears some resemblance to the frequency locking phenomena , although in the frequency locking case we are dealing with a system with two non - zero frequencies and their ratio becomes constant in a region of parameter space ( a resonance horn ) , whereas here we are dealing with a single frequency crossing zero . in the present paper , we analyze the breaking of @xmath0 symmetry in a dynamical system close to a hopf bifurcation whose frequency changes sign along a curve in parameter space . the analysis shows that breaking @xmath0 symmetry is much more complex than expected , resulting in a bifurcation of high codimension ( about nine ) . although it is not possible to analyze in detail such a complex and high - codimension bifurcation , we present here the analysis of five different ways to break @xmath0 symmetry . this is done by introducing into the normal form all the possible terms , up to and including second order , that break the symmetry , and analyzing each of these five terms separately . three of these particular cases have already been analyzed in completely different contexts unrelated to the pinning phenomenon @xcite . in the present study , we extract the common features that are associated with the pinning . in all cases , we find that a band of pinning solutions appears around the zero frequency curve from the symmetric case , and that the band is delimited by curves of infinite - period bifurcations . the details of what happens when the infinite - period bifurcation curves approach the hopf bifurcation curve are different in the five cases , and involve complicated dynamics with several codimension - two bifurcations occurring in a small region of parameter space as well as several global bifurcations . interest in the present analysis is two - fold . first of all , although the details of the bifurcational process close to the zero - frequency hopf point are very complicated and differ from case to case , for all cases we observe the appearance of a pinning band delimited by infinite - period bifurcations of homoclinic type that , away from the small region of complicated dynamics , are snic bifurcations ( saddle - node on an invariant circle bifurcation , e.g. see * ? ? ? secondly , some of the scenarios analyzed are important _ per se _ , as they correspond to the generic analysis of a partial breaking of the @xmath0 symmetry , so that after the introduction of perturbations , the system still retains a discrete symmetry ( the @xmath2 case is analyzed in detail ) . the paper is organized as follows . in section [ sec_perfect_hopf ] the properties of a hopf bifurcation with @xmath0 symmetry with the precession frequency crossing through zero are summarized , and the general unfolding of the @xmath0 symmetry breaking process is discussed . the next sections explore the particulars of breaking the symmetry at order zero ( [ sec_epsilon ] ) , one ( [ sec_bar_z ] ) and two ( [ sec_quadratic ] ) . sections [ sec_bar_z ] and [ sec_z3 ] are particularly interesting because they consider the symmetry - breaking processes @xmath3 and @xmath4 which are readily realized experimentally . section [ sec_general ] extracts the general features of the pinning problem from the analysis of the specific cases carried out in the earlier sections . section [ sec_experiments ] presents comparisons with experiments and numerical computations in two real problems in fluid dynamics , illustrating the application of the general theory developed in the present study . finally , in [ conclusions ] , conclusions and perspectives are presented .

their precession frequency changes with parameters and it may change sign , passing through zero . this is the so - called pinning phenomenon . in this study , we analyze the breaking of the symmetry in a dynamical system close to a hopf bifurcation whose frequency changes sign along a curve in parameter space . the problem is very complex , as it involves the complete unfolding of high codimension . a detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite - period bifurcation curves appears in all cases . complex bifurcational processes , strongly dependent on the specifics of the symmetry breaking , appear very close to the intersection of the hopf bifurcation and the pinning region . scaling laws of the pinning region width , and partial breaking of to , are also considered .

rotating waves are periodic solutions in equivariant dynamical systems . their precession frequency changes with parameters and it may change sign , passing through zero . when this happens , the dynamical system is very sensitive to imperfections that break the symmetry and the waves may become trapped by the imperfections , resulting in steady solutions that exist in a finite region in parameter space . this is the so - called pinning phenomenon . in this study , we analyze the breaking of the symmetry in a dynamical system close to a hopf bifurcation whose frequency changes sign along a curve in parameter space . the problem is very complex , as it involves the complete unfolding of high codimension . a detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite - period bifurcation curves appears in all cases . complex bifurcational processes , strongly dependent on the specifics of the symmetry breaking , appear very close to the intersection of the hopf bifurcation and the pinning region . scaling laws of the pinning region width , and partial breaking of to , are also considered . previous and new experimental and numerical studies of pinned rotating waves are reviewed in light of the new theoretical results .

0910.1674

i

extended rpa theories such as second rpa ( srpa ) @xcite , which go beyond first - order rpa , are often used to describe the strength , decay width and fine structure of nuclear giant resonances ( grs ) and other collective low - lying states . they also appear particularly useful in the case of unitarily transformed realistic interactions , which have not been calibrated for first - order rpa methods , but rather rely on extended model spaces to provide converged results . such interactions also make self - consistent " extended - rpa applications possible , in the sense that the ground state and the residual couplings can be described by the same hamiltonian . first applications using a renormalized argonne v18 potential , derived with the unitary correlation operator method ( ucom ) @xcite , were presented in ref . @xcite . self - consistent extended - rpa applications in large spaces without arbitrary truncations can be envisioned , in principle , with any properly constructed finite - range effective interaction . however , they are hardly ever performed for various technical and conceptual reasons . phenomenological effective interactions are fitted to sets of experimental data using mostly hartree - fock(-bogoliubov ) and selected ( quasi - particle ) rpa results . their range of applicability is then restricted to the selected observables and many - body methods . zero - range effective interactions , which greatly simplify numerical applications , can not be employed in second - order rpa methods , because they do not provide a natural cutoff in momentum space . consequently , no effective interactions have been fitted to calculations beyond first - order rpa and consistency in the treatment of the ground and excited states is ordinarily abandoned in practical applications of such methods . it is the purpose of the present work to perform and analyze large - scale ( i.e. , without arbitrary truncations ) , self - consistent " ( i.e. , with a single interaction as the sole input ) srpa calculations . we employ mostly the @xmath0 interaction used in ref . it is derived from the argonne v18 potential by means of a unitary transformation , which renormalizes it , while preserving the phase shifts and retaining the complex structure of the realistic interaction . we also use the brink - boeker interaction , @xmath1 @xcite , which is a simple , central , phenomenological effective interaction . no explicit three - body force is used at this point . we will not focus on producing realistic results and comparing them with data , as was done in ref . @xcite , but rather on technical and physical aspects of the method . we present how the large - scale eigenvalue problems that srpa involves can be treated , demonstrate how the method operates in producing self - energy corrections and fragmentation , and discuss consistency and stability problems . in the next section we present the srpa formalism and in sec . [ s : solve ] the methods we have used to solve the srpa eigenvalue problem . in sec . [ s : res ] we discuss our results with the help of illustrative examples . we conclude in sec . [ s : concl ] .

second rpa ( srpa ) calculations of nuclear response are performed and analyzed . unlike in most other srpa applications , the ground state , approximated by the hartree - fock ( hf ) ground state , and the residual couplings are described by the same hamiltonian and no arbitrary truncations are imposed on the model space . finite - range interactions are used and thus divergence problems are not present . we employ a realistic interaction , derived from the argonne v18 potenial using the unitary correlation operator method ( ucom ) , as well as the simple brink - boeker interaction . representative results are discussed , mainly on giant resonances and low - lying collective states . the focus of the present work is not on the comparison with data , but rather on technical and physical aspects of the method . we present how the large - scale eigenvalue problem that srpa entails can be treated , and demonstrate how the method operates in producing self - energy corrections and fragmentation .

second rpa ( srpa ) calculations of nuclear response are performed and analyzed . unlike in most other srpa applications , the ground state , approximated by the hartree - fock ( hf ) ground state , and the residual couplings are described by the same hamiltonian and no arbitrary truncations are imposed on the model space . finite - range interactions are used and thus divergence problems are not present . we employ a realistic interaction , derived from the argonne v18 potenial using the unitary correlation operator method ( ucom ) , as well as the simple brink - boeker interaction . representative results are discussed , mainly on giant resonances and low - lying collective states . the focus of the present work is not on the comparison with data , but rather on technical and physical aspects of the method . we present how the large - scale eigenvalue problem that srpa entails can be treated , and demonstrate how the method operates in producing self - energy corrections and fragmentation . the so - called diagonal approximation is conditionally validated . stability problems are traced back to missing ground - state correlations .

1309.3021

i

we have simulated systems of self - propelled particles with preferred circular trajectories ( circle spps ) interacting via a velocity - trajectory coordination rule , and systems of curved flagella propelled by a sinusoidal beating motion . in both systems , we observe the formation of vortex arrays , controlled by particle density , interaction range , and diameter of the preferred circular trajectory . for the circle - spp systems , the vortex array shows liquid - like rather than hexagonal spatial order . the diameter of the vortices , @xmath114 , is about the diameter of a single particle trajectory @xmath7 with a slight increase with the diameter of the interaction region @xmath8 , but is not sensitive to the particle density @xmath98 . the average distance between neighbor vortices , @xmath136 , is also not sensitive to @xmath98 , but increases quickly with increasing @xmath8 . a transition from a light - vortex - dominated state ( at low @xmath98 and small @xmath8 ) to a heavy - vortex - dominated state ( at high @xmath98 or large @xmath8 ) is observed . we use an order parameter @xmath2 to characterize the degree of the vortex formation . by comparing the time evolution of @xmath2 , we find that the vortex formation can be divided into three time periods . during period i , the particles collect neighbor ones to form vortices and @xmath2 increase quickly with time . the increase of @xmath183 during period i is slightly elevated with @xmath98 , but is not sensitive to @xmath8 . in the subsequent period ii , @xmath183 increases very slowly . in period iii , the vortex mass increases again more rapidly through vortex collision and fusion . note that environmental noise is not described in our model . therefore the fission , fusion and displacement of vortices is purely the result of multi - particle interactions of circle spps . in order to compare with the experiments of sperm cells near surfaces , we have also studied a more detailed model of curved , sinusoidally beating flagella . vortex patterns in this system emerge from the hard - core repulsion of the curved body of the elongated self - propelled particles moving in a viscous environment . in the simulations with anisotropic frictions , the collective motion of the curved flagella system agrees very well with the behavior of the circle spps system , as well as the phenomenon observed in the sea - urchin sperm experiments @xcite . as in the circle spps system , the average size of the vortices @xmath114 equals approximately @xmath7 , and slightly increases with the flagellum density . by comparing @xmath136 with the circle spps systems , we find that the size of the effective interaction region of a curved flagellum can be approximately identified with @xmath253 . the order parameter @xmath2 increases with @xmath98 as well as @xmath7 . the fraction @xmath235 coincides the value @xmath254 calculated by using the data from @xcite for sea - urchin sperm system . in conclusion , the collective motion of self - propelled particles , which leads to the formation of vortex arrays , can be well reproduced by circle spps with a velocity - trajectory coupling interaction . the velocity - trajectory coordination rule is a different interaction type than the velocity coordination rules employed since the vicsek model @xcite for the simulations of collective motion . such an interaction mimics , for example , the hard - core interaction of curved , sinusoidal beating flagella . the analysis of a more specific model of beating flagella allows to elucidate the features related to an explicit propulsion mechanism and physical interactions .

if the particles interact via a velocity - trajectory coordination " rule within neighboring particles , a self - organized vortex pattern emerges . we also study a semi - dilute solution of curved , sinusoidal - beating flagella , as an example of circling self - propelled particles with explicit propulsion mechanism and excluded - volume interactions .

self - propelled point - like particles move along circular trajectories when their translocation velocity is constant and the angular velocity related to their orientation vector is also constant . we investigate the collective behavior of ensembles of such circle swimmers by brownian dynamics simulations . if the particles interact via a velocity - trajectory coordination " rule within neighboring particles , a self - organized vortex pattern emerges . this vortex pattern is characterized by its particle - density correlation function , the density correlation function of trajectory centers , and an order parameter representing the degree of the aggregation of the particles . here , we systematically vary the system parameters , such as the particle density and the interaction range , in order to reveal the transition of the system from a light - vortex - dominated to heavy - vortex - dominated state , where vortices contain mainly a single and many self - propelled particles , respectively . we also study a semi - dilute solution of curved , sinusoidal - beating flagella , as an example of circling self - propelled particles with explicit propulsion mechanism and excluded - volume interactions . our simulation results are compared with previous experimental results for the vortices in sea - urchin sperm solutions near a wall . the properties of the vortices in simulations and experiments are found to agree quantitatively .

1607.07586

i

let @xmath5 be a finite group , and @xmath6 be two complex representations of @xmath5 with characters @xmath7 . we will study the quantities @xmath8 specifically , let @xmath9 be the minimum of @xmath10 as @xmath6 range over pairs of inequivalent irreducible @xmath0-dimensional representations of @xmath5 , with the convention that @xmath11 if there are no such pairs @xmath6 . note that @xmath9 tells us what fraction of elements of @xmath5 we must check to distinguish irreducible degree @xmath0 characters . put @xmath12 . an elementary consequence of orthogonality relations is [ prop1 ] we have @xmath13 . buzzard , edixhoven and taylor constructed examples to show this bound is sharp when @xmath0 is a power of 2 , which serre generalized this to arbitrary @xmath0 ( see @xcite ) . [ thm : serre ] for any @xmath0 , there exists @xmath5 such that @xmath14 , so @xmath15 . in particular , the infimum is a minimum . we will recall the proof of proposition [ prop1 ] and serre s construction in section [ sec : serre ] . for now , the main points to note are that serre s examples must be solvable and the representations are induced . in this paper , we consider two kinds of refinements of determining @xmath16 , and give an application to a strong local - global phenomenon for galois representations . the first refinement is about restricting to primitive representations and the second is about restricting to certain families of groups . define @xmath17 to be the infimum of @xmath10 where @xmath6 range over pairs of inequivalent irreducible primitive @xmath0-dimensional complex representations of @xmath5 . let @xmath18 . using the classical fact that the number of finite primitive subgroups of @xmath19 is bounded for a given @xmath0 , it is not hard to show that this infimum is also a minimum . from serre s theorem , we get a trivial bound @xmath20 . here is our first main result ( see theorems [ thm : deg2 ] and [ thm : deg3 ] ) . [ thm1 ] we have @xmath21 , @xmath22 and @xmath23 . furthermore @xmath24 if and only if @xmath5 is an extension of @xmath25 $ ] or @xmath26 $ ] , and @xmath27 if and only if @xmath5 is an extension of @xmath28 . by @xmath5 being an extension of @xmath29 ( by a normal subgroup @xmath30 ) , we mean @xmath31 . the groups @xmath25 $ ] and @xmath26 $ ] are the two groups of order 48 which are extensions of @xmath32 by the cyclic group @xmath33 and contain @xmath34 . the @xmath35 case is already contained in proposition [ prop1 ] as @xmath36 . for @xmath37 , these bounds are much better than the trivial bounds @xmath38 and @xmath39 . for @xmath40 , some related results were previously obtained by the second author in @xcite and will be discussed below . note that while @xmath16 is a strictly decreasing sequence for @xmath41 , our result says this is not the case for @xmath42 . in a slightly different direction , one can look for stronger lower bounds than @xmath43 for certain families of groups . we do not begin a serious investigation of this here , but just treat two basic families of finite groups of lie type which are related to the calculations for @xmath44 and @xmath45 . [ thm2 ] we compute @xmath9 and @xmath46 where @xmath47 and @xmath48 ; for @xmath0 not listed explicitly , @xmath49 . for @xmath50 with @xmath51 arbitrary or for @xmath47 with @xmath51 even , @xmath52 and @xmath53 whereas @xmath54 . for @xmath47 and @xmath51 odd , @xmath55 and @xmath56 whereas @xmath54 we remark that we completely determine @xmath57 for @xmath48 and @xmath2 in section [ sec : sl2q ] , but the exact formulas are a bit complicated and depend on divisibility conditions of @xmath58 . in particular , @xmath59 if and only if @xmath60 , and @xmath61 if and only if @xmath62 . the values for @xmath3 immediately give the following bounds . @xmath63 for @xmath51 any odd prime power greater than 3 . note the upper bound in the corollary for @xmath64 is the exact value of @xmath65 . even though theorem [ thm1 ] implies @xmath42 is not a decreasing sequence for @xmath41 , this corollary at least suggests the possibility of @xmath66 as @xmath67 . the proof of theorem [ thm1 ] relies on consideration of various cases according to the possible finite primitive subgroups of @xmath68 and @xmath69 , and about half of these are of the form @xmath2 or @xmath3 ( or @xmath70 ) for @xmath71 . thus theorem [ thm2 ] is a generalization of one of the ingredients for theorem [ thm1 ] . however , the main work in proving theorem [ thm1 ] is dealing with extensions of finite subgroups of @xmath68 and @xmath69 . one reason for interest in these questions is an application to density questions for galois and automorphic representations . namely , let @xmath72 be a number field and @xmath6 be irreducible @xmath0-dimensional artin representations for @xmath72 , i.e. , irreducible @xmath0-dimensional continuous complex representations of the absolute galois group @xmath73 of @xmath72 . for almost all places @xmath74 of @xmath72 , we can associate a well - defined frobenius conjugacy class @xmath75 of @xmath73 . the local invariant @xmath76 is of interest in number theory . the bound @xmath77 implies that if @xmath78 for a set of primes of density strictly greater than @xmath79 , then @xmath80 . on the other hand , there also exist inequivalent @xmath81 such that @xmath78 on a set of primes of density @xmath82 , so this bound is sharp . an analogous result for @xmath83-adic galois representations is due to rajan @xcite . ramakrishnan @xcite conjectured an analogous `` refined strong multiplicity one '' statement for cuspidal automorphic representations of @xmath84 , again with density bounds @xmath82 that should be sharp , and proved this for @xmath40 in @xcite . recently , in @xcite the second author showed that when @xmath40 one can in fact obtain stronger bounds under various assumptions , e.g. , the bound @xmath85 may be replaced by @xmath86 if one restricts to non - dihedral representations or by @xmath87 if the representations are not twist - equivalent . ( these bounds are also sharp . ) here non - dihedral is the analogue of primitive . all of these refined strong multiplicity one statements can be interpreted as stating , given an @xmath88-function @xmath89 associated to some object @xmath90 , how many euler factors @xmath91 one needs to know to determine @xmath92 . this project arose as an attempt to gain insight into what a conjectural analogue of @xcite ( specifically , the @xmath93 bound for non - dihedral representations ) might be for @xmath94 . since the problem for automorphic representations seems hard for @xmath95 , here we just settle for some results about artin representations as a test case . let @xmath81 , @xmath96 be inequivalent irreducible primitive @xmath0-dimensional artin representations for @xmath72 . suppose @xmath78 for a set of primes @xmath74 of @xmath72 of density @xmath97 . 1 . if @xmath40 and @xmath98 , then @xmath80 . if @xmath99 and @xmath100 , then @xmath80 . this follows immediately from the chebotarev density theorem which says that if @xmath101 is a finite normal extension with galois group @xmath5 and @xmath102 is a conjugacy class in @xmath5 , then the image of @xmath75 in @xmath103 lies in @xmath102 for a set of primes @xmath74 of density @xmath104and theorem [ thm1 ] . in general , chebotarev s theorem implies that if @xmath81 and @xmath96 are irreducible @xmath0-dimensional artin representations for @xmath72 which both factor through a finite galois extension @xmath101 with galois group @xmath5 , then @xmath105 implies @xmath80 ( with @xmath97 as in the corollary ) . when @xmath40 , if @xmath81 and @xmath96 are automorphic , i.e. , correspond to cuspidal automorphic representations of @xmath106 , then the above result already follows by @xcite . the strong artin conjecture asserts that all artin representations are automorphic . when @xmath40 , the strong artin conjecture for @xmath81 is known in many cases for instance , if @xmath81 has solvable image by langlands @xcite and tunnell @xcite , or if @xmath107 and @xmath81 is `` odd '' via serre s conjecture by khare - wintenberger @xcite . we remark that the methods of @xcite are quite different than ours here . the above corollary then suggests the following statement may be true : if @xmath108 are cuspidal automorphic representations of @xmath109 which are not induced from characters and @xmath110 for a set of primes @xmath74 of density @xmath111 , then @xmath112 . of course , not all cuspidal @xmath108 come from galois representations , so the @xmath113 bound may not be sufficient for general @xmath108 . however , it seems reasonable to think that coincidences of a large fraction of euler factors only happen for essentially algebraic reasons , so the density bounds are likely to be the same in both the galois and automorphic cases . the first author was partially supported by a simons collaboration grant . the second author was supported by forschungskredit grant k-71116 - 01 - 01 of the university of zrich and partially supported by grant snf pp00p2 - 138906 of the swiss national foundation .

serre obtained a sharp bound on how often two irreducible degree complex characters of a finite group can agree , which has applications to a refined local - global principle for galois representations . we answer this question for , the families and for general , and conclude a local - global application to primitive galois ( artin ) representations . this provides some insight on refined strong multiplicity one phenomena for automorphic representations of .

serre obtained a sharp bound on how often two irreducible degree complex characters of a finite group can agree , which has applications to a refined local - global principle for galois representations . we consider the more delicate question of finding a sharp bound when the characters are primitive . we answer this question for , the families and for general , and conclude a local - global application to primitive galois ( artin ) representations . this provides some insight on refined strong multiplicity one phenomena for automorphic representations of .

1607.05602

i

simultaneous wireless information and power transfer ( swipt ) has recently attracted significant attention in academia , with works addressing many scenarios , a.o . mimo broadcasting @xcite , architecture @xcite , interference channel @xcite , broadband system @xcite , relaying @xcite . wireless power transfer ( wpt ) is a fundamental building block of swipt and the design of an efficient swipt architecture fundamentally relies on the ability to design efficient wpt . the major challenge with wpt , and therefore swipt , is to find ways to increase the dc power level at the output of the rectenna without increasing the transmit power . to that end , the vast majority of the technical efforts in the literature have been devoted to the design of efficient rectennas . the rectenna is made of a non - linear device followed by a low - pass filter to extract a dc power out of an rf input signal . the amount of dc power collected is a function of the input power level and the rf - to - dc conversion efficiency . interestingly , the rf - to - dc conversion efficiency is not only a function of the rectenna design but also of its input waveform @xcite . this observation has triggered very recent interests on wireless power waveform design in the signal processing literature @xcite . the objective is to understand how to make the best use of a given rf spectrum in order to deliver a maximum amount of dc power at the output of a rectenna . this problem can be formulated as a link optimization where transmit waveforms are adaptively designed as a function of the channel state information ( csi ) so as to maximize the dc power at the output of the rectifier . in @xcite , the waveform design problem for wpt has been tackled by introducing a simple and tractable analytical model of the non - linearity of the diode through the second and higher order terms in the taylor expansion of the diode characteristics . comparisons were also made with a linear model of the rectifier , that only accounts for the second order term . assuming perfect channel state information at the transmitter ( csit ) can be attained , relying on both the linear and non - linear models , an optimization problem was formulated to adaptively change on each transmit antenna a multisine waveform as a function of the csi so as to maximize the output dc current at the energy harvester . important conclusions of @xcite are that 1 ) multisine waveforms designed accounting for nonlinearity are spectrally more efficient that those designed based on a linear model of the rectifier , 2 ) the linear model does not characterize correctly the rectenna behaviour and leads to inefficient multisine waveform design , 3 ) rectifier nonlinearity is key to design efficient wireless powered systems . interestingly , the swipt literature has so far entirely relied on the aforementioned linear model of the rectifier , e.g. @xcite and subsequent works . the problem of swipt waveform and transceiver design that accounts for the nonlinearity of the rectifier has indeed never been addressed so far . in view of the recent results in @xcite , it is expected that accounting for the rectifier nonlinearity is key to efficient swipt design . in this paper , we address the important problem of waveform and transceiver design for swipt . the contributions of the paper are summarized as follows . first , we leverage the analytical model of the rectenna non - linearity introduced in @xcite and investigate how a communication waveform ( ofdm ) and a power waveform ( multisine ) compare with each other in terms of harvested energy . comparison is also made with the linear model commonly used in the swipt literature @xcite . scaling laws of the harvested energy with multisine and ofdm waveforms are analytically derived as a function of the number of sinewaves and the propagation conditions . we show that with the nonlinear model of the rectifier , there is a clear benefit of using a deterministic multisine over an ofdm waveform for wpt . on the other hand , the benefits vanish when we consider the linear model . second , we introduce a novel swipt transceiver architecture relying on the superposition of multisine and ofdm waveforms at the transmitter and a power - splitter receiver equipped with an energy harvester and an information decoder . both cases where the receiver does and does not have the capability of cancelling the multisine waveform are considered . the swipt multisine / ofdm waveforms and the power splitter are jointly optimized so as to maximize the rate - energy region of the whole system . the superposed swipt waveforms are adaptive to the channel state information and result from a posynomial maximization problem that originates from the non - linearity of the energy harvester . third , numerical results illustrate the performance of the derived waveforms and swipt architecture . key observations are that 1 ) a power waveform ( superposed to a communication waveform ) is always useful to enlarge the rate - energy region of swipt , 2 ) a combination of power splitting and time sharing is in general the best strategy , 3 ) a non - zero mean gaussian input distribution outperforms the conventional capacity - achieving zero - mean gaussian input distribution . those observations are consequences of the non - linearity of the rectifier and highlights that exploiting the nonlinearity of the rectifier is essential to design an efficient swipt architecture . _ organization : _ section [ ms_vs_ofdm ] introduces the multisine and ofdm waveforms for wpt , section [ section_eh ] introduces the rectenna model , section [ wpt_design ] optimizes multisine and ofdm waveforms for wpt and discusses the impact of the waveform type ( multisine vs ofdm ) on the harvested energy . section [ swipt_section ] introduces the swipt architecture , section [ section_swipt_waveform ] addresses the swipt waveform design , section [ simulations ] evaluates the performance and section [ conclusions ] concludes the work . _ notations : _ bold lower case and upper case letters stand for vectors and matrices respectively whereas a symbol not in bold font represents a scalar . @xmath0 refers to the frobenius norm a matrix . @xmath1 refers to the dc component of a signal . @xmath2 refers to the expectation operator taken over the distribution of the random variable @xmath3 ( @xmath3 may be omitted for readability if the context is clear ) . @xmath4 refers to the conjugate of a scalar . @xmath5 and @xmath6 represent the transpose and conjugate transpose of a matrix or vector respectively .

simultaneous wireless information and power transfer ( swipt ) has attracted significant attention in the communication community . the problem of waveform design has however never been addressed so far . in this paper , we first investigate how a communication waveform ( ofdm ) and a power waveform ( multisine ) compare with each other in terms of harvested energy . we show that due to the non - linearity of the rectifier and the randomness of the information symbols , the ofdm waveform is less efficient than the multisine waveform for wireless power transfer . this observation motivates the design of a novel swipt transceiver architecture relying on the superposition of multisine and ofdm waveforms at the transmitter and a power - splitter receiver equipped with an energy harvester and an information decoder . the superposed swipt waveform is optimized so as to maximize the rate - energy region of the whole system . its design is adaptive to the channel state information and result from a posynomial maximization problem that originates from the non - linearity of the energy harvester . numerical results illustrate the performance of the derived waveforms and swipt architecture . key ( and refreshing ) observations are that 1 ) a power waveform ( superposed to a communication waveform ) is useful to enlarge the rate - energy region of swipt , 2 ) a combination of power splitting and time sharing is in general the best strategy , 3 ) exploiting the nonlinearity of the rectifier is essential to design efficient swipt architecture , 4 ) a non - zero mean gaussian input distribution outperforms the conventional capacity - achieving zero - mean gaussian input distribution .

simultaneous wireless information and power transfer ( swipt ) has attracted significant attention in the communication community . the problem of waveform design has however never been addressed so far . in this paper , we first investigate how a communication waveform ( ofdm ) and a power waveform ( multisine ) compare with each other in terms of harvested energy . we show that due to the non - linearity of the rectifier and the randomness of the information symbols , the ofdm waveform is less efficient than the multisine waveform for wireless power transfer . this observation motivates the design of a novel swipt transceiver architecture relying on the superposition of multisine and ofdm waveforms at the transmitter and a power - splitter receiver equipped with an energy harvester and an information decoder . the superposed swipt waveform is optimized so as to maximize the rate - energy region of the whole system . its design is adaptive to the channel state information and result from a posynomial maximization problem that originates from the non - linearity of the energy harvester . numerical results illustrate the performance of the derived waveforms and swipt architecture . key ( and refreshing ) observations are that 1 ) a power waveform ( superposed to a communication waveform ) is useful to enlarge the rate - energy region of swipt , 2 ) a combination of power splitting and time sharing is in general the best strategy , 3 ) exploiting the nonlinearity of the rectifier is essential to design efficient swipt architecture , 4 ) a non - zero mean gaussian input distribution outperforms the conventional capacity - achieving zero - mean gaussian input distribution .

0910.2270

i

massive star - forming regions ( msfrs ) with o stars are usually identified by a group of hypercompact ( hc ) h ii or ultracompact ( uc ) h ii regions found together , deeply embedded in a dense molecular cloud @xcite . that several h ii regions are typically found within each star - forming region indicates that massive stars form together in small clusters . furthermore , the infrared luminosity and radio continuum brightness of the individual h ii regions suggest that some of them may themselves contain more than one massive star . thus , the spatial structure of massive star - forming regions is clustered and hierarchical : the star - forming regions contain a number of separate hc and uc h ii regions , each of which may in turn contain a few massive stars . low angular resolution , single - dish , molecular line surveys of msfrs show evidence for large scale contraction of the embedding molecular clouds @xcite . higher angular resolution observations of some of these regions identify velocity gradients consistent with rotation and inflow . in addition to the accretion flows seen on the large - scale ( @xmath5 pc ) of the embedding molecular cloud ( g10.6 - 0.4 : ho & haschick 1986 , keto et al . 1987a , keto 1990 ; g29.96 - 0.02 : olmi et al . 2003 ) , accretion flows are also seen on smaller ( @xmath6 pc ) scales around individual hc and uc h ii regions ( g10.6 - 0.4 : keto et al . 1988 , sollins et al . 2005a ; w3(oh ) : keto et al . 1987b , keto et al . 1995 ; w51e2 : zhang & ho 1997 , young et al . 1998 ; g28.20 - 0.05 : sollins et al . 2005b ; g24.78 + 0.08 : beltrn et al . 2004 , 2005 , 2006 , galvn - madrid et al . 2008 ; g29.96 - 0.02 : beuther et al . 2007 ) . it is unclear how the flows on different length scales are related . in the case of g10.6 - 0.4 , the cluster - scale accretion flow can be traced down from the largest cloud scale to the small scale of the brightest h ii region , but it is not known whether this holds for other objects . for example , in a survey of msfrs , selected on the basis of iras colors and specifically excluding those with h ii regions , multiple bipolar molecular outflows ( implying the presence of accretion flows ) are seen in random orientations @xcite . the different orientations of these smaller - scale flows suggest separate , individual centers of collapse . this comparison raises the question whether a large - scale coherent flow is required for the formation of the most massive stars , o stars ( @xmath7 @xmath8 ) capable of producing bright h ii regions , whereas b stars require only smaller scale flows . it is also unclear what happens in an accretion flow when the inflowing molecular gas reaches the boundary of an embedded h ii region . previous observations suggest that the h ii regions in an msfr that are surrounded by accretion flows , may be best understood as deriving from the continuous ionization of the accretion flow @xcite , rather than as a dynamically separate expanding bubble of ionized gas within the flow . part of the ionized gas may continue to the central star or stars and part escapes off the rotationally flattened accretion flow as a photoevaporative outflow perpendicular to the plane of rotation @xcite . the outflow is accelerated to supersonic speeds by the density gradient maintained by the stellar gravity @xcite . because the extent of an ionized outflow is generally larger than the region of ionized inflow , in most cases the outflow should be detected more easily than the inflow . h ii regions classified as broad recombination line objects " ( brlo ) @xcite show steep density gradients and supersonic flows @xcite , consistent with photoevaporation and acceleration . it is not known whether all brlo are associated with accretion . if the accretion surrounding an o star cluster is continuous from the largest to the smallest scales , this must be the case . there are only a handful of radio recombination line ( rrl ) observations that spatially resolve the ionized flow within an hc h ii region . velocity gradients consistent with outflow and rotation in the ionized gas have been previously reported for w3(oh ) @xcite , w51e2 @xcite , and g28.20 - 0.05 @xcite . observations of the very massive and spatially large g10.6 - 0.4 h ii region made at the vla in the highest possible angular resolution are able to map the inflowing ionized gas @xcite . in order to study the accretion dynamics over a range of scales in a msfr , from the cluster scale down to the scale of individual hc h ii regions and within the ionized gas , we set up a program of radio frequency molecular line , recombination line , and continuum observations at two telescopes and with several different angular resolutions . for this study we chose the massive star formation region g20.08 - 0.14 north ( hereafter g20.08n ) , identified by three uc and hc h ii regions detected in the cm continuum by @xcite . the total luminosity of the region is @xmath9 @xmath10 for a distance of 12.3 kpc . kpc ) is the most commonly quoted in the previous literature . in contrast , @xcite and @xcite report that this region is at the far kinematic distance ( @xmath11 kpc ) . we will assume the far distance throughout the rest of the paper . for reference , a scale of @xmath12 corresponds to @xmath13 au ( 0.03 pc ) . the total luminosity of the region was estimated to be @xmath14 @xmath10 assuming the near kinematic distance @xcite . correcting for the location at the far distance , the luminosity is @xmath9 @xmath10 . ] previous observations suggest accretion in the g20.08n cluster . molecular - line observations show dense gas embedding the h ii regions @xcite . molecular masers , generally associated with ongoing massive - star formation , have been detected in a number of studies ( oh : ho et al . 1983 ; h@xmath3o : hofner & churchwell 1996 ; and ch@xmath0oh : walsh et al . @xcite observed large - scale inward motions consistent with an overall contraction of the embedding molecular cloud . those authors also observed sio line profiles suggestive of massive molecular outflows , further evidence for accretion and star formation . the recombination line spectra show broad lines @xcite , presumably due to large , organized motions in the ionized gas . however , the previous observations do not have the angular resolution and the range of spatial scales needed to confirm the presence of accretion flows and study them in detail . in this paper we report on several observations of g20.08n and discuss our findings . we confirm active accretion within the cluster . furthermore , we find that the parsec - scale accretion flow fragments into smaller flows around the individual hc h ii regions , and that the gas probably flows from the largest scale down to the smallest scale . this continuous and hierarchical accretion may be necessary to supply enough mass to the small - scale flows to form o - type stars , in contrast to low- and intermediate - mass star - forming regions with stars no more massive than @xmath15 @xmath8 , where isolated accretion flows around individual protostars may be sufficient .

spectral line and continuum observations of the ionized and molecular gas in g20.08 - 0.14 n explore the dynamics of accretion over a range of spatial scales in this massive star - forming region . millimeter radio recombination line ( rrl ) observations at angular resolution indicate rotation and outflow of the ionized gas within the brightest h ii region ( a ) . these observations are consistent with photoevaporation of the inner part of the rotationally flattened molecular accretion flow .

spectral line and continuum observations of the ionized and molecular gas in g20.08 - 0.14 n explore the dynamics of accretion over a range of spatial scales in this massive star - forming region . very large array observations of nh at angular resolution show a large - scale ( 0.5 pc ) molecular accretion flow around and into a star cluster with three small , bright h ii regions . higher resolution ( ) observations with the submillimeter array in hot core molecules ( chcn , ocs , and so ) and the vla in nh , show that the two brightest and smallest h ii regions are themselves surrounded by smaller scale ( 0.05 pc ) accretion flows . the axes of rotation of the large and small scale flows are aligned , and the timescale for the contraction of the cloud is short enough , 0.1 myr , for the large - scale accretion flow to deliver significant mass to the smaller scales within the star formation timescale . the flow structure appears to be continuous and hierarchical from larger to smaller scales . millimeter radio recombination line ( rrl ) observations at angular resolution indicate rotation and outflow of the ionized gas within the brightest h ii region ( a ) . the broad recombination lines and a continuum spectral energy distribution ( sed ) that rises continuously from cm to mm wavelengths , are both characteristic of the class of h ii regions known as `` broad recombination line objects '' . the sed indicates a density gradient inside this h ii region , and the rrls suggest supersonic flows . these observations are consistent with photoevaporation of the inner part of the rotationally flattened molecular accretion flow . we also report the serendipitous detection of a new nh ( 3,3 ) maser .

0910.2270

r

figure [ fig2 ] shows the 1.3-cm continuum ( contours ) obtained from the vla - bna observations overlaid with the 1.3-mm continuum from the sma - vex data ( color scale ) . at 1.3 cm we resolve the g20.08n system into the three components reported by @xcite . h ii region a is the brightest , westernmost peak . h ii region b is the slightly broader peak @xmath40 to the se of a. h ii region c is the more extended uc h ii further to the se . its brightest , eastern rim is detected at the @xmath41 @xmath30 level in our 1.3-mm observations . the continuum of h ii region a is unresolved at 1.3 cm ; at 1.3 mm it shows a core - halo morphology . the 1.3-mm core is unresolved ( gaussian fits yield a deconvolved size at half power fwhm @xmath42 ) . the low - intensity halo has a diameter of @xmath43 ( see fig . [ fig2 ] ) . the h@xmath20 emission is confined to the unresolved core ( [ ionized ] ) and the warm molecular gas ( [ smallscale ] ) coincides with the extended continuum halo . this indicates that the unresolved h ii region a is surrounded by a dust cocoon . h ii region b is barely resolved in the 1.3-cm vla bna map ( deconvolved fwhm @xmath44 ) . the peak position of h ii region a is identical at 1.3 cm and 1.3 mm : @xmath45 @xmath46 @xmath47 , @xmath48 @xmath49 @xmath50 , within the positional uncertainty of the reference quasars ( in the range @xmath51 ) . previous observations of the recombination lines at 2 and 6 cm @xcite put the h ii regions in g20.08n in the class known as `` broad recombination line objects '' ( although those observations did not have sufficient angular resolution to separate h ii regions a , b , and c ) . the large widths in cm - wavelength recombination lines are due to pressure broadening at high gas densities ( @xmath52 @xmath53 ) as well as unresolved supersonic motions @xcite . these h ii regions also have continuum spectral energy distributions ( seds ) that increase with frequency through the mm wavelengths , evidence for a steep density gradient in the ionized gas @xcite . our new vla and sma observations , at 1.3 cm and 1.3 mm respectively , extend the sed to millimeter wavelengths . we find that the flux density of h ii region a continues to rise from cm to mm wavelengths ( fig . [ fig2 ] ) , and we analyze this characteristic in detail below . the flux densities of h ii region b at 1.3 mm ( @xmath54 mjy ) and 1.3 cm ( @xmath55 mjy ) imply a spectral index ( @xmath37 , where @xmath56 ) of @xmath57 , roughly consistent with the expected index of @xmath58 of optically thin gas . h ii region c is more extended and most of the 1.3-mm flux is resolved out . at wavelengths shorter than 1 mm , thermal dust emission contributes significantly to the continuum . we estimate the relative contributions of dust and free - free emission at 1.3 mm from our recombination line observations ( described in [ ionized ] ) and the theoretically expected line - to - continuum ratio . in the optically thin limit ( a good approximation at 1.3 mm ) the free - free line - to - continuum flux ratio @xmath59 is given by the ratio of the opacities @xmath60 @xcite : @xmath61 = \frac{\pi h{^}3 e{^}2 } { ( 2\pi m_e k){^}{3/2 } m_e c } n_1{^}2 f_{n_1,n_2 } \phi_\nu \frac{n_e n_i}{t{^}{3/2 } } \nonumber \\ \times \exp{\biggl(\frac{e_{n_1}}{kt}\biggr ) } \bigl(1- e{^}{-h\nu /kt}\bigr ) , ~ ~ ~ ~ ~ ( 1a ) \nonumber \\ \biggl[\frac{\kappa_c}{\mathrm{cm}{^}{-1}}\biggr ] = 9.77 \times 10{^}{-3 } \frac{n_e n_i}{\nu{^}2 t{^}{3/2 } } \biggl[17.72 + \ln{\frac{t{^}{3/2}}{\nu } } \biggr ] , ~ ~ ~ ~ ~ ( 1b ) \nonumber \label{eq : kappac}\end{aligned}\ ] ] where all the units are in cgs , the physical constants have their usual meanings , @xmath62 for h @xmath20 , @xmath63 for @xmath37 lines , @xmath64 for hydrogen , @xmath65 000 k , and @xmath66 is the normalized line profile . the main source of uncertainty in equations [ eq : kappal ] and [ eq : kappac ] is the temperature of the ionized gas . assuming that the line profile is gaussian and correcting for 8 @xmath67 helium in the gas , the expected ratio at the line center is @xmath68 for @xmath69 k , or @xmath70 for @xmath71 000 k. the observed ratio is @xmath72 therefore , assuming that the rrls are in lte , the free - free contribution to the 1.3-mm flux of h ii region a is @xmath73 for the assumed temperature range . figure [ fig3 ] shows a model sed for h ii region a in which 70 @xmath67 ( 355 mjy ) of the 1.3-mm flux is produced by free - free from an h ii region with a density gradient and 30 @xmath67 ( 142 mjy ) by warm dust . assuming radiative equilibrium , we set the dust temperature @xmath74 to 230 k , the average temperature of the dense gas at the same scales ( [ small - parms ] ) . the modeling procedure is described in @xcite and @xcite . table 3 summarizes the model . the total gas mass inferred from the dust emission is too large ( @xmath75 @xmath8 ) for the h ii region alone , so most of the dust must be in the cocoon around the h ii region . the calculated mass range takes into account uncertainties in the dust emissivity , but not in the temperature . the density gradient derived for the ionized gas in h ii region a is @xmath76 , with @xmath77 . equilibrium between recombination and ionization in this model h ii region requires an ionizing flux equivalent to an o7.5 star ( using the computations of * ? ? ? * ) , although this ionizing flux could be made up of several stars of slightly later spectral type . the model for the sed assumes spherical geometry and a static h ii region with no inflow of neutral gas into the h ii region . in contrast , h ii region a is embedded in a rotationally flattened accretion flow ( see [ smallscale ] ) , so the determination of the stellar spectral type is only approximate . the large - scale molecular cloud is detected by the nh@xmath0 vla - d observations . from these data we find the presence of a parsec - scale accretion flow surrounding the cluster of h ii regions . in [ large - dyn ] we first estimate the systemic velocity @xmath78 of the cloud with respect to the local standard of rest ( lsr ) , and then analyze the line velocities to determine rotation and infall following the procedure used in measuring accretion flow velocities in previous papers ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in [ large - parms ] we derive the physical properties of the cloud : temperature , mass , ammonia abundance , and density . figure [ fig4 ] shows the channel maps of the @xmath79 main hyperfine line . the most notable feature is a velocity gradient along the major axis of the cloud , consistent with rotation . the redshifted emission is toward the ne , while the blueshifted gas is toward the sw . also , there is strong absorption against the free - free background of the h ii regions at the center of the cloud , which are unresolved at @xmath80 resolution . the separation between the emission peaks on either side of the absorption is @xmath81 , or 0.6 pc . the symmetry of the channel maps suggests a systemic velocity of about @xmath82 @xmath19 . a gaussian fit to the emission spectrum integrated in a box covering the entire cloud , and clipping out the redshifted absorption , gives a centroid velocity of @xmath83 @xmath19 . we adopt a systemic velocity for the parsec - scale cloud of @xmath84 @xmath19 , in agreement with that reported by @xcite ( 41.9 @xmath19 ) based on observations of cs @xmath85 . figure [ fig5 ] shows position - velocity ( pv ) diagrams across cuts at pa @xmath86 ( sw - ne , major axis ) and pa @xmath87 ( nw - se , minor axis ) . the rotation is seen in the sw - ne cut as a shift in the velocity of the emission contours from one side of the absorption to the other . the velocity offset with respect to @xmath78 seen in the emission contours increases inward , suggesting that the gas rotates faster with decreasing radius . under the assumption that the velocity gradient seen in emission along the major axis is dominated by rotation , the redshifted absorption in the pv diagrams ( fig . [ fig5 ] ) is also evidence for inward flow toward the central h ii regions , as there is an excess of redshifted absorption . this is more clearly seen in fig . [ fig6 ] , which shows the spectra toward the absorption center . the nh@xmath0 ( 2,2 ) main hyperfine absorption peak is redshifted by 2.3 kms@xmath88 with respect to the systemic velocity . an infall velocity @xmath89 @xmath19 is also seen in the nh@xmath0 ( 3,3 ) line , although the spectrum is contaminated by an nh@xmath0 ( 3,3 ) maser ( see description in fig . [ fig6 ] ) . the maser is confirmed by our high angular resolution nh@xmath0 observations ( [ 33maser ] ) . if the rotation were seen edge - on , there would not be a velocity gradient across the h ii region along the minor axis ( nw - se ) . at an oblique viewing angle a velocity gradient along the minor axis is created by the inflow . the velocity gradient along both the minor and major axes ( fig . 5 ) implies that the rotationally flattened flow is tipped with respect to the line of sight . the optical depth of the gas can be determined from the brightness ratios of the hyperfine lines . from their optical depth ratio the rotational temperature between the @xmath90 and @xmath91 transitions can be determined ( see * ? ? ? * ; * ? ? ? * for details of the procedure ) . this temperature can be considered as a first - order approximation to the kinetic temperature ( @xmath92 ) of the molecular gas . @xcite suggest that an improved estimate of the kinetic temperature ( @xmath92 ) is obtained by accounting for the populations in the upper states of the k - ladders rather than assuming that all states above the lowest are negligibly populated . including this correction , we obtain an average kinetic temperature @xmath93 k for the parsec - scale cloud . the high - resolution data discussed in [ smallscale ] show that higher gas temperatures are found closer to the h ii regions . the mean column density of nh@xmath0 is @xmath94 @xmath95 . we can determine the abundance of ammonia @xmath96 by comparing the nh@xmath0 and h@xmath3 column densities . the mass of the cloud can be estimated from the observed velocity dispersion ( @xmath97 kms@xmath88 ) , the radius of the cloud ( @xmath98 au ) , and the virial theorem : @xmath99 . similarly , from the observed velocity gradient , the rotation velocity is @xmath100 @xmath19 at a radius @xmath101 au . equating the centripetal and gravitational forces , the gas mass inside @xmath102 is @xmath103 @xmath8 . therefore , we estimate the average column density of h@xmath3 to be @xmath104 @xmath95 and @xmath105 , within a factor of three of the value estimated for g10.60.4 @xcite . the mean h@xmath3 density in the large - scale cloud is @xmath106 @xmath53 . our sma very extended ( vex ) and vla - bna observations provide a rich view of the molecular environment close to the h ii regions . the lines detected with the sma that have peak intensities @xmath107 and are not blended with any other line are listed in the top part of table 2 . we follow a similar outline as for the large - scale cloud . figure [ fig7a ] shows the channel maps of ocs @xmath108 , so@xmath3 @xmath109 , ch@xmath0cn @xmath110 , and ch@xmath0cn @xmath111 . these maps show that the line emission from these hot - core molecules is considerably brighter around h ii region a. all the molecules show a velocity gradient across this source , from the southwest to northeast , in a similar orientation as the larger , cluster - scale flow . we do not detect molecular emission around h ii region b. at this high angular resolution we are not sensitive to brightness temperatures of less than @xmath41 k ( @xmath112 ) for the mm lines . figure [ fig8 ] shows the velocity - integrated intensity ( moment 0 ) and the intensity - weighted mean velocity ( moment 1 ) maps of the four lines previously shown in fig . [ fig7a ] . the integrated emission of ch@xmath0cn @xmath113 is brightest in front of the h ii region , while for the other molecules the brightness peak is slightly offset from the continuum . these differences reflect the relative brightness of each molecule with respect to the continuum emission of h ii region a. the velocity gradient across h ii region a is also seen . figure [ fig9 ] shows the velocity - integrated ( moment 0 ) and velocity dispersion ( moment 2 ) maps for the same lines as fig . the line widths increase toward the continuum peak , indicating that unresolved motions increase closer to the h ii region . figure 10 shows the position - velocity ( pv ) diagrams for the lines of figure 7 in cuts at position angles pa @xmath114 and pa @xmath115 across the continuum peak of hii region a. the cuts at @xmath116 show the velocity gradient also seen in the channel maps of ocs and both of the ch@xmath0cn lines . the pv diagram of ch@xmath0cn 12(4)-11(4 ) has a feature suggestive of a velocity gradient in the perpendicular direction pa @xmath117 , with an excess of redshifted emission toward the nw . consistent with our interpretation of the nh@xmath0 vla - d data , this suggests inward motion in a rotationally - flattened flow that is seen not quite edge - on . the same redshifted feature is also marginally detected in the lower excitation ch@xmath0cn transition as well as the ocs line . however , the infall signature in emission is only tentative , and a clearer indication of infall at small scales comes from the redshifted nh@xmath0 absorption in the vla - bna data ( see below ) . in general , observational experience suggests that ch@xmath0cn , along with nh@xmath0 , is a reliable tracer of high - density molecular mass and accretion flows @xcite . ch@xmath0cn has recently been detected in the outflow of the nearby low - mass star l1157 @xcite , but at a very low brightness ( @xmath118 k ) . the distribution of the ocs molecule in our observations is very similar to the ch@xmath0cn , but the so@xmath3 velocities do not show the same pattern , and are more difficult to interpret . the so@xmath3 may be more easily affected by the excitation conditions , and part of the observed emission could arise from the shocked boundaries of outflows . from gaussian fits to the ch@xmath0cn @xmath119 and 4 emission lines at the position of the continuum peak , the systemic velocity at small scales is estimated to be @xmath120 . figure [ fig11 ] shows the ch@xmath0cn spectra and their gaussian fits . at subarcsecond angular resolution , our nh@xmath0 observations are sensitive to emission of brightness temperature above @xmath121 k. therefore the thermal nh@xmath0 is detected only in absorption against the bright continuum . as in [ large - parms ] , a comparison between the nh@xmath0 absorption line velocity and @xmath78 shows an inward velocity of @xmath122 in front of h ii region a ( figure [ fig12 ] ) . the nh@xmath0 ( 2,2 ) absorption line in front of h ii region b is redshifted by @xmath123 @xmath19 with respect to @xmath78 , implying inward motion and accretion toward h ii region b as well ( figure [ fig12 ] ) . the ( 3,3 ) absorption in front of h ii region b is mixed with nh@xmath0 maser emission ( [ 33maser ] ) , and the determination of the inward velocity is uncertain . more sensitive observations are needed to constrain the properties of the molecular gas around h ii region b. we estimate the dynamical mass @xmath124 ( gas plus stars ) within the smaller accretion flow in the same way as with the large - scale flow ( see [ large - parms ] ) . at a radius @xmath125 au the rotation velocity is @xmath126 @xmath19 . therefore , @xmath127 . this is consistent with the lower limit to the stellar mass , @xmath128 @xmath8 , required for ionization equilibrium ( [ sed ] ) . the estimate is also consistent with the gas mass derived from the mm continuum once the free - free contribution has been properly subtracted , @xmath129 ( [ sed ] ) . the mean h@xmath3 density is @xmath130 @xmath53 . we derive the temperature in the dense gas surrounding h ii region a from the rotational energy diagram of the lines of the ch@xmath0cn @xmath131 k - ladders ( see e.g. , * ? ? ? * ; * ? ? ? figure [ fig13 ] shows this diagram for two cases : one considering all the @xmath132 lines , and the other including only the @xmath133 lines , which have lower optical depths than the low - number k lines ( also , the @xmath134 lines are blended , separated by only 5.8 @xmath19 ) . the rotational temperature obtained for the former case is @xmath135 k , while for the latter it is @xmath136 k. the difference between the two values given above appears to be caused by optical depth effects ( the rotational diagram analysis assumes that the emission is optically thin ) . although our sensitivity level does not permit us to detect the lines of the isotopologue ch@xmath137cn and measure the optical depth of the ch@xmath0cn emission , the upper limits are not restrictive ( @xmath138 ) . high optical depths are also suggested by the flat slope of the k ladders ( fig . 1 ) . fitting the k ladders taking into account the opacities @xcite yields a kinetic temperature close to the lower estimation , @xmath139 k , and optical depths are @xmath140 ( keping qiu 2009 , personal communication ) . the rotational temperatures are higher if we use only the brightest pixels instead of averaging over all the emission . this suggests a temperature gradient toward the center of the h ii region . we derive a ch@xmath0cn column density of @xmath141 @xmath95 assuming @xmath142 k. comparison of the ch@xmath0cn column density with the dynamical mass implies an abundance @xmath143(ch@xmath0cn ) @xmath144 for the range of masses quoted above . abundance estimates in other msfrs cover a range of values : @xmath145 inside the orion hot core and @xmath146 outside @xcite ; @xmath147 inside the orion hot core and @xmath148 in the orion ridge @xcite ; @xmath149 in sgr b2(n ) @xcite ; @xmath150 in w51e1/e2 @xcite . the optical depth of nh@xmath0 in absorption toward h ii region a is @xmath151 , @xmath152 . the mean column density is @xmath153 @xmath95 . if the ammonia abundance at these small scales is in the range @xmath154 , then the molecular hydrogen column density is @xmath155 @xmath95 . this implies a molecular gas mass of @xmath156 @xmath8 . the kinetic temperature obtained from the nh@xmath0 is @xmath157 k , considerably cooler than that obtained for ch@xmath0cn and implying that most of the nh@xmath0 column density is further away from the h ii region than the ch@xmath0cn . the distribution of the warm molecular gas around h ii region a appears to be rotationally flattened ( figs . [ fig7a ] , [ fig8 ] , [ fig9 ] ) , but the observed size is slightly larger than the radius at which the accretion flow is expected to become centrifugally supported ( i.e. , a `` disk '' ) , @xmath158 au for a star of mass @xmath159 and @xmath160 . actually , the disk scale matches the size of the h ii region ( table 3 , [ ionized ] ) . the mass - inflow rate toward h ii region a can be estimated from the high - resolution nh@xmath0 absorption . from an inflow velocity of @xmath161 and spherical geometry , the mass - inflow rate is @xmath162 yr@xmath88 ( for the @xmath163 of molecular gas detected in ammonia absorption ) . this estimate may be an upper limit because the hot molecular core is flattened rather than spherical . in [ sed ] we inferred a density gradient inside the hc h ii region a. in this section , we derive the internal dynamics of this h ii region based on multifrequency rrls . the mm / sub - mm lines are especially important because they are much less affected by pressure broadening and preferentially trace denser gas . while subarcsecond resolution studies at wavelengths longer than 7 mm have been available for many years @xcite , similar studies at shorter wavelengths have had limited angular resolution ( e.g. , * ? ? ? @xcite presented the first results of high - frequency , high - resolution ( @xmath164 ) , multifrequency rrl observations in a sample of 5 msfrs with similar characteristics to g20.08n a. they were able to separate the contributions of pressure broadening and large - scale motions to the line width , even when the h ii regions were unresolved . we follow their procedure to analyze our rrl data . we observed the h30@xmath37 ( @xmath165 ghz ) and h66@xmath37 ( @xmath166 ghz ) lines at subarcsecond angular resolution ( see table 2 ) . because both the line - to - continuum ratio and the continuum intensity are lower at 22 ghz than at 231 ghz , the h66@xmath37 line is much weaker than the h@xmath20 line . this is somewhat alleviated by the better sensitivity of the vla , but the signal - to - noise ratio ( s / n)in the high - frequency line is still better . figure [ fig14 ] shows the moment 0 and moment 1 maps of the h@xmath20 line . although the emission is unresolved at half power , there is a slight indication of a velocity gradient in the ionized gas that agrees ( not perfectly ) with the rotation seen in ch@xmath0cn and ocs . figure [ fig15 ] shows the h@xmath20 and h@xmath167 spectra toward h ii region a and their gaussian fits . the h@xmath167 line shows evidence of a blueshifted wing , suggesting either inflow or outflow in addition to rotation . within the uncertainties of the fits , both the h66@xmath37 and h30@xmath37 lines have the same line width ( table 4 ) . assuming that the dynamical broadening @xmath168 ( caused by turbulence and ordered motions ) and the thermal broadening @xmath169 are gaussian , and that the pressure broadening @xmath170 is lorentzian , the rrl has a voigt profile with line width @xcite : @xmath171 where all the widths are fwhm . for the h@xmath20 line at 231.9 ghz the pressure broadening is less than the thermal broadening at electron densities below @xmath172 @xmath53 @xcite . our sed modeling indicates lower densities over most of the hii region . therefore , the observed line width can be attributed to thermal plus dynamical broadening . the electron temperature @xmath173 in uc h ii regions is typically @xmath174 000 k , with a small gradient as a function of galactocentric radius @xcite . we adopt @xmath175 k ( @xmath176 k for h30@xmath37 because of the low optical depth and @xmath177 filling factor ) , which translates into a thermal fwhm of @xmath178 . therefore , from eq . [ eq : voigt ] , we obtain a dynamical width of @xmath179 . from the velocity gradient ( fig . [ fig14 ] ) it is seen that @xmath180 @xmath19 of @xmath168 can be in the form of rotation . the rest could be caused by inflowing or outflowing ionized gas , as suggested by the blueshifted ( @xmath181 @xmath19 ) mean velocities of the rrls , and by the blue wing in the h@xmath167 spectrum ( fig . [ fig15 ] ) . most of the ionized gas that we see should be outflow . inflow inside the h ii region is expected within the radius where the escape velocity from the star exceeds the sound speed of the ionized gas . this is approximately the bondi - parker transonic radius @xcite , @xmath182 au @xmath183 , or about 190 au for h ii region a , assuming a sound speed @xmath184 kms@xmath88 and stellar mass @xmath159 . h ii region a extends out to @xmath185 au , so most of the gas is not gravitationally bound to the star and flows outward . in this model , the outflow is continuously supplied by photoevaporation off the rotationally flattened accretion flow ( t. peters et al . 2009 , in preparation ) . the somewhat misaligned velocity gradient in the ionized gas ( fig . 14 ) derives from a combination of the rotation and outflow blended together in the observing beam . low angular resolution ( hpbw @xmath186 ) , single - dish ( jcmt ) observations of sio ( 8 - 7 ) show evidence for large - scale molecular outflows in g20.08n @xcite . although the standard outflow tracers @xmath187co @xmath188 and @xmath137co @xmath188 are in our passband , we do not detect any co in emission . the @xmath28 coverage of our sma - vex observations is incapable of imaging structures larger than @xmath189 ; therefore , the co emission from the molecular cloud and molecular outflow must be on larger scales . @xmath187co and @xmath137co are seen in our data in absorption at the position of h ii region a , at several different velocities in the range @xmath190 . some co absorption features are at the same velocities as the hi absorption features of @xcite and are therefore due to foreground gas that is not related to g20.08n but rather to intervening galactic spiral arms . a handful of nh@xmath0 masers have been reported in the literature , always associated with massive star formation ( e.g. , * ? ? ? many of the known nh@xmath0 masers are from non - metastable ( @xmath191 ) transitions . the first clear detection of a metastable ( @xmath192 ) nh@xmath0 ( 3,3 ) maser was reported by @xcite toward dr 21(oh ) . most of the detections point toward a shock excitation origin for the population inversion , inasmuch as the maser spots are invariably associated with outflow indicators such as bipolar co and/or sio structures , class i methanol masers , and/or water masers @xcite . we report the serendipitous detection of a new nh@xmath0 ( 3,3 ) maser toward g20.08n . the maser spot is relatively weak , and is spatially centered at @xmath45 @xmath46 @xmath193 , @xmath48 @xmath49 @xmath194 , close in projection to the center of h ii region b. the maser spot is spatially unresolved even in uniform weighting maps of the vla - bna data ( hpbw = @xmath195 , pa = @xmath196 ) . if the deconvolved source size is limited to half the beam size , then the peak brightness temperature of the spot is constrained to @xmath197 k. the high intensity , together with the absence of similar emission in our ( 2,2 ) maps at high angular resolution , confirm the maser nature of the ( 3,3 ) emission . the spectral feature is also very narrow ( fig . [ fig16 ] ) , typical of maser emission , although it shows evidence of line wings . from a gaussian fit to the line profile , the velocity of the maser is @xmath198 ( accurate only to 20 % @xmath199 40 % ) . the fwhm is @xmath200 , after deconvolving the channel width of @xmath201 . owing to its position , it is probable that the maser is excited by h ii region b. we do not have sufficient data , however , to assert that it is excited in a shock .

the broad recombination lines and a continuum spectral energy distribution ( sed ) that rises continuously from cm to mm wavelengths , are both characteristic of the class of h ii regions known as `` broad recombination line objects '' . the sed indicates a density gradient inside this h ii region , and the rrls suggest supersonic flows . we also report the serendipitous detection of a new nh ( 3,3 ) maser .

spectral line and continuum observations of the ionized and molecular gas in g20.08 - 0.14 n explore the dynamics of accretion over a range of spatial scales in this massive star - forming region . very large array observations of nh at angular resolution show a large - scale ( 0.5 pc ) molecular accretion flow around and into a star cluster with three small , bright h ii regions . higher resolution ( ) observations with the submillimeter array in hot core molecules ( chcn , ocs , and so ) and the vla in nh , show that the two brightest and smallest h ii regions are themselves surrounded by smaller scale ( 0.05 pc ) accretion flows . the axes of rotation of the large and small scale flows are aligned , and the timescale for the contraction of the cloud is short enough , 0.1 myr , for the large - scale accretion flow to deliver significant mass to the smaller scales within the star formation timescale . the flow structure appears to be continuous and hierarchical from larger to smaller scales . millimeter radio recombination line ( rrl ) observations at angular resolution indicate rotation and outflow of the ionized gas within the brightest h ii region ( a ) . the broad recombination lines and a continuum spectral energy distribution ( sed ) that rises continuously from cm to mm wavelengths , are both characteristic of the class of h ii regions known as `` broad recombination line objects '' . the sed indicates a density gradient inside this h ii region , and the rrls suggest supersonic flows . these observations are consistent with photoevaporation of the inner part of the rotationally flattened molecular accretion flow . we also report the serendipitous detection of a new nh ( 3,3 ) maser .

0910.2270

c

we report radio and mm observations of the molecular and ionized gas toward the o - star cluster g20.08n , made with an angular resolution from @xmath225 pc to @xmath226 pc . our main findings can be summarized as follows : 1 . we find a large - scale ( @xmath203 pc ) accretion flow around and into a star cluster with several o - type stars , identified by one uc and two hc h ii regions . this flow is rotating and infalling towards its center . the two hc h ii regions are surrounded by smaller accretion flows ( @xmath227 pc ) , each of them with the signature of infall too . the brightest ( toward h ii region a ) is detected in mm emission lines , and rotates in concordance with the large - scale flow . the similar orientations of the flows at small and large scales , as well as their dynamical timescales ( @xmath210 yrs and @xmath211 yrs respectively ) , and masses ( @xmath228 and @xmath229 respectively ) , suggest that , if o stars are forming in g20.08n ( as it is observed ) , then the smaller scales ought to be resupplied from the larger scales . the same result has been found in recent numerical simulations of massive star formation in clusters . the brightest hc h ii region ( a ) has a rising sed from cm to mm wavelengths and broad hydrogen recombination lines . both characteristics suggest density gradients and supersonic flows inside the h ii region . a tentative velocity gradient is detected in the recombination line emission of this source , suggesting rotation and outflow in the ionized gas at the innermost scales . h ii region a can be interpreted as the inner part of the surrounding molecular accretion flow , with the observed ionization being produced by photoevaporation . ccccccc [ tab1 ] 2003 apr 28 & vla - d & 18 28 10.384 & @xmath230 28 48.65 & 3c454.3 & @xmath231 & @xmath232 + 2003 may 13 & vla - d & 18 28 10.384 & @xmath230 28 48.65 & 3c454.3 & @xmath233 & @xmath234 + 2003 oct 09 & vla - bna & 18 28 10.384 & @xmath230 28 48.65 & 3c454.3 & @xmath233 & @xmath234 + 2003 oct 10 & vla - bna & 18 28 10.384 & @xmath230 28 48.65 & 3c454.3 & @xmath233 & @xmath234 + 2006 jun 25 & sma - vex & 18 28 10.38 & @xmath230 28 48.60 & 3c273 & @xmath235 & @xmath235 + 2006 jun 25 & sma - vex & 18 28 10.76 & @xmath230 29 27.60 & 3c273 & @xmath235 & @xmath235 + 2006 jul 06 & sma - vex & 18 28 10.38 & @xmath230 28 48.60 & 3c454.3 & @xmath236 & @xmath236 + 2006 jul 06 & sma - vex & 18 28 10.76 & @xmath230 29 27.60 & 3c454.3 & @xmath236 & @xmath236 + 2007 oct 26 & vla - b & 18 28 10.400 & @xmath230 28 49.00 & 3c454.3 & @xmath237 & @xmath234 + 2007 oct 27 & vla - b & 18 28 10.400 & @xmath230 28 49.00 & 3c454.3 & @xmath237 & @xmath234 + + cccccc [ tab2 ] h & 66@xmath37 & 22.364178 & vla - b & @xmath238 ; 3 + nh@xmath0 & @xmath90 & 23.722633 & vla - d & @xmath239 ; 236 + nh@xmath0 & @xmath91 & 23.870129 & vla - d & @xmath240 ; 8 + nh@xmath0 & @xmath90 & 23.722633 & vla - bna & @xmath241 ; @xmath242 + nh@xmath0 & @xmath91 & 23.870129 & vla - bna & @xmath243 ; @xmath244 + @xmath137co & 2 - 1 & 220.398681 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(4)-11(4 ) & 220.679297 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(3)-11(3 ) & 220.709024 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(2)-11(2 ) & 220.730266 & sma - vex & @xmath245 ; @xmath246 + so@xmath3 & 11(1,11)-10(0,10 ) & 221.965200 & sma - vex & @xmath247 ; @xmath246 + co & 2 - 1 & 230.538000 & sma - vex & @xmath248 ; @xmath249 + ocs & 19 - 18 & 231.060991 & sma - vex & @xmath248 ; @xmath249 + h & 30@xmath37 & 231.9009 & sma - vex & @xmath248 ; @xmath249 + + + ch@xmath0cn & 12(7)-11(7 ) & 220.539340 & sma - vex & @xmath245 ; @xmath246 + hnco & 10(1,9)-9(1,8 ) & 220.584762 & sma - vex & @xmath247 ; @xmath246 + ch@xmath0cn & 12(6)-11(6 ) & 220.594438 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(5)-11(5 ) & 220.641096 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(1)-11(1 ) & 220.743015 & sma - vex & @xmath245 ; @xmath246 + ch@xmath0cn & 12(0)-11(0 ) & 220.747265 & sma - vex & @xmath245 ; @xmath246 + ch@xmath3chcn & 24(0,24)-23(0,23 ) & 221.76598 & sma - vex & @xmath245 ; @xmath246 + @xmath137cs & 5 - 4 & 231.220768 & sma - vex & @xmath250 ; @xmath249 + + ccc [ tab3 ] hii radius ( au ) & & 2530 + electron density ( @xmath251 @xmath53 ) & & 1.4 + exponent & & 1.3 + gas mass ( @xmath8 ) & & 35 - 95 + spectral type & & o7.5 + stellar mass ( @xmath8 ) & & 34 + hii mass ( @xmath8 ) & & 0.05 + ccccc [ tab4 ] h & 66@xmath37 & @xmath252 & @xmath253 & @xmath254 + h & 30@xmath37 & @xmath255 & @xmath256 & @xmath257 + ch@xmath0cn & 12(4)-11(4 ) & @xmath258 & @xmath259 & @xmath260 + ch@xmath0cn & 12(3)-11(3 ) & @xmath261 & @xmath262 & @xmath263 + ch@xmath0cn & 12(2)-11(2 ) & @xmath261 & @xmath264 & @xmath265 + . the question mark ( _ ? _ ) in the upper sideband ( _ top _ frame ) might be a superposition of lines of ch@xmath0och@xmath0 and ch@xmath0ch@xmath3cn . s _ at the center of the lower sideband ( _ bottom _ frame ) could be from vibrationally excited ch@xmath0cn . _ in the upper sideband close to the so@xmath3 might be from ch@xmath0cch . ] to the se of a. h ii region c is the more extended emission to the se of b. the color scale goes linearly from 8 to 430 @xmath30 ( the rms noise in the mm image is 2 @xmath30 ) . contours are placed at @xmath266 @xmath267 @xmath30 , the noise of the cm image . the sma - vex beam ( empty ellipse ) encircles the vla - bna beam ( filled ellipse ) at the bottom - left of the image . ] and @xmath268 uncertainty expected in the vla and sma flux measurements , respectively . the _ red dashed _ line shows the flux of an h ii region with a density gradient . the _ black dotted _ line is the flux from the warm dust component . the _ solid blue _ line is the sum of the two components . the relative contributions of free - free ( 70 @xmath67 ) and dust ( 30 @xmath67 ) to the 1.3-mm flux were estimated from the observed h@xmath20 line - to - continuum ratio , and are marked with _ diamonds_. ] ( 3,3 ) observations . emission is in _ solid _ contours and absorption in _ dashed _ contours . the star covers the h ii regions shown in fig . contour levels are at @xmath269 @xmath270 @xmath30 . a clear velocity gradient in emission is seen from one side of the absorption to the other . the lsr systemic velocity of the molecular gas is @xmath271 @xmath19 . the original maps at 0.3 @xmath19 spectral resolution were smoothed to 0.6 @xmath19 for clarity . ] ( 2,2 ) and ( 3,3 ) from the vla - d data . the cuts were done at pa=45@xmath272 ( _ bottom _ row ) and pa=135@xmath272 ( _ top _ row ) . _ dashed _ contours are absorption , _ solid _ contours are emission . contouring is at @xmath273 @xmath267 @xmath30 . only one inner satellite line is covered in the velocity range . in the sw - ne cuts ( across the major axis of the cloud ) the difference in the velocity of the emission with respect to @xmath84 @xmath19 increases closer to the position center . this can be interpreted as spin up with decreasing distance from the center . however , the same trend is present in the nw - se cuts ( along the minor axis of the cloud ) , although only in the stronger , blueshifted side of the emission . this suggests that besides rotation , radial motions in the frame of the central stars are also present . ] spectra from the vla - d observations toward the center of the absorption in g20.08n . the vertical line marks the systemic velocity ( @xmath274 @xmath19 ) . the small peak near the middle of the ( 3,3 ) absorption is due to maser emission ( confirmed in the high - resolution , vla - bna data , see [ 33maser ] ) . the absorption peaks in the main ( 2,2 ) and ( 3,3 ) lines are redshifted with respect to @xmath78 , indicating the presence of inflow in the kinematics of the parsec - scale molecular cloud . the other weak absorption component seen in the ( 2,2 ) spectrum is one of the inner satellites . the absorption component at @xmath275 @xmath19 in the ( 3,3 ) spectrum is also an inner satellite . the weaker absorption at @xmath276 @xmath19 in the ( 3,3 ) spectrum may arise from an outflow . the blueshifted absorption in the main lines closest to @xmath78 might arise from blending with the rotation seen in emission . ] from the sma - vex observations . contours are @xmath277 @xmath278 ( negative in @xmath279 , and positive in @xmath280 ) . the peak intensity is @xmath281 . the numbers in the upper left corner indicate the central lsr velocity of the channel . the two stars mark the positions of h ii regions a ( west ) and b ( east ) . ] ( 2,2 ) and ( 3,3 ) spectra toward the absorption peak of h ii region a in the vla - bna observations . the vertical line marks the systemic velocity ( @xmath289 ) of the molecular gas at scales comparable to the h ii region . the centers of the absorption lines are redshifted with respect to @xmath78 , indicating inflow of molecular gas toward h ii region a at small scales . the ( 3,3 ) absorption is broader ( fwhm @xmath290 ) than the ( 2,2 ) ( fwhm @xmath291 ) , probably caused by larger motions closer to the center . _ bottom _ panel : nh@xmath0 ( 2,2 ) spectrum toward h ii region b. the absorption , considerably fainter than for h ii region a , is also redshifted . ] rrl emission toward g20.08n . contours are at @xmath292 @xmath293 @xmath294 . although the emission is unresolved at half power , the moment 1 map hints at the presence of a velocity gradient in the ionized gas similar to that seen in ch@xmath0cn and ocs . ] ( _ top _ panel ) and h@xmath167 ( _ bottom _ panel ) lines toward g20.08n a. error bars denote the @xmath287 noise in the channels . the channel spacing is @xmath288 for h@xmath20 and @xmath295 for h@xmath167 . the flux was integrated over a 0.5 square box centered on h ii region a. ]

very large array observations of nh at angular resolution show a large - scale ( 0.5 pc ) molecular accretion flow around and into a star cluster with three small , bright h ii regions . the flow structure appears to be continuous and hierarchical from larger to smaller scales .

spectral line and continuum observations of the ionized and molecular gas in g20.08 - 0.14 n explore the dynamics of accretion over a range of spatial scales in this massive star - forming region . very large array observations of nh at angular resolution show a large - scale ( 0.5 pc ) molecular accretion flow around and into a star cluster with three small , bright h ii regions . higher resolution ( ) observations with the submillimeter array in hot core molecules ( chcn , ocs , and so ) and the vla in nh , show that the two brightest and smallest h ii regions are themselves surrounded by smaller scale ( 0.05 pc ) accretion flows . the axes of rotation of the large and small scale flows are aligned , and the timescale for the contraction of the cloud is short enough , 0.1 myr , for the large - scale accretion flow to deliver significant mass to the smaller scales within the star formation timescale . the flow structure appears to be continuous and hierarchical from larger to smaller scales . millimeter radio recombination line ( rrl ) observations at angular resolution indicate rotation and outflow of the ionized gas within the brightest h ii region ( a ) . the broad recombination lines and a continuum spectral energy distribution ( sed ) that rises continuously from cm to mm wavelengths , are both characteristic of the class of h ii regions known as `` broad recombination line objects '' . the sed indicates a density gradient inside this h ii region , and the rrls suggest supersonic flows . these observations are consistent with photoevaporation of the inner part of the rotationally flattened molecular accretion flow . we also report the serendipitous detection of a new nh ( 3,3 ) maser .

astro-ph9708263

i

starbursts are defined as brief episodes ( @xmath6 10@xmath3 years ) of intense star - formation that occur in the central - most 0.1 to 1 kpc- scale regions of galaxies and dominate the integrated emission from the galaxy . they are a significant component of the present - day universe : they provide roughly 10% of the bolometric emissivity of the local universe and are the sites of @xmath025% of the high- mass star - formation . thus , they deserve to be understood in their own right . they also offer unique ` laboratories ' for testing our ideas about star formation , the evolution of high - mass stars , and the physics of the interstellar medium . they serve as local analogs of the processes that were important in the origin and early evolution of galaxies and in the heating and chemical enrichment of the inter- galactic medium ( igm ) . in this contribution i have reviewed starbursts from this broad cosmogonical perspective , stressing several key lessons we have learned from starbursts : + * i ) violent , transient events play a significant role in the origin and evolution of galaxies . * rather than simply evolving in a steady ` clockwork ' fashion , galaxies also evolve discontinuously through powerful bursts of star - formation , triggered by galaxy interactions . + * ii ) galaxies do not evolve as ` island universes ' or ` closed boxes . ' * powerful starbursts are triggered by galaxy interactions and mergers that can create an elliptical galaxy out of two spirals . the starbursts produce outflows of hot metal - enriched gas ( ` superwinds ' ) that pollute the inter - galactic medium . there is now direct observational evidence for a metal - enriched igm and for the outflows at low- and high - redshift that are responsible for this enrichment . study of superwinds in the local universe suggest that galaxy formation may have been an inefficient process with the majority of gas being ejected . dust dramatically affects of view of high - mass star- formation in starbursts and ( probably ) in high - redshift galaxies . * powerful starbursts in the present universe emit almost all their light in the far - infrared . an ultraviolet census of the local universe would significantly underestimate the true star - formation- rate and could systematically under - represent the most powerful , most metal - rich starbursts occuring in the most massive galaxies . applying the empirical relations followed by local starbursts to the uv - selected galaxies at high - redshift implies that the latter typically suffer 2 to 3 magnitudes of extinction , and that the star - formation rate in the universe need not be smaller at z@xmath0 3 than at z@xmath01 . the high - z galaxies would then have estimated bolometric surface - brightnesses and sizes consistent with a population of forming elliptical galaxies . + * iv ) space - based observations are crucial in understanding starbursts . * x - ray data ( rosat , asca , axaf , xmm ) are vital for studying the superwind phenomenon , since they directly probe the hot gas that comprises most of the mass and energy in the flow . ultraviolet data ( iue , hst , hut , fuse ) offer detailed information about both the hot stars that power the starburst and the dynamics of the interstellar medium . visible observations with the high - angular resolution of hst have revealed the importance of galaxy interactions and mergers at low and medium redshift and given us a tantalizing glimpse of the star - forming history of the early universe . finally , the infrared ( iras , iso , cobe , wire , sirtf , sofia , ngst ) represents the primary channel for energy loss for the dusty , metal - rich starbursts . such data not only document the presence of dusty starbursts in the local universe ( z @xmath46 1 ) , but also constrain their global importance at high - redshift .

starbursts are episodes of intense star - formation that occur in the central regions of galaxies , and dominate the integrated emission from the galaxy . they are a significant component of the present- day universe , being the site of 25% of the high - mass star- formation . they offer unique ` laboratories ' for testing our ideas about star - formation , the evolution of high - mass stars , and the physics of the interstellar medium . they serve as local analogs of the processes that were important in the origin and early evolution of galaxies and in the heating and chemical enrichment of the inter - galactic medium . in this contribution i review starbursts from this broad cosmogonical perspective , stressing several key lessons we have learned from starbursts : 1 ) violent , transient events play a significant role in the origin and evolution of galaxies . 2 ) galaxies do not evolve as ` island universes ' : starbursts are triggered by galaxy interactions and produce outflows of hot chemically - enriched gas that ` pollute ' the inter- galactic medium . 3 ) dust dramatically affects of view of high - mass star - formation in starbursts and ( probably ) in high - redshift galaxies . throughout this review i emphasize the importance of space - based observations in understanding starbursts .

starbursts are episodes of intense star - formation that occur in the central regions of galaxies , and dominate the integrated emission from the galaxy . they are a significant component of the present- day universe , being the site of 25% of the high - mass star- formation . they offer unique ` laboratories ' for testing our ideas about star - formation , the evolution of high - mass stars , and the physics of the interstellar medium . they serve as local analogs of the processes that were important in the origin and early evolution of galaxies and in the heating and chemical enrichment of the inter - galactic medium . in this contribution i review starbursts from this broad cosmogonical perspective , stressing several key lessons we have learned from starbursts : 1 ) violent , transient events play a significant role in the origin and evolution of galaxies . 2 ) galaxies do not evolve as ` island universes ' : starbursts are triggered by galaxy interactions and produce outflows of hot chemically - enriched gas that ` pollute ' the inter- galactic medium . 3 ) dust dramatically affects of view of high - mass star - formation in starbursts and ( probably ) in high - redshift galaxies . throughout this review i emphasize the importance of space - based observations in understanding starbursts .

0811.1159

i

interacting fermionic particles play a central role in the structure of matter and exist over a very broad range of energies , from extremely low temperature trapped atomic fermi gases , where @xmath10 k @xcite , to very high temperature primordial matter , like quark - gluon plasmas , where @xmath11 k @xcite . for all of these systems , the most intriguing physics is related to very strong interactions between fermionic particles , such as the strong coupling between electrons in high-@xmath8 superconductors and the strong interactions between neutrons in neutron matter . current many - body quantum theories face great challenges in solving problems for strongly interacting fermi systems , due to the lack of a small coupling parameter . for example , the critical temperature of a superfluid - normal fluid transition in a strongly interacting fermi gas has been controversial for many years . the critical temperature @xmath12 has been predicted to have values in the range between 0.15 and 0.35 by different theoretical methods @xcite . a complete understanding of the physics of strongly interacting systems can not yet be obtained from a theoretical point of view . there is a pressing need to investigate strongly interacting fermions experimentally . in recent years , based on progress in optical cooling and trapping of fermionic atoms , a clean and controllable strongly interacting fermi system , comprising a degenerate , strongly interacting fermi gas @xcite , is now of interest to the whole physics community . strongly interacting fermi gases are produced near a broad feshbach resonance @xcite , where the zero energy s - wave scattering length @xmath13 is large compared to the interparticle spacing , while the interparticle spacing is large compared to the range of the two - body interaction . in this regime , the system is known as a unitary fermi gas , where the properties are universal and independent of the details of the two - body scattering interaction @xcite . in contrast to other strongly interacting fermi systems , in atomic gases , the interactions , energy , and spin population can be precisely adjusted , enabling a variety of experiments for exploring this model system . intense studies of strongly interacting fermi gases have been implemented over the past several years from a variety of perspectives . some of the first experiments observed the expansion hydrodynamics of the strongly interacting cloud @xcite . evidence for superfluid hydrodynamics was first observed in collective modes @xcite . collective modes were later used to study the @xmath14 equation of state throughout the crossover regime @xcite . recently , measurements of sound velocity have also been used to explore the @xmath14 equation of state @xcite . below a feshbach resonance , fermionic atoms join to form stable molecules and molecular bose - einstein condensates @xcite . fermionic pair condensation has been observed by projection experiments using fast magnetic field sweeps @xcite . above resonance , strongly bound pairs have been probed by radio frequency and optical spectroscopy @xcite . phase separation has been observed in spin polarized samples @xcite . rotating fermi gases have revealed vortex lattices in the superfluid regime @xcite as well as irrotational flow in both the superfluid and normal fluid regimes @xcite . measurement of the thermodynamic properties of a strongly interacting fermi gas was first accomplished by adding a known energy to the gas , and then determining an empirical temperature that was calibrated using a pseudogap theory @xcite . recent model - independent measurements of the energy and entropy @xcite provide a very important piece of the puzzle , because they enable direct and precision tests that distinguish predictions from recent many - body theories , without invoking any specific theoretical model @xcite . one of the major challenges for the experiments in strongly interacting fermi gases is the lack of a precise model - independent thermometry . two widely - used thermometry methods are model - dependent , in that they rely on theoretical models for calibration . the first relies on adiabatic magnetic field sweeps between the molecular bec regime and the strongly interacting regime @xcite . subsequently , the temperature of the strongly interacting gas is estimated from the measured temperature in the bec regime using a theoretical model of the entropy @xcite . the second method , used by our group @xcite , is based on determining an empirical temperature from the cloud profiles that is calibrated by comparing the measured density distribution with a theoretical model for the density profiles . currently two model - independent thermometry methods have been reported for strongly - interacting gases . one is the technique employed by the mit group @xcite , which is only applicable to imbalanced mixtures of spin - up and spin - down atoms . that method is based on fitting the noninteracting edge for the majority spin after phase separation . another model - independent method is demonstrated in ref . @xcite , which is applicable to both balanced and imbalanced mixtures of spin - up and spin - down fermions . the energy @xmath1 and entropy @xmath2 are measured and then parameterized to determine a smooth curve @xmath4 . then the temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation @xmath5 . in this paper , we will describe our model - independent thermodynamic experiments on a strongly interacting fermi gas of @xmath0li , which we have conducted at duke university . first , we will describe our measurements of both the total energy @xmath1 and the total entropy @xmath2 of a trapped strongly - interacting fermi gas tuned near a feshbach resonance . then , we determine the temperature @xmath5 after showing that the @xmath4 data are very well parameterized by using two different power laws that are joined with continuous @xmath1 and @xmath6 at a certain entropy @xmath7 that gives the best fit . to examine the sensitivity of the temperature to the form of the fit function , we employ two different fit functions that allow for a heat capacity jump or for a continuous heat capacity at @xmath7 . we find that the @xmath6 values closely agree for both cases . we find a significant change in the scaling of @xmath1 with @xmath2 above and below @xmath7 , in contrast to the behavior for an ideal fermi gas , where a single power - law well parameterizes @xmath4 over the same energy range . by interpreting @xmath7 as the critical entropy for a superfluid - normal fluid transition in the strongly interacting fermi gas , we estimate the critical energy @xmath15 and critical temperature @xmath8 . both the model - independent @xmath4 data and the estimated critical parameters are compared with several recent many - body theories based on both analytic and quantum monte carlo methods . we also show how parameterizing the @xmath4 data provides experimental temperature calibrations , which helps to unify , in a model - independent way , the results obtained by several groups @xcite . first we relate the endpoint temperatures for adiabatic sweeps of the bias magnetic field between the strongly interacting and ideal noninteracting regimes , as used in the jila experiments to characterize the condensed pair fraction @xcite . this enables the ideal gas temperature observed for the onset of pair condensation @xcite to be related to the critical temperature of the strongly interacting fermi gas . the temperature obtained by parameterizing the strongly interacting gas data also calibrates the empirical temperature based on the cloud profiles , as used in our previous studies of the heat capacity @xcite . these temperature calibrations yield values of @xmath8 close to that estimated from our @xmath4 data . next , we discuss three different methods for determining the universal many - body parameter , @xmath16 @xcite , where @xmath17 is the energy per particle in a uniform strongly interacting fermi gas at @xmath14 in units of the energy per particle of an ideal fermi gas at the same density . first , we describe the measurement of the sound velocity at resonance and its relationship to @xmath16 . then , we determine @xmath16 from the ground state energy @xmath18 of the trapped gas . here , @xmath18 is obtained by extrapolating the @xmath4 data to @xmath9 , as suggested by hu et al . this avoids a systematic error in the sound velocity experiments arising from the unknown finite temperature . finally , to explore the systematic error arising from the measurement of the number of atoms , @xmath16 is determined in a number - independent manner from the ratio of the cloud sizes in the strongly and weakly interacting regimes . all three results are found to be in very good agreement with each other and with recent predictions . finally , we obtain three universal thermodynamic functions from the parameterized @xmath4 data , the energy @xmath19 , heat capacity @xmath20 , and global chemical potential @xmath21 .

strongly interacting fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature , from high temperature superconductors to neutron matter and quark - gluon plasmas . we conduct a series of measurements on the thermodynamic properties of this unique quantum gas , including the energy , entropy , and sound velocity . our model - independent measurements of and enable a precision study of the finite temperature thermodynamics . the temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation by parameterizing the data using two different power laws that are joined with continuous and at a certain entropy , where the fit is optimized . we observe a significant change in the scaling of with above and below . taking the fitted value of as an estimate of the critical entropy for a superfluid - normal fluid phase transition in the strongly interacting fermi gas , we estimate the critical parameters . our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our data . we also calibrate the empirical temperature employed in studies of the heat capacity and obtain nearly the same . we determine the ground state energy by three different methods , using sound velocity measurements , by extrapolating to and by measuring the ratio of the cloud sizes in the strongly and weakly interacting regimes . pacs numbers : 03.75.ss

strongly interacting fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature , from high temperature superconductors to neutron matter and quark - gluon plasmas . model - independent thermodynamic measurements , which do not require theoretical models for calibrations , are very important for exploring this important system experimentally , as they enable direct tests of predictions based on the best current non - perturbative many - body theories . at duke university , we use all - optical methods to produce a strongly interacting fermi gas of spin-1/2-up and spin-1/2-downli atoms that is magnetically tuned near a collisional ( feshbach ) resonance . we conduct a series of measurements on the thermodynamic properties of this unique quantum gas , including the energy , entropy , and sound velocity . our model - independent measurements of and enable a precision study of the finite temperature thermodynamics . the data are directly compared to several recent predictions . the temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation by parameterizing the data using two different power laws that are joined with continuous and at a certain entropy , where the fit is optimized . we observe a significant change in the scaling of with above and below . taking the fitted value of as an estimate of the critical entropy for a superfluid - normal fluid phase transition in the strongly interacting fermi gas , we estimate the critical parameters . our data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes . this enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation , where the ideal fermi gas temperature is measured before sweeping the magnetic field to the strongly interacting regime . our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our data . we also calibrate the empirical temperature employed in studies of the heat capacity and obtain nearly the same . we determine the ground state energy by three different methods , using sound velocity measurements , by extrapolating to and by measuring the ratio of the cloud sizes in the strongly and weakly interacting regimes . the results are in very good agreement with recent predictions . finally , using universal thermodynamic relations , we estimate the chemical potential and heat capacity of the trapped gas from the data . pacs numbers : 03.75.ss

0811.1159

c

we have studied the thermodynamic properties of a strongly interacting fermi gas by measuring both the energy and the entropy . the model - independent data obtained in both the superfluid and the normal fluid regimes do not employ any specific theoretical calibrations , and therefore can be used as a benchmark to test the predictions from many - body theories and simulations . parameterizing the energy - entropy data determines the temperature of the strongly interacting fermi gas and also yields estimates of the critical parameters . we use the measured data to calibrate two different temperature scales that were employed in observations of the onset of pair condensation and in heat capacity studies . these calibrations yield critical temperatures in good agreement with the results estimated from our energy - entropy data . our data does not determine whether the heat capacity exhibits a jump or is continuous at the critical temperature . however , for a finite system with nonuniform density , the latter is most likely . considering that there is huge interest in determining the detailed behavior of the superfluid transition in a strongly interacting fermi gas @xcite , more precise determinations of the critical temperature , the heat capacity , and the chemical potential near the critical point , as well as the high temperature behavior and the approach to the ideal gas limit , will be important topics for future research .

model - independent thermodynamic measurements , which do not require theoretical models for calibrations , are very important for exploring this important system experimentally , as they enable direct tests of predictions based on the best current non - perturbative many - body theories . at duke university , we use all - optical methods to produce a strongly interacting fermi gas of spin-1/2-up and spin-1/2-downli atoms that is magnetically tuned near a collisional ( feshbach ) resonance .

strongly interacting fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature , from high temperature superconductors to neutron matter and quark - gluon plasmas . model - independent thermodynamic measurements , which do not require theoretical models for calibrations , are very important for exploring this important system experimentally , as they enable direct tests of predictions based on the best current non - perturbative many - body theories . at duke university , we use all - optical methods to produce a strongly interacting fermi gas of spin-1/2-up and spin-1/2-downli atoms that is magnetically tuned near a collisional ( feshbach ) resonance . we conduct a series of measurements on the thermodynamic properties of this unique quantum gas , including the energy , entropy , and sound velocity . our model - independent measurements of and enable a precision study of the finite temperature thermodynamics . the data are directly compared to several recent predictions . the temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation by parameterizing the data using two different power laws that are joined with continuous and at a certain entropy , where the fit is optimized . we observe a significant change in the scaling of with above and below . taking the fitted value of as an estimate of the critical entropy for a superfluid - normal fluid phase transition in the strongly interacting fermi gas , we estimate the critical parameters . our data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes . this enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation , where the ideal fermi gas temperature is measured before sweeping the magnetic field to the strongly interacting regime . our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our data . we also calibrate the empirical temperature employed in studies of the heat capacity and obtain nearly the same . we determine the ground state energy by three different methods , using sound velocity measurements , by extrapolating to and by measuring the ratio of the cloud sizes in the strongly and weakly interacting regimes . the results are in very good agreement with recent predictions . finally , using universal thermodynamic relations , we estimate the chemical potential and heat capacity of the trapped gas from the data . pacs numbers : 03.75.ss

1302.6603

r

the main finding is that on terrestrial exoplanets having atmospheres ranging from reducing to oxidizing , the primary sulfur emission from the surface ( e.g. , and ) is chemically short - lived . the sulfur emission leads to photochemical formation of elemental sulfur ( ) and sulfuric acid ( ) , which would condense to form aerosols if saturated in the atmosphere . in reducing atmospheres ( e.g. , atmospheres ) , aerosols are photochemically formed based on and emission ; and in oxidized atmospheres ( e.g. , and atmospheres ) , both and aerosols may be formed ( see figure [ sulfur_s ] ) . in general , the higher the surface sulfur emission , the more aerosols exist in the atmosphere ( see figure [ sulfur_s ] ) . as a result of photochemical production of elemental sulfur and sulfuric acid , terrestrial exoplanets with a habitable surface temperature ( e.g. , @xmath46 k ) and substantial sulfur emission from the surface are likely to have hazy atmospheres . in this paper , we use hazy " to describe an atmosphere that has significant aerosol opacities at visible wavelengths ( e.g. , 500 nm ) . we find that even with an earth - like surface sulfur emission , 1-bar dominated atmospheres on habitable rocky exoplanets are hazy with aerosols ( see figure [ sulfur_s ] ) . we also find that if the sulfur emission rate is @xmath47 times more than the earth s current volcanic sulfur emission rate , photochemical aerosols become optically thick at visible wavelengths in oxidized atmospheres including and atmospheres ( see figure [ sulfur_s ] ) . the key parameters that determine the aerosol opacity in the atmosphere are the surface sulfur emission rate , the dry deposition velocity , and the aerosol particle size . first , a higher surface sulfur emission rate leads to more sulfur and sulfate aerosols in anoxic atmospheres ( e.g. , figure [ sulfur_s ] and figure [ sulfur_gms ] ) . second , larger dry deposition velocities of and cause more rapid removal of these sulfur compounds from the atmosphere , which reduces the chance of converting them into condensable molecules ( i.e. , and ) . therefore , larger dry deposition velocities of and result in lower aerosol loading and aerosol opacities in the atmospheres , as shown in figure [ sulfur_vb ] . third , we find that the particle size has only secondary effects on the chemical composition of the atmosphere ( i.e. , by increasing the penetration of ultraviolet radiation ) , but has a primary effect on the aerosol optical depth . for mean particle diameter varying in the range of @xmath48 @xmath1 m ( i.e. , typical particle sizes of photochemical aerosols on earth ( e.g. , seinfeld & pandis 2006 ) and titan ( e.g. , rages et al . 1983 ) ) , we do not see a notable variation in the yield of elemental sulfur , but we see an enhancement of production with large particles ( figure [ sulfur_gms ] ) . even with the same aerosol abundances , however , micron - sized particles cause lower opacities at the visible wavelengths and higher opacities in mir compared with submicron - sized particles ( figure [ sulfur_gms ] ) . we capture the effects of the three key parameters on the aerosol opacity in anoxic atmospheres on terrestrial exoplanets by fitting the following power - law formula , i.e. , @xmath49 where @xmath50 is the vertical optical depth due to aerosols at 1 bar , @xmath51 is the total sulfur emission rate , @xmath52 is the dry deposition velocities of and with respect to current earth values , @xmath53 is the mean particle diameter of aerosols , @xmath54 , @xmath55 , and @xmath56 are positive numbers , and @xmath57 is a constant that covers other uncertainties . we have fit the empirical relation ( [ eqnsyn ] ) through an extensive parameter exploration using photochemistry models ( see figure [ sulfur_s ] - [ sulfur_vb ] for examples ) and determined the values of @xmath57 , @xmath54 , @xmath55 and @xmath56 for dominated reducing atmospheres and for and dominated oxidized atmospheres . we summarize graphically the parameter regime in which sulfur emission leads to a hazy atmosphere in figure [ syn ] . here we use @xmath58 and @xmath59 as the representatives for aerosol opacities at visible wavelengths and mir wavelengths ; due to the complex nature of the extinction cross sections of aerosol particles ( figure [ cross_compare ] ) , it is not practical to fold the full wavelength dependency into the empirical formula . also , we find that it is always true that @xmath60 for mean particle diameter in the order of 10 @xmath1 m and @xmath61 for mean particle diameter in the order of 0.1 @xmath1 m . for atmospheres , and mean particle diameter @xmath62 in the the range of @xmath48 @xmath1 m , @xmath63 and for @xmath62 in the the range of @xmath64 @xmath1 m , @xmath65 for and atmospheres , and @xmath62 in the the range of 0.1 and 1 @xmath1 m , @xmath66 and for @xmath62 in the the range of @xmath64 @xmath1 m , @xmath67 the constant @xmath57 in equations ( [ h2_syn1 ] - [ n2_syn2 ] ) spans about one order of magnitude , which covers the variation of the following model inputs : * the / ratio in the surface sulfur emission , ranging from 0.01 to 10 ; * temperature profiles deviating from the adopted temperature profile by @xmath68 k that controls the mixing ratio of water vapor in the atmosphere by the cold trap ; * stellar ultraviolet radiation received by the planet , ranging from the habitable zone of solar - like stars to the habitable zone of quiet m dwarfs with an effective temperature of 3100 k ; * eddy diffusion coefficients ranging from 0.1 to 100 times the values of earth s atmosphere ; * sulfur polymerization reaction rates ( reactions [ sp0 ] - [ sp4 ] ) ranging by one order of magnitude . to summarize , we find that the emission of and from the surface is readily converted into sulfur ( ) and sulfate ( ) in anoxic atmospheres of terrestrial exoplanets . the photochemical sulfur and sulfate would condense to form aerosols if saturated in the atmosphere , which is likely to occur on a planet in the habitable zone of either a sun - like star or a quiet m star . the aerosol layer is optically thick at the visible and nir wavelengths if the surface sulfur emission is comparable to earth s volcanic sulfur emission in the atmosphere , and more than @xmath47 times of the earth s volcanic sulfur emission in other anoxic atmospheres , depending on the dry deposition velocities of sulfur compounds and particle size of the aerosols . the sulfur emission from surface shapes the spectra of terrestrial exoplanets at the visible and nir wavelengths , mostly through the photochemical formation of and aerosols . we use the model outputs from the photochemistry models to compute the transmission , reflection , and thermal emission spectra of a terrestrial exoplanet with various levels of sulfur emission , and show examples of the computed spectra in figure [ spec ] . we see that submicron - sized aerosols dominate the transmission and reflection spectra at wavelengths from visible up to 3 @xmath1 m , if the sulfur emission is more than about two orders of magnitude higher than earth s volcanic sulfur emission . in general , an atmosphere with high sulfur emission and therefore high aerosol loading generally exhibits a flat transmission spectrum ( the features at nir muted ) , and a high visible albedo ( see figure [ spec ] ) . notably , aerosols are purely reflective at 500 nm but absorptive at 300 nm . the absorption edge of aerosols in 300 - 400 nm is evident in the reflection spectra for planets with enhanced sulfur emission ( figure [ spec ] ) , which is a potential diagnostic feature for aerosols . although opaque at visible wavelengths , the atmospheres with enhanced sulfur emission are likely to be transparent in the mir wavelengths ( @xmath69 @xmath1 m ) . the spectral features of aerosols depend on their particle sizes , so we now consider two possibilities : if the particles are submicron - sized , the aerosol molecules have negligible cross sections at mir ( see figure [ cross_compare ] ) ; or if the particles are micron - sized , the falling velocity of aerosol particles is large enough to rapidly remove aerosols from the atmosphere , as implied by equation ( [ h2_syn2 ] ) and equation ( [ n2_syn2 ] ) that are applicable for micron - sized particles . therefore in both cases the aerosol opacities at mir are minimal even for very high sulfur emission rates ( see figure [ spec ] for examples of atmospheres , and atmospheres are qualitatively similar ) . the only exception , in which aerosols indeed affect mir spectra , is the case of abundant aerosols . the main spectral effect of aerosols is absorption at mir wavelengths ( @xmath70 @xmath1 m ; figure [ spec ] ) . however , the column - average mixing ratio of needs to be larger than 0.1 ppm in order to produce significant aerosol absorption at mir . we find with numerical exploration that such a high abundance of aerosols is only possible in highly oxidizing dominated atmospheres without reducing gas emission ( see paper i for an example of such atmospheres ) . with reducing gas emission ( i.e. , and ) , it is unlikely that mixing ratio exceeds 0.01 ppm in anoxic atmospheres for a wide range of sulfur emission rates ( see figure [ sulfur_s ] ) . in summary we expect the spectral effects of and aerosols to be minimal at mir for most cases . we now turn to consider the direct spectral features of and . it has been previously proposed that and can be detectable on terrestrial exoplanets by their spectral features ( kaltenegger & sasselov 2010 ) . however , our photochemistry models show that both and are chemically short - lived in the atmospheres , which implies that that substantial surface emission is required to maintain a detectable level of either or in the atmosphere . has diagnostic absorption features at 7.5 @xmath1 m and 20 @xmath1 m ( see figure [ spec ] ) . for these features to be detectable the mixing ratio of needs to be larger than 0.1 ppm , which corresponds to sulfur emission rates 1000 times more than current earth s sulfur emission rates for , , and atmospheres ( see figure [ sulfur_s ] ) . the spectral feature of is the pseudo - continuum absorption at wavelengths longer than 30 @xmath1 m , which coincides with the rotational bands of . we find that the only scenario in which may be directly detected is the case with extremely high sulfur emission rates ( i.e. , 3000 times higher than the current earth s sulfur emission rate ) on a highly desiccated planet without liquid water ocean so that there is no water vapor contamination . we therefore conclude that direct detection of and is tricky : they are chemically short - lived so that extremely large surface emission is required for a detectable mixing ratio in the atmosphere , and their spectral features may be contaminated by other gases in the atmosphere . finally , we suggest that the emission of sulfur compounds might be indirectly inferred by detecting sulfur and sulfate aerosols . our numerical exploration reveals a monotonic relationship between the abundance of aerosols in the atmosphere and the emission rates of sulfur compounds ( see figure [ sulfur_s ] ) , and the composition of aerosols is correlated with the / ratio of the surface emission ( see figure [ n2_ratio ] ) . a combination of featureless low atmospheric transmission ( large planet radius viewed in transits ) and high planetary albedo ( large planetary flux at the visible wavelengths viewed in occultations ) may establish the existence of aerosols in the atmosphere . in particular , elemental sulfur ( ) aerosols are absorptive at wavelengths shorter than 400 nm and therefore might be identified by the absorption edge ( see figure [ spec ] ) . sulfate aerosols ( ) , if abundant in the atmosphere , lead to absorption features at the mir wavelengths ( @xmath71 - 10 @xmath1 m ) . however , none of these features are uniquely diagnostic of certain types of aerosols . the identification of aerosol composition , therefore , is by no means straightforward . we learn from the solar system exploration that the discriminating piece of information for aerosol identification comes from polarization of reflected stellar light . historically , the bright clouds on venus were identified to be mainly composed of droplets after the phase curve of the planet in polarized light had been observed ( e.g. , young 1973 ; hansen & hovenier 1974 ) . we therefore postulate that aerosol identification on terrestrial exoplanets and the inference of surface sulfur emission might require observation of polarized reflected light as a function of planetary illumination phase .

we study the atmospheric composition and the spectra of terrestrial exoplanets with sulfur compounds ( i.e. , and ) emitted from their surfaces . the most important finding is that both and are chemically short - lived in virtually all types of atmospheres on terrestrial exoplanets , based on models of , , and atmospheres . this implies that direct detection of surface sulfur emission is unlikely , as their surface emission rates need to be extremely high ( times earth s volcanic sulfur emission ) for these gases to build up to a detectable level . we also find that sulfur compounds emitted from the surface lead to photochemical formation of elemental sulfur and sulfuric acid in the atmosphere , which would condense to form aerosols if saturated . for terrestrial exoplanets in the habitable zone of sun - like stars or m stars , earth - like sulfur emission rates result in optically thick haze composed of elemental sulfur in reducing -dominated atmospheres for a wide range of particle diameters ( 0.1 - 1 m ) , which is assumed as a free parameter in our simulations . in oxidized atmospheres composed of and , optically thick haze , composed of elemental sulfur aerosols ( ) or sulfuric acid aerosols ( ) , will form if the surface sulfur emission is 2 orders of magnitude more than the volcanic sulfur emission of earth .

sulfur gases are common components in the volcanic and biological emission on earth , and are expected to be important input gases for atmospheres on terrestrial exoplanets . we study the atmospheric composition and the spectra of terrestrial exoplanets with sulfur compounds ( i.e. , and ) emitted from their surfaces . we use a comprehensive one - dimensional photochemistry model and radiative transfer model to investigate the sulfur chemistry in atmospheres ranging from reducing to oxidizing . the most important finding is that both and are chemically short - lived in virtually all types of atmospheres on terrestrial exoplanets , based on models of , , and atmospheres . this implies that direct detection of surface sulfur emission is unlikely , as their surface emission rates need to be extremely high ( times earth s volcanic sulfur emission ) for these gases to build up to a detectable level . we also find that sulfur compounds emitted from the surface lead to photochemical formation of elemental sulfur and sulfuric acid in the atmosphere , which would condense to form aerosols if saturated . for terrestrial exoplanets in the habitable zone of sun - like stars or m stars , earth - like sulfur emission rates result in optically thick haze composed of elemental sulfur in reducing -dominated atmospheres for a wide range of particle diameters ( 0.1 - 1 m ) , which is assumed as a free parameter in our simulations . in oxidized atmospheres composed of and , optically thick haze , composed of elemental sulfur aerosols ( ) or sulfuric acid aerosols ( ) , will form if the surface sulfur emission is 2 orders of magnitude more than the volcanic sulfur emission of earth . although direct detection of and by their spectral features is unlikely , their emission might be inferred by observing aerosol - related features in reflected light with future generation space telescopes .

1101.2642

i

counting the real solutions of polynomial equations in one variable is a fundamental ingredient behind many deeper tasks and applications involving the topology of real algebraic sets . however , the intrinsic complexity of this basic enumerative problem becomes a mystery as soon as one considers the input representation in a refined way . such complexity questions have practical impact for , in many applications such as geometric modelling or the discretization of physically motivated partial differential equations , one encounters polynomials that have sparse expansions relative to some basis . so we focus on new , exponential speed - ups for counting the real roots of certain sparse univariate polynomials of high degree . sturm sequences @xcite , and their later refinements @xcite , have long been a centrally important technique for counting real roots of univariate polynomials . in combination with more advanced algebraic tools such as a grbner bases or resultants @xcite , sturm sequences have even been applied to algorithmically study the topology of real algebraic sets in arbitrary dimension ( see , e.g. , ( * ? ? ? * chapters 2 , 5 , 11 , and 16 ) ) . however , as we will see below ( cf . examples [ ex : tri ] and [ ex : tetra1 ] ) , there are obstructions to attaining polynomial intrinsic complexity , for _ sparse _ polynomials , via sturm sequences . so we must seek alternatives . more recently , relating multivariate positive polynomials to sums of squares has become an important algorithmic tool in optimizing real polynomials over semi - algebraic domains @xcite . however , there are also obstructions to the use of sums of squares toward speed - ups for sparse polynomials ( see theorem [ thm : neg ] below ) . discriminants have a history nearly as long as that of sturm sequences and sums of squares , but their algorithmic power has not yet been fully exploited . our main result is that _ @xmath4-discriminants _ @xcite yield an algorithm for counting real roots , with average - case complexity polynomial in the _ logarithm _ of the degree , for certain choices of probability distributions on the input ( see theorem [ thm : pos ] below ) . the use of randomization is potentially inevitable in light of the fact that even detecting real roots becomes @xmath7-hard already for moderately sparse multivariate polynomials @xcite . the classical technique of sturm sequences @xcite reduces counting the roots of a polynomial @xmath0 in a half - open interval @xmath8 to a gcd - like computation , followed by sign evaluations for a sequence of polynomials . a key difficulty in these methods , however , is their apparent super - linear dependence on the degree of the underlying polynomial . consider the following two examples ( see also ( * ? ? ? * example 1 ) ) . [ ex : tri ] _ setting @xmath9 , the realroot command in maple 14 ( which is an implementation of sturm sequences ) results in an out of memory error after about @xmath10 seconds . the polynomials in the underlying computation , while quite sparse , have coefficients with hundreds of thousands of digits , thus causing this failure . on the other hand , via more recent work @xcite , one can show that when @xmath11 and @xmath12 , @xmath13 has exactly @xmath14 , @xmath15 , or @xmath16 positive roots according as @xmath17 is less than , equal to , or greater than @xmath18 . in particular , our @xmath0 has exactly @xmath16 positive roots . ( we discuss how to efficiently decide the size of monomials in rational numbers with rational exponents in algorithm [ algor : sign ] of section [ sub : bit ] below . ) @xmath19 _ [ ex : tetra1 ] _ going to tetranomials , consider @xmath20 with @xmath21 . then ( via the classical descartes rule of signs ) such an @xmath0 has exactly @xmath15 or @xmath22 positive roots , but the inequalities characterizing which @xmath23 yield either possibility are much more unwieldy than in our last example : there are at least @xmath16 , involving polynomials in @xmath24 and @xmath25 having tens of thousands of terms . in particular , for @xmath26 , sturm sequences on maple 14 result in an out of memory error after about 122 seconds . @xmath19 _ we have discovered that @xmath4-discriminants , reviewed in section [ sec : back ] , enable algorithms with complexity polynomial in the _ logarithm _ of the degree . _ for any @xmath27 , we define @xmath28 and let the _ stable log - uniform measure _ on @xmath29 ( resp . @xmath30 ) be the probability measure @xmath31 ( resp . @xmath32 ) defined as follows : @xmath33^d)}{(2m)^d}$ ] ( resp . @xmath34 ) , where @xmath35 denotes the standard lebesque measure on @xmath36 and @xmath37 denotes set cardinality . @xmath19 _ note that the stable log - uniform measure is finitely additive ( but not countably additive ) , and is invariant under reflection across coordinate hyperplanes . [ thm : pos ] let @xmath38 be positive integers , + @xmath39 + with @xmath40 being independent stable log - uniform random variables chosen from @xmath41 ( resp . @xmath42 ) , and define @xmath43 . then there is a deterministic algorithm , with complexity polynomial in @xmath3 ( resp . @xmath44 and @xmath3 ) , that computes a number in @xmath45 that , with probability @xmath15 , is exactly the number of real roots of @xmath0 . the underlying computational model is the bss model over @xmath41 ( resp . the turing model ) . the key idea is that while the regions of coefficients determining polynomials with a constant number of real roots become more complicated as the number of monomial terms increases , one can nevertheless efficiently characterize large subregions _ chamber cones _ where the number of real roots is very easy to compute . this motivates the introduction of probability and average - case complexity . the @xmath4-discriminant allows one to make this approach completely precise and algorithmic . in fact , our framework enables us to transparently extend theorem [ thm : pos ] to @xmath5-variate @xmath6-nomials ( see theorem [ thm : nplus3 ] of section [ sub : can ] ) . our focus on the stable log - uniform measure simplifies our development and has some practical motivation : when one considers @xmath46-bit floating - point numbers with uniformly random exponent and mantissa , taking @xmath47 and suitably rescaling yields exactly the stable log - uniform measure on @xmath42 . the stable log - uniform measure has also been used in work of avendao and ibrahim to study the expected number of roots of sparse polynomial systems over local fields other than @xmath41 @xcite . it is of course quite natural to ask how the expected complexity in theorem [ thm : pos ] behaves under other well - known measures , e.g. , uniform or gaussian . unfortunately , the underlying calculations become much more complicated . on a deeper level , it is far from clear what a truly `` natural '' probability measure on the space of tetranomials is . for instance , for non - sparse polynomials , it is popular to use specially weighted independent gaussian coefficients since the resulting measure becomes invariant under a natural orthogonal group action ( see , e.g. , @xcite ) . however , we are unaware of any study of the types of distributions occuring for the coefficients of polynomials actually occuring in physical applications . the speed - ups we derive actually hold in far greater generality : see @xcite for the case of @xmath5-variate @xmath48-nomials with @xmath49 , section [ sec : chambercones ] here for connections to @xmath5-variate @xmath6-nomials , the forthcoming paper @xcite for the general univariate case , and the forthcoming paper @xcite for chamber cone theory for @xmath50 sparse polynomial systems . one of the main goals of our paper is thus to illustrate and clarify the underlying theory in a non - trivial special case . we now state our second main result . recent advances in semidefinite programming have produced efficient algorithms for finding sum of squares representations of certain nonnegative polynomials , thus enabling efficient polynomial optimization under certain conditions . when the input is a sparse polynomial it is then natural to ask if there is a sum of squares representation that also respects sparseness . indeed , it is well - known that a nonnegative univariate polynomial can always be written as a sum of two squares of , usually non - sparse , polynomials ( see , e.g. , @xcite for refinements ) . the following result demonstrates that a sparse analogue is either unlikely or much more subtle . [ thm : neg ] there do _ not _ exist absolute constants @xmath51 and @xmath52 with the following property : any trinomial @xmath53 $ ] that is positive on @xmath41 can be written in the form @xmath54 , for some @xmath55 $ ] with @xmath56 having at most @xmath52 terms for all @xmath57 . were there to be a sufficiently efficient representation of positive sparse polynomials as sums of squares , one could then try to use semidefinite programming to find such a representation explicitly for a given polynomial . this in turn could yield an efficient reduction from deciding the existence of real roots to a ( small ) semidefinite programming problem , similar to the techniques of @xcite . our last theorem thus reveals an obstruction to this sums of squares approach . the best known algorithms for real root counting lack speed - ups for sparse polynomials like the average - case complexity bound from our first main result . for example , in the notation of theorem [ thm : pos ] , @xcite gives an arithmetic complexity bound of @xmath58 which , via the techniques of @xcite , yields a bit complexity bound super - linear in @xmath59 . no algorithm with complexity polynomial in @xmath3 ( deterministic , randomized , or average - case ) appears to have been known before for tetranomials . ( see @xcite for recent speed benchmarks of univariate real solvers . ) as for alternative approaches , softening our concept of sparse sum of squares representation may still enable speed - ups similar to theorem [ thm : pos ] via semidefinite programming . for instance , one could ask if a positive trinomial of degree @xmath1 always admits a representation as a sum of @xmath60 squares of polynomials with @xmath60 terms . this question appears to be completely open . [ ex : log ] _ observe that a quick derivative computation yields that + @xmath61 + attains a unique minimum value of @xmath14 at @xmath62 . so this @xmath0 is nonnegative . on the other hand , one can prove easily by induction that @xmath63 , thus yielding an expression for @xmath0 as a sum of @xmath64 _ bi_nomials with @xmath65 . @xmath19 _ note also that while we focus on speed - ups that replace the polynomial degree @xmath1 by @xmath3 in this paper , other practically important speed - ups combining semidefinite programming and sparsity are certainly possible ( see , e.g. , @xcite ) .

suppose is a real univariate polynomial of degree with exactly monomial terms . we present an algorithm , with complexity polynomial in on average ( relative to the stable log - uniform measure ) , for counting the number of real roots of . the best previous algorithms had complexity super - linear in . we also discuss connections to sums of squares and-discriminants , including explicit obstructions to expressing positive definite sparse polynomials as sums of squares of few sparse polynomials . our key tool is the introduction of efficiently computable _ chamber cones _ , bounding regions in coefficient space where the number of real roots of can be computed easily . much of our theory extends to-variate-nomials .

suppose is a real univariate polynomial of degree with exactly monomial terms . we present an algorithm , with complexity polynomial in on average ( relative to the stable log - uniform measure ) , for counting the number of real roots of . the best previous algorithms had complexity super - linear in . we also discuss connections to sums of squares and-discriminants , including explicit obstructions to expressing positive definite sparse polynomials as sums of squares of few sparse polynomials . our key tool is the introduction of efficiently computable _ chamber cones _ , bounding regions in coefficient space where the number of real roots of can be computed easily . much of our theory extends to-variate-nomials . @matrix[1][c]- ifnextchar@ifnextchar [ section ] [ thm]algorithm [ thm]corollary [ thm]lemma [ thm]proposition [ thm]question [ thm]conjecture [ thm]problem [ thm]definition [ thm]remark [ thm]example [ thm]remark

1402.3783

i

in recent years significant attention has been devoted to the development of accurate and low cost wireless localization systems for indoor civilian applications , since they can be employed to provide a number of new services , like asset tracking and tracking of people with special needs @xcite . in these services estimated positions need always to be related to a surrounding infrastructure ( e.g. , rooms and corridors ) to be useful to their end users , so that the knowledge of the map of the environment where users are expected to move ( e.g. , the plan of a building floor ) is required . in principle , map knowledge ( i.e. , _ map - awareness _ ) can be also exploited to improve the estimation accuracy of a localization system . in fact , any wireless localization system first acquires a set of point - to - point measurements related to user position ( first step ; technology - dependent ) and then processes such measurements for _ bi - dimensional _ ( 2-d ) or three - dimensional position estimation by means of a proper localization technique ( second step ; technology - agnostic ) ( * ? ? ? 4 ) . maps can play a significant role in the second step , since they provide information about environmental obstructions ( e.g. , walls ) which interfere with signal propagation ; however , a full exploitation of these information requires a ) the availability of _ map - aware statistical models _ for the acquired measurements and b ) the development of localization techniques explicitly based on these models . at present the only available map - aware statistical models are the model ( * ? ? ? * eq . ( 6 ) ) and the model ( * ? ? ? 4.11.5 ) ( also known as _ wall - attenuation _ model or _ multi - wall _ model @xcite ) ; these models have been developed for and localization systems , respectively , and are based on experimental evidence . this preliminary work shows that map - awareness can significantly improve localization accuracy by compensating for the so called _ bias _ , which is a major source of error . however , as far as we know , the accuracy and validity of the above mentioned models in real world localization systems is under - explored and , generally speaking , there is a lack of experimental results supporting them in the technical literature . in fact , most of the state - of - the - art localization methods rely on _ map - unaware models_. for instance , the well known _ log - distance propagation model _ @xcite ( or , in some cases , models based on polynomial series expansions @xcite ) are adopted to relate rss to distance . similar comments hold for those models relating and to distance ; in this case additive error terms are usually represented by gaussian _ random variables _ ( rvs ) * eq . ( 6 ) ) , @xcite , although more refined models accounting for propagation are also available ( see @xcite and references therein ) . it is also worth mentioning that map - awareness is implicitly employed in _ fingerprinting_-based localization systems to select fingerprint locations @xcite . in those systems no statistical modelling of acquired measurements is needed ( even if combined fingerprinting / statistical approaches are possible @xcite ) ; however , extensive and time consuming measurement campaigns ( which may be very sensitive to environmental changes ) are necessary to achieve an acceptable accuracy , since the localization error of fingerprinting methods is roughly bounded by the spacing between calibration sites . the aim of this manuscript is twofold . first of all , a novel _ unified statistical map - aware model _ for , or measurements is proposed and is validated exploiting a set of rss and toa data acquired in indoor environments . secondly , the improvement in localization accuracy provided by optimal localization algorithms based on the novel map - aware modelling with respect to their counterparts relying on map - unaware modelling is quantified ; this unveils that , specially in rss systems , the accuracy improvement justifies the increased complexity of map - aware modelling . the proposed map - aware model has the following relevant features : a ) it relates the nlos bias affecting measurements to map geometrical features ; b ) it can be employed in localization systems based on ranging techniques ( i.e. , toa , tdoa and rss , but not angle of arrival @xcite ) provided that their radio signals mainly propagate through obstructions ; c ) it contains few parameters to be estimated from measurements ; d ) even if its validity is assessed for narrowband low - frequency rss measurements and for toa measurements , its use can be envisaged for other technologies , like _ wireless local area network _ toa / tdoa or even non - radio - based technologies ( e.g , ultra - sound ) , since it does not rely on technology - specific properties ; e ) likelihood functions based on it can be employed in navigation systems ( where mobile agents are considered ) . this manuscript is organized as follows . in section [ sec : statistical_model ] , the localization system we consider is described and general statistical models for map - aware and map - unaware scenarios are proposed . specific models for rss and toa measurements , based on our experimental data , are illustrated in section [ sec : experimental_results ] . in section [ sec : accuracy_results ] map - aware and map - unaware optimal localization algorithms are derived , their performance is assessed and compared , and some indications about their computational complexity are provided . finally , section [ sec : conclusions ] offers some conclusions . _ notations _ : the probability density function ( pdf ) of the rv @xmath0 evaluated at the point @xmath1 is denoted @xmath2 ; @xmath3 denotes the pdf of a gaussian rv having mean @xmath4 and variance @xmath5 , evaluated at the point @xmath1 ; @xmath6 denotes the pdf of an exponential rv translated by @xmath7 and having mean @xmath8 , evaluated at the point @xmath1 , so that @xmath9 , where @xmath10 denotes the heaviside step function ; @xmath11 denotes the cardinality of the set @xmath12 ; @xmath13 denotes the floor of the real parameter @xmath14 ; @xmath15 denotes the convolution integral .

this result can be achieved by developing novel localization techniques that rely on proper map - aware statistical modelling of the measurements they process . in this manuscript a unified statistical model for the measurements acquired in map - aware localization systems based on _ time - of - arrival _ and _ received signal strength _ techniques is developed and its experimental validation is illustrated . finally , the accuracy of the proposed map - aware model is assessed and compared with that offered by its map - unaware counterparts . localization , map - aware , toa , rss , nlos .

the accuracy of indoor wireless localization systems can be substantially enhanced by _ map - awareness _ , i.e. , by the knowledge of the map of the environment in which localization signals are acquired . in fact , this knowledge can be exploited to cancel out , at least to some extent , the signal degradation due to propagation through physical obstructions , i.e. , to the so called _ non - line - of - sight _ bias . this result can be achieved by developing novel localization techniques that rely on proper map - aware statistical modelling of the measurements they process . in this manuscript a unified statistical model for the measurements acquired in map - aware localization systems based on _ time - of - arrival _ and _ received signal strength _ techniques is developed and its experimental validation is illustrated . finally , the accuracy of the proposed map - aware model is assessed and compared with that offered by its map - unaware counterparts . our numerical results show that , when the quality of acquired measurements is poor , map - aware modelling can enhance localization accuracy by up to 110% in certain scenarios . localization , map - aware , toa , rss , nlos .

1211.6078

i

over the last decade , observational evidence has suggested that soft gamma - ray repeaters ( sgrs ) and anomalous x - ray pulsars ( axps ) belong to a particular class of pulsars . the sgrs / axps are understood as slowly rotating neutron stars ( nss ) that , in contrast to rotation powered radio pulsars and accretion powered x - ray pulsars , are not powered by their spin - down energy losses , but by the energy stored in their extremely large magnetic fields @xmath0 g. they are known as very slow rotating isolated pulsars with rotational periods in the range of @xmath14 s , a narrow range comparing to ordinary pulsars ; and spin - down rates of @xmath15 s / s , in contrast to @xmath16 s / s for ordinary pulsars . their persistent x - ray luminosity , as well as the bursts and flares typical of these sources , are believed to be powered by the decay of their ultra strong magnetic fields ( see mereghetti 2008 for review ) . sgrs are observed with their bright and short bursts of soft @xmath17-rays and x - ray radiation and hence they are considered as a subclass of gamma - ray bursts ( grbs ) . moreover , their generally large spin - down rates , strong outburst energies of @xmath18 erg and giant flares of @xmath19 erg , make them different from the ordinary pulsars . however , the giant flares have been observed so far only from sgrs . axps , on the other hand , are distinguished from x - ray binaries by their narrow period distribution , soft x - ray spectrum , faint optical counterparts , and long term spin - down . however , observations performed over the last few years have led to new discoveries pointing out many similarities between these two classes of sources . the magnetar model , firstly developed for the sgrs , has also been applied to the axps and hence they are often classified together , suggesting that axps and sgrs belong to the same family . in the twisted magnetosphere model of magnetars , the observed x - ray luminosity @xmath10 is determined both by its surface temperature and by magnetospheric currents , the latter due to the twisted dipolar field structure ( see @xcite ; @xcite ) . the luminosity from the hard tails observed in the x - ray spectra contributes significantly to the total energy output in axps / sgrs , indicating the presence of non - thermal phenomena in the magnetosphere of underlying axps / sgrs . the surface temperature in turn is determined by the energy output from within the star due to magnetic field decay , as well as by the nature of the atmosphere and the stellar magnetic field strength . this surface thermal emission is resonantly scattered by the magnetospheric current , thus resulting in an overall spectrum similar to a comptonized blackbody ( see e.g. , @xcite ; @xcite ) . in addition , the surface heating by return currents is believed to contribute substantially to @xmath10 , at least at the same level as the thermal component induced from the interior field decay . magnetar outbursts in this picture occur with sudden increases in twist angle , consistent with the generic hardening of magnetar spectra during outbursts ( e.g. , @xcite ; @xcite ) . furthermore , the strong magnetic field explains the confinement of the hot plasma , required for the subsequent tail with a softer spectrum pulsating at the ns rotation period , and the short bursts in almost all axps / sgrs with peak luminosity exceeding the eddington limit for a ns by a few orders of magnitude , and high frequency quasi - periodic oscillations ( qpos ) ( see @xcite ) . the origin of the quasi - periodic oscillations ( qpos ) observed in the giant flares of soft gamma - ray repeaters ( sgrs ) remains uncertain . current models explore the idea that long - term quasi - periodic oscillations are trapped at the turning points of the continuum of torsional magneto - elastic oscillations in the magnetar s interior . recently , efforts have been made using two - dimensional , general - relativistic , magneto - hydrodynamical simulations , coupled to the evolution of shear waves in the solid crust , in order to explore the viability of this model when a purely dipolar magnetic field is assumed ( see @xcite ; @xcite ) . they showed that axisymmetric , torsional , magneto - elastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasi - periodic oscillations in the giant flares of soft gamma - ray repeaters . there exist constant phase , magneto - elastic qpos at both low ( @xmath20hz ) and high frequencies ( @xmath21hz ) , in full agreement with observations . the range of magnetic field strengths required to match the observed qpo frequencies agrees with that from spin - down estimates . the recent discovery of radio - pulsed emission in four of this class of sources , where the spin - down rotational energy lost @xmath22 is larger than the x - ray luminosity @xmath10 during the quiescent state - as in normal pulsars - opens the question of the nature of these radio sources in comparison to the other sgrs / axps ( we have also recently studied this point in @xcite ) . according to the fundamental plane for magnetars , a plot of @xmath10 versus the spin - down luminosity ( see @xcite for details ) , four of a total of about 20 sgrs / axps should have radio - pulsed emission : xte j1810 - 197 , 1e 1547.0 - 5408 , psr j1622 - 4950 , and sgr 1627 - 41 . basically , is propose that the magnetar radio activity can be predicted from the knowledge of the star s rotational period , its time derivative , and the quiescent x - ray luminosity , when @xmath23 . it is true that for one of these sources , sgr 1627 - 47 , no radio emission has been detected yet , because it is unfavorably affected by distance , scattering , or lack of sensitive observations at the time its pulsed radio emission was possibly expected to be brighter . furthermore , the discovery of 3.76 s pulsations from the new burst source at the galactic center , using data obtained with the _ nustar _ observatory was recently reported . sgr j174529 is the fourth magnetar detected in radio wavelengths , very similar to the other radio sgrs / axps , where also @xmath24 is less than one . the _ swift _ satellite has also observed the sudden turn - on of a new radio source near sgr a*. this result , combined with the detection of a short hard x - ray burst from a position consistent with the new radio sgr , suggests that this source is in fact a new sgr in the galactic center . the combination of a magnetar - like burst , periodicity and spectrum led to the identification of the transient as a likely new magnetar in outburst ( see the recent works about this new sgr in @xcite ; @xcite ) . however , the pulsar s unusually large faraday rotation used to estimate the magnetic field indicates a quite low value @xmath25 @xmath26 , in comparison with all the others magnetars . extra information about the gas in the central 10 pc of the galactic center must be used for a more robust estimate of the magnetic field ( see @xcite ) . the condition @xmath23 proposed in rea et al . ( 2012 ) that magnetars need to satisfy in order to explain the radio emission for some of these sources , in our understanding it is not well justified in the magnetar model . the basic assumption of this model is that steady x - ray luminosity and not only x - ray burst and flares are powered by ultra strong magnetic fields of the star . thus , the connection proposed between the x - ray steady luminosity and the spin - down rate of the rotational energy for the radio magnetars seems to be in contradiction with the basic assumptions of this model , where these two quantities are not correlated . it is appropriate to recall now a few other difficulties of the magnetar model in fitting observations , following malheiro , rueda and ruffini ( 2012 ) ( see references therein ) . in particular , e.g. : ( 1 ) as recalled by mereghetti ( 2008 ) , up to now , attempts to estimate the magnetic field strength through the measurement of cyclotron resonance features , as successfully done for accreting pulsars , have been inconclusive ; ( 2 ) the prediction of the high - energy gamma ray emission expected in the magnetars has been found to be inconsistent with the recent observation of the fermi satellite ( see e.g. , @xcite ; @xcite ) ; ( 3 ) it has been shown that the attempt to relate magnetars to the energies of the supernova remnants ( see e.g. , @xcite ; @xcite ; @xcite ; @xcite ) or the formation of black holes is not viable ( see @xcite ) . * _ alternative models_. * thus , even if the magnetar model has been quite successful in explaining the phenomenology of sgrs / axps , no conclusive , direct measure of the surface magnetic field has been claimed yet . furthermore , we can not ignore that the recent astronomical observations of old sgrs ( characteristic age @xmath27 myr ) with low surface magnetic field ( see section 3 ) , as well as the four sgrs / axps showing radio emission pointed out above , have opened space for alternative models , such as the possible presence of a fallback disk slowing down the neutron star pulsar up to the current spin period ( see e. g. , @xcite ; @xcite ) , or more exotic scenarios involving the hypothesis of quark stars ( see e.g. , @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) to explain these types of sources ( see e.g. , @xcite ) . * _ the white dwarf model_. * an alternative description of the sgrs / axps based on rotating highly magnetized and very massive white dwarfs has been proposed recently by malheiro , rueda and ruffini ( 2012 ) , following previous work by morini et al . ( 1988 ) and paczynski ( 1990 ) . moreover , observations of massive fast rotating highly magnetized white dwarfs by dedicated missions as that of the x - ray japanese satellite suzaku ( see e.g. , @xcite ; @xcite ; @xcite ; @xcite ) has led to a confirmation of the existence of wds sharing common properties with ns pulsars , hence called wd pulsars ( see @xcite , for a latest review about white dwarf pulsars ) . in this new description several observational features are easy understood and well explained as a consequence of the large radius of a massive white dwarf , which manifests itself as a new scale of mass density , moment of inertia , rotational energy , and magnetic dipole momentum in comparison with the case of neutron stars : \a ) the existence of stable wds can explain , the range of long rotation periods @xmath28 seconds observed in sgrs and axps . in particular , the fact we do not observe any sgrs / axps with @xmath29 s is a consequence of the low surface gravity and density of a white dwarf compared with those of neutron stars . boshkayev et al . ( 2012 ) performed a self consistent calculation of dense and very fast rotating white dwarfs and obtained the minimum rotational periods @xmath30 , @xmath31 , @xmath32 and @xmath33 seconds for @xmath34 , and @xmath35 wds respectively . \b ) the long standing puzzle of the energetic balance of the sgrs and axps pulsars is solved : the steady x - ray luminosity @xmath10 observed is smaller than the loss of rotational energy of the white dwarf , @xmath36 , because @xmath22 is @xmath37 orders of magnitude larger due to the wd moment of inertia in comparison with the neutron star one . sgrs and axps are rotation - powered massive white dwarf pulsars in complete analogy with neutron star pulsars . \c ) the large steady luminosity @xmath38 erg / s , for such slow pulsars ( @xmath39 hz ) is also understood , as a consequence of the large radius of the dense wd that produces a large magnetic dipole moment , in the range of these magnetic wds , as we will discuss in this paper . it has usually been thought that white dwarfs could also behave as pulsar since their magnetic fields could be sufficiently strong to produce pulsar emission . in the white dwarf model , since sgrs / axps are magnetic white dwarfs , they are spinning too fast , close to the kepler frequency , and not slow as in the case of neutron stars . these high wd rotational frequencies together with their large radii in comparison to the ns ones , will produce strong potential energy differences , if they are very magnetized wd , and will be able to emitted from x - rays to even gamma - rays ( see @xcite ) . as we will see in the section 3 , several wds were recently observed with magnetic fields up to @xmath40 g , and if sgrs / axps are white dwarfs , the @xmath11 field are even larger @xmath41 g , large enough to power the pulsar emission . \d ) the large @xmath5 observed ( @xmath42 s / s ) are also a consequence of the large wd magnetic dipole moment , as well as of the large radius and the momentum of inertia , and not only of the magnetic field , as is the case for neutron stars in the magnetar model . overcritical magnetic fields of the order of @xmath43 g are no longer needed to explain the large spin - down breaking of the sgrs and axps pulsars : they can be understood as highly magnetized wds with large magnetic fields ( @xmath44 ) g. magnetic white dwarfs tend to be more massive and smaller ( @xcite ) , exactly the properties shared by sgrs and axps as rotationally powered dense white dwarfs ( @xcite ) . recent studies predicted that the masses of high - field magnetic wds should be larger than the average mass of wds ( see e.g. , @xcite ; @xcite ) . \e ) the burst activity quite frequent in these sources is a consequence of their large angular velocity , near to break - up and close to rotational instability . in this critical situation , gravity can stress the star , producing glitches ( associated sudden shortening of the period ) and giving origin to the outburst and large flares observed ( @xcite ; @xcite ) . the scale of the rotational energy delivery by these glitches is also in agreement with the outburst and giant flare energies observed of @xmath45 erg , since the wd rotational energies is at least @xmath46 larger than that of the ns due to the large momentum of inertia ( see figs . ( 4 ) and ( 7 ) of malheiro , rueda and ruffini 2012 ) . the occurrence of these glitches can be explained by the release of gravitational energy associated with a sudden contraction and decrease of the moment of inertia of the white dwarf , consistent with the conservation of angular momentum . the energetics of steady emission as well as that of the outbursts following the glitch can be simply explained in term of the loss of rotational energy , in view of the moment of inertia of the white dwarfs , being much larger than that of neutron stars . \f ) the small population of sgrs and axps observed , only @xmath47 in more than 1800 pulsars , is also understood , since these wd pulsars are quite fast and very magnetic , and as a consequence rarely formed ( @xcite ) . moreover , astronomical observations indicate that isolated magnetic white dwarfs with high magnetic field are only 10@xmath48 of the total magnetic stars found ( see @xcite ) . recently , the sloan digital sky survey ( sdss ) found six very massive white dwarfs with @xmath49 g ( see @xcite ) . furthermore , as explained in malheiro , rueda and ruffini ( 2012 ) , a possible formation mechanism of fast wds originates in a binary system composed of a wd and a late evolved companion star , close to the process of gravitational collapse . we can not discard the possibility that a wd can be captured by a star cluster to form such a binary system . moreover , according to the mcgill sgr / axp online catalog , there are currently twenty confirmed magnetars , consisting of nine soft gamma repeaters and eleven anomalous x - ray pulsars , as well as six magnetar candidates ( four sgr and two axp candidates ) . these numbers are small relative to the total number of known rotation - powered pulsars , nearly 2000 , according to the online atnf pulsar catalog ( see @xcite ) . thus , this uncommon phenomena is consistent with the possibility of a rare capture . the origin of fast white dwarfs generated by supernovae ia has also been investigated , where the rapidly rotating wd is formed shortly after the stellar formation episode , and the delay from stellar formation to explosion is basically determined by the spin - down time of the rapidly rotating merger remnant ( see e.g. , @xcite ) . it has been only shown recently that high - field magnetic white dwarfs ( hfmwds ) might be the result of white dwarf mergers as was long - suspected ( see @xcite ) . rueda et al . ( 2013 ) showed that the merger of a double degenerate system can explain the characteristics of the magnetar axp 4u 0142 + 61 , consistent with an approximate 1.2 @xmath50 white dwarf , resulting from the merger of two otherwise ordinary white dwarfs of masses 0.6 @xmath50 and 1.0 @xmath50 , surrounded by the heavy accretion disk produced during the merger . it is worth pointing out , before opening a discussion concerning difficulties of the white dwarf model in fitting observations , that the description of sgrs / axps as very massive and magnetized white dwarfs ( @xmath51 g ) is quite plausible and can be seen as a natural extrapolation of the star surface magnetic field of magnetized and isolated white dwarfs recently discovered , with @xmath11 from @xmath52 g all the way up to @xmath53 g ( see the recent work of @xcite ) . it is also worth mentioning the fact that most of the observed magnetized white dwarfs are massive ; see e.g. rej 0317 - 853 with @xmath54 @xmath55 and @xmath56 g ( see e.g. , @xcite ; @xcite ) ; pg 1658 + 441 with @xmath54 @xmath57 and @xmath58 g ( see e.g. , @xcite ; @xcite ) , and pg 1031 + 234 with the highest magnetic field @xmath40 g ( see e.g. , @xcite ; @xcite ) . it is also appropriate to recall the main difficulties concerning the white dwarf model , in order to explain some of the phenomenology of sgrs / axps : \a ) _ association of supernova remnants ( snr ) _ in two or three of the magnetars , is usually advocated as an indication of a neutron star nature for these sources , since snr are considered clear signs of the collapse of a massive star . the formation mechanism of fast wds based on a binary system proposed by malheiro , rueda and ruffini ( 2012 ) , is compatible with a snr due to the collapse of the late evolved wd companion star . furthermore , the magnetar association to snr is only robust in three cases ( see @xcite ) , but not considered significant in several other cases that were proposed in the past ( see e.g. , @xcite ) . the case of the association of axp 1e 2259 + 586 with snr g109.1 - 1.0 ( ctb 109 ) was analyzed by paczynski ( 1990 ) assuming the merger of a binary system of an ordinary white dwarf of mass @xmath59 , leading both to the formation of a fast rotating white dwarf , and to the supernova remnant ( see section 8 of @xcite ) . the second case concerns the axp 1e 1841 - 045 associated with the snr kes 73 ( see @xcite ) where a pulsar psr j1841 - 0500 was recently found located at only 4 from this axp , supporting the binary scenario discussed before ( see note added after submission of @xcite ) . thus , the existence of snr near to the sgrs / axps can not be used to clearly exclude a white dwarf nature of these sources . the third case concerns the axp 1e 1547.0 - 5408 sited at the center of snr g327.24 - 0.13 ( see e.g. @xcite ) , which is one of the magnetars that emitted in radio as discussed before . in our understanding , this source is in fact a neutron star pulsar , as are the others radio magnetars presented recently in coelho & malheiro ( 2013 ) , and can not be identified with a massive white dwarf . its outburst activity , well studied by bernardine et al . ( 2011 ) , is due to the high surface magnetic field of this star , similar to the magnetospheric activity also observed in the sun . we claim that this source is a high-@xmath11 pulsar , but not a magnetar , since its steady luminosity can be well explained in terms of the neutron star spin - down rate energy ( @xmath60 ) , and does not require magnetic energy to produce this luminosity . \b ) _ sgrs and axps are associated with massive , young star clusters , but white dwarfs are usually old . _ recently , two sgrs with low magnetic fields were found with characteristic ages much higher ( myr ) than those of the others ( see mcgill catalog ) . the few possible associations of sgrs / axps with clusters of massive stars does not exclude the possibility that a white dwarf can be captured by a star cluster and form the binary system that will give origin to the fast white dwarf formation mechanism already discussed . since , several axps are not located in young star clusters , the merger of two usually older white dwarfs , can also explain the small characteristic ages of these sources . as we already discussed , recently @xcite showed that the merger of a double degenerate system can explain the characteristic age of the axp 4u 0142 + 61 , @xmath61 kyr , consistent with the characteristic ages of several magnetars . \c ) _ the magnetic fields of white dwarfs are not strong enough to produce pulsar emission at the slow periods associated with axps . _ we have already commented on this point before and will dedicate more discussions to it when we present the values for the dipole magnetic moments of isolated and very magnetic white dwarfs . kashiyama et al . ( 2011 ) address this point in their paper , and showed that because of the large radii and momenta of inertia of wds , magnetic fields of @xmath62 g ( exactly the ones obtained for sgrs / axps ) , can produce high potential energies as in normal neutron star pulsars in order to explain their large emission , from x - rays up to gamma - rays . \d ) _ axps have been shown to vary their x - ray luminosity . in particular the transient axps seem to contradict the assumption that quiescent x - ray luminosity is ascribed to spin - down luminosity_. as explained in mereghetti ( 2008 ) , in the best theory available , the long - term variations of x - ray emission on magnetars comes from currents supported in twisted magnetosphere or sudden reconfigurations of the magnetosphere when unstable conditions are reached . the star heated in these events will pass by through a subsequent cooling process that could explain the observed long - term decays in the soft x - ray emissions of axps . thus , the origin of the x - ray variability comes essentially from magnetospheric effects and reconnections expected to occur on very magnetized wds . this is not correlated directly to the quiescent x - ray luminosity that is associated to the spin - down luminosity for the case of the white dwarf model . furthermore , it is interesting to pointed out that almost all the transient axps that show a large luminosity range variability are the some that emit in radio ( except the axp cxo j164710.2 - 455216 in the massive star cluster westerlund ) , exactly the ones that we have already discussed , for which @xmath60 , with @xmath22 calculated as neutron stars . this is a strong indication that the energy source for the x - ray variability and the steady luminosity have different origins : the first due to the large magnetic fields of the magnetosphere ( this is expected to also happen in the magnetosphere of very magnetized rotating white dwarfs , as found in the transient radio source gcrt j1745 - 3009 by @xcite ) , and the second from the spin - down luminosity ( only possible in the white dwarf model , with the exception of the radio axps that , as discussed in @xcite , obey a linear log - log relation between @xmath10 and @xmath22 , as expected for neutron star pulsars ) . \e ) _ the quasi - periodic oscillations ( qpos ) at frequencies almost up to 1 khz in sgrs following giant flares , are very high - frequency oscillations to be supported by a white dwarf_. as we already discussed , axisymmetric , torsional , magneto - elastic oscillations of neutron stars can explain these qpos . however , we do not observe directly the vibration of the crust , but only their effect on the x - ray emission . this is testified by the sporadic nature of the observed signals , that could be originated by the geometry of the magnetic field and its complex effect on the radiation beam patterns ( see @xcite ) . thus , the origin of the qpos is possibly not associated with magneto - elastic oscillations of the star surface , but instead with more complex process due to the hot plasma of the star and magnetospheric oscillations , since the giant flare tail emission is thought to originate in the fraction of the energy released in the initial spike that remains trapped in the star magnetosphere , forming an optically thick photon - pair plasma . the same effect for very magnetized white dwarfs , optically thick pairs in equilibrium with radiation trapped by magnetic fields may also be present in the magnetosphere if the wd magnetic fields are high @xmath63 g , in the range of the values obtained for sgrs / axps in the white dwarf model . furthermore , as we already pointed out , pair production activities in the magnetosphere of a rotating white dwarf have already been observed in the transient radio source gcrt j1745 - 3009 by zhang & gil ( 2005 ) , and also in the ae aquarii ( see e.g. , @xcite ; @xcite ; @xcite ; @xcite ) . thus , we can not exclude the high frequencies of the qpos from occurring in very massive and fast white dwarfs if they are very magnetized . \f ) _ hard x - ray emission ( up to 1 mev ) which is highly pulsed and at a luminosity that is often more than the soft x - ray luminosity_. such a spectral feature is clearly already in evidence for rotating white dwarfs , in particular the wd ae aquarii observed by the suzaku satellite , following the work of terada et al . it was concluded , as presented in more detail in malheiro , rueda and ruffini ( 2012 ) , that the hard x - ray pulsations observed on this white dwarf , in addition to the thermal modulation of the softer x - ray band , should have no thermal origin , but possibly the synchrotron emission with sub mev electrons . since the magnetic fields for almost all sgrs / axps as white dwarfs are at least two orders of magnitude higher than the one of ae aquarii ( see table 1 ) we would expected an even harder x - ray emission spectrum up to mev . in this work , we will discuss the magnetic dipole moment @xmath2 of neutron stars and magnetic white dwarfs , to stress that the values obtained for @xmath2 for sgrs and axps as white dwarfs are in agreement with those of polar and isolated magnetic wds . using the catalog of the sloan digital sky survey ( sdss ) project , we selected from the sample of 480 white dwarfs that have high magnetic field strength in the range of @xmath46 to @xmath53 g ( @xcite ) , 82 wds for which both period @xmath4 and magnetic field @xmath11 are known . these recent astronomical observations of white dwarfs allow us to conclude that the range of the magnetic dipole moment of polar and isolated _ magnetic _ white dwarfs is @xmath6 and also almost independent of the star period . this systematic study of magnetic white dwarfs applied to sgrs / axps described as white dwarf pulsars was not performed in our previous works ( @xcite ; @xcite ) . for the first time , we will show that sgrs / axps as white dwarf pulsars also have the same magnetic dipole moment of the magnetic wds even with much small periods ( @xmath13 s ) . thus , the astronomical observation that the wd magnetic dipole moment for polar and isolated white dwarfs is always in the range indicated before , despite the fact that their rotational periods change from @xmath46 to @xmath64 s , is an important evidence that also suggests the wd nature of sgrs / axps , since they share these same properties . for both millisecond and long period nss pulsars , we do not see this phenomenology , since they have quite different magnetic moments that increase with the period . the larger values of the magnetic dipole moment for a white dwarf compared to those of neutron star x - ray pulsars ( @xmath65 emu ) , can explain for instance the large steady luminosity @xmath66 seen in sgrs / axps of @xmath38 erg / s , for very slow pulsars rotational frequencies ( @xmath39 hz ) . furthermore , we extend the comparison done in malheiro , rueda and ruffini ( 2012 ) of the observational properties of one low-@xmath11 sgr and one fast white dwarf , including the recent observations of one more low-@xmath11 sgr and two other fast , magnetic white dwarfs . we conclude that several features of these two sgrs with low magnetic fields are still very similar to those of fast , magnetic white dwarfs , an important result that shows some of the sgrs / axps , at least these sgrs with low-@xmath11 , could be identified with very fast and magnetic massive white dwarfs . * this work is organized as follow : * in section 2 , we discuss the standard magnetic dipole model for rotation - powered pulsars in order to show the scale of the dipole magnetic moment in wds and nss . in section 3 , we present the recent discoveries of sgr 0418 + 5729 ( see @xcite ) and swift j1822.3 - 1606 ( see @xcite ; @xcite ) with low magnetic field sharing some properties ( @xcite ; @xcite ) with the recent detected fast wd pulsars ae aquarii and rxj 0648.0 - 4418 , and the candidate euve j0317 - 855 , supporting the description of some sgrs / axps as white dwarf pulsars . in section 3 , we present the wds magnetic dipole moments in comparison to the nss ones , suggesting the possibility of some sgrs / axps belonging to a class of very fast , magnetic massive white dwarfs . finally , in section 4 we summarize our conclusions .

the anomalous x - ray pulsars ( axps ) and soft gamma - ray repeaters ( sgrs ) are some of the most interesting groups of pulsars that have been intensively studied in the recent years . they are understood as neutron stars ( nss ) with super strong magnetic fields , namely g. however , in the last two years two sgrs with low magnetic fields g have been detected . moreover , three fast and very _ magnetic _ white dwarfs ( wds ) have also been observed in the last years . based on these new pulsar discoveries , we compare and contrast the magnetic fields , magnetic dipole moment , characteristic ages , and x - ray steady luminosities of these two sgrs ( in the wd model ) with three fast white dwarfs , to conclude that they show strong similarities corroborating an alternative description of several sgrs / axps as very massive and magnetic white dwarfs . the pulsar magnetic dipole moment depending only on the momentum of inertia , and observational properties , such as the period and its first time derivative , can help to identify the scale of for sgrs / axps . we analyze the pulsar magnetic dipole moment of sgrs and axps when a model based on a massive fast rotating highly magnetized white dwarf is considered .

the anomalous x - ray pulsars ( axps ) and soft gamma - ray repeaters ( sgrs ) are some of the most interesting groups of pulsars that have been intensively studied in the recent years . they are understood as neutron stars ( nss ) with super strong magnetic fields , namely g. however , in the last two years two sgrs with low magnetic fields g have been detected . moreover , three fast and very _ magnetic _ white dwarfs ( wds ) have also been observed in the last years . based on these new pulsar discoveries , we compare and contrast the magnetic fields , magnetic dipole moment , characteristic ages , and x - ray steady luminosities of these two sgrs ( in the wd model ) with three fast white dwarfs , to conclude that they show strong similarities corroborating an alternative description of several sgrs / axps as very massive and magnetic white dwarfs . the pulsar magnetic dipole moment depending only on the momentum of inertia , and observational properties , such as the period and its first time derivative , can help to identify the scale of for sgrs / axps . we analyze the pulsar magnetic dipole moment of sgrs and axps when a model based on a massive fast rotating highly magnetized white dwarf is considered . we show that the values for obtained for several sgrs and axps are in agreement with the observed range of isolated and polar magnetic white dwarfs . this result together with the fact that for _ magnetic _ white dwarfs g their magnetic dipole moments are almost independent of the star rotation period ( ) - a phenomenology not shared by neutron stars pulsars - suggests a possible _ magnetic _ white dwarf nature for some of sgrs / axps that have much smaller periods ( s ) . moreover , since for pulsars the dipole radiation power is proportional only to and to the rotational star frequency , we can explain in the wd model - considering only the different scales of the magnetic dipole moment for wds and nss - why the steady luminosity for several sgrs / axps ( and in particular the low- sgrs ) compared to those of x - ray dim isolated neutron stars ( xdins ) and high- pulsars obey the ratio : all these x - ray sources have essentially the same rotational periods ( s ) and the x - ray luminosity is correlated to the spin - down luminosity which is equal to the dipole radiation power in the dipole model .

1211.6078

c

we have studied the possibility of describing several sgrs / axps as belonging to a class of massive , fast - rotating , highly magnetized white dwarfs , following the alternative description of sgrs / axps proposed recently in malheiro , rueda and ruffini ( 2012 ) , and showed that the values for @xmath2 obtained for several sgrs and axps are in agreement with the observed , range @xmath6 of those of isolated and polar magnetic white dwarfs . this result , together with the fact that for _ magnetic _ white dwarfs @xmath7 g their magnetic dipole moments are almost independent of the star rotation period ( @xmath8 ) , a phenomenology not seen in neutron star rotation - powered pulsars , suggests a possible _ magnetic _ white dwarf nature for several sgrs / axps that have much smaller periods ( @xmath9 s ) . thus , the astronomical observation that the wd magnetic dipole moment for polar and isolated white dwarfs is always in the range indicated before , despite the fact that their rotational period changes from @xmath46 to @xmath64 s , is an important evidence that suggests the wd nature of sgrs / axps , since they share these some properties , a result that constitutes one of novelties of our work . furthermore , we showed that the scale of the dipole magnetic moment in wd is @xmath89 times larger than that for neutron stars , exactly the factor seen in the x - ray luminosity of sgrs / axps described as white dwarfs when compared with the @xmath10 of slow neutron star pulsars , such as xdins , and high-@xmath11 pulsars that have essentially the same period ( @xmath901 to 10 s ) as those of sgrs / axps . we also presented the recent discoveries of sgr 0418 + 5729 and swift j1822.3 - 1606 with low magnetic fields , sharing some properties with the recently detected fast wd pulsar ae aquarii and rxj 0648.0 - 4418 , and the candidate euve j0317 - 855 , to support the wd description of sgrs and axps . in table 1 we compared the parameters of these two sgrs with low magnetic fields described in the white dwarf model with three fast white dwarfs . we concluded from table 1 that several features of the two sgrs with low magnetic fields are very similar to those of fast , magnetic white dwarfs , for sure one of the most novel aspects of our work . they are old , with characteristic ages of myr , low quiescent x - ray luminosity @xmath120 , magnetic fields of @xmath121 g and magnetic dipole moments of @xmath109 emu . moreover , the large steady x - ray emission @xmath119 erg / s observed in the sgrs / axps is now well understood as a consequence of the fast white dwarf rotation ( @xmath9 s ) , since the magnetic dipole moment @xmath2 is of the same scale as that observed for the very magnetic and not so fast white dwarfs . all these findings support the description of some sgrs / axps as belonging to a class of very fast and magnetic massive white dwarfs , in line with important and recent astronomical observations of massive fast rotating highly magnetized white dwarfs . we encourage future observational campaigns to verify the radius of these sources , in order to clarify the nature of sgrs / axps . the authors acknowledges the financial support of the brazilian agency capes , cnpq and fapesp ( so paulo state agency , thematic project 2007/03633 - 3 ) . we are grateful to y. terada by the data points of the figure in this paper , and also by the valuable discussions in the 13th marcel grossmann meeting . alcock , c. , farhi , e. , & olinto , a. 1986 , , 310 , 261 allen , m. p. , & horvath , j. e. 2004 , , 616 , 346 alpar , m. a. , ertan , @xmath122 , & @xmath123ali@xmath124kan , @xmath125 . 2011 , , 732 , l4 angel , j. r. p. , borra , e. f. , & landstreet , j. d. 1981 , , 45 , 457 barstow , m. a. , jordan , s. , odonoghue , d. , burleigh , m. r. , napiwotzki , r. , & harrop - 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we show that the values for obtained for several sgrs and axps are in agreement with the observed range of isolated and polar magnetic white dwarfs . this result together with the fact that for _ magnetic _ white dwarfs g their magnetic dipole moments are almost independent of the star rotation period ( ) - a phenomenology not shared by neutron stars pulsars - suggests a possible _ magnetic _ white dwarf nature for some of sgrs / axps that have much smaller periods ( s ) .

the anomalous x - ray pulsars ( axps ) and soft gamma - ray repeaters ( sgrs ) are some of the most interesting groups of pulsars that have been intensively studied in the recent years . they are understood as neutron stars ( nss ) with super strong magnetic fields , namely g. however , in the last two years two sgrs with low magnetic fields g have been detected . moreover , three fast and very _ magnetic _ white dwarfs ( wds ) have also been observed in the last years . based on these new pulsar discoveries , we compare and contrast the magnetic fields , magnetic dipole moment , characteristic ages , and x - ray steady luminosities of these two sgrs ( in the wd model ) with three fast white dwarfs , to conclude that they show strong similarities corroborating an alternative description of several sgrs / axps as very massive and magnetic white dwarfs . the pulsar magnetic dipole moment depending only on the momentum of inertia , and observational properties , such as the period and its first time derivative , can help to identify the scale of for sgrs / axps . we analyze the pulsar magnetic dipole moment of sgrs and axps when a model based on a massive fast rotating highly magnetized white dwarf is considered . we show that the values for obtained for several sgrs and axps are in agreement with the observed range of isolated and polar magnetic white dwarfs . this result together with the fact that for _ magnetic _ white dwarfs g their magnetic dipole moments are almost independent of the star rotation period ( ) - a phenomenology not shared by neutron stars pulsars - suggests a possible _ magnetic _ white dwarf nature for some of sgrs / axps that have much smaller periods ( s ) . moreover , since for pulsars the dipole radiation power is proportional only to and to the rotational star frequency , we can explain in the wd model - considering only the different scales of the magnetic dipole moment for wds and nss - why the steady luminosity for several sgrs / axps ( and in particular the low- sgrs ) compared to those of x - ray dim isolated neutron stars ( xdins ) and high- pulsars obey the ratio : all these x - ray sources have essentially the same rotational periods ( s ) and the x - ray luminosity is correlated to the spin - down luminosity which is equal to the dipole radiation power in the dipole model .

hep-ph0507270

i

it had been proved that the b - meson wf is renormalizable after taking into account the rg evolution effects @xcite , and the undesirable feature @xcite of the b - meson da can be removed under evolution . therefore , to keep the @xmath4 dependence in both the hard scattering amplitude and the wavefunction is necessary . it was found that the transverse and longitudinal momentum dependence in the b - meson wf under the ww approximation is correlated through a @xmath77-function , @xmath268 . in the paper , we show that the transverse momentum distribution of the b - meson wf can be broadened to be a hyperbola - like curve by including 3-particle fock state , rather than a simple @xmath77-function . the solutions in this paper provide a practical framework for constructing the b - meson lc wfs @xmath0 and hence are meaningful for phenomenological applications . and we have constructed a new model for the b - meson wavefunction in the compact parameter @xmath26-space as shown in eqs.([newmodel1],[newmodel2 ] ) based on these solutions . there are uncertainties caused by two unknown parameters @xmath239 and @xmath77 . however , since the b - meson wfs are universal , we can determine them by global fitting of the experimental data . by taking @xmath7 transition form factor as an example , we show that if the 3-particle wavefunctions contributions are less than @xmath269 of that of the ww case , then one may observe that the preferable values for these two parameters are @xmath270 and @xmath271 . the reasonable inclusion of the 3-particle fock states in b - meson wfs provides us with the chance to make a more precise evaluation on the b meson decays . further studies on the b - meson wfs with higher fock states and its phenomenological implications are still necessary .

our results show that the use of gluon equation of motion can give a constraint on the transverse momentum dependence of the b - meson wavefunctions , whose distribution tends to be a hyperbola - like curve under the condition , which is quite different from the ww type wavefunctions , whose transverse momentum dependence is merely a delta function .

the b - meson light - cone wavefunctions , , are investigated up to the next - to - leading order in fock state expansion in the heavy quark limit . in order to know the transverse momentum dependence of the b - meson wavefunctions with 3-particle fock states contributions , we make use of the relations between 2- and 3- particle wavefunctions derived from the qcd equations of motion and the heavy quark symmetry , especially two constraints derived from the gauge field equation of motion are employed . our results show that the use of gluon equation of motion can give a constraint on the transverse momentum dependence of the b - meson wavefunctions , whose distribution tends to be a hyperbola - like curve under the condition , which is quite different from the ww type wavefunctions , whose transverse momentum dependence is merely a delta function . based on the derived results , we propose a simple model for the b - meson wavefunctions with 3-particle fock states contributions . + * pacs numbers : * 12.38.aw , 12.39.hg , 14.40.nd * keywords : * b - meson wavefunction , 3-particle fock state , heavy quark symmetry # 1#1 # 1 _

astro-ph0109068

c

our abundance analysis based on high - resolution optical spectra of iras 05113 + 1347 and iras 22272 + 5435 shows that these stars classified as pagb stars have the surface composition expected of a highly - evolved agb star : carbon and nitrogen enrichments ( relative to their presumed initial abundances ) are identified as products of the third and first dredge - ups , respectively , and a strong @xmath0-process enrichment is also attributable to the third dredge - up . an intriguing lithium enrichment may reflect lithium production from @xmath68he in the agb or pagb star . the two stars analysed in this paper seem typical of the sample ( now , 11 stars in total analysed ) of c - rich pagb stars . if the transition from agb to pagb star was made without drastic alterations of surface composition , the immediate progenitor of a c - rich pagb was a cool carbon star of the n - type . bright cool carbon stars analysed by lambert et al . ( 1986 ) and ohnaka , tsuji , & aoki ( 2000 ) have c , n , and o abundances quite similar to the pagbs , and are @xmath0-process enriched to similar levels too . however , the carbon stars are of approximately solar metallicity ( lambert et al . 1986 ; abia et al . 2001 ) not metal - poor like the pagbs . lithium provides a discordant note . the n - type stars are not lithium rich . the lithium - rich carbon stars are the j - type stars rich in @xmath45c and with no @xmath0-process enhancement . there are metal - poor carbon stars in the halo that are as metal - poor as the pagbs : kipper et al . ( 1996 ) analysed 5 stars with [ fe / h ] from @xmath190.7 to @xmath191.2 , all with considerable @xmath0-process enrichments . with one exception , the carbon abundances are similar to those of the pagbs . but with the same exception , the nitrogen abundances are much less than those of the pagbs . in two of the stars li was found to be enhanced ( log @xmath28(li ) @xmath46 1.7 ) . the noticeable difference is that the @xmath1c/@xmath45c ratio of the carbon stars are much lower ( 5 to 10 ) than the limits set for the pagbs . in summary , the immediate progenitors of the pagbs have yet to be identified . this is odd given that the pagbs evolve rapidly and probably more rapidly than their agb progenitor . it is quite possible that the progenitor is shrouded by dust . we acknowledge the support of national science foundation ( grant ast-9618414 ) and the robert a. welch foundation of houston , texas . we thank dr . pandey and dr . allende prieto for many helpful comments . this research has made use of the simbad database , operated at cds , strasbourg , francs , and the nasa ads service , usa . abia , c. , busso , m. , gallino , r. , domnguez , i. , straniero , o. , & isern , j. 2001 , apj , ( in press ) andersen , j. , gustafsson , b. , & lambert , d.l . 1984 , a&a , 136 , 75 angulo , c. , arnould , m. , rayet , m. , ( nacre collaboration ) , 1999 , nuclear physics a , 656 , 1 bakker , e.j . , van dishoek , e. f. , waters , l.b.f.m . , & schmaker , t. 1997 , a@xmath5a , 323 , 469 blackwell , d.e . , booth , a.j . , menon , s.l.r . , & petford , a.d . 1986a , mnras , 220 , 303 blackwell , d.e . , booth , a.j . , menon , s.l.r . , & petford , a.d . 1986b , mnras , 220 , 289 bhm - 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j . , & boothroyd , a.i . 1992 , apj , 392 , l71 shetrone , m.d . , & sneden , c. , & pilachowski , c.a . 1993 , pasp , 105 , 337 siess , l. , & livio , m. 1999 , mnras , 304 , 925 smith , v.v . , & lambert , d.l . 1989 , apj , 345 , l75 smith , v.v . , & lambert , d.l . 1990 , apj , 361 , l69 smith , g. , & raggett , d.st.j . 1981 , j.phys.b 14 , 4015 smith , v.v . , shetrone , m.d . , & keane , m.j . 1999 , apj , 516 , 73 sneden , c. 1973 , ph.d . thesis , univ . of texas at austin tull , r.g . , macqueen , p.j . , sneden , c. , & lambert , d.l . 1995 , pasp , 107 , 251 van winckel , h & reyniers , m. 2000 , a&a , 354 , 135 waelkens , c. , van winckel , h. , bogaert , e. , & trams , n.r . 1992 , a&a , 264 , 159 whaling , w. , hannaford , p. , lowe , r.m . , bimont , e. , & grevesse , n. 1985 , a&a , 153 , 109 wallace , l. , hinkle , k. , & livingston , w. 1993 , an atlas of the spectrum of the solar photosphere wiese , w.l . , fuhr , j.r . , & deters , t.m . 1996 , atomic transition probabilities of carbon , nitrogen , and oxygen : a critical data compilation , american chemical society .. for nist , 453 wyller , a.a . 1966 , apj , 143 , 828 zas , l. , klochkova , v.g . , & panchuk , v.e . 1995 , mnras , 275,764 ccccccc + & & & & + @xmath69 & lep & & @xmath32 & & @xmath32 + ( ) & ( ev ) & log @xmath8 & ( m ) & log @xmath28(x ) & ( ) & log @xmath28(x ) + & & & & & & + 6363.63 & 1.12 & -1.419 & 35.0 & 1.64 & 28 & 1.92 + 6413.68 & 1.13 & -0.853 & ... & ... & 36 & 1.49 + 6281.28 & 0.96 & -0.570 & 117.0 & 1.36 & ... & ... + 6165.89 & 0.92 & -0.205 & 199.0 & 1.59 & 166 & 1.74 + 6093.06 & 1.46 & -0.648 & 39.0 & 1.32 & ... & ... + 6087.53 & 1.12 & -0.618 & 124.0 & 1.66 & ... & ... + 6086.18 & 1.30 & -0.801 & 92.0 & 1.81 & ... & ... + 6016.51 & 1.00 & -0.798 & 152.0 & 1.92 & ... & ... + 6182.34 & 1.44 & -0.387 & ... & ... & 33.0 & 1.31 + 6046.65 & 1.12 & -0.686 & ... & ... & 58.0 & 1.60 + & & & & & & + 6248.27 & 1.22 & -1.600 & 93.0 & 2.56 & 60 & 2.67 + 6250.44 & 1.16 & -1.620 & 112.0 & 2.66 & 79 & 2.80 + 6591.43 & 0.20 & -2.510 & 126.0 & 2.54 & 76 & 2.66 + 6637.19 & 1.45 & -1.080 & 143.0 & 2.63 & 125 & 2.88 + 6650.52 & 1.95 & -0.170 & 184.0 & 2.60 & 147 & 2.64 + 6669.63 & 1.04 & -1.720 & 115.0 & 2.61 & 83 & 2.78 + 6680.14 & 1.69 & -0.810 & 148.0 & 2.66 & ... & ... + 6698.64 & 1.64 & -1.360 & 80.0 & 2.65 & 63 & 2.86 + & & & & & & + 7085.49 & 1.07 & -1.963 & 100.0 & 2.52 & ... & ... + 6844.70 & 1.36 & -1.529 & 95.0 & 2.38 & ... & ... + 6734.05 & 1.37 & -1.400 & 106.0 & 2.37 & 83 & 2.53 + 6731.81 & 1.17 & -1.372 & 145.0 & 2.38 & 117 & 2.55 + 6694.72 & 1.37 & -2.209 & 30.0 & 2.43 & ... & ... + 6693.56 & 1.69 & -1.089 & 104.0 & 2.39 & ... & ... + 6679.22 & 1.07 & -1.691 & 108.0 & 2.34 & ... & ... + 6632.27 & 1.67 & -1.344 & 53.0 & 2.19 & 38 & 2.33 + 6616.61 & 1.35 & -2.220 & 30.0 & 2.42 & ... & ... + 6544.61 & 1.17 & -2.180 & 30.0 & 2.18 & 13 & 2.14 + 6542.76 & 1.17 & -1.737 & 77.0 & 2.26 & 45 & 2.31 + 6484.55 & 1.26 & -1.792 & 81.0 & 2.46 & ... & ... +

the stars are c , n , and-process enriched suggesting efficient operation of the third - dredge up in the agb star following a first dredge - up that increased the n abundance . a common history is indicated and , in particular , the-abundances , especially the relative abundances of light to heavy-process elements , follow recent predictions for the third dredge - up in agb stars .

the chemical compositions of the c - rich pagb stars iras 05113 + 1347 and iras 22272 + 5424 are determined from high - resolution optical spectra using standard lte model atmosphere - based techniques . the stars are c , n , and-process enriched suggesting efficient operation of the third - dredge up in the agb star following a first dredge - up that increased the n abundance . lithium is present with an abundance requiring li manufacture . with this pair , abundance analyses are now available for 11 c - rich pagbs . a common history is indicated and , in particular , the-abundances , especially the relative abundances of light to heavy-process elements , follow recent predictions for the third dredge - up in agb stars .

1612.07648

i

in 1963 g. grtzer and e.t . schmidt proved that every algebraic lattice is isomorphic to the congruence lattice of some algebra ( @xcite ) . since the algebras constructed by them were infinite , the result immediately raised the question : does every finite lattice occur as the congruence lattice of a _ finite _ algebra ? the problem remained open till today , and it is usually referred as the _ finite lattice representation problem_. it is an abstract representation problem because it asks for a solution up to isomorphism . the concrete version is the more involved question : given a sublattice @xmath3 of the the partition lattice @xmath4 of all equivalence relations on a set @xmath0 , does there exist an algebra on the same base set @xmath0 , such that @xmath3 _ equals _ the congruence lattice of this algebra ( in @xcite such lattices @xmath3 are characterized by closure properties ) . the subject of the present paper is related to the finite representation problem in its concrete version . for a fixed finite set @xmath0 we consider all possible congruence lattices of algebras with base set @xmath0 . these congruence lattices ( ordered by inclusion ) form itself a lattice @xmath1 and we are going to investigate this lattice . an important tool is our knowledge about the lattice @xmath5 of all quasiorder lattices of algebras defined on the set @xmath0 described in @xcite ( using some techniques developed previously in the papers @xcite and @xcite ) . these two lattices are strongly interrelated : there is a residual mapping from @xmath5 to @xmath1 . therefore , in section [ sec:2 ] , we investigate on abstract level , how lattice properties ( which are relevant for us ) behave under residual mappings ( for instance , the coatoms of @xmath1 directly can be obtained from the coatoms of @xmath5 , see [ b1 ] ) . based on preliminary results from section [ sec:1 ] and the results of @xcite and section [ sec:2 ] , we describe the atoms ( @xmath6-irreducible elements ) , coatoms ( section [ sec:3 ] ) and further @xmath7-irreducible elements ( sections [ sec:4 ] and [ sec:4a ] ) of the lattice @xmath1 . finally , in section [ sec:5 ] , we investigate several lattice theoretic properties of @xmath1 , e.g. , it is tolerance simple , but has no properties related with modularity .

the congruence lattices of all algebras defined on a fixed finite set ordered by inclusion form a finite atomistic lattice . each meet - irreducible element of being determined by a single unary mapping on , we characterize completely those which are determined by a permutation or by an acyclic mapping on the set . using these characterisations we deduce several properties of the lattice ; in particular , we prove that is tolerance - simple whenever .

the congruence lattices of all algebras defined on a fixed finite set ordered by inclusion form a finite atomistic lattice . we describe the atoms and coatoms . each meet - irreducible element of being determined by a single unary mapping on , we characterize completely those which are determined by a permutation or by an acyclic mapping on the set . using these characterisations we deduce several properties of the lattice ; in particular , we prove that is tolerance - simple whenever .

1608.06418

i

we presented here the results of a rigorous rr lyrae search in the corot archive . we found nine rrab stars in the data base that have not been studied and seven of them are new discoveries . three stars show the blazhko effect . the cycle - to - cycle variation of these blazhko effects are evident either for amplitude or frequency modulations or both which rises the possibility of their multiperiodic ( or irregular / chaotic ) nature . the fourier spectrum of star # 132 contains small amplitude ` additional ' frequencies which can be identified as the consequence of the period doubling effect and the excitation of the second radial overtone mode . the later mode identification is strengthened by pulsation modeling , since the observed period ratio is unusually high ( @xmath41 ) , but linear pulsation models at least do not exclude this period ratio . the other two blazhko stars show no significant additional frequencies . the light curve stability and period changes were studied for non - blazhko stars . we detected a significant cycle - to - cycle fluctuation of the pulsation period ( cycle length ) of cm ori . this is the first case that random jitter has been detected for an rr lyrae star . the fluctuation rate is tiny : at longest 1 - 2 seconds per cycles . long term period changes were also investigated for the two known rr lyrae stars cm ori and v2042 oph . their o@xmath7c diagrams cover more than 80 and almost 70 years , respectively . both stars show a slight period increase with rates which agree well with the prediction of the stellar evolution theory for normal red - ward evolution . the fourier amplitude and phase difference distribution with respect to the harmonic order have been studied for the first time on a larger set of non - blazhko stars . we found a common amplitude decline feature . the phase differences show a split distribution . the observed distributions were compared theoretical works . our conclusion is that the recent model calculations reproduce the main features but the fine structures can not be described properly . these amplitude and phase distribution diagrams could be potential diagnostic tools for constraining pulsation models , because of their high sensitivity of the fine structure of the light curves . we successfully transformed the corot unfiltered light curves , and their fourier parameters to the johnson _ v _ curves , and parameters . as a by - product of the use of the interrelations we found possible flux loss for several stars . such an effect was shown for high amplitude variables of the _ kepler _ telescope , but has not documented yet in the case of corot satellite . by using empirical formulae we estimated the basic physical parameters of the complete corot rrab sample . the estimated physical parameters define two subgroups of the sample . ( 1 ) a shorter period and lower metallicity and ( 2 ) a longer period higher metallicity groups . the physical parameters of both groups , however , are within the canonical ranges of rr lyrae stars .

seven of them are new discoveries . the harmonic amplitude and phase declines with the harmonic order were studied for non - blazhko stars . we discovered significant random period fluctuation for one of the two oversampled target , cm ori . after a successful transformation of the corot band parameters to the johnson the sample can be divided into two subgroups with respect to the metallicity but otherwise the physical parameters are in the canonical range of rr lyrae stars .

the corot satellite supplied the scientific community with a huge data base of variable stars . among them the rr lyrae stars have intensively been discussed in numerous papers in the last few years , but the latest runs have not been checked to find rr lyrae stars up to now . our main goal was to fill this gap and complete the corot rr lyrae sample . we found nine unstudied rr lyrae stars . seven of them are new discoveries . we identified three new blazhko stars . the blazhko effect shows non - strictly repetitive nature for all stars . the frequency spectrum of the blazhko star corot 104948132 contains second overtone frequency with the highest known period ratio . the harmonic amplitude and phase declines with the harmonic order were studied for non - blazhko stars . we found a period dependent but similar shape amplitude decline for all stars . we discovered significant random period fluctuation for one of the two oversampled target , cm ori . after a successful transformation of the corot band parameters to the johnson _ v _ values we estimated the basic physical properties such as mass , luminosity , metallicity . the sample can be divided into two subgroups with respect to the metallicity but otherwise the physical parameters are in the canonical range of rr lyrae stars . [ firstpage ] stars : variables : rr lyrae stars : oscillations stars : interiors techniques : photometric space vehicles

1012.0039

c

studying the physics in the outer regions of clusters is very important to understand how clusters are formed , how the the intracluster gas is heated , as well as to constrain the formation of large - scale structure . because of the very low density in cluster outer regions , the collisional timescales are very long and comparable to the cluster age . electrons and ions passed through the accretion shocks may not have enough time to reach equipartition and the ions may be under - ionized . in a previous paper @xcite , we have studied the non - equipartition effects on clusters using one - dimensional hydrodynamic simulations . in this paper , we systematically studied non - equilibrium ionization effects on clusters and the x - rays signatures using the same set of simulations we have developed @xcite . by using semi - analytic arguments together with numerical simulations , we have shown that the non - equilibrium ionization effect is nearly independent of cluster mass but depends strongly on redshift . in particular , non - equilibrium ionization effects are stronger for low - redshift clusters . therefore , the brighter massive clusters at low - redshifts are good candidates for studying the non - equilibrium ionization effects . we systematically studied non - equilibrium ionization signatures in x - rays for a massive cluster with @xmath184 . we first calculated the ionization fractions for 11 elements heavier than he following the electron temperature and density evolutions of each fluid element . we then calculated the x - ray emissivity of each fluid element and the resulting projected spectra for the cluster . since the electron temperature profiles depend on electron heating efficiency @xmath27 , we have considered three different possibilities which represent a very low heating efficiency ( @xmath29 ) , an intermediate heating efficiency ( @xmath30 ) , and equipartition , @xmath31 . we also considered models which assume equilibrium ionization for comparison . at a radius ( e.g. , 2 mpc ) where the ionization timescale is long , the overall spectra for the nei and cie non - eq models are very similar . this is because of the dominant free - free emission , and both models assume the same electron temperature . however , in the outer regions , e.g , at @xmath185 mpc which is between @xmath5 and @xmath186 , the soft emission in the nei model is dominated by line emission , where the cie non - eq spectrum is still dominated by the continuum free - free emission . by analyzing the surface brightness profiles , we found that soft emission ( 0.31.0 kev ) for the nei model can be enhanced by more than 20% at around 3 mpc , and up to nearly an order of magnitude near the shock radius compared to the cie non - eq model . the soft emission enhancement is mainly due to the line emission from under - ionized ions . the non - equilibrium ionization effects on the medium ( 1.02.0 kev ) and hard ( 2.010.0 kev ) band emissions are smaller . the overall x - ray band ( 0.310.0 kev ) emission is dominated by the soft emission , and the total x - ray emission for the nei model decrease much slower than that of the cie non - eq model . thus , if cluster outer regions are in non - equilibrium ionization , the shock region will be much more luminous compared to the cie non - eq model . by inspecting a number of spectra , we found that the most prominent non - equilibrium ionization signature in line emission is the line ratio of the he - like triplets and the h - like doublets , @xmath136@xmath137@xmath110 . the line ratios for the cie models are higher than 10 for most regions between @xmath187 14 mpc , while the line ratios are smaller than 10 for the nei models . the differences in the line ratios between the nei and cie models increase with radius , and the differences are more than an order of magnitude for radii beyond @xmath188 mpc . these results are insensitive to the degree of non - equipartition or electron heating efficiency @xmath27 . we suggest that the line ratios can be used to distinguish between the nei and cie models . the electron temperature profile can be determined from fits to the continuum spectra of the outer regions of clusters , allowing the cie line ratios to be determined . comparison to the observed ratios should show the effects of non - equilibrium ionization . note that a line ratio of @xmath136@xmath189@xmath190 in the outer region of a massive clusters is a clear signal of nei . we have also studied the detectability of the and lines around cluster accretion shock regions with _ ixo _ , as well as the test for non - equilibrium ionization using the line ratio . for our optimum model , we found that with the xms core array , an exposure time of 220 ksec is need to have a 3.0-@xmath169 detection of the lines and about 180 ksec is need to have @xmath191 counts for a 3.2-@xmath169 detection of the lines . the uncertainties in nxb and gxb will not affect the results significantly . for the xms full array while we assume the spectral resolution to be the same as the outer array throughout the detector , we found that the signal - to - noise ratios for our optimum model are higher for the same exposure time as the xms core array . in particular , only about 130 ( 100 ) ksec is needed to detect the ( ) line . the xms full array is only slightly more subject to nxb and gxb uncertainties due to the poorer spectral resolution . to test the non - equilibrium ionization model without ambiguity requires measurements of both the electron temperature ( or hardness ratio ) and the line ratio so that the measured line ratio can be compared to the cie line ratio inferred by the electron temperature . we have shown that this can be done within @xmath172 mpc of a cluster by the _ ixo _ with sufficient confidence . beyond @xmath170 mpc where the surface brightness may be too low and measuring the electron temperature may be difficult , we have shown that if the line ratio is measured to be as low as @xmath8 at 3-@xmath169 ( @xmath192@xmath137@xmath174 \sim 2/3 $ ] at 1-@xmath169 ) in the outermost regions , this will rule out the cie model at a 3-@xmath169 level since the cie line ratios are always higher than 4 for realistic cluster temperatures . a 3 or 4-@xmath169 measurement of such a low line ratio is sufficient to provide a strong test of the non - equilibrium ionization . if the line ratio is measured to be even lower ( e.g. , @xmath175 ) , only a 2 or 3-@xmath169 will be sufficient to rule out the cie model . on the other hand , if the line ratio is measured to be as high as 4 , a 6-@xmath169 measurement ( @xmath173@xmath137@xmath110 ] = 2/3 at 1-@xmath169 ) will be necessary to rule out the nei low line ratio of @xmath8 at a 3-@xmath169 level . we found that an observation with about 130 ( 220 ) ksec with the xms full ( core ) array is enough to measure the line ratio at 2.3-@xmath169 . for a 3-@xmath169 measurement of the line ratio , about 230 ( 380 ) ksec will be needed for the xms full ( core ) array , and this will provide a strong test for non - equilibrium ionization . in summary , detecting the and lines around the cluster accretion shock regions and testing non - equilibrium ionization in cluster outer regions with _ ixo _ are promising . it is expected that the and lines from whim will also be strong . because of the high spectral resolution of the xms , emissions from different redshifts should be easily separated . only the emission from whim immediately surrounding the target cluster will be potentially confused with the emission from cluster outer regions . to observe the and lines and study nei effects in cluster accretion shock regions , it will be best to avoid observing directions along the filaments where it is believed that denser preheated whims and subclusters are preferentially accreted onto more massive and relaxed galaxy clusters . what do we learn about clusters from the ionization state of the outer gas ? since collisional ionization and recombination rates involve straightforward atomic physics , the processes are not in question and the rates are reasonably well - known . unlike shock electron heating or rates for transport processes like thermal conduction , the basic physics is not uncertain and magnetic fields do not affect the results in a significant way . what we mainly learn about is the pre - shock physical state of materials which are being accreted by the cluster . if most of the whim is ionized beyond , then the effects described in this paper will be greatly reduced . if most of the material currently being accreted by clusters comes in through filaments which have a higher ionization , then nei effects will be diminished significantly . if most of the gas being added to clusters at present comes in through mergers with groups which deposit most of the gas in the inner regions of clusters , the gas will achieve cie quickly . from the theoretical point of view , with the increasing number of observations of galaxy cluster outer regions ( @xmath193 ) and the potential to extend observations out to the shock radius with _ ixo _ in the future , it is necessary to perform more detailed simulations than ours . it is also interesting to extend our work to study the connections between the shocked icm and the more diffuse whim surrounding clusters . three - dimensional simulations will be essential to understand the effects of mergers or filament accretion on the degree of ionizations in different regions of clusters . this will allow us to characterize the variation of non - equilibrium signatures in the clusters ; such calculations are essential to compare observational signatures with our understanding of the cluster physics near the accretion shocks . cosmological simulations have been performed recently to study the nei signatures @xcite . these studies have shown that both non - equipartition and non - equilibrium ionization effects are important in cluster outer regions ; although they focus more on the lower density and lower temperature whim . high resolution simulations were also performed for studying nei effects in clusters , but these are limited to binary mergers with idealized initial conditions and focus on the denser merger shocks @xcite . re - simulating representative clusters and the surrounding whim from cosmological simulations with higher resolutions and including realistic physics ( e.g. , cooling , conduction , turbulent pressure , magnetic pressure , and relativistic support by cosmic rays ) will be necessary to provide realistic model images and spectra . the different observational signatures and connections between the icm and the more diffuse whim can also be addressed self - consistently by these simulations . we thank daniel wang and todd tripp for helpful discussions . support for this work was provided by nasa through _ chandra _ grants go7 - 8129x , go7 - 8081a , go8 - 9083x , go9 - 0135x , and go9 - 0148x , _ xmm - newton _ grants nnx08az34 g , and nnx08aw83 g , and _ suzaku _ grants nnx08az99 g , nnx09ah25 g , and nnx09ah74 g . we thank the referee for helpful comments . smith , r. k. , bautz , m. w. , bookbinder , j. , garcia , m. r. , guainazzi m. , & kilbourne , c. a. 2010 , spie , 7732 , 773246 ( http://ixo.gsfc.nasa.gov/resources/published_papers/docs/ spie_2010/ixo - bkgnd - spie.pdf ) ( equation [ ion_eq : iontime ] ) versus radius @xmath19 scaled to the cluster shock radius @xmath104 for cluster models with total accreted masses of @xmath196 ( dashed line ) , 1.53 ( solid line ) , and 3.06 ( dotted line ) @xmath197 @xmath198 at a redshift of @xmath45 . the shock radii for the three clusters from small to high mass are @xmath199 , and 5.41 mpc , respectively . all three lines lie almost on top of one another . , width=453 ] for versus the scaled radius ( @xmath103 ) for clusters with total accreted masses of @xmath200 ( dashed line ) , 1.53 ( solid line ) , and 3.06 ( dotted line ) @xmath197 @xmath198 at a redshift of @xmath45 . models with @xmath29 ( non - equipartition ) and @xmath31 ( equipartition ) are shown in thick and thin lines , respectively . , width=453 ] for versus the scaled radius ( @xmath103 ) for clusters at different redshifts . the cluster model with a total accreted mass @xmath201 at @xmath45 is used . models with @xmath29 ( non - equipartition ) and @xmath31 ( equipartition ) are shown in thick and thin lines , respectively . , width=453 ] ) for clusters with total accreted masses of @xmath200 ( dashed line ) , 1.53 ( solid line ) , and 3.06 ( dotted line ) @xmath197 @xmath198 at a redshift of @xmath45 . models with @xmath29 ( non - equipartition ) and @xmath31 ( equipartition ) are shown in thick and thin lines , respectively . , width=453 ] ) for clusters at different redshifts . the cluster model with a total accreted mass @xmath201 at @xmath45 is used . models with @xmath29 ( non - equipartition ) and @xmath31 ( equipartition ) are shown in thick and thin lines , respectively . , width=453 ] at @xmath45 are shown at two projected radii ( left : 2 mpc ; right : 3.5 mpc ) . upper panels : the nei model with @xmath140 and non - equipartition of electrons and ions . lower panels : projected rest frame spectra for the cie model with the same @xmath27 and non - equipartition . , width=453 ] ( thick lines ) and the cie non - eq model ( thin lines ) . upper right panel : rest frame projected surface brightness profiles for the nei model with @xmath140 ( thick lines ) and the cie eq model ( thin lines ) . lower left panel : ratios of the surface brightness profiles @xmath126 . lower right panel : ratios of the surface brightness profiles @xmath127 . , width=453 ] . middle panel : projected rest frame spectra for the nei model with @xmath202 . lower panel : projected rest frame spectra for the cie non - eq model with @xmath29 . all spectra are for the @xmath184 at @xmath45 , and are for a projected radius of @xmath121 mpc . the spectra are binned with @xmath203 ev . , width=453 ] @xmath137@xmath110 for the nei models with @xmath29 ( solid ) , 0.5 ( dash - dotted ) , and 1.0 ( dash - dot - dotted ) . line ratios for the cie non - eq ( dashed ) and cie eq ( dotted ) models are also shown . , width=453 ]

we have studied systematically the effects of non - equilibrium ionization for relaxed clusters in thecdm cosmology using one - dimensional hydrodynamic simulations . we found that non - equilibrium ionization effects do not depend on cluster mass but depend strongly on redshift which can be understood by self - similar scaling arguments . soft emission ( 0.31.0 kev ) is enhanced significantly by under - ionization , and the enhancement can be nearly an order of magnitude near the shock radius . the most prominent non - equilibrium ionization signature we found is the and line ratio . the ratios for non - equilibrium ionization and collisional ionization equilibrium models are different by more than an order of magnitude at radii beyond half of the shock radius . we have also calculated the detectability of the and lines with the future _ international x - ray observatory _ ( _ ixo _ ) . depending on the line ratio measured , we conclude that an exposure of ksec on a moderate - redshift , massive regular cluster with the x - ray microcalorimeter spectrometer ( xms ) on the _ ixo _ will be sufficient to provide a strong test for the non - equilibrium ionization model .

the densities in the outer regions of clusters of galaxies are very low , and the collisional timescales are very long . as a result , heavy elements will be under - ionized after they have passed through the accretion shock . we have studied systematically the effects of non - equilibrium ionization for relaxed clusters in thecdm cosmology using one - dimensional hydrodynamic simulations . we found that non - equilibrium ionization effects do not depend on cluster mass but depend strongly on redshift which can be understood by self - similar scaling arguments . the effects are stronger for clusters at lower redshifts . we present x - ray signatures such as surface brightness profiles and emission lines in detail for a massive cluster at low redshift . in general , soft emission ( 0.31.0 kev ) is enhanced significantly by under - ionization , and the enhancement can be nearly an order of magnitude near the shock radius . the most prominent non - equilibrium ionization signature we found is the and line ratio . the ratios for non - equilibrium ionization and collisional ionization equilibrium models are different by more than an order of magnitude at radii beyond half of the shock radius . these non - equilibrium ionization signatures are equally strong for models with different non - adiabatic shock electron heating efficiencies . we have also calculated the detectability of the and lines with the future _ international x - ray observatory _ ( _ ixo _ ) . depending on the line ratio measured , we conclude that an exposure of ksec on a moderate - redshift , massive regular cluster with the x - ray microcalorimeter spectrometer ( xms ) on the _ ixo _ will be sufficient to provide a strong test for the non - equilibrium ionization model .

0903.0505

i

one of the main sources of gravitational radiation for the future esa - nasa gravitational wave observatory , the laser interferometer space antenna ( lisa ) @xcite , is the capture and inspiral of a stellar - mass compact object ( sco ) , with masses in the range @xmath0 , into a massive black hole ( mbh ) in a galactic centre , with masses in the range @xmath1 . these systems are usually known as extreme - mass - ratio inspirals ( emris ) since the mass ratios involved are in the range @xmath2 . during the inspiral phase the system is driven by the emission of gravitational radiation , and hence there is loss of energy and angular momentum that makes the orbit shrink until the sco plunges into the mbh . it is expected that lisa will be able to detect @xmath3 emri@xmath4 @xcite up to distances within @xmath5 @xcite ( see also @xcite for more details on the astrophysics of emris ) . recently , it has been suggested @xcite that inspirals of scos into intermediate - mass black holes , with masses in the range @xmath6 and presumably located in globular clusters , could be detected by future second - generation ground interferometers like advanced ligo @xcite and advanced virgo @xcite . the mass ratios are in the range @xmath7 , and in consequence they are called intermediate - mass - ratio inspirals ( imris ) . it is expected that techniques to describe emris may also been used for imris , at least to a certain degree of precision . during the long inspiral , an emri will spend many cycles inside the lisa band , of the order of @xmath8 during the last year before plunge into the mbh @xcite . however , the gravitational - wave signals from emris will be buried in the lisa data stream with the instrumental noise and the gravitational wave foreground ( produced by compact binaries in the lisa band ) . to extract these signals and the relevant physical parameters that characterize them , we need to have a very precise _ a priori _ theoretical knowledge of the gravitational waveforms . this means to describe the inspiral of the sco taking into account the gravitational backreaction , that is , the influence of the sco gravitational field on its own motion . this is an interesting but difficult theoretical problem , and different methods have been developed to solve it ( see @xcite ) . while techniques for constructing templates good enough for detection are getting ready , mainly based on the use of the adiabatic approximation @xcite , methods to build templates good enough for extraction of physical information are not yet fully developed . the main difficulty being that one requires a more precise treatment of the self - gravity of the sco and its impact on the gravitational waveform . in relation to this fact , there is currently a significant activity on the study of the accuracy of the different types of adiabatic approximations that have been introduced @xcite . on the other hand , the _ self - force _ approach to the equations of motion @xcite ( see also @xcite ) is an step forward to a precise estimation of the radiation - reaction effects and in consequence , towards the construction of accurate waveform templates . in this approach the backreaction effects on the sco are described as the action of a local force , the _ self - force _ , which can be computed in terms of the perturbations generated by the sco with respect the mbh background spacetime . in practice , to compute the self - force one needs to regularize the perturbations , similarly as it happens in electromagnetism @xcite . to that end , a _ mode sum _ regularization scheme has been designed ( in the gravitational case it has been formulated in the lorenz gauge ) @xcite . it tells us how to subtract , mode by mode ( for a schwarzschild mbh the modes correspond to a harmonic decomposition of the perturbations ) , the singular part of the perturbations that does not contribute to the self - force . therefore , what we need is a method of computing the full retarded solution of the perturbative equations for applying the mode - sum regularization scheme and obtain in this way the self - force . the perturbative field equations are a set of ten linear partial differential equations ( pdes ) for the metric perturbations @xmath9 ( @xmath10 at linear order , where @xmath11 is the spacetime metric and @xmath12 is the background metric describing the mbh ) , which only in certain gauges ( e.g. , the regge - wheeler gauge @xcite ) can be decoupled . in any case , to solve them completely we need to resort to numerical methods . following the initial studies of black hole quasinormal modes , frequency methods were used successfully @xcite , and it was found they provide accurate results for emris with moderate eccentricities . however , the frequency domain approach has more difficulties with highly eccentric orbits , which are of interest for lisa , since one has to sum over a large number of modes to obtain a good accuracy , and convergence may be an issue . this has opened the door to time - domain methods , which are not affected much by the eccentricity of the orbit and may be more efficient for the case of high - eccentricity emris . in the last years there has been an intense activity on this front , both for a nonrotating background @xcite , and for a rotating background @xcite . the main drawbacks of time - domain methods have mainly two origins : ( i ) the fact that one has to resolve very different physical scales ( both spatial and temporal ) present in the problem due to the extreme mass ratios involved ( see , e.g. @xcite ) . that is , using a standard numerical discretization of the problem we are led to resolve the typical gravitational wavelengths ( comparable to the size of the mbh ) and , at the same time , scales in the vicinity of the sco , which are crucial for evaluating the self - force . this translates in a demanding requirement of computational resources . ( ii ) the fact that the sco is described as a point - like object . this introduces dirac delta distributions in the sco energy - momentum distribution that lead to loss of differentiability in the solution of the perturbative field equations . this fact can degrade the convergence properties of the numerical algorithms used . moreover , such a localized distribution of matter can also introduce spurious high - frequency modes that contaminate the numerical solution and , in consequence , degrade its accuracy . recently , there have been different proposals to improve the performance of time domain methods . barack and goldbourn @xcite have introduced a new technique to compute the scalar field generated by a pointlike scalar charge orbiting a black hole . this technique consists in subtracting from each azimuthal mode ( in the kerr geometry the field equations are not fully separable in the time domain and one has to tackle them in 2 + 1 dimensions ) of the retarded field a piece that describes the singular behavior near the particle . this is done through a careful analytical study of the scalar field near the particle , using a _ puncture _ scheme which resembles the puncture model used for simulations in numerical relativity @xcite . this technique has been extended to the electromagnetic and gravitational cases by barack , goldbourn and sago @xcite . on the other hand , vega and detweiler @xcite have introduced another new method for regularizing the solution of the field equations . their approach , tested on a simplified model of a charged particle orbiting a nonrotating black hole , regularizes the retarded field itself by identifying and removing first , in an analytical way , the singular part of the retarded field . this alternative approach to the mode - sum regularization scheme yields a finite and differentiable remainder from which the self - force can be computed . this remainder is the solution to a field equation with a nonsingular source , which avoid the problem ( ii ) above . finally , lousto and nakano @xcite have also introduced an analytical technique to remove the particle singular behaviour . their method is global and also produces a well behaved source for the field equations . whereas these new techniques help in dealing with problem ( ii ) above , they do not completely solve the problem ( i ) since the regular source terms that these new schemes produce still have associated with them a length scale ( or , from the numerical point of view , there are still special spatial resolution requirements associated with those source terms ) . in this paper , we introduce a new time - domain scheme towards the computation of the self - force which , for the case of a nonrotating black hole , eliminates completely any length scale associated with the sco . this is done by using multiple subdomains and locating the particle in the interface between two of them ( this has similarities with what was done in @xcite using the finite element method , where in one of the numerical schemes proposed the particle was located between two elements ) . in this way , the dirac delta distributions do not appear in our equations and the presence of the sco enters through the boundary conditions that communicate the solutions at the different subdomains . as a consequence , we are solving wave - type equations with smooth solutions , which avoid the problems described in ( ii ) ( preliminary results have been reported in @xcite ) . regarding ( i ) , we just need to provide the numerical resolution to describe the field near the particle , but not the particle itself , which makes the computation much more efficient . our numerical algorithms are based on the pseudospectral collocation ( psc ) method ( see , e.g. @xcite ) , which has been applied to numerical relativity @xcite , and recently it has also been used in @xcite for one - dimensional head - on collisions of black - holes . and very recently , in @xcite , a discontinuous galerkin method has been introduced and some gravitational waveforms for extreme - mass - ratio binaries are computed . this work uses similar techniques to the ones introduced in @xcite and the ones that we present here . in this paper , we describe a set of techniques and methods to use the psc for the computation of the self - force on a charged scalar particle in circular orbits around a non - rotating black hole . we also show some results of the numerical implementation . the organization of the paper is as follows : in section [ modeldescription ] we introduce the basics of the model of a charged scalar particle orbiting a nonrotating black hole , including the basic formulae for the computation of the self - force via the mode - sum regularization scheme . in section [ timedomainframework ] we introduce all the ingredients of a new time - domain numerical framework for the computation of the self - force in such scenario , from the mathematical foundations to the practical implementation of the computations . in section [ results ] we show the performance of a numerical code we have designed to implement the new scheme , and results of the computation of the self - force , in particular for the innermost stable circular orbit . in section [ discussion ] we draw conclusions from the results shown and discuss possible future avenues in the development of these techniques for the simulations of emris in relevant physical situations . throughout this paper we use the metric signature @xmath13 and geometric units in which @xmath14 .

the description of the inspiral of a stellar - mass compact object into a massive black hole sitting at a galactic centre is a problem of major relevance for the future space - based gravitational - wave observatory lisa ( laser interferometer space antenna ) , as the signals from these systems will be buried in the data stream and accurate gravitational - wave templates will be needed to extract them . the main difficulty in describing these systems lies in the estimation of the gravitational effects of the stellar - mass compact object on his own trajectory around the massive black hole , which can be modeled as the action of a local force , the _ self - force_. in this paper , we present a new time - domain numerical method for the computation of the self - force in a simplified model consisting of a charged scalar particle orbiting a nonrotating black hole . we eliminate completely the presence of a small length scale associated with the need of resolving the particle . this technique also avoids the problems associated with the impact of a low differentiability of the solution in the accuracy of the numerical computations . we show how this special framework can provide very efficient and accurate computations in the time domain , which makes the technique amenable for the intensive computations required in the astrophysically - relevant scenarios for lisa .

the description of the inspiral of a stellar - mass compact object into a massive black hole sitting at a galactic centre is a problem of major relevance for the future space - based gravitational - wave observatory lisa ( laser interferometer space antenna ) , as the signals from these systems will be buried in the data stream and accurate gravitational - wave templates will be needed to extract them . the main difficulty in describing these systems lies in the estimation of the gravitational effects of the stellar - mass compact object on his own trajectory around the massive black hole , which can be modeled as the action of a local force , the _ self - force_. in this paper , we present a new time - domain numerical method for the computation of the self - force in a simplified model consisting of a charged scalar particle orbiting a nonrotating black hole . we use a multi - domain framework in such a way that the particle is located at the interface between two domains so that the presence of the particle and its physical effects appear only through appropriate boundary conditions . in this way we eliminate completely the presence of a small length scale associated with the need of resolving the particle . this technique also avoids the problems associated with the impact of a low differentiability of the solution in the accuracy of the numerical computations . the spatial discretization of the field equations is done by using the pseudospectral collocation method and the time evolution , based on the method of lines , uses a runge - kutta solver . we show how this special framework can provide very efficient and accurate computations in the time domain , which makes the technique amenable for the intensive computations required in the astrophysically - relevant scenarios for lisa .

0706.2760

i

the understanding of quantum tunneling in mesoscopic systems has made huge progress in the past decades , to the point that nanofabricated devices are now being exploited as coherently tunneling two - level systems ( tlss ) for quantum information purposes.@xcite conceptually , a first breakthrough was the proper description of the coupling of an effective tls to an environment described by an oscillator bath.@xcite whether the system is an intrinsic tls ( e.g. a spin @xmath8 ) or the low - energy truncation of a more complicated entity ( e.g. the flux state of a squid ) , one can generally apply the oscillator bath theory when the environment is described by delocalized modes ( conduction electrons , phonons , photons , etc . ) and the couplings of the tls to each oscillator are weak . in many solid - states systems , however , it can be necessary to account for localized environmental excitations whose couplings to the tls are not weak . this type of environment is called `` spin bath '' @xcite and can not be mapped onto an oscillator bath . importantly , a spin bath environment can cause decoherence even at @xmath9 and is therefore of great relevance for quantum systems that are designed to show coherent dynamics , like qubits for quantum computation . the prototypical realization of a tunneling tls coupled to a spin bath is the giant spin of a single - molecule magnet ( smm).@xcite these molecular systems consist of a core of strongly interacting transition metal ions , surrounded by organic ligands . at sufficiently low temperatures the core of the molecule behaves effectively like a single large spin @xmath10 . when uniaxial magnetic anisotropy is present , the reversal of the spin direction requires - classically - a large energy , so that the spin direction can be frozen at very low @xmath3 . however , in the presence of a transverse magnetic field or a biaxial anisotropy , the spin direction can be reversed by tunneling through the anisotropy barrier.@xcite the electronic spins that form the smm are magnetically coupled to the nuclear spins that either belong to the magnetic ions themselves ( @xmath2mn , @xmath11fe , ) or to the surrounding ligand molecules ( @xmath6h , @xmath12c , ) . as a consequence of these couplings , the observation of macroscopic quantum tunneling of magnetization in smms @xcite can not be understood without invoking the dynamics of the nuclear spins themselves.@xcite the theoretical predictions for the role of nuclear spins in the magnetization tunneling of smms @xcite have been verified by a series of experiments on the fe@xmath13 compound.@xcite most remarkably , this material allows to change the isotopic composition of the sample , both by strengthening ( @xmath11fe @xmath14 @xmath15fe substitution ) and weakening ( @xmath6h @xmath14 @xmath7h substitution ) the hyperfine couplings , while leaving the electronic structure of the smms unaffected . as predicted , the rate of quantum relaxation of the magnetization was found to be directly related to the nuclear isotopic composition of the sample.@xcite more recently , the effect of isotopic substitution has been observed in the low-@xmath3 electronic specific heat of fe@xmath13 ( ref . ) and in the dephasing time of coherent electron spin precession in cr@xmath16ni.@xcite nuclear spin effects were also invoked in the interpretation of @xmath17sr data in isotropic molecules,@xcite and in an alternative description of the short - term magnetic relaxation in smms.@xcite all these works have analyzed the effect of the nuclei on the dynamics of the `` central spin '' , but a crucial aspect of the theory of the spin bath is that the tunneling of the central system has repercussion on the dynamics of the bath itself , so that the latter can not be simply regarded as an independent source of `` noise '' . until now , the experiments to probe the electron spin dynamics have not been able to test this delicate aspect of the theory . to understand the details of the nuclear spin fluctuations , one should then look _ directly _ at the nuclear spins by means of low - temperature nmr experiments , performed under different regimes for the quantum dynamics of the electron spin . these experiments have been carried out by several groups,@xcite but an accurate analysis of their implications for the more general theory of nuclear - spin mediated quantum tunneling is still lacking . in this work , we present a comprehensive set of experiments on the dynamics of @xmath2mn nuclear spins in the mn@xmath0-ac smm , and we use our results for a critical assessment of the theory of the spin bath . our data provide definitive proof that the nuclear spin dynamics is strongly correlated with that of the central spin , that is , it can not be treated as an independent source of noise . indeed , we find that the nuclear spin fluctuations change dramatically when the tunneling dynamics of the central spin is modified , e.g. by an external magnetic field . in addition , we shall demonstrate that the nuclear spins remain in thermal equilibrium with the phonon bath down to the lowest temperatures ( @xmath1 mk ) accessible to our experiment , where the thermal fluctuations of the electron spins are entirely frozen out . this implies that there is a mechanism for exchanging energy between nuclei , electrons and phonons _ through the nuclear - spin mediated quantum tunneling of the central spin_. this is the point where the current theoretical description of macroscopic quantum tunneling in the presence of a spin bath needs to be improved . as regards the `` macroscopicness '' of the quantum effects observed in smms , we adopt leggett s view that the most stringent criterion is the `` disconnectivity'',@xcite @xmath18 , which roughly speaking is the number of particles that behave differently in the two branches of a quantum superposition . for instance , while a cooper pair box@xcite is a relatively large , lithographically fabricated device , the quantum superposition of its charge states involves in fact only one cooper pair , i.e. two electrons , and its disconnectivity is only @xmath19 . the matter - wave interference in fullerene molecules,@xcite for instance , is a much more `` quantum macroscopic '' phenomenon , since it means that 60 @xmath20 ( 12 nucleons + 6 electrons ) = 1080 particles are superimposed between different paths through a diffraction grating . for the spin tunneling in mn@xmath0-ac smms discussed here , we have 44 electron spins simultaneously tunneling between opposite directions , which places this system logarithmically halfway between single particles and fullerenes on a macroscopicness scale . the paper is organized as follows . section [ experimental ] describes the physical properties of the sample used in the experiments , the design and performance of our measurement apparatus , and the methods of data analysis . section [ nsd ] presents the experimental results on the nuclear spin dynamics , starting with the nmr spectra , the longitudinal and transverse relaxation rates in zero field , and their dependence on a longitudinal external field . we also study the nuclear relaxation in different mn sites within the cluster , and the effect of isotopic substitution in the ligand molecules . in section [ spint ] we discuss the thermal equilibrium between nuclear spins and phonon bath , the experimental challenges in optimizing it , and the indirect observation of magnetic avalanches during field sweeps . in section [ theory ] we give an introductory review of the theory of the spin bath , and apply its predictions to the calculation of the nuclear relaxation rate as observed in our experiments . together with the information on the thermal equilibrium of the nuclear spins , this will allow us to draw clear - cut conclusions on the status of our current theoretical understanding of quantum tunneling of magnetization . we conclude with a summary and implications of the results in section [ conclusions ] .

most of the attention is usually given to the dynamics of the `` central spin '' ( i.e. , the qubit ) , while little is known about the spin bath itself . here we present a detailed study of the dynamics of the nuclear spin bath in the mn-ac single - molecule magnet , probed by nmr experiments down to very low temperatures ( mk ) . we find that the longitudinal relaxation rate of themn nuclei in mn-ac becomes roughly-independent below k , and can be strongly suppressed with a longitudinal magnetic field . we also show that the isotopic substitution ofh byh leads to a slower nuclear longitudinal relaxation , consistent with the decreased tunneling probability of the molecular spin . finally , we demonstrate that , even at the lowest temperatures - where only-independent quantum tunneling fluctuations are present - the nuclear spins remain in thermal equilibrium with the lattice phonons , and we investigate the timescale for their thermal equilibration . after a review of the theory of macroscopic spin tunneling in the presence of a spin bath , we argue that most of our experimental results are consistent with that theory , but the thermalization of the nuclear spins is not .

the description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest , and is relevant for many solid - state qubit designs . most of the attention is usually given to the dynamics of the `` central spin '' ( i.e. , the qubit ) , while little is known about the spin bath itself . here we present a detailed study of the dynamics of the nuclear spin bath in the mn-ac single - molecule magnet , probed by nmr experiments down to very low temperatures ( mk ) . the results are critically analyzed in the framework of the prokofev - stamp theory of nuclear - spin mediated quantum tunneling . we find that the longitudinal relaxation rate of themn nuclei in mn-ac becomes roughly-independent below k , and can be strongly suppressed with a longitudinal magnetic field . this is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin , and we attribute the tunneling fluctuations to the minority of fast - relaxing molecules present in the sample . the transverse nuclear relaxation is also-independent for k , and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules . this intercluster nuclear spin diffusion mechanism is an essential ingredient for the global relaxation of the nuclear spin bath . we also show that the isotopic substitution ofh byh leads to a slower nuclear longitudinal relaxation , consistent with the decreased tunneling probability of the molecular spin . finally , we demonstrate that , even at the lowest temperatures - where only-independent quantum tunneling fluctuations are present - the nuclear spins remain in thermal equilibrium with the lattice phonons , and we investigate the timescale for their thermal equilibration . after a review of the theory of macroscopic spin tunneling in the presence of a spin bath , we argue that most of our experimental results are consistent with that theory , but the thermalization of the nuclear spins is not . this calls for an extension of the spin bath theory to include the effect of spin - phonon couplings in the nuclear - spin mediated tunneling process .

0706.2760

c

the purpose of the research presented here is to illustrate and analyze a prototypical example of quantum tunneling of a macroscopic variable ( the giant spin of single - molecule magnet ) in the presence of a spin bath environment . instead of looking at the macroscopic variable itself and deducing the effect of the environment on its dynamics , as is most often done , we have directly observed the behavior of the spin bath by means of low - t nmr experiments . we have provided compelling evidence that the longitudinal nuclear spin relaxation in the @xmath2mn nuclei of mn@xmath0-ac is driven by electron - spin quantum tunneling fluctuations . the nuclear lsr rate , @xmath76 , indeed contains all the features that are expected to be associated with tunneling of the molecular spin : i ) a @xmath3-independent plateau of the lsr rate for @xmath216 k ; ii ) a strong dependence of @xmath76 on a longitudinal magnetic field , that destroys the resonance condition for electron spin tunneling ; iii ) the slowing down of the nuclear lsr upon isotropic substitution of @xmath6h by @xmath7h in the ligands , by an amount identical to the slowing down of the quantum relaxation of the magnetization observed in similar systems . because of the short timescale of the observed lsr , we argued that the tunneling fluctuations must take place in a minority of fast - relaxing molecules , which are indeed known to be present in mn@xmath0-ac . for these fluctuations to relax the nuclear magnetization in the entire sample , an additional mechanism is required which equilibrates the nuclear spin polarization across neighboring molecules , i.e. intercluster nuclear spin diffusion . our data on the transverse nuclear spin relaxation show that the intercluster spin diffusion is indeed present and effective . all the above observations confirm and support the picture of nuclear - driven quantum tunneling of magnetization as originally formulated by prokofev and stamp . however , a crucial outcome of our experiments is the demonstration that the nuclear spins are in thermal equilibrium with the lattice phonons down to the lowest temperatures , where only quantum tunneling fluctuations of the electron spins are still present . this observation can not be explained within the present theory of the spin bath . the implications of our results are potentially very profound , particularly because of the growing interest toward a coherent manipulation of spins for quantum information processing . the spin - bath environment , describing localized two - level systems , has been repeatedly identified as the most important source of decoherence in solid - state qubits . this includes superconducting systems,@xcite quantum dots,@xcite nv centers in diamond@xcite and , of course , molecular magnets.@xcite we have investigated here the incoherent tunneling regime , but the theoretical formalism to describe the coupling between central spin and spin bath is identical in the case of coherent spin dynamics . therefore , the main finding of our work - that the role of phonons in the nuclear - spin mediated tunneling is currently lacking a proper description - suggests that also the contribution of the nuclear spin bath to the decoherence rate of realistic spin qubits may need to be revisited . we are indebted to o. n. bakharev , h. b. brom , d. bono , n. j. zelders and g. frossati for experimental help and extensive discussions . continuous and illuminating theoretical support from p. c. e. stamp and i. s. tupitsyn is gratefully acknowledged , and so are discussions with w. wernsdorfer , s. hill , n. v. prokofev , b. v. fine , m. evangelisti , a. j. leggett , y. imry , m. schechter and a. l. burin . we also thank k. awaga and k. takeda for useful correspondence about their results in ref . . the mn@xmath0-ac samples were supplied by r. sessoli and a. caneschi ( crystallites , natural and deuterated ) and a. millan ( single crystal ) . + this work is part of the research program of the `` stichting fom '' and is partially funded by the ec - rtn `` quemolna '' and ec - network of excellence `` magmanet '' ( no.515767 - 2 ) .

the description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest , and is relevant for many solid - state qubit designs . this is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin , and we attribute the tunneling fluctuations to the minority of fast - relaxing molecules present in the sample . this calls for an extension of the spin bath theory to include the effect of spin - phonon couplings in the nuclear - spin mediated tunneling process .

the description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest , and is relevant for many solid - state qubit designs . most of the attention is usually given to the dynamics of the `` central spin '' ( i.e. , the qubit ) , while little is known about the spin bath itself . here we present a detailed study of the dynamics of the nuclear spin bath in the mn-ac single - molecule magnet , probed by nmr experiments down to very low temperatures ( mk ) . the results are critically analyzed in the framework of the prokofev - stamp theory of nuclear - spin mediated quantum tunneling . we find that the longitudinal relaxation rate of themn nuclei in mn-ac becomes roughly-independent below k , and can be strongly suppressed with a longitudinal magnetic field . this is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin , and we attribute the tunneling fluctuations to the minority of fast - relaxing molecules present in the sample . the transverse nuclear relaxation is also-independent for k , and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules . this intercluster nuclear spin diffusion mechanism is an essential ingredient for the global relaxation of the nuclear spin bath . we also show that the isotopic substitution ofh byh leads to a slower nuclear longitudinal relaxation , consistent with the decreased tunneling probability of the molecular spin . finally , we demonstrate that , even at the lowest temperatures - where only-independent quantum tunneling fluctuations are present - the nuclear spins remain in thermal equilibrium with the lattice phonons , and we investigate the timescale for their thermal equilibration . after a review of the theory of macroscopic spin tunneling in the presence of a spin bath , we argue that most of our experimental results are consistent with that theory , but the thermalization of the nuclear spins is not . this calls for an extension of the spin bath theory to include the effect of spin - phonon couplings in the nuclear - spin mediated tunneling process .

1004.4207

i

the second science run of the zeplin iii project will feature two main upgrades : lower background photomultiplier tubes and the use of an active veto . here , the design of the veto has been presented , together with details of the radiological content and performance of the components to be used . detailed geant4 monte carlo simulations have been used to aid in the characterisation of the veto , and to estimate its overall performance . in addition to providing valuable diagnostic information , it is expected that the veto will be able to reject over 65% of neutrons , and over 15% of @xmath1-rays from background radioactivities , whilst contributing negligibly to the zeplin iii acceptance region background , expected to be @xmath00.4 events per year . the veto will reduce this background to less than @xmath00.14 events per year . this is a significant factor in the event of a non - zero observation . the veto has been fully assembled and systems integrated , and will be installed around zeplin iii shortly for the commencement of the second science run as this instrument probes yet greater sensitivity . the uk groups acknowledge the support of the science & technology facilities council ( stfc ) for the zeplin iii project and for maintenance and operation of the underground palmer laboratory which is hosted by cleveland potash ltd ( cpl ) at boulby mine , near whitby on the north - east coast of england . the project would not be possible without the co - operation of the management and staff of cpl . we also acknowledge support from a joint international project award , held at itep and icl , from the russian foundation of basic research ( 08 - 02 - 91851 ko a ) and the royal society . lip coimbra acknowledges financial support from fundao para a cincia e tecnologia ( fct ) through the project - grants cern / fp/83501/2008 and cern / fp/109320/2009 , as well as the postdoctoral grants sfrh / bpd/27054/2006 and sfrh / bpd/47320/2008 . this work was supported in part by sc rosatom ; by russian grant ss-1329.2008.2 and by the russian ministry of education and science contract 02.740.11.0239 . the university of edinburgh is a charitable body , registered in scotland , with the registration number sc005336 . _ , sources4c : a code for calculating ( @xmath20,n ) spontaneous fission and delayed neutron sources and spectra , american nuclei society / radiation protection and shielding division , 2002 .

iii from.4 to.14 events per year in the wimp acceptance region , a significant factor in the event of a non - zero observation . furthermore , in addition to providing valuable diagnostic capabilities , the veto is capable of tagging over 15% for-ray rejection , all whilst contributing no significant additional background . in conjunction with the replacement of the internal zeplin

the design , optimisation and construction of an anti - coincidence veto detector to complement the zeplin iii direct dark matter search instrument is described . one tonne of plastic scintillator is arranged into 52 bars individually read out by photomultipliers and coupled to a gadolinium - loaded passive polypropylene shield . particular attention has been paid to radiological content . the overall aim has been to achieve a veto detector of low threshold and high efficiency without the creation of additional background in zeplin iii , all at a reasonable cost . extensive experimental measurements of the components have been made , including radioactivity levels and performance characteristics . these have been used to inform a complete end - to - end monte carlo simulation that has then been used to calculate the expected performance of the new instrument , both operating alone and as an anti - coincidence detector for zeplin iii . the veto device will be capable of rejecting over 65% of coincident nuclear recoil events from neutron background in the energy range of interest in zeplin iii . this will reduce the background in zeplin iii from.4 to.14 events per year in the wimp acceptance region , a significant factor in the event of a non - zero observation . furthermore , in addition to providing valuable diagnostic capabilities , the veto is capable of tagging over 15% for-ray rejection , all whilst contributing no significant additional background . in conjunction with the replacement of the internal zeplin iii photomultiplier array , the new veto is expected to improve significantly the sensitivity of the zeplin iii instrument to dark matter , allowing spin independent wimp - nucleon cross sections below 10 pb to be probed .

1512.01264

i

the composition of the short - duration , hard - spectrum gamma - ray burst ( grb ) population is not yet fully understood . it is believed that most of the bursts are generated in compact binary mergers @xcite and while the handful of optical counterparts and host galaxies discovered to date does not contradict this view , it is also thought that the population probably contains up to 8% extragalactic giant magnetar flares as well @xcite . for the majority of the short - duration grb population , however , there is simply not enough evidence to determine their origin unambiguously . hawking radiation from primordial black holes ( hereafter pbh ) was one of the very first explanations proposed for cosmic gamma - ray bursts @xcite , and it continues to be proposed today @xcite . the pbh lifetime and burst duration depend on its mass , so pbhs bursting today have similar masses and durations , and release similar energies , making them in essence ` standard candles ' . the typical pbh gamma - ray burst is not expected to be accompanied by detectable intrinsically - generated extended emission or have an afterglow , although accompanying bursts at other wavelengths or afterglows may arise if , for example , the pbh is embedded in a high density magnetic field or plasma @xcite . in the standard emission scenario , so - called because it uses the standard model of particle physics @xcite , the pbh gamma - ray burst is strongest in the final second of the burst lifetime , has a hard energy spectrum , and should be detectable in the vicinity of the earth . for a typical interplanetary network detector sensitive to bursts of fluence 10@xmath3 erg @xmath4 and above , pbh events could in principle be detected out to a distance of a few parsecs , depending on the emission model . pbhs evaporating today do not have enough luminosity to be detected at cosmological distances even by the most sensitive current instruments , so searching for them locally is a logical step . when observed by a single detector , the properties of a pbh burst might not appear to be significantly different from those of other short bursts ; instruments with localization or imaging capabilities would obtain their arrival directions as they would for an infinitely distant source . indeed many attempts to find evidence for the existence of pbh bursts have to date been based mainly on the spatial distribution and time histories of a subset of short bursts @xcite . other search methods have employed atmospheric cherenkov detectors @xcite , air shower detectors @xcite , radio pulse detection @xcite , spark chamber detection @xcite , and grb femtolensing @xcite . table [ comparison ] gives a comparison of these various methods . to widely spaced interplanetary network ( ipn ) detectors , however , a local pbh burst could look significantly different when compared with bursts from distant sources , due to the curvature of the received wavefront . in this paper , we use this fact to explore the possibility that some short bursts may originate in the solar neighborhood , and estimate lower limits to the pbh burst evaporation rate assuming these bursts are real pbh bursts . this paper is organized as follows . in section [ blackhole ] we derive the fluence expected in the detector from a pbh burst using the standard emission model and , as a maximal alternative , the hagedorn emission model . in section [ methodology ] we explain how we localized the detected bursts in 3d relaxing the assumption that they are at infinite distances . the detailed discussion of the methodology is given in appendix a. our data selection criteria are described in section [ data_selection ] . our results and pbh burst rate limit calculation are given in section [ results ] . in section [ discussion ] , we discuss implications and limitations of our results .

the detection of a gamma - ray burst ( grb ) in the solar neighborhood would have very important implications for grb phenomenology . the leading theories for cosmological grbs would not be able to explain such events . the final bursts of evaporating primordial black holes ( pbhs ) , however , would be a natural explanation for local grbs .

the detection of a gamma - ray burst ( grb ) in the solar neighborhood would have very important implications for grb phenomenology . the leading theories for cosmological grbs would not be able to explain such events . the final bursts of evaporating primordial black holes ( pbhs ) , however , would be a natural explanation for local grbs . we present a novel technique that can constrain the distance to gamma - ray bursts using detections from widely separated , non - imaging spacecraft . this method can determine the actual distance to the burst if it is local . we applied this method to constrain distances to a sample of 36 short duration grbs detected by the interplanetary network ( ipn ) that show observational properties that are expected from pbh evaporations . these bursts have minimum possible distances in the 10 cm ( 710 au ) range , consistent with the expected pbh energetics and with a possible origin in the solar neighborhood , although none of the bursts can be unambiguously demonstrated to be local . assuming these bursts are real pbh events , we estimate lower limits on the pbh burst evaporation rate in the solar neighborhood .

1512.01264

r

according the methodology described in section [ methodology ] and appendix a , we have calculated the minimum possible distances to the sample of 36 bursts selected in section [ data_selection ] . this burst sample is shown in table [ distances ] and the 12 columns give : 1 . the date of the burst , in ` yymmdd ` format , with suffix a or b where appropriate , 2 . the universal time of the burst at earth , in seconds of day , 3 . the spacecraft which were used for the triangulation ; a complete list of the spacecraft which detected the burst may be found on the ipn website ( ` http://ssl.berkeley.edu/ipn3/index.html ` ) , 4 . the burst duration , in seconds , 5 . the fluence of the burst in erg @xmath4 , 6 . the energy range over which the duration and fluence were measured , in kev , 7 . the lower limit to the burst distance , obtained by triangulation , in cm , 8 . the distance to which this burst could have been detected if it were a pbh burst of energy 10@xmath25 erg , assuming that all the energy went into the measured fluence ( this is essentially the maximum possible detectable distance ) , 9 . the maximum detectable distance assuming the sem model ( equation [ eq : semdmax ] ) in terms of the undetermined parameter @xmath26 , 10 . the maximum detectable distance assuming the hm model ( equation [ eq : hdmax ] ) in terms of the undetermined parameter @xmath27 , 11 . whether or not counterpart searches took place and if so , their references , 12 . references to the duration , peak flux , and/or fluence measurements , and/or to the localization . the shortest burst in table [ distances ] has a duration of 60 ms . due to the relatively coarse time resolutions of interplanetary detectors , bursts with shorter durations must have greater intensities to be detected , effectively setting a higher detection threshold for very short events . the weakest event has a fluence of @xmath28 . the bursts in table [ distances ] could not have come from distances less than the distance lower limits in column 7 ; however , all of them have time delays which are also consistent with infinite distances . figure [ fig : pbh_min_dist_histo ] shows a histogram of these minimum distances . the detector - dependent distance upper limits in column 8 are calculated assuming the extreme case that these events are caused by @xmath29 erg hm - type bursts from primordial black holes of mass @xmath30 g and that all of the emitted energy spectrum is contained within the detector measurement limits . table [ localizations ] gives the coordinates of the centers and corners of the error boxes for the events in table [ distances ] , assuming that the sources are at infinity . if in fact the sources are local , the arrival directions are distance - dependent , and different from the ones in table [ localizations ] . these coordinates represent the intersections of annuli , and in some cases the curvature of the annuli would make it inaccurate to construct an error box by connecting the coordinates with straight - line segments . all previous direct pbh burst searches resulted in null detections @xcite . in this case , one can derive an upper limit on the local pbh burst rate density , that is , an upper limit on the number of pbh bursts per unit volume per unit time in the local solar neighborhood . however , in our case , we have pbh burst candidates with short duration , no known afterglow detection and minimum distances that are sub - light - years . since we have pbh candidates , we should be able to derive an actual measurement of the pbh burst rate density under the assumption that the candidates are actual pbh bursts . thus , the actual pbh burst rate density is @xmath31 where @xmath32 is the number of pbh bursts , @xmath33 is the effective pbh detectable volume and @xmath34 is the observed duration . the selection efficiency of the ipn is @xmath35 . if all the candidates identified in section [ data_selection ] are real pbh bursts , then we have 36 pbh bursts , i.e. , @xmath3636 . hence , our pbh burst rate density estimate is , @xmath37 next we need to estimate the values of @xmath34 , @xmath33 , and @xmath35 . because we have studied ipn bursts collected over 21.75 years ( the 2.5 year ipn non sensitivity period is excluded ) , our observed duration is @xmath34=21.75 years . the effective pbh detectable volume , @xmath33 , calculation for this 21.75 year period , however , is not obvious . each pbh candidate has a distance consistent with some minimum distance up to infinity . we also know that pbh bursts are not bright enough to be detected from large distances . the maximum possible detectable distance of a pbh burst depends on the high - energy physics model used to calculate the final pbh burst spectrum @xcite . currently there are no accurate calculations for final pbh burst photon spectra in the kev - mev energy range . thus as a conservative maximum possible detectable pbh burst distance , we can take the maximum value of the minimum distances in our candidate pbh burst sample . this corresponds to a distance of 0.47 parsecs ( @xmath38 cm ) . because all the pbh burst candidates in the sample are actual ipn detections , this distance value is model - independent . on the other hand , it is important to note that the ipn is not capable of detecting all the bursts within this distance over the entire observation duration due to various factors such as the orientation of the satellites , and/or instrument duty cycles . thus the effective volume calculated from the above maximum possible detectable pbh burst distance is an overestimate . hence the pbh burst rate calculated in equation [ pbh_rate_36 ] is in reality a lower limit on the pbh burst rate density , @xmath39 in section [ data_selection ] , we made a rough estimate of the selection efficiency of ipn , @xmath35 , for pbh bursts . however , we note that it is very challenging to calculate @xmath35 accurately due to a number of unknown factors such as the fraction of bursts without ee , the fraction of bursts without afterglows , the fraction of bursts to which the ipn is not sensitive ( for example due to orientation or deadtime ) , etc . using the estimated effective pbh detectable volume @xmath33 , observed duration @xmath34 , and selection efficiency @xmath35 , we can now estimate the lower limit of the pbh burst rate in the best case scenario where all the pbh burst candidates are actual pbh bursts . in this case , our pbh burst lower limit is @xmath40158.5 bursts @xmath41 . if we assumed 100% efficiency then the pbh burst lower limit is @xmath40 3.6 bursts @xmath41 . if only one of the candidates is an actual pbh burst then the value of the rate density lower limit depends on the minimum distance to that particular burst . if the burst with the largest minimum distance ( grb 140807 ) is the pbh burst , then the pbh burst rate density lower limit is @xmath40 0.1 bursts @xmath41 . if the burst with the smallest minimum distance ( grb 970902 ) is real then the pbh burst rate density lower limit is @xmath42 bursts @xmath41 ( this value is excluded by other high - energy experiments , however ) . all these estimates assume that pbhs are distributed uniformly in the solar neighborhood . the ipn pbh burst rate density lower limit values are shown in figure [ fig : pbh - limit - final ] . pbh burst upper limits from various other searches are also shown in the figure . in the worst case scenario where none of our candidates is a real pbh burst , we can not estimate a lower limit to the pbh burst rate density and instead consider to estimate an upper limit to the pbh burst rate density . however , the assumption that none of the bursts in the sample is real but still we have candidates implies that our criteria to identify pbh bursts defined in section [ data_selection ] is not sufficient . this means our method is not capable of setting an upper limit on the pbh burst rate density .

these bursts have minimum possible distances in the 10 cm ( 710 au ) range , consistent with the expected pbh energetics and with a possible origin in the solar neighborhood , although none of the bursts can be unambiguously demonstrated to be local . assuming these bursts are real pbh events , we estimate lower limits on the pbh burst evaporation rate in the solar neighborhood .

the detection of a gamma - ray burst ( grb ) in the solar neighborhood would have very important implications for grb phenomenology . the leading theories for cosmological grbs would not be able to explain such events . the final bursts of evaporating primordial black holes ( pbhs ) , however , would be a natural explanation for local grbs . we present a novel technique that can constrain the distance to gamma - ray bursts using detections from widely separated , non - imaging spacecraft . this method can determine the actual distance to the burst if it is local . we applied this method to constrain distances to a sample of 36 short duration grbs detected by the interplanetary network ( ipn ) that show observational properties that are expected from pbh evaporations . these bursts have minimum possible distances in the 10 cm ( 710 au ) range , consistent with the expected pbh energetics and with a possible origin in the solar neighborhood , although none of the bursts can be unambiguously demonstrated to be local . assuming these bursts are real pbh events , we estimate lower limits on the pbh burst evaporation rate in the solar neighborhood .

1406.3258

i

modern biology , especially genetics and fmri analysis , has motivated a great deal of theoretical and applied research in detection of local signals in large fields of data . see , for example , lander and botstein ( 1989 ) , karlin , dembo and kawabata ( 1990 ) , feingold et al . ( 1993 ) worsley ( 1992 ) , siegmund and worsley ( 1995 ) . typically , the random field representing the data is standardized , say , to have mean zero when there is no signal and to have mean different from zero in neighborhoods of signals . these signal detection problems are statistically irregular , since the parameters quantifying the magnitude and location of each signal are confounded . in many formulations the random field is assumed to be gaussian , often because of arguments based on the central limit theorem . control for the multiple comparisons involved in searching the field for local signals is achieved by using the theory of maxima of gaussian fields to obtain a significance threshold that controls the overall false positive rate . this requires that the normal distribution provide an adequate approximation in the extreme tail of the distribution , which in turn suggests that one be skeptical of the accuracy of the resulting thresholds , especially in many cases where poisson like data are involved and the poisson rate is not large . papers containing more precise asymptotic analyses under various special conditions are rabinowitz and siegmund ( 1995 ) , tang and siegmund ( 2001 ) , peng and siegmund ( 2005 ) , chan and zhang ( 2006 ) , siegmund , yakir and zhang ( 2011 ) . this paper is motivated by a number of problems arising from high - throughput dna sequencing data , where the random field is assumed to be a poisson process , possibly non - homogeneous , or in some cases a mixture of poisson processes to deal with over - dispersion . the signal to be detected involves a local change in the rate of the poisson process . such scans for local signals arise in the detection of dna copy number variations in dna sequencing , transcription factor binding sites in chromatin immuno - precipitation followed by sequencing ( chip - seq , see for example schwarzman et al . 2013 ) , alternative transcription start and end sites in rna sequencing , and genomic insertions and deletions in paired - end dna sequencing . a brief description of these motivating applications is given in the next section , but our focus will be on the last problem , also referred to as dna structural variant detection . although these problems differ in biological context and model formulation , they can be studied by closely related statistical methods . we propose a framework for detecting local signals in poisson - like data . scan statistics for the applications mentioned in the preceding paragraph can be cast in the proposed framework . we derive approximations for the false positive rates of likelihood ratio- and score - based scan statistics for reasonably general poisson random fields . we also study the power of these statistics as a function of the baseline rate and other parameters . for the structural variant detection problem , we first introduce , as illustration , a toy mixture model that can be directly compared to some simple models for which there is existing theory . we then consider more complex models that are more carefully tailored to the specific features of paired end reads of dna sequencing data . this paper is organized as follows . first , we describe some motivating applications in section [ sec : examples ] . in section [ sec : model ] , we give a general framework for scans of poisson random fields , first illustrating it on a simple mixture model ( section [ sec : simple ] ) and then on a more complex and realistic model for the problem of structural variant detection ( section [ sec : bettermodel ] ) . the simple mixture model has the benefit of being more transparent and allowing more direct comparisons to some existing scan statistics , while also lending qualitative insights that are transferable to more complex settings . in sections 4 and 5 , we describe the procedure for p - value approximation for scan statistics on poisson random fields . these approximations are derived for the simple mixture model in section 6 , with their accuracy examined by numerical experiments . even for the simple mixture model , it is not clear how to design the scan statistic with respect to the unknown parameters to maximize power under the different types of alternatives . in section [ sec : power ] , we explore some of the complicated issues relating to power . in section 7 , we return to the more realistic models for structural variant detection formulated in section [ sec : bettermodel ] . their p - value approximations are given , the power of various scan regimes under current experimental designs are studied , and and the analysis of a real data set from illumina s platinum genomes is described . we conclude with a discussion in section [ sec : discussion ] . the theory and methods described in this paper are at the core of ` swan ` , a comprehensive statistical pipeline for genomic structural variant detection . ` swan ` is an open source r library available at : ` https://bitbucket.org/charade/swan/wiki/home ` .

the detection of local genomic signals using high - throughput dna sequencing data can be cast as a problem of scanning a poisson random field for local changes in the rate of the process . we propose a likelihood - based framework for for such scans , and derive formulas for false positive rate control and power calculations . the framework can also accommodate mixtures of poisson processes to deal with over - dispersion . as a specific , detailed example , we consider the detection of insertions and deletions by paired - end dna - sequencing . we propose several statistics for this problem , compare their power under current experimental designs , and illustrate their application on an illumina platinum genomes data set . , ,

the detection of local genomic signals using high - throughput dna sequencing data can be cast as a problem of scanning a poisson random field for local changes in the rate of the process . we propose a likelihood - based framework for for such scans , and derive formulas for false positive rate control and power calculations . the framework can also accommodate mixtures of poisson processes to deal with over - dispersion . as a specific , detailed example , we consider the detection of insertions and deletions by paired - end dna - sequencing . we propose several statistics for this problem , compare their power under current experimental designs , and illustrate their application on an illumina platinum genomes data set . , ,

1009.0350

i

according to a standard picture of the mixed state in bulk type - ii superconductors the abrikosov vortices penetrating the homogeneous sample form a periodic arrangement called a flux lattice @xcite . the magnetic flux through the unit cell of such flux line lattice equals to the flux quantum @xmath1 : we have one vortex per unit cell . there are a few examples of rather exotic superconducting systems which may provide a possibility to observe a different vortex lattice periodicity , namely the structures with more than one vortices per unit cell . in particular , the phase transitions to such multiquanta flux lattices can occur , e.g. , for superconductors with unconventional pairing @xcite or 2d fulde - ferrell - larkin - ovchinnikov superconductors @xcite . the goal of this work is to suggest an alternative scenario of the phase transitions between the flux structures with different number of vortices per unit cell which can be realized in thin films of anisotropic superconductors . the underlying physical mechanism for this scenario arises from the interplay between the long range attraction and repulsion between tilted vortex lines in thin films discussed recently in ref . . the unusual attractive part of the vortex vortex interaction potential is known to be a distinctive feature of anisotropic superconductors and the value of the attractive force is controlled by the tilting angle of the vortex line with respect to the anisotropy axis @xcite . the origin of the long range intervortex repulsion in thin films has been analyzed in the pioneering work @xcite by pearl in 1964 . this repulsion force always overcomes the attraction at rather large distances because of the different power decay laws of these contributions . note that , of course , the short range interaction between vortices is also repulsive . finally , this balance between the repulsion and attraction can result in the formation of the nonmonotonic interaction potential @xmath2 vs the intervortex distance @xmath3 . increasing the vortex tilting angle we first strengthen the attraction force between vortices and , thus , the minimum in the vortex interaction potential can appear only for rather large tilting angles when the attraction overcomes the pearl s repulsion . this minimum shifts towards the larger intervortex distances with the further increase in the tilting angle and , finally , at rather large distances the attraction appears to be suppressed due to the exponential screening effect . as a consequence , the minimum in the interaction potential exists only for a certain restricted range of the vortex tilting angles which shrinks with the decrease of the system anisotropy parameter . the appearance of a minimum in the interaction potential points to the possibility to get a bound vortex pair ( or even the clusters with higher vorticities ) for a certain range of vortex tilting angles . for a flux line lattice such vortex vortex interaction potential can cause an instability with respect to the unit cell doubling , i.e. the phase transition to the multiquanta vortex lattices . in this paper we use two theoretical approaches to describe the peculiarities of the intervortex interaction and resulting formation of clusters and multiquanta lattices . one of them is a standard london model accounting for an anisotropic mass tensor which is adequate for the superconductors with moderate anisotropy . this approach assumes that the superconducting coherence length in all directions exceeds the distance between the atomic layers and obviously breaks down in the limit of strong anisotropy , i.e. , for josephson coupled layered structures . in the latter case we choose to apply another phenomenological model , namely the so called lowrence doniach theory @xcite . for rather small intervortex distances this theory can be simplified neglecting the effects of weak interlayer josephson coupling . this approach of josephson decoupled superconducting layers is known to be useful in studies of the vortex lattice structure at low fields @xcite . considering thin film samples in tilted magnetic fields we do not restrict ourselves by the case of only straight vortex lines and study the problem of the energetically favorable vortex line shape in the presence of the inhomogeneous supercurrent screening the field component @xmath4 parallel to the film plane . previously this problem has been addressed in ref . for rather small deviations of the vortex line from the direction normal to the film plane . such approximation is obviously valid only for the @xmath5 values much smaller than the critical field @xmath6 of the penetration of vortices parallel to the film plane . for anisotropic london model this analysis of ref . has been previously generalized for the case of a strongly distorted vortex line ( see ref . ) . for the sake of completeness we present here the calculations of the shape of an isolated vortex line for arbitrary fields @xmath7 within both theoretical models describing the limits of strong and moderate anisotropy . as a next step , we calculate the vortex - vortex interaction potential for such strongly deformed vortex lines . further analysis in the paper includes the calculations of energy of finite size vortex clusters as well as the energy of vortex lattices with different number of vortices per unit cell . experimentally the visualization of unconventional vortex arrangements could be carried out by a number of methods which provided convincing evidence for the existence of vortex chains in bulk anisotropic superconductors caused by the intervortex attraction phenomenon ( such as the decoration technique in @xmath8 @xcite , scanning - tunneling microscopy in @xmath9 @xcite , scanning hall - probe @xcite and lorentz microscopy measurements in @xmath8 @xcite ) . the paper is organized as follows . in sec . ii we find the energetically favorable shape of an isolated vortex line . in sec . iii we calculate the vortex vortex interaction potential and prove the existence of a potential minimum for a certain range of field tilting angles and parameters . the sec . iv is devoted to the calculation of energy of vortex clusters . finally , in sec . v we present our analysis of the phase transition between the vortex lattices with one and two flux quanta per unit cell . the results are summarized in sec . vi . some of the calculation details are presented in the appendices [ apx - a ] and [ apx - b ] .

this minimum appears to exist only for a certain restricted range of the vortex tilting angles which shrinks with the decrease of the system anisotropy parameter . tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or / and can arrange into multiquanta flux lattice . the magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number of flux quanta .

the distinctive features of equilibrium vortex structures in thin films of anisotropic superconductors in tilted magnetic fields are studied for the limits of moderate and strong anisotropy . the energetically favorable shape of isolated vortex lines is found in the framework of two particular models describing these limiting cases : london theory with an anisotropic mass tensor and london - type model for a stack of josephson decoupled superconducting layers . the increase of the field tilting is shown to result in qualitative changes in the vortex vortex interaction potential : the balance between long range attractive and repulsive forces occurs to be responsible for a formation of a minimum of the interaction potential vs the intervortex distance . this minimum appears to exist only for a certain restricted range of the vortex tilting angles which shrinks with the decrease of the system anisotropy parameter . tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or / and can arrange into multiquanta flux lattice . the magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number of flux quanta . thus , the increase in the field tilting should be accompanied by the series of the phase transitions between the vortex lattices with different .

cond-mat9609286

i

the investigation of the transport properties of highly correlated fermionic systems has attracted much attention in recent years . a thorough understanding of the conductivity in particular is essential for the technical application of materials such as metallic oxides in electronic devices . the development of a new analytic approach , the limit of infinite dimension for fermionic systems @xcite , allowed the numerical description of the metal - insulator occuring in the half - filled hubbard model in @xmath4 for higher values of the interaction @xmath5 assuming a homogeneous phase @xcite . the latter assumption means that one deliberately ignores the possible occurence of symmetry breaking for the sake of simplicity . it is argued that on frustrated lattices symmetry breaking is suppressed so that the metal - insulator transition occurs at higher temperatures than those at which symmetry breaking sets in . with this background in mind , it is the aim of this work to extend and to complement the results known so far into two directions . first , the finite dimensionality of realistic systems , i.e.mostly @xmath6 , shall be included at least to lowest non - trivial order in an expansion in @xmath2 . much care is used in including these correction without physical and/or analytic inconsistencies . it is shown that it is _ not _ sufficient to use a conserving , @xmath7-derivable approximation in the sense of baym / kadanoff . furthermore , the true three - dimensional dos will be used . second , the influence of symmetry breaking on the conductivity , especially the question of possible metal - insulator transitions induced by symmetry breaking shall be investigated . to this end , the model of spinless fermions with repulsive interaction for particles on adjacent sites is considered on a generic bipartite lattice , namely the simple cubic lattice . its hamiltonian at half - filling @xmath8 reads @xmath9 where @xmath10 creates ( annihilates ) a fermion at site @xmath11 . the sum @xmath12 runs over all sites @xmath11 and @xmath13 which are nearest neighbors . the coordination number @xmath14 appears for the proper scaling of the kinetic energy @xcite and for the proper scaling of the potential energy @xcite . the interaction constant is @xmath5 . in this model the symmetry is broken yielding an ab - cdw at half - filling @xcite for infinitesimal values of the interaction at @xmath15 and for sufficiently large interaction at all finite temperatures . the ab - cdw consists of alternating sites with a particle density above ( below ) average . the order parameter @xmath16 is the absolute deviation of the particle density from its average @xcite . as far as the occurence of a symmetry broken phase is concerned , the model of spinless fermions at half - filling is similar to the hubbard model at half - filling which displays antiferromagnetic behavior . the main differences are that the broken symmetry for spinless fermions is discrete whereas it is continuous in the hubbard model , and the fact that a local interaction like the one in the hubbard model does not favor a spatial order by itself . the latter fact leads to a value of @xmath17 for large @xmath5 in the hubbard model whereas one has @xmath18 in the spinless fermions model . the article is organized as follows . succeeding this introduction it is discussed how a thermodynamically and analytically consistent extension of the limit @xmath19 can be performed . next the basic equations for the extension to linear order @xmath20 are derived and their numerical evaluation is sketched . this third section contains also results for the dos and the corresponding proper self - energy . in sect . 4 the bethe - salpeter equation is set up and solved for the conductivity @xmath0 . the preservation of the f - sum rule is discussed . numerical results for the dc- and the ac - conductivity are presented in sect . the findings are summarized and dicussed in the final section . all energies ( temperatures , respectively ) throughout this article will be given in units of the root - mean - square of the `` free '' , i.e. non - interacting , density - of - states of the lattice model concerned . all conductivities will be given in units of @xmath21 where @xmath22 is the lattice constant . the constants @xmath22 , @xmath23 , and @xmath24 ( boltzmann s constant ) are set to unity .

the model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice . the investigated symmetry broken phase is the charge density wave ( cdw ) with wave vector which occurs at half - filling . special care is paid to the setup of a conserving approximation in the sense of baym / kadanoff without inconsistencies .

the dynamic conductivity of strongly correlated electrons in a symmetry broken phase is investigated in the present work . the model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice . the investigated symmetry broken phase is the charge density wave ( cdw ) with wave vector which occurs at half - filling . the calculations are based on the high dimensional approach , i.e.an expansion in the inverse dimension is used . the finite dimensionality is accounted for by the inclusion of linear terms in and the true finite dimensional dos . special care is paid to the setup of a conserving approximation in the sense of baym / kadanoff without inconsistencies . the resulting bethe - salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase ( ab - cdw ) . the dc - conductivity is reduced drastically in the cdw . yet it does not vanish in the limit due to a subtle cancellation of diverging mobility and vanishing dos . in the dynamic conductivity the energy gap induced by the symmetry breaking is clearly discernible . in addition , the vertex corrections of order lead to an excitonic resonance lying within the gap .

cond-mat9609286

r

in this section we present and discuss results which follow from the general equations derived in the previous section . all results are calculated at half - filling and for @xmath6 . ( 8.2,7)(0,0.7 ) ( 8.3,0 ) in fig . [ fi : res1 ] , the real part of the dynamic conductivity is depicted in the non symmetry broken phase for different temperatures , i.e. the occurrence of a symmetry broken phase at low temperature is discarded deliberately for the moment . they are compared with results of pruschke , cox , and jarrell @xcite for the half - filled hubbard model in @xmath4 , obtained in the non - crossing approximation . in both cases the interaction value is @xmath217 ( in our units ) which is just below the value where the mott - hubbard transition occurs in the hubbard model @xcite . for spinless fermions the drude peak is absolutely dominant . its weight is very large . its width is given by the imaginary part of the self - energy at the fermi level @xmath218 ( see ( [ basis0 ] ) with @xmath219 or eq . ( 14 ) in ref . 26 ) , i.e. the width is proportional to @xmath220 . the shape of the drude peak corresponds very well to a lorenzian . only at low temperatures a shoulder emerges . this shoulder is the effect of interaction induced scattering . the fluctuations are not particularly strong . it was already shown previously @xcite that the average over the @xmath221 interaction partners reduces the relative fluctuations . there is no mott - hubbard transition without symmetry breaking in the spinless fermion model because an increasing interaction enhances not only the fluctuations but also the fock term ( absent in the hubbard model ) which stabilizes the fermi liquid phase . these features are particularly obvious in the comparison with the hubbard model data . in this model , the drude peak is very reduced at all displayed temperatures since much of the weight is shifted to the peaks induced by the strong local particle density fluctuations . besides the difference shoulder vs. peak it is interesting to note the difference in energy scales . in the hubbard model , it is more or less @xmath5 which sets the energy at which the peak occurs . this can be understood as the energetic effect of whether or not an electron with a different spin is present . the typical energy for the shoulder is obviously much smaller . this in turn can be understood in the same way as before but it has to be taken into account that the number of possible interaction partners @xmath221 leads to a reduction of the relative fluctuations of the order of @xmath222 . this yields an energy of roughly @xmath223 in the particular example which is in good agreement with the numerical result . due to the nesting at half - filling , the system of spinless fermions undergoes a transition to a spontaneously broken translation symmetry for all ( positive ) values of the interaction on lowering the temperature . this spontaneously broken discrete symmetry implies the occurrence of a gap which grows exponentially @xmath224 for low values of the interaction at @xmath15 ( see ref . 6 and refs . therein ) . it is visible in the dynamic conductivity@xcite . in fig . [ fi:23 ] , its growth on decreasing temperature is shown in four snap - shots . ( 8.2,15)(0,0.7 ) ( -0.7,7.5 ) ( 8.3,7.5 ) ( -0.7,0 ) ( 8.3,0 ) in fig . [ fi:23](a ) , @xmath153 is still above its critical value . no structure is visible except for the dominant drude peak already discussed in fig . [ fi : res1 ] . in figs . [ fi:23](b)-(d ) the gap is present and discernible . its value is approximately @xmath225 if @xmath144 is the value of the energy gap in the dos , see figs . [ fi:7 ] and [ fi:8 ] . but there is also some weight within the gap for @xmath226 since the correlation contribution blurred already the gap in the dos . note in passing that the f - sum rule can be verified numerically on the results shown in fig . [ fi:23 ] very accurately ( to the fraction of a percent at @xmath15 ; to the fraction of a permille in the homogeneous phase ) . the drude peak does not vanish immediately in the ab - cdw . it becomes smaller and narrower on decreasing temperature . its maximum value does not vanish for @xmath3 ( see below ) but its weight does . in fig . [ fi:24 ] , ( 8.2,7)(0,0.7 ) ( -0.7,0 ) ( 8.3,0 ) two frequency intervals are shown in detail for a fairly low temperature . [ fi:24](a ) displays the drude peak again . the interesting feature is its small width ( compared with the width of the drude peaks in figs . [ fi:23](b ) and ( c ) ) . it can not be explained by a factor of @xmath220 but corresponds to an exponential shrinking @xmath227 . as already observed in the one - particle properties , an increasing gap reduces the influence of the fluctuations . [ fi:24](b ) shows a very interesting feature below the proper band edge at @xmath228 . this resonance is also visible in fig . [ fi:23](c ) whereas the resonance and the band edge are not resolved at a higher temperature , fig.[fi:23](b ) . the resonance can very well be approximated by a lorenzian . at @xmath15 , it is also present as a @xmath229-peak ( not shown in fig . [ fi:23](d ) ) . it originates from a zero of the denominator in ( [ vollchi2 ] ) . at @xmath226 , only the real part of the denominator vanishes and its imaginary part leads to the observed broadening which depends strongly , namely exponentially , on the temperature . physically the resonance can be interpreted as a bound state , an exciton , between a particle in the upper band and a hole in the lower band in the reduced brillouin zone of the ab - cdw . the energy difference between the position of the exciton and the band edge is its binding energy . the type of diagrams which yield the denominator in ( [ vollchi2 ] ) corroborates the interpretation as an exciton . the vertical interaction lines stand for the repeated interaction between particle and hole in the two propagators involved in the calculation of @xmath166 . it should be noted that , for instance , for the parameters of fig . [ fi:23](d ) about 70% of the weight of the conductivity are found in the excitonic resonance ( one may not be misled by the logarithmic scale ) . this means that the excitonic effect is not at all a small side effect . concluding the part on the dynamic conductivity , we discuss fig . [ fi:25 ] ( 8.2,7)(0,0.7 ) ( 8.3,0 ) which shows results for a large interaction value @xmath5 . due to the induced large gap and due to the narrow effective band width several frequency intervals of absorption are well separated . the peaks are caused by the convolution of the satellite band presented for the one - particle properties . note , however , that the weight of these satellites decreases rapidly by a factor of 100 from peak to peak . these small amplitudes render an experimental verification certainly extremely difficult if not impossible . nevertheless , it would be interesting to know whether such satellites exist . their existence would support the application of a self - consistent approximation since the non self - consistent calculation yields only two peaks besides the @xmath229-peak which is not shown . since the dc - conductivity in absence of symmetry breaking has been extensively discussed in ref . 26 we will treat here exclusively the case with symmetry breaking . the result of ( [ dcltf1 ] ) and ( [ dcltf2 ] ) is depicted in fig . [ fi:26 ] ( 8.2,7)(0,0.7 ) ( -0.7,0 ) ( 8.3,0 ) for weak and strong interaction @xcite . to the right of the cusp the system is in the non symmetry broken phase . the conductivity is essentially proportional @xcite to @xmath220 . on entering the symmetry broken phase with gap , the conductivity falls drastically since the energy gap reduces the dos at the fermi level . surprisingly , however , the conductivity does _ not _ vanish for @xmath3 although the dos vanishes in this limit . there is even a very slight uprise of @xmath230 close to @xmath15 . this phenomenon is again a manifestation of the suppression of correlation effects by the energy gap . the dos is reduced by a factor of @xmath227 but so is the imaginary part of the self - energy in ( [ basis0 ] ) which is responsible for the quasi - particle life - time . these two effects cancel exactly . put differently , an exponentially small number of quasi - particles of exponentially large life - time carries a constant current ( but see discussion below ) . it remains an algebraic dependence on @xmath153 of the dc - conductivity . the constant term and the linear one can be computed analytically and where used to complete the curves in fig . [ fi:26 ] for small values of @xmath153 where the numerical calculation is no longer precise enough due to extinction . the limit value @xmath231 is given in fig . [ fi:27 ] ( 8.2,7)(0,0.7 ) ( 8.3,0 ) as function of @xmath5 . as expected it decreases rapidly for @xmath232 . note the logarithmic scale . what do the above findings for @xmath230 imply for the existence of a metal - insulator transition ? seemingly , even spontaneous symmetry breaking does not suffice to render the system insulating . but it must be noted that the `` residual '' conductivity @xmath231 is infinitely fragile : any other arbitrarily weak scattering mechanism which does not die out on @xmath3 e.g. disorder or scattering at the borders of the sample , will take over . the exponentially vanishing dos will yield an exponentially vanishing dc - conductivity . this is reflected in the exponentially decreasing width of the drude peak which , at constant height , implies an exponentially decreasing weight . experimentally , very pure samples might allow to see the beginning of the plateaus in fig . [ fi:26 ] before the above cited other scattering mechanism reduce the conductivity . this behavior is in complete analogy to the one observed for the shear viscosity @xmath233 of helium 3 in the b phase @xcite . in this system like in the system of spinless fermions in the ab - cdw one observes an exponentially diverging mean free path since the collision between ( quasi-)particles is suppressed by a gap . in the so - called `` knudsen regime '' collisions of quasi - particles with the wall of the container dominate the collisions _ between _ the quasi - particles . in helium 3 , one observes a sharp drop below @xmath234 and then the beginning of a plateau before finally @xmath233 vanishes rapidly . the theoretical result for the infinite system predicts a gentle uprise just like the one we predict in fig . [ fi:26 ] . in both cases , a factor @xmath227 in the dos cancels with the same factor in the scattering rate @xcite . this interesting analogy underlines the validity of the results of our @xmath2 approach .

the dynamic conductivity of strongly correlated electrons in a symmetry broken phase is investigated in the present work . the resulting bethe - salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase ( ab - cdw ) . in addition , the vertex corrections of order lead to an excitonic resonance lying within the gap .

the dynamic conductivity of strongly correlated electrons in a symmetry broken phase is investigated in the present work . the model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice . the investigated symmetry broken phase is the charge density wave ( cdw ) with wave vector which occurs at half - filling . the calculations are based on the high dimensional approach , i.e.an expansion in the inverse dimension is used . the finite dimensionality is accounted for by the inclusion of linear terms in and the true finite dimensional dos . special care is paid to the setup of a conserving approximation in the sense of baym / kadanoff without inconsistencies . the resulting bethe - salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase ( ab - cdw ) . the dc - conductivity is reduced drastically in the cdw . yet it does not vanish in the limit due to a subtle cancellation of diverging mobility and vanishing dos . in the dynamic conductivity the energy gap induced by the symmetry breaking is clearly discernible . in addition , the vertex corrections of order lead to an excitonic resonance lying within the gap .

astro-ph0011101

c

through uv - optical imaging and spectroscopy , we have found new evidence for bar - mediated resonances as the primary drivers of evolution in m94 at the present epoch . our observational results include evidence for ( 2 . ) an inner disk with diffuse fuv emission in concentric arcs that do not match the fine - scale structures or reddened structures at visible wavelengths . since @xmath86 is observed in absorption here , the uit / fuv image represents the first view of this non - ionizing but relatively young disk component . uv - optical colors and spectral indices in the nucleus and inner disk that indicate b and a - type stars in the presence of modest extinction ( a@xmath87 @xmath281 mag ) along with some liner activity from the nucleus itself . ( 4 . ) a 2.2 kpc diameter starbursting ring at the perimeter of the inner disk that is bright at fuv , h@xmath0 , and radio - continuum wavelengths . the level of starbirth activity in this inner ring rivals the levels observed in starbursting irregular galaxies such as ngc 1569 and ngc 4449 . the inferred star formation rate within the ring and inner disk amounts to 1.5 m@xmath35 yr@xmath13 sufficient to build up the stellar mass of the inner disk and bulge in @xmath210@xmath60 yr . two 500-pc size fuv - emitting knots exterior to the ring on diametrically opposite sides of the nucleus . the bisymmetric knots and starburst ring appear to be especially prominent parts of a complex spiral arm structure , as revealed in a spatially - filtered b - band image . the starburst ring , bi - symmetric knots , oval disk , and outer pseudo - ring as signposts of resonant dynamics in the disk of m94 . more specifically , the radii of these features match those of various orbital resonances , given a pattern speed of 35 km s@xmath13 kpc@xmath13 at our adopted distance and inclination . these orbital resonances are most likely driven by some combination of the nuclear mini - bar and oval distortion in the disk . ( 8 . ) a shallow minimum of gravitational stability at the radius of the starburst ring that extends inward into the inner disk . although too broad to explain the discrete starburst ring , the shallow minimum may help to explain the 10@xmath88-yr old stellar population interior to the ring . although we can set a limit on the speed of outward or inward propagating star formation in the ring , we can not preclude the existence of such a mode . at a propagation speed of 35 km / s , a wave initiated in the nucleus could traverse the inner disk to the radius of the current starburst ring in only 31 myr . therefore , it is possible that the @xmath89-yr old stellar population detected in the inner disk is the result of such an outward propagating wave . the striking difference in emission morphologies at fuv and red wavelengths provides further support for the starburst ring being a transient phenomenon which does not persist at any one radius for very long . either these resonant phenomena come and go , as the oval distortions undergo secular evolution , or their operating radii migrate in response to other dynamical influences on the stars and gas ( cf . combes 1994 ; combes et al . 1995 ; friedli & benz 1995 ) . otherwise , one must invoke strong radial inflows of stars from the starburst ring to populate the inner disk and bulge , a feat requiring unusual circumstances e.g. mergers . the results reported herein may have important implications with regard to observations of the most distant observable galaxies . at redshifts of 15 , the 2-kpc diameter starburst ring in m94 would subtend angles of only ( 0.7@xmath1 1.0@xmath1)h@xmath7/75 in an einstein - de sitter universe ( q@xmath7 = 1/2 ) and ( 0.3@xmath1 0.2@xmath1)h@xmath7/75 in an open ( milne ) universe ( q@xmath7 = 0 ) ( cf . narlikar 1983 ) . the uv - bright nuclear rings evident in ngc 1097 , ngc 1317 , ngc 1433 , ngc 1512 , ngc 2997 , ngc 4321 , and ngc 5248 ( maoz et al . 1995 ; maoz et al . 1996 ; kuchinsky et al . 2000 ; marcum et al . 2000 ) would subtend even smaller angles at the same redshifts . moreover , nuclear rings tend to have higher fuv surface brightnesses than their larger counterparts the inner ring in m94 being a remarkable exception . therefore , some of the `` core - halo '' morphologies that are evident at high - redshift in the restframe fuv ( cf . giavalisco et al . 1997 ) may , in fact be marginally - resolved representations of galaxies with starburst rings in their centers . gravitationally - lensed galaxies are fortuitously magnified , enabling resolutions of their structure at high s / n . an important precedent in this regard is the gravitationally - lensed `` pretzel galaxy '' which lies behind the galaxy cluster 0024 + 1654 at an estimated redshift of 1.2 1.8 ( colley et al . 1996 ; tyson et al . 1997 ) . detailed reconstructions of the multiply - lensed galaxy show a clear annular morphology on a scale of several kpc . if m94 and other nearby ringed galaxies can be used as current - epoch analogues , the `` pretzel galaxy '' and perhaps other marginally - resolved `` core - halo '' galaxies at high redshift may represent youthful inner disks and bulges growing under the organizing influence of oval or bar asymmetries(friedli & benz 1995 ; waller et al . conversely , if evidence for starburst rings at high redshift proves to be sparse , then massive inner disks featuring ring - bar dynamics have yet to form in most systems , or starbursting bulges are masking their presence . we thank david adler , gene byrd , francoise combes , daniel friedli , and david westpfahl for generously providing consultation on the dynamics of ringed - barred spiral galaxies . whw is grateful to john huchra and the oir division of the harvard - smithsonian center for astrophysics for their kind hospitality during his visiting appointment at the cfa . whw also thanks eric murphy and christine winslow , tufts undergraduates who helped craft some of the graphics . uit research is funded through the spacelab office at nasa headquarters under project number 440 - 51 . we are deeply grateful to the crew of sts-67 and the many people who helped make the _ astro-2 _ mission a success . whw acknowledges partial support from nasa s astrophysics data program ( 071 - 96adp ) . giavalisco , m. , et al . 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , eds . w. h. waller , m. n. fanelli , j. e. hollis , & a. c. danks ( new york : aip press ) , p. 221 marcum , p. m , et al . 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , eds . w. h. waller , m. n. fanelli , j. e. hollis , & a. c. danks ( new york : aip press ) , p. 88 oconnell , r. w. 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , eds . w. h. waller , m. n. fanelli , j. e. hollis , & a. c. danks ( new york : aip press ) , p. 11 tyson , j. a. , kochanski , g. , & dellantonio , i. 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , eds . w. h. waller , m. n. fanelli , j. e. hollis , & a. c. danks ( new york : aip press ) , p. 204 waller , w. h. , et al . 1997 , in the ultraviolet universe at low and high redshift : probing the progress of galaxy evolution , eds . w. h. waller , m. n. fanelli , j. e. hollis , & a. c. danks ( new york : aip press ) , p. 39 waller , w. h. , varosi , f. , boulanger , f. , & digel , s. w. 1998 , in new horizons from multi - wavelength sky surveys , iau symp . 179 , eds . b. j. mclean , d. a. golombek , j. e. hayes , & h. e. payne b. lasker & m. postman ( dordrecht : kluwer ) , p. 194 , ( astro - ph/9612233 )

the dynamic orchestration of starbirth activity in the starburst - ringed galaxy m94 ( ngc 4736 ) is investigated using images from the ultraviolet imaging telescope ( fuv - band ) , hubble space telescope ( nuv - band ) , kitt peak 0.9-m telescope ( h , r , and i bands ) , and palomar 5-m telescope ( b - band ) , along with spectra from the international ultraviolet explorer and lick 1-m telescopes . optical and iue spectroscopy of the nucleus and diffuse inner disk indicates a yr - old stellar population from low - level starbirth activity blended with some liner activity . the inner starburst ring and bi - symmetric knots at intermediate radius , in particular , argue for bar - mediated resonances as the primary drivers of evolution in m94 at the present epoch . similar processes may be governing the evolution of the `` core - dominated '' galaxies that have been observed at high redshift . the gravitationally - lensed `` pretzel galaxy '' ( 0024 + 1654 ) at a redshift of.5 provides an important precedent in this regard .

the dynamic orchestration of starbirth activity in the starburst - ringed galaxy m94 ( ngc 4736 ) is investigated using images from the ultraviolet imaging telescope ( fuv - band ) , hubble space telescope ( nuv - band ) , kitt peak 0.9-m telescope ( h , r , and i bands ) , and palomar 5-m telescope ( b - band ) , along with spectra from the international ultraviolet explorer and lick 1-m telescopes . the wide - field uit image shows fuv emission from ( a ) an elongated nucleus , ( b ) a diffuse inner disk , where h is observed in _ absorption _ , ( c ) a bright inner ring of h ii regions at the perimeter of the inner disk ( r = 48 = 1.1 kpc ) , and ( d ) two 500-pc size knots of hot stars exterior to the ring on diametrically opposite sides of the nucleus ( r = 130 = 2.9 kpc ) . the hst / foc image resolves the nuv emission from the nuclear region into a bright core and a faint 20-long `` mini - bar '' at a position angle of 30 deg . optical and iue spectroscopy of the nucleus and diffuse inner disk indicates a yr - old stellar population from low - level starbirth activity blended with some liner activity . analysis of the h , fuv , nuv , b , r , and i - band emission along with other observed tracers of stars and gas in m94 indicates that most of the star formation is being orchestrated via ring - bar dynamics involving the nuclear mini - bar , inner ring , oval disk , and outer ring . the inner starburst ring and bi - symmetric knots at intermediate radius , in particular , argue for bar - mediated resonances as the primary drivers of evolution in m94 at the present epoch . similar processes may be governing the evolution of the `` core - dominated '' galaxies that have been observed at high redshift . the gravitationally - lensed `` pretzel galaxy '' ( 0024 + 1654 ) at a redshift of.5 provides an important precedent in this regard .

hep-ph0107034

i

the observation of clear signatures for the chiral phase transition still remains one of the outstanding challenges of hadron physics . there is hope that the extreme energy densities located inside the spatial region between receding baryonic slabs shortly after ultrarelativistic baryon or heavy - ion collision may provide physical conditions for such a phase transition to take place . from the theoretical point of view we are dealing with a complex dynamical system , strongly interacting quantum fields with many different fermionic and bosonic degrees of freedom , far from equilibrium , creating and emitting baryons and mesons from a rapidly expanding and cooling spatial volume . correspondingly , there is a vast theoretical literature ranging from cascade models in the colored partonic degrees of freedom to hydrodynamic flow models for hadronic currents , which might be applicable at different stages and shed light on different aspects during the time evolution of such events . if within the hot fireball chiral symmetry indeed is restored then the dynamics of its spontaneous breaking and formation of a chiral condensate is one important aspect of the cooling process in which the highly excited spatial volume returns back to normal physical vacuum . a possible strategy which has proven useful for many other cases of phase transitions in microscopically very complex systems is to comprise the essential phenomenology into an effective action for an ordering parameter field . for the hadron phenomenology near @xmath2 a chiral field with spontaneously broken @xmath3-symmetry has become a standard and successful tool , so it is natural to try to extend and apply this concept to the temperature region where the chiral phase transition is expected . in its most simple version the effective action then consists of the ( 3 + 1)dimensional @xmath3 linear @xmath4-model , with a suitable temperature - dependent @xmath1-potential for the spontaneous symmetry breaking . depending on the ratio between relaxation and cooling times , the dynamics of the ordering field then follows the cooling quench imposed on the temperature dependence of the potential . as in other cases of multi - component field ordering , it is characterized by formation and growth of misaligned domains separated by domain walls or other topologically nontrivial structures , depending on field and space dimensionality @xcite . numerical simulations in this classical framework have been performed and they confirm the transient formation of domains of false vacuum , in which the condensate is approaching its vacuum value while the direction of the aligned field still deviates from the surrounding vacuum @xcite . the possible influence of quantum- and thermal effects has been investigated , mostly in mean - field approximation @xcite . it has been suggested that pions emitted from these domains of disoriented chiral condensate ( dcc ) carry the misalignment in their isospin multiplicities , and in this way may provide a signature of the phase transition @xcite . a peculiar feature of the chiral @xmath3-field in 3 spatial dimensions is that its winding density may be identified with baryon density @xcite . this has led to a most interesting and remarkably successful model for baryon structure and dynamics at @xmath2 . the corresponding topological arguments @xcite have been used @xcite to estimate nascent baryon - antibaryon multiplicities in random chiral field configurations at high temperature ; of course , the first few time steps in an ordering evolution lead to an almost instantaneous reduction of the initially large and rapidly fluctuating winding densities . strictly , the topological conservation of the total winding number is limited to a field manifold where the point @xmath5 is excluded . in numerical simulations of field evolutions on a discrete spatial lattice , however , even topological conservation laws have to be enforced by constraint , because arguments based on continuity can not be applied . therefore there is no principal difference for implementing on a lattice the conservation of winding number in the nonlinear or linear realization of the @xmath3-symmetry . this allows to study formation of condensate and disoriented domains during the phase transition with simultaneously forming baryons plus antibaryons such that the total baryon number is fixed to any desired value . it is well known that topological textures play an important role in ordering transitions , so it is of special interest to study how the stabilization of extended baryonic structures and baryon number conservation may affect the growth laws of dcc domains , and possible dcc signatures in the emitted radiation . for this purpose it is necessary to include in the effective action terms which stabilize the spatial size of the baryons generated in the course of the ordering evolution . scaling arguments show that an additional four - derivative term is sufficient for soliton stabilization in 2- and 3-dimensional @xmath6 models . a different extension , the inclusion of the anomaly term , has been advocated to increase the probability of dcc - formation @xcite . the linear @xmath4-model ( even with explicite inclusion of quarks ) sometimes has been used @xcite to investigate the possibility of dcc - signals by considering spatially averaged fields , only . naturally , within such an approximation the effects we are investigating here , are lost . on the other hand , there is no immediate need to explicitly include fermionic degrees of freedom in our present approach . before embarking on a full - scale simulation of the ( 3 + 1)-dimensional @xmath3 case it is helpful to analyse the relevant questions in the ( 2 + 1)-dimensional @xmath0 model @xcite . it shares all essentials with the higher - dimensional case . although it represents an efficient tool for the description of 2-dimensional spin systems in its own right @xcite , we here discuss it mainly in view of its hadron physics generalization . that is , we denote the order parameter field as chiral meson field , we call the fluctuations pions with internal isospin components , and @xmath4-mesons , which aquire mass through spontaneous breaking of the chiral @xmath0-symmetry , and we call the domains with small values of the condensate and unbroken symmetry bags , in which the baryonic winding density is confined . although there is no compelling connection to fix the parameters of the model from its higher - dimensional analogue , we choose them in correspondence to simulate relative sizes and masses for baryons and mesons . various features of the static solutions of this model , and their formation in relaxation processes after a quench have been studied in @xcite . in the present investigation we discuss in more detail the different stages which characterize the long - time ordering evolution under dissipative dynamics , the dependence of the relevant times on model parameters , different types of symmetry breaking , and quench rates . our main aim , however , is an attempt to extract from the dynamics of the evolution the possibility of a dcc - signal . generally , the emission of radiation from a moving source is determined by quantum - field - theoretic amplitudes which require a separation of the time - dependent field into a classically moving part and quantum fluctuations . the result is commonly put into the statement that the intensity of pion radiation is proportional to the square of the classical pion field @xcite . this argument is the basis of the interest in dcc - pions . we analyse the validity of this statement under the assumption of dissipative dynamics , i.e. assuming that the energy loss of the relaxing and ordering classical configurations is carried away by propagating fluctuations . under this assumption we obtain the timing and strength and isospin distribution of dcc - pions from purely classical considerations . this general dynamical scheme is outlined in sect.2 , while the specifics of the model and the observables of interest are defined in sect.3 . the essential features of configurations during the course of the transition , the growth of angular correlations , decrease of numbers of textures , saturation of condensate and average orientation , formation of baryonic clusters , are presented in chpts.4,5 , and 6 , in dependence on parameters of the model , symmetry breaking , and cooling rates . finally , in sect.7 , we analyse the rates of energy loss with respect to possible dcc pion pulses , and extract the isospin distributions from large ensembles of events . conclusions are drawn in sect.8 .

the dynamics of symmetry - breaking after a quench is numerically simulated on a lattice for the ( 2 + 1)-dimensional model . the total winding number can be conserved by constraint . as a model for the chiral phase transition during the cooling phase after a hadronic collision this allows to investigate the interference of baryon - antibaryon production with the developing disoriented aligned domains . the growth of angular correlations , condensate , average orientation is studied in dependence of texture size , quench rate , symmetry breaking .

the dynamics of symmetry - breaking after a quench is numerically simulated on a lattice for the ( 2 + 1)-dimensional model . in addition to the standard sigma - model with temperature - dependent-potential the energy functional includes a four - derivative current - current coupling to stabilize the size of the emerging extended topological textures . the total winding number can be conserved by constraint . as a model for the chiral phase transition during the cooling phase after a hadronic collision this allows to investigate the interference of baryon - antibaryon production with the developing disoriented aligned domains . the growth of angular correlations , condensate , average orientation is studied in dependence of texture size , quench rate , symmetry breaking . the classical dissipative dynamics determines the rate of energy emitted from the relaxing source for each component of the 3-vector field which provides a possible signature for domains of disoriented chiral condensate . we find that the pions are emitted in two distinct pulses ; for sufficiently small lattice size the second one carries the dcc signal , but it is strongly suppressed as compared to simultaneous sigma-meson emission . we compare the resulting anomalies in the distributions of dcc pions with probabilities derived within the commonly used coherent state formalism .

1603.00178

c

the comparative study of single - qubit - based and entangled - state - based schemes of secure quantum communication performed in the present work has lead to a number of interesting conclusions . firstly , the equivalence observed in the ideal noiseless scenario is lost in more practical scenarios where noise is present . next , it is observed that it is not possible to say unambiguously that in a noisy environment entangled - state - based protocols perform better than the single - qubit - based protocols or vice versa . in fact , it depends on the nature of the noise present in the channel . specifically , single - qubit - based schemes are generally found to be the suitable choice in the presence of ad and/or pd noises , while entanglement - based protocols turns out to be preferable in the presence of collective noises . as sgad and gad channels are generalizations of the ad channel , conclusions similar to that for the ad channel are also applicable to them . however , with an increase in temperature , fidelity is seen to decay . squeezing is seen to play the role of a beneficial quantum resource , in a host of scenarios , in practical quantum communication . also , it is observed that the effect of noise depends upon the number of rounds ( how many times a travel qubit travels through the noisy channel ) of quantum communication involved . for instance , qkd protocols are least affected by noise , while qd protocols are most affected as in qkd protocols a travel qubit travels only once through the noisy channel , whereas in ba an protocol of qd , it travels twice through the noisy channel . further , the single - qubit - based qd scheme involves three rounds of communication as it requires alice to bob and bob to alice transmission of qubits and an additional alice to bob travel of equal number of qubits . as a consequence , single - qubit - based qd scheme is found to be the most affected among the four different single - qubit - based schemes for secure quantum communication discussed in this paper . 10 bennett , c. h. , brassard , g. : quantum cryptography : public key distribution and coin tossing . in : proceedings of the ieee international conference on computers , systems , and signal processing , bangalore , india , p. 175 ( 1984 ) yuan , h. , song , j. , zhou , j. , zhang , g. , wei , x. : high - capacity deterministic secure four - qubit w state protocol for quantum communication based on order rearrangement of particle pairs . int . * 50 * , 2403 ( 2011 ) sharma , r. d. , thapliyal , k. , pathak , a. , pan , a. k. , de , a. : which verification qubits perform best for secure communication in noisy channel ? quantum inf . process . ( 2015 ) doi 10.1007/s11128 - 015 - 1207 - 6 bourennane , m. , eibl , m. , gaertner , s. , kurtsiefer , c. , cabello , a. , weinfurter , h. : decoherence - free quantum information processing with four - photon entangled states . lett . * 92 * , 107901 ( 2004 ) chiuri , a. , rosati , v. , vallone , g. , p@xmath140dua , s. , imai , h. , giacomini , s. , macchiavello , c. , mataloni , p. : experimental realization of optimal noise estimation for a general pauli channel . * 107 * , 253602 ( 2011 ) turchette , q. a. , myatt , c. j. , king , b. e. , sackett , c. a. , kielpinski , d. , itano , w. m. , monroe , c. , wineland , d. j. : decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs . a * 62 * , 053807 ( 2000 ) ; myatt , c. j. , king , b. e. , turchette , q. a. , sackett , c. a. , kielpinski , d. , itano , w. m. , monroe , c. , wineland , d. j. : decoherence of quantum superpositions through coupling to engineered reservoirs . nature * 403 * , 269 ( 2000 ) thapliyal , k. , pathak , a. : applications of quantum cryptographic switch : various tasks related to controlled quantum communication can be performed using bell states and permutation of particles . quantum inf . process . * 14 * , 2599 ( 2014 )

the comparative study reported here has revealed that single - qubit - based schemes are generally found to perform better in the presence of amplitude damping , phase damping , squeezed generalized amplitude damping noises , while entanglement - based protocols turn out to be preferable in the presence of collective noises . it is also observed that the effect of noise entirely depends upon the number of rounds of quantum communication involved in a scheme of quantum communication .

the effect of noise on various protocols of secure quantum communication has been studied . specifically , we have investigated the effect of amplitude damping , phase damping , squeezed generalized amplitude damping , pauli type as well as various collective noise models on the protocols of quantum key distribution , quantum key agreement , quantum secure direct quantum communication and quantum dialogue . from each type of protocol of secure quantum communication , we have chosen two protocols for our comparative study ; one based on single qubit states and the other one on entangled states . the comparative study reported here has revealed that single - qubit - based schemes are generally found to perform better in the presence of amplitude damping , phase damping , squeezed generalized amplitude damping noises , while entanglement - based protocols turn out to be preferable in the presence of collective noises . it is also observed that the effect of noise entirely depends upon the number of rounds of quantum communication involved in a scheme of quantum communication . further , it is observed that squeezing , a completely quantum mechanical resource present in the squeezed generalized amplitude channel , can be used in a beneficial way as it may yield higher fidelity compared to the corresponding zero squeezing case .

cond-mat0310541

m

in this atomistic - level study of void growth , the simulations have been done using empirical embedded - atom ( eam ) potentials in classical molecular dynamics @xcite following the scheme developed earlier . @xcite the copper eam potential we have used is due to oh and johnson . @xcite the system , in which the simulations are done , is a three - dimensional single - crystal face - centered - cubic ( fcc ) lattice in a cubic box with @xmath9 faces . periodic boundary conditions are used in all the three directions so that there are no free boundaries in the system apart from the void . equivalently the system can be imagined to consist of an infinite periodic array of voids . note that periodic boundary conditions have also been used in continuum models of void growth , but in the continuum modeling of void growth in isotropic materials the calculations are done in a reduced cell , which exhibits one quarter of the box in two dimensions , and one eighth in three dimensions , and the behavior of other areas are derived from the symmetries . we use the full cubic box because the cubic symmetry present in the continuum is broken in md at finite temperature , and processes such as dislocation nucleation at the void surface would be over - constrained in a reduced simulation box . in the simulations , the system is brought to thermal equilibrium at room temperature , @xmath10 k , with a commonly used thermostat @xcite and at ambient pressure , @xmath11 mpa , keeping the volume constant . after that a spherical void is cut in the middle of the system , later the thermostat is turned off , and the dilational strain is applied uniformly with a constant strain - rate @xmath2 . the removal of the atoms in the spherical region may be considered to simulate the instantaneous separation of the matrix material from an infinitely weakly bound inclusion . the uniform expansion in these strain - controlled simulations is applied through rescaling the coordinates as in the parrinello - rahman method . @xcite technically the three cartesian coordinates of the atoms are rescaled to the unit - box , each coordinate @xmath12 . when calculating the forces and velocities , as well as updating the new positions of the atoms , the unit - box is multiplied by a diagonal scaling matrix @xmath13 , where @xmath14 s are the simulation box s side lengths , to compute the true positions of the atoms , @xmath15 this scaling matrix @xmath16 is updated each time - step , when the load is applied , by multiplying the initial matrix @xmath17 with the sum of the unit matrix and the strain matrix @xmath18 , @xmath19 for our purposes the strain - rate matrix @xmath20 is always diagonal , since neither rotation nor simple shear type strains are studied . in the triaxial case all the terms in the diagonal are equal ; in the uniaxial there is a single non - zero term ; and in the biaxial case two of the three diagonal terms differ from zero and are equal . prior to expansion the system is cubic , its scaling matrix @xmath17 is diagonal , and all the terms are equal and correspond to the equilibrium size at ambient pressure . hence the scaling matrix @xmath16 remains diagonal throughout the simulation , and the strain in each case is in a @xmath21 direction . in fracture and plasticity simulations the first quantity to consider is the stress - strain behavior . with the strain as an input parameter , here we have to measure the stress . in this study of the stress - triaxiality we are interested in both mean and shear stresses . therefore the whole stress tensor @xmath22 is needed . the stress tensor ( the negative of the pressure ) can be calculated atomistically on each time - step using the virial formula : @xcite @xmath23 the first term in the stress tensor is the kinetic contribution of atoms denoted with @xmath24 and having masses @xmath25 and momenta @xmath26 . the second term , a microscopic _ virial _ potential stress , consists of sums of interatomic forces @xmath27 of atom pairs @xmath28 with corresponding distances @xmath29 . it should be noted , that here and in the rest of the article @xmath24 and @xmath30 denote the atoms , and @xmath31 and @xmath32 the cartesian coordinates . note that the thermal stress is included , although in practice in these simulations it contributes less than 1 gpa , less than 10% of the yield stress value , and never dominates the changes in stress . typically in the simulations carried out here , the cube consists of 60 fcc unit cells in each direction , giving 864 000 atoms . the equilibrium side - length of such a copper system is @xmath33 nm at room temperature and ambient pressure . the radius of the spherical void cut from the system , unless otherwise noted , is 0.1 of the side - length of the box ; thus @xmath34 nm . after the void is cut , there are 860 396 atoms in the system . the relatively inexpensive potential used enables us to do extensive simulations in time . a single time - step takes typically about 40 sec of cpu - time in a system with 864 000 atoms in a linux workstation with intel xeon 1700mhz processor . the longest calculation required 835 050 time - steps corresponding to 5.6 nanoseconds . the time - step was @xmath35 femtoseconds . as mentioned earlier , in order to study the effects of the stress - triaxiality and different modes of expansion on the void - growth , we have applied three different types of expansion , namely uniaxial , biaxial , and triaxial . the strain - rates used for each of the three modes of expansion are @xmath36/sec , @xmath37/sec , @xmath38/sec , @xmath8/sec , and @xmath0/sec . for the lowest strain - rate , the md code was parallelized in order to take advantage of massively parallel computers . the parallelization was done using a spatial domain - decomposition , and was shown to scale nearly linearly up to 128 processors . the parallel code was used in the case with 835 050 time - steps mentioned above , for example . for comparison in the elastic regime , we have also performed simulations without a void in all three modes of expansion . these simulations have been used to determine the bulk , elastic stress - strain response of the eam copper and hence the elastic constants . without a void , the system is not so strain - rate and system size dependent , at least up to the point of failure , so the so - called `` no void '' simulations have been performed with a smaller system size , 45 fcc - cells in each direction ( 364 500 atoms ) and at the single strain - rate @xmath39/sec . a uniaxial study of the 60@xmath40 system size , but with a smaller initial void radius of @xmath41 nm , was carried out with the strain - rate @xmath42/sec in order to study the void - size dependence . in this case the system with the void contains 863 543 atoms . it should be mentioned , too , that all of the intermediate strain - rate simulations ( @xmath43/sec and @xmath38/sec ) expansion were not started from equilibrium conditions at @xmath44 mpa , but from systems expanded previously at the strain - rate @xmath39/sec . these simulations have been restarted well before yielding , when the system s behavior is rate independent , and relaxed for 2000 time - steps , or 13.4 picoseconds , without expansion before continuing the expansion at the intermediate strain rates . the energy is conserved during the relaxation in md simulations . these restarts have been accomplished at strain values @xmath45 % , @xmath46 % , and @xmath47 % in uniaxial , biaxial , and triaxial cases , respectively .

the effect of stress - triaxiality on growth of a void in a three dimensional single - crystal face - centered - cubic ( fcc ) lattice has been studied . molecular dynamics ( md ) simulations using an embedded - atom ( eam ) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from/sec to/sec . void growth has been simulated in three different conditions , namely uniaxial , biaxial , and triaxial expansion .

the effect of stress - triaxiality on growth of a void in a three dimensional single - crystal face - centered - cubic ( fcc ) lattice has been studied . molecular dynamics ( md ) simulations using an embedded - atom ( eam ) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from/sec to/sec . strain - rates of these magnitudes can be studied experimentally , _ e.g. _ using shock waves induced by laser ablation . void growth has been simulated in three different conditions , namely uniaxial , biaxial , and triaxial expansion . the response of the system in the three cases have been compared in terms of the void growth rate , the detailed void shape evolution , and the stress - strain behavior including the development of plastic strain . also macroscopic observables as plastic work and porosity have been computed from the atomistic level . the stress thresholds for void growth are found to be comparable with spall strength values determined by dynamic fracture experiments . the conventional macroscopic assumption that the mean plastic strain results from the growth of the void is validated . the evolution of the system in the uniaxial case is found to exhibit four different regimes : elastic expansion ; plastic yielding , when the mean stress is nearly constant , but the stress - triaxiality increases rapidly together with exponential growth of the void ; saturation of the stress - triaxiality ; and finally the failure .

cond-mat0310541

c

in this article void growth in copper has been studied in a high range of strain - rates at the atomistic level . the model has been designed to simulate the growth of a void nucleating from a very weakly bound inclusion during strain - controlled dynamic fracture . in order to see the effect of various modes of expansion and the related stress - triaxiality , three different modes have been applied , namely uniaxial , biaxial , and triaxial . the molecular dynamics method developed here has been shown to be efficient enough to explore the different loading conditions and strain - rates varying over four orders of magnitude . a uniform expansive loading of a system with periodic boundary conditions has been implemented using a well defined scaling matrix method . for the longest calculations , the md method was parallelized successfully . the macroscopic observables mean stress , von mises stress , stress - triaxiality , mean plastic strain , equivalent plastic strain , plastic work , and temperature have been calculated and compared with the microscopic quantities measured at the atomistic - level , such as the volume of the void and its shape change . a method to describe the shape changes in the void is introduced and employed , namely calculations of the multipole moments of the void based on spherical harmonics in polynomial , not trigonometric , form . when calculating the volume of the void with an unknown shape or defining solid surface for the multipole moment calculation a useful method , namely optimal triangular tessellation , has been introduced . this method has been extended from the usual planar case to non - planar objects such as the surface of the void . when the different measured quantities are compared with each other during an md simulation in uniaxial expansion , it is found that at early stages of plasticity von mises stress , and thus also stress - triaxiality , plays a more significant role to the void growth and its shape change than expected . on the other hand , most of the macroscopic plastic quantities as mean and equivalent plastic strain as well as plastic work and temperature , seem to be more dependent on the simultaneous saturation of the mean stress . these calculations show a counter - intuitive behavior , observed previously in continuum void growth modeling , @xcite that a prolate - to - oblate transition occurs . when the system starts to yield , the expansion of the void switches from its original elastic extension in the direction of the load to transverse plastic expansion . the yield stress values for the lowest strain - rates @xmath0/sec are in reasonable agreement with the experimentally measured spall strength . @xcite the fact that mean plastic strain can be mapped to the growth of the void is consistent with continuum models . @xcite this study leaves many open questions . for instance related to the void growth are the dislocations , which occur when the system yields . since the fcc crystal studied here is perfect apart from the void , the dislocations form from void s surface . they are also responsible for its growth by carrying material away . thus the characterization of plasticity surrounding a growing void at the level of dislocations should be investigated , too , especially with respect to the stress - triaxiality . these investigations are underway . @xcite their results are beyond the scope of this article , other than to mention that the identification of the yield point in this article does indeed correspond to the point of initial nucleation of dislocations . another topic that is beyond the scope of this article and needs further investigation , but is closely related to the studies here , is the quantitative connection between the shear stress , and thus the mode of the loading , and the onset of the void growth and the resulting change in the stress state . other areas where this study can be extended are different materials including different lattice structures such as body - centered cubic ( bcc ) lattices ; in the uniaxial case other orientations of the lattice as @xmath177 and @xmath178 ; continuously changing stress - triaxiality in order to create the full yield surface to the stress space similarly as in gurson type of continuum studies ; @xcite to include grain boundaries , defects , pre - existing dislocations , several voids , etc . this work was performed under the auspices of the u.s . of energy by the university of california , lawrence livermore national laboratory , under contract number w-7405-eng-48 . the authors would like to thank dr . richard becker bringing to our attention refs . and that find the prolate - oblate transition in continuum modeling .

also macroscopic observables as plastic work and porosity have been computed from the atomistic level . the stress thresholds for void growth are found to be comparable with spall strength values determined by dynamic fracture experiments . the conventional macroscopic assumption that the mean plastic strain results from the growth of the void is validated .

the effect of stress - triaxiality on growth of a void in a three dimensional single - crystal face - centered - cubic ( fcc ) lattice has been studied . molecular dynamics ( md ) simulations using an embedded - atom ( eam ) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from/sec to/sec . strain - rates of these magnitudes can be studied experimentally , _ e.g. _ using shock waves induced by laser ablation . void growth has been simulated in three different conditions , namely uniaxial , biaxial , and triaxial expansion . the response of the system in the three cases have been compared in terms of the void growth rate , the detailed void shape evolution , and the stress - strain behavior including the development of plastic strain . also macroscopic observables as plastic work and porosity have been computed from the atomistic level . the stress thresholds for void growth are found to be comparable with spall strength values determined by dynamic fracture experiments . the conventional macroscopic assumption that the mean plastic strain results from the growth of the void is validated . the evolution of the system in the uniaxial case is found to exhibit four different regimes : elastic expansion ; plastic yielding , when the mean stress is nearly constant , but the stress - triaxiality increases rapidly together with exponential growth of the void ; saturation of the stress - triaxiality ; and finally the failure .

1308.1223

c

we have studied the electronic structure , magnetic interaction , and thermodynamic properties of gd - doped and eu - rich euo using first - principles calculations . homogeneous electron doping of euo , which was modeled in the virtual crystal approximation , leads to a broad maximum in @xmath0 . this maximum is due to the competition between the monotonically increasing indirect exchange contribution and the @xmath1-@xmath2 hopping mechanism , which generates ferromagnetism in pure euo but is suppressed at large doping concentrations . calculations with variable polarization of the @xmath3 shell reveal a pronounced non - heisenberg character of the indirect exchange interaction at small doping concentrations in agreement with the model of mauger,@xcite which leads to strongly enhanced @xmath0 and an anomaly in the @xmath4 curve . we have analyzed the electronic structure of isolated gd impurities and o vacancies in euo . both these defects donate one electron to the conduction band in the ferromagnetic state . an o vacancy introduces an exchange - split @xmath123 center - like level , which is half - filled in the ground state . estimates based on the key parameters extracted from our calculations suggest that in the limit of low vacancy concentrations the impurity state should become doubly occupied , assuming that the @xmath3 spins are fully disordered . this is consistent with the `` he atom model '' of the metal - insulator transition observed in the bulk samples of eu - rich euo @xcite and with no enhancement of @xmath0 in such samples . however , the estimated 0.05 ev activation energy in the paramagnetic state is too low compared to the transport measurements , and we can not rule out the formation of bound magnetic polarons . at higher vacancy concentrations typical for eu - rich euo films , the impurity states broaden into impurity bands , the upper one of which remains partially filled in the paramagnetic state . the impurity states behave as anderson local moments in this regime . this is consistent with the observed strong enhancement of @xmath0 in eu - rich euo films . localized states on o vacancies could also provide the bound states observed in arpes in gd - doped euo . @xcite to go beyond the homogeneous doping model , we employed a magnetostructural cluster expansion ( msce ) approach , which explicitly includes the effect of local chemical environment on the magnetic interaction . for the case of gd - doped euo we constructed an msce based on the input data from first - principles calculations that covers a wide range of gd concentration of up to 25% . for eu - rich euo , we set up a simple msce based on the data for one supercell with a single vacancy . the resulting hamiltonians were used in monte carlo simulations . the curie temperature in gd - doped euo was found to behave similar to the virtual crystal approximation , exhibiting a maximum as a function of gd concentration . the results suggest that the intrinsic limit @xcite of @xmath0 in gd - doped euo is approximately 150 k. oxygen vacancies induce a sharper rise in @xmath0 compared to a similar concentration of gd dopants due to the strong exchange coupling of the neighboring eu atoms mediated by the polarized impurity levels . microscopic inhomogeneity does not lead to any anomalies in the @xmath4 curves , at least in the random alloys that we have considered . we thank s. v. barabash , p. a. dowben , and a. g. petukhov for useful discussions . this work was supported by dtra ( grant no . hdtra1 - 07 - 1 - 0008 ) and nsf ( grant no . dmr-1005642 ) . computations were performed utilizing the holland computing center at the university of nebraska . k. d. b. acknowledges support from the research corporation through the cottrell scholar award .

linear response calculations in the virtual crystal approximation show a broad maximum in the curie temperature as a function of doping , which results from the combination of the saturating contribution from indirect exchange and a decreasing contribution from the- hopping mechanism . when the spins are disordered , the impurity state goes from single to double occupation , but correlated bound magnetic polarons are not ruled out . at higher vacancy concentrations typical for eu - rich euo films , the impurity states broaden into bands and remain partially filled . to go beyond the homogeneous doping picture , the curie temperature for gd - doped euo agrees with the results of the virtual crystal approximation and shows a maximum of about 150 k. at 3.125% vacancy concentration the increases to 120 k , consistent with experimental data for eu - rich film samples .

the effects of gd doping and o vacancies on the magnetic interaction and curie temperature of euo are studied using first - principles calculations . linear response calculations in the virtual crystal approximation show a broad maximum in the curie temperature as a function of doping , which results from the combination of the saturating contribution from indirect exchange and a decreasing contribution from the- hopping mechanism . non - heisenberg interaction at low doping levels and its effect on are examined . the electronic structure of a substitutional gd and of an o vacancy in euo are evaluated . when the spins are disordered , the impurity state goes from single to double occupation , but correlated bound magnetic polarons are not ruled out . at higher vacancy concentrations typical for eu - rich euo films , the impurity states broaden into bands and remain partially filled . to go beyond the homogeneous doping picture , magnetostructural cluster expansions are constructed , which describe the modified exchange parameters near gd dopants or o vacancies . thermodynamic properties are studied using monte carlo simulations . the curie temperature for gd - doped euo agrees with the results of the virtual crystal approximation and shows a maximum of about 150 k. at 3.125% vacancy concentration the increases to 120 k , consistent with experimental data for eu - rich film samples .

math-ph0204006

i

in the early sixties , dyson predicted that the local correlations between the eigenvalues of ensembles of random matrices , when their size tends to infinity , have universal behavior in the bulk of the spectrum . he expected that this universal behavior depends only on the type of the ensemble : orthogonal , unitary or symplectic . this constitutes the famous conjecture of universality in the theory of random matrices . for the classical ensembles ( hermite , laguerre and jacobi ) , this conjecture has been proven , see for example @xcite . for the unitary ensembles much more is known due to the connection with orthogonal polynomials , and the universality conjecture in the bulk of the spectrum is proved for a wide class of unitary ensembles , see @xcite . at the edge of the spectrum this universal behavior breaks down . for hermite ensembles , it is known that the local correlations ( at the soft edge ) can be expressed in terms of airy functions @xcite , and for jacobi and laguerre ensembles ( at the hard edge ) in terms of bessel functions @xcite . for example , for the jacobi unitary ensemble @xmath3 where @xmath4 is the jacobi weight , the eigenvalue correlations near @xmath5 are expressed in terms of the bessel kernel @xmath6 as @xmath7 . @xmath8 is the usual bessel function of the first kind and order @xmath9 . the order agrees with the exponent of @xmath10 in the jacobi weight . nagao and wadati ( * ? ? ? * @xmath11 ) expect that a universality result persists for more general jacobi - like ensembles , in the sense that the local form of the weight function near @xmath5 determines the eigenvalue correlation near @xmath5 . it is the aim of this paper to prove this universal behavior for a generalization of the jacobi unitary ensemble , which we call the modified jacobi unitary ensemble ( mjue ) . the mjue is given by ( [ jue ] ) with modified jacobi weight @xmath12 where @xmath13 and the extra factor @xmath1 is real analytic and strictly positive on @xmath2 $ ] . the modified jacobi ensemble is a probability measure on the space of @xmath14 hermitian matrices with all eigenvalues in @xmath15 . the mjue gives rise to a probability density function of the @xmath16 eigenvalues @xmath17 given by @xmath18 with @xmath19 and @xmath20 a normalizing constant . dyson @xcite showed , see also @xcite , that we can express the correlation functions @xmath21 @xmath22 in terms of orthogonal polynomials . denote the @xmath16th degree orthonormal polynomial with respect to the modified jacobi weight @xmath23 by @xmath24 , @xmath25 . then @xmath26 , where @xmath27 by the christoffel - darboux formula , we have @xmath28 which shows that asymptotic properties of @xmath29 are intimately related with asymptotics of the orthogonal polynomials @xmath30 as @xmath7 . in a previous paper with k.t - r mclaughlin and w. van assche @xcite , we studied the asymptotics of the polynomials that are orthogonal with respect to the modified jacobi weight . we used the riemann - hilbert formulation for orthogonal polynomials of fokas , its , and kitaev @xcite and the steepest descent method for riemann - hilbert problems of deift and zhou @xcite . in @xcite we concentrated on the asymptotics of the polynomials away from the interval @xmath2 $ ] , but the riemann - hilbert method gives uniform asymptotics in all regions in the complex plane . here we are interested in the behavior on @xmath2 $ ] , and in particular near the endpoints @xmath31 . the riemann - hilbert method was applied before to orthogonal polynomials by deift and co - authors @xcite . they studied orthogonal polynomials on the real line with varying weights , and used the asymptotics to prove the universality in the bulk of the spectrum for the associated unitary ensembles . we apply the same method to prove the universality at the edge of the spectrum for the mjue . our main result is the following . [ theoremuniversalityedge ] let @xmath23 be the modified jacobi weight ( [ definitiew ] ) and let @xmath29 be the kernel ( [ definitiekn ] ) associated with @xmath23 . then the following holds . 1 . for @xmath32 , we have as @xmath7 , @xmath33 the error term is uniform for @xmath34 in compact subsets of @xmath15 . 2 . let @xmath35 . then for @xmath32 and @xmath36 , we have as @xmath7 , @xmath37 the error term is uniform for @xmath34 in compact subsets of @xmath15 and for @xmath38 in compact subsets of @xmath39 . 3 . for @xmath40 , we have as @xmath7 , @xmath41 where @xmath42 is the bessel kernel given by ( [ besselkern ] ) . the error term is uniform for @xmath38 in bounded subsets of @xmath43 . note that the error term in ( [ universalnear1 ] ) holds uniformly for @xmath38 in _ bounded _ subsets of @xmath43 , not just in compact subsets . by symmetry , there is a corresponding universality result near @xmath44 . the eigenvalue density is the 1point correlation function @xmath45 , see for example @xcite . therefore , part ( a ) of the theorem yields the asymptotic eigenvalue density @xmath46 as @xmath47 . this result is in agreement with @xcite . the scaling in ( [ universalbulk ] ) has the effect that @xmath34 is the new origin and that the asymptotic eigenvalue density at @xmath34 is 1 . at the endpoints , ( [ densityofstates ] ) breaks down , and the eigenvalue density is @xmath48 as @xmath47 , near the endpoints , see for example @xcite . this explains the scaling in ( [ universalnear1 ] ) . part ( b ) of the theorem states the universality ( independent of the choice of @xmath49 and @xmath34 ) for @xmath29 in the bulk of the spectrum . it extends the result of nagao and wadati ( * ? ? ? * ( 4.19 ) ) for the case that @xmath50 . at the edge 1 of the spectrum we have a universality class for @xmath29 ( independent of the choice of @xmath51 and @xmath1 ) which is only affected by the local form of the modified jacobi weight near 1 , see part ( c ) . using theorem [ theoremuniversalityedge ] we can answer local statistical quantities concerning the eigenvalues . here we follow @xcite . the probability @xmath52 that there are no eigenvalues in the interval @xmath53 is given by @xmath54 where @xmath29 is the trace class operator with integral kernel @xmath55 acting on @xmath56 , and where @xmath57 is the fredholm determinant . for a fixed interval @xmath58 we have that @xmath59 , as @xmath47 . so , to understand the asymptotic behavior of @xmath60 at the edge of the spectrum , we will look at intervals near the edges which shrink with @xmath16 , and we are led to consider the asymptotic behavior of @xmath61 as @xmath47 , where @xmath62 . we have the following universality for @xmath60 at the edge 1 of the spectrum , depending on the parameter @xmath9 but independent of the choice of @xmath51 and @xmath1 . [ corollary2universalityedge ] for @xmath62 , we have @xmath63 where @xmath64 is the integral operator with kernel @xmath65 acting on @xmath66 , and @xmath67 is the fredholm determinant . as mentioned before , our main tool in proving theorem 1.1 is the asymptotic analysis of the riemann - hilbert problem for the orthogonal polynomials with respect to the modified jacobi weight , as developed in @xcite . we give an overview of this work in section 2 . this approach is able to give strong and uniform asymptotics for the orthogonal polynomials in every region in the complex plane , which we also review in section 2 . the proofs of theorem 1.1 and corollary 1.2 are given in section 3 .

the eigenvalue correlations of random matrices from the jacobi unitary ensemble have a known asymptotic behavior as their size tends to infinity . in the bulk of the spectrum the behavior is described in terms of the sine kernel , and at the edge in terms of the bessel kernel . we will prove that this behavior persists for the modified jacobi unitary ensemble . this generalization of the jacobi unitary ensemble is associated with the modified jacobi weight where the extra factor is assumed to be real analytic and strictly positive on $ ] . we use the connection with the orthogonal polynomials with respect to the modified jacobi weight , and recent results on strong asymptotics derived by k.t - r mclaughlin , w. van assche and the authors . * universality for eigenvalue correlations from the modified jacobi unitary ensemble * a.b.j .

the eigenvalue correlations of random matrices from the jacobi unitary ensemble have a known asymptotic behavior as their size tends to infinity . in the bulk of the spectrum the behavior is described in terms of the sine kernel , and at the edge in terms of the bessel kernel . we will prove that this behavior persists for the modified jacobi unitary ensemble . this generalization of the jacobi unitary ensemble is associated with the modified jacobi weight where the extra factor is assumed to be real analytic and strictly positive on $ ] . we use the connection with the orthogonal polynomials with respect to the modified jacobi weight , and recent results on strong asymptotics derived by k.t - r mclaughlin , w. van assche and the authors . * universality for eigenvalue correlations from the modified jacobi unitary ensemble * a.b.j . kuijlaars + _ department of mathematics , katholieke universiteit leuven , + celestijnenlaan 200 b , 3001 leuven , belgium + [email protected] + and + m. vanlessen + _ department of mathematics , katholieke universiteit leuven , + celestijnenlaan 200 b , 3001 leuven , belgium + [email protected]__ +

1104.1645

i

non - equilibrium phenomena on the nanoscale increasingly gain interest as more and more devices are based on nanoscale electronics . the ongoing miniaturization trend results in state - of - the - art transistors , used for information processing , in which only a small number of electrons is moving through a conducting channel at a given time . semiconductor - based quantum information processing relies on the coherent dynamics in nanostructures . for both classical and , in particular , quantum circuits the detection of information relies on electronic signals strong enough to be measurable . an inevitable consequence are interactions in nonequilibrium giving rise to quantum noise and back - action . our experiments aim at understanding the underlying physics of interacting nanoscale circuits where only few electrons far from thermal equilibrium carry the information . we study in transport experiments at low temperatures the simplest case of individual nonequilibrium electrons . after their injection these `` hot '' electrons move at first ballistically with well - defined , high kinetic energy before they relax in an otherwise degenerate fermi liquid interested in the case of a high mobility 2des since here electrons near the fermi edge have a momentum mean - free path @xmath1 of several micrometers and therefore move ballistically through the mesoscopic device . the scattering length of the hot electrons , however , at first strongly decreases as a function of kinetic energy as the phase space for scattering processes grows . for larger kinetic energies the electron - electron scattering length increases again because of the high velocity and short interaction times . in a magnetic field perpendicular to the plane of the 2des , the lorentz force tends to guide hot electrons to move along the edges of the conducting mesa of the 2des . in this article we focus on the transition between two - dimensional scattering in a low magnetic field to quasi one - dimensional scattering in the quantum limit of edge channel transport of the hot electrons . one - dimensional '' refers to a situation where the lateral width of the effective transport channel still exceeds the magnetic length . relevant energy - loss mechanisms of hot electrons in a 2des are the emission of plasmons , acoustic or optical phonons , or scattering with `` cold '' equilibrium electrons in the degenerate fermi sea . the radiation of photons is strongly suppressed because of the momentum missmatch . the emission of plasmons by hot electrons is particularly hard to capture in pure transport experiments so we will address plasmons only briefly from the theoretical point of view in this article . the interaction between hot electrons and acoustic phonons constitutes a minor contribution to the relaxation of hot electrons in our nonequilibrium experiments . it therefore wo nt be a focus here , but detailed investigations in zero magnetic field have already been conducted on comparable samples by using a novel phonon spectroscopy technique.@xcite it is worth mentioning , however , that acoustic phonons play a major role in interactions between _ electrically separated _ nanostructures in nonequilibrium without@xcite and with@xcite a perpendicular magnetic field applied . the emission of optical phonons has been studied in zero magnetic field in various types of experiments since the 1960 s . it usually shows up as a very weak oscillatory signal as a function of the kinetic energy of hot electrons , with an oscillation frequency equal to the phonon energy . it has been observed in several materials including gaas in photoconductivity,@xcite in raman scattering experiments@xcite as well as in pure transport experiments in which electrons tunnel vertically between layers of a heterostructure.@xcite later the emission of optical phonons has also been observed in lateral devices defined in gaas - based heterostructures.@xcite the scattering of hot electrons in zero magnetic field with a cold 2des has been experimentally investigated in lateral three - terminal devices where the three regions have been separated by electrostatic barriers.@xcite it has been demonstrated that the electron - electron interaction in such mesoscopic three - terminal devices gives rise to effects such as a `` negative resistance''@xcite and can be used for avalanche amplification of a current of hot injected electrons.@xcite building on refs . and here we find that the transition from two - dimensional to one - dimensional scattering , as a perpendicular magnetic field is increased , goes along with a change in the importance of electron - electron scattering versus the emission of optical phonons . these two processes dominate the scattering dynamics of hot electrons in a degenerate two- or one - dimensional electron system in the whole range of available magnetic fields . at low fields hot electrons relax mainly via electron - electron scattering while the emission of optical phonons becomes more and more important at high fields . still , amplification of the injected electron current based on electron - electron scattering occurs even in a large perpendicular magnetic field . our measurements indicate that the scattering time between hot electrons and optical phonons strongly decreases as a function of the perpendicular magnetic field while the electron - electron scattering time increases . our experimental results are backed up by numerical calculations of the electron - electron scattering time and the emission rate of optical phonons as a function of the perpendicular magnetic field . finally , changing the magnetic field direction reveals a contribution of hopping transport via high energy localized bulk states of the 2des where a strong perpendicular magnetic field hinders the screening of disorder .

the energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two - dimensional electron system are investigated in transport experiments in a mesoscopic three - terminal device . one - dimensional scattering of the hot electrons in a strong magnetic field . in the two - dimensional case electron - electron scattering is the dominant relaxation mechanism , while the emission of optical phonons becomes more and more important as the magnetic field is increased . numerical calculations of electron - electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one - dimensional dynamics .

the energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two - dimensional electron system are investigated in transport experiments in a mesoscopic three - terminal device . we observe a transition from two dimensions at zero magnetic field to quasi one - dimensional scattering of the hot electrons in a strong magnetic field . in the two - dimensional case electron - electron scattering is the dominant relaxation mechanism , while the emission of optical phonons becomes more and more important as the magnetic field is increased . the observation of up to 11 optical phonons emitted per hot electron allows us to determine the onset energy of lo phonons in gaas at cryogenic temperatures with a high precision ,mev . numerical calculations of electron - electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one - dimensional dynamics .

math0109166

i

the orientation - preserving free actions of a finite group @xmath0 on 3-dimensional orientable handlebodies have a close connection with a long - studied concept from group theory , namely _ nielsen equivalence _ of generating sets . indeed , as we observe in section [ sec : theory ] below , the free actions of @xmath0 on the handlebody of genus @xmath7 , up to equivalence , correspond to the nielsen equivalence classes of @xmath3-element generating sets of @xmath0 , where @xmath4 . we will utilize this to prove a number of results about equivalence and weak equivalence of free actions . these results are summarized in concise form in section [ sec : results ] , which also contains precise definitions of equivalence , weak equivalence , and other concepts that we shall use . a special feature of free actions on handlebodies is that there is a stabilization process relating actions on different genera . when a handlebody @xmath10 with a free @xmath0-action contains a @xmath0-invariant handlebody @xmath11 such that @xmath12 consists of disjoint @xmath13-handles , the action on @xmath10 is called a stabilization of the action on @xmath11 . inequivalent actions can become equivalent after stabilization , indeed we do not know an example of actions that remain inequivalent after even an elementary stabilization ( i. e. a stabilization for which @xmath12 consists of @xmath14 @xmath13-handles ) . such an example could not involve a solvable group , since a result of m. dunwoody implies that for solvable @xmath0 , any two actions on a handlebody of more than the minimum possible genus for a @xmath0-action are equivalent ( see corollary [ coro : solvable corollary 2 ] below ) . for an arbitrary @xmath0 , proposition [ prop : stabilization ] shows that any two actions become equivalent after @xmath15 elementary stabilizations , where @xmath15 is the minimum number of generators of @xmath0 . we remark that there is an interesting theory of stabilization of actions on @xmath16-manifolds @xcite . the connection between free actions on handlebodies and nielsen equivalence is well - known in some circles , although we can not find an explicit statement in the literature . it was known to j. kalliongis and a. miller and is is a direct consequence of theorem 1.3 in their paper @xcite ( for free actions , the graph of groups will have trivial vertex and edge groups , and the equivalence of graphs of groups defined there is readily seen to be the same as nielsen equivalence on generating sets of @xmath0 ) . indeed , more delicate classifications of nonfree actions on handlebodies have been examined in considerable depth . a general theory of actions was given in @xcite and @xcite , and the actions on very low genera were extensively studied in @xcite . actions with the genus small relative to the order of the group are investigated in @xcite , and the special case of orientation - reversing involutions is treated in @xcite . the first focus on free actions seems to be @xcite , where it was proven that for a cyclic group , any free action on a handlebody of genus above the minimal one is the stabilization of an action on minimal genus , and that any two free actions on a handlebody are weakly equivalent . these results were generalized to dihedral and abelian groups in @xcite , whose results are reconfirmed and extended in section [ sec : abelian and dihedral ] below . some of the arguments in this paper can be shortened by invoking results from @xcite . since the general theory given there is much more elaborate than the elementary methods needed for the present work , we have chosen to make our arguments self - contained . after giving some more precise definitions and stating our main results in section [ sec : results ] , we develop the general theory relating free actions to nielsen equivalence in section [ sec : theory ] . we apply this in section [ sec : solvable groups ] to treat the case when @xmath0 is solvable , and in section [ sec : abelian and dihedral ] we examine the specific cases of abelian and dihedral groups . in section [ sec : free actions of psl(2,3p ) ] , we show that for @xmath6 prime , two free actions of @xmath5 on a handlebody of genus above the minimal one are equivalent . by work of evans @xcite and gilman @xcite , it is known that the same is true for @xmath17 ( for all @xmath18 ) and @xmath19 ( for @xmath6 prime ) . section [ sec : stabilization of actions ] gives some general results on stabilization , in particular , we prove that if the genus of @xmath10 is at least @xmath20 , where @xmath9 is the maximum length of a decreasing chain of nonzero subgroups of @xmath0 , then any two free @xmath0-actions are equivalent . in section [ sec : questions ] , we state some open problems . in particular , do there even exist inequivalent actions that are not minimal genus actions ?

the equivalence ( or weak equivalence ) classes of orientation - preserving free actions of a finite group on an orientable-dimensional handlebody of genus can be enumerated in terms of sets of generators of . there is only one equivalence class of actions on the genus handlebody if is at least , where is the maximal length of a chain of subgroups of . there is a stabilization process that sends an equivalence class of actions to an equivalence class of actions on a higher genus , and some results about its effects are obtained .

the equivalence ( or weak equivalence ) classes of orientation - preserving free actions of a finite group on an orientable-dimensional handlebody of genus can be enumerated in terms of sets of generators of . they correspond to the equivalence classes of generating-vectors of elements of , where , under nielsen equivalence ( or weak nielsen equivalence ) . for abelian and dihedral , this allows a complete determination of the equivalence and weak equivalence classes of actions for all genera . additional information is obtained for solvable groups and for the groups with prime . for all , there is only one equivalence class of actions on the genus handlebody if is at least , where is the maximal length of a chain of subgroups of . there is a stabilization process that sends an equivalence class of actions to an equivalence class of actions on a higher genus , and some results about its effects are obtained .

astro-ph0309411

i

there is growing evidence in cosmology for the existence of nearly massless scalar fields in our universe . on the one hand , a host of observations , from supernovae luminosity - distance measurements @xcite to the cosmic microwave background anisotropy @xcite , suggests that 70% of the current energy budget consists of a dark energy fluid with negative pressure . while observations are consistent with a non - zero cosmological constant , the dark energy component is more generally modeled as quintessence : a scalar field rolling down a flat potential @xcite . in order for the quintessence field to be evolving on cosmological time scales today , its mass must be of order @xmath0 , the present hubble parameter . on the other hand , recent measurements of absorption lines in quasar spectra suggest that the fine - structure constant @xmath2 has evolved by roughly one part in @xmath3 over the redshift interval @xmath4 @xcite . time - variation of coupling constants are generally modeled with rolling scalar fields @xcite , and the recent evidence for a time - varying @xmath2 requires the mass of the corresponding scalar field to be of order @xmath0 @xcite . in either case , the inferred scalar field is essentially massless on solar system scales , and therefore subject to tight constraints from tests of the equivalence principle ( ep ) @xcite . the current bound on the e@xmath5tv@xmath5s parameter , @xmath6 , which quantifies the deviation from the universality of free - fall , is @xmath7 , from the e@xmath5t - wash experiment @xcite . from a theoretical standpoint , massless scalar fields or moduli are abundant in string and supergravity theories . indeed , generic compactifications of string theory result in a plethora of massless scalars in the low - energy , four - dimensional effective theory . however , these massless fields generally couple directly to matter with gravitational strength , and therefore lead to unacceptably large violations of the ep . therefore , if the culprit for quintessence or time - varying @xmath2 is one of the moduli of string theory , some mechanism must effectively suppress its ep - violating contributions . for instance , damour and polyakov @xcite ( see also @xcite ) have proposed a dynamical mechanism to suppress the coupling constants @xmath8 between the various matter fields and the dilaton of string theory . alternatively , the suppression could be the result of approximate global symmetries @xcite . in a recent paper @xcite , we presented a scenario in which scalar fields can evolve cosmologically while having couplings to matter of order unity , _ i.e. , _ @xmath9 . this is because the scalar fields acquire _ a mass whose magnitude depends on the local matter density_. in a region of high density , such as on earth , the mass of the fields is large , and thus the resulting violations of the ep are exponentially suppressed . in the solar system , where the density is much lower , the moduli are essentially free , with a compton wavelength that can be much larger than the size of the solar system . finally , on cosmological scales , where the density is very low , the mass can be of the order of the present hubble parameter , thereby making the fields potential candidates for causing the acceleration of the universe or the time - evolution of the fine - structure constant . while the idea of density - dependent mass terms is not new @xcite , the novelty of our work lies in that the scalar fields can couple directly to baryons with gravitational strength . in our scenario , scalar fields that have cosmological effects , such as quintessence , do not result in large violations of the ep in the laboratory because we happen to live in a very dense environment . thus , the main constraint on our model is that the mass of the field be sufficiently large on earth to evade ep and fifth force constraints @xcite . the generation of a density - dependent mass for a given modulus @xmath10 results from the interplay of two source terms in its equation of motion . the first term arises from self - interactions , described by a monotonically - decreasing potential @xmath11 which is of the runaway form ( see fig . [ pot ] ) . in particular , we underscore the fact that the potential need not have a minimum ; rather , it must be monotonic . the second term arises from the conformal coupling to matter fields , of the form @xmath12 . the coupling constants @xmath8 need not be small , however , and values of order unity or greater are allowed . although these two contributions are both monotonic functions of @xmath10 , their combined effect is that of an effective potential which does display a minimum ( see fig . [ poteff ] ) . furthermore , since this effective potential depends explicitly on the local matter density @xmath13 , both the field value at the minimum and the mass of small fluctuations depend on @xmath13 as well , with the latter being an increasing function of the density . although the scalar fields are quite massive on earth , their behavior is strikingly different in the solar system where the local matter density is much smaller . thus our model makes a crucial prediction for near - future experiments that will test gravity in space . for example , consider the see project @xcite which among other things will measure newton s constant to an unprecedented accuracy . our scenario generically predicts that the see experiment should observe corrections of order unity to newton s constant compared to its measured value on earth , due to fifth - force contributions which are important in space but exponentially suppressed on earth . moreover , three satellite experiments to be launched in the near future , step @xcite , galileo galilei ( gg ) @xcite and microscope @xcite , will test the universality of free - fall in orbit with expected accuracy of @xmath14 , @xmath15 and @xmath16 , respectively . we predict that these experiments should observe a strong ep - violating signal . in fact , for a wide range of parameters , our model predicts that the signal will be larger than the ground - based e@xmath5t - wash bound of @xmath17 . if see does measure an effective newton s constant different from that on earth , or if step observes an ep - violating signal larger than thought permitted by the e@xmath5t - wash experiment , this will strongly indicate that a mechanism of the form proposed here is realized in nature . for otherwise it would be hard to explain the discrepancies between measurements in the laboratory and those in orbit . these new and surprising outcomes are a direct consequence of the fact that scalar fields in our model have drastically different behavior in regions of high density than in regions of low density . we refer to @xmath10 as a `` chameleon '' field , since its physical properties , such as its mass , depend sensitively on the environment . moreover , in regions of high density , the chameleon `` blends '' with its environment and becomes essentially invisible to searches for ep violation and fifth force . even though we predict significant violations of the ep in space , all existing constraints from planetary orbits @xcite , such as those from lunar laser ranging @xcite , are easily satisfied in our model . this is because of the fact that the chameleon - mediated force between two large objects , such as the earth and the sun , is much weaker than one would naively expect . to see this , we use calculus and break up the earth into a collection of infinitesimal volume elements . consider one such volume element located well - within the earth . since the mass of the chameleon is very large inside the earth , the @xmath10-flux from this volume element is exponentially suppressed and therefore contributes negligibly to the @xmath10-field outside the earth . this is true for all volume elements within the earth , except for those located in a thin shell near the surface . infinitesimal elements within this shell are so close to the surface that they do not suffer from the bulk exponential suppression . thus , the exterior field is generated almost entirely by this thin shell , whereas the bulk of the earth contributes negligibly . a similar argument applies to the sun . consequently , the chameleon - mediated force between the earth and the sun is suppressed by this thin - shell effect , which thereby ensures that solar system tests of gravity are satisfied . however , note that this only applies to large objects , such as planets . sufficiently small objects do not suffer from thin - shell suppression , and thus their entire mass contributes to the exterior field . in particular , a small satellite in orbit , such as see , may not exhibit a thin - shell effect . this is why the orbits of the planets are essentially unaffected by the @xmath10-force , whereas the fifth force between two test particles in the see capsule is significant . since @xmath10 couples directly to matter fields , all mass scales and coupling constants of the standard model depend on space and time . once again due to the thin - shell mechanism described above , spatial variations of constants are sufficiently small in our model to satisfy current experimental bounds , for instance from the vessot - levine experiment @xcite . time variation of coupling constants are also not a problem since , during most of the history of the universe , the various couplings actually change by very little . thus the bounds from big bang nucleosynthesis , for instance , are easily satisfied . this will be described in more detail in a separate paper dealing with the cosmological evolution in our model @xcite . in sec . [ setups ] , we describe the ingredients of the scenario , focusing on a single modulus @xmath10 for simplicity . we show how the dynamics of @xmath10 are governed by an effective potential that depends on the local matter density . in sec . [ compact ] , we derive approximate solutions for @xmath10 for a compact object such as the sun , for instance , and describe the thin - shell mechanism mentioned earlier . in sec . [ earth ] , we specialize the solution for @xmath10 to the case of the earth , and apply the results in sec . [ tests ] to derive constraints on the parameters of the theory based on laboratory tests of the ep and searches for a fifth force . we then show in sec . [ condmass ] that , for a potential of power - law form , @xmath18 , these constraints translate into the requirement that the energy scale @xmath19 be less than an inverse millimeter or so . curiously , this is also the scale associated with the cosmological constant today . in sec . [ solar ] , we argue that our model easily satisfies constraints from solar system tests of gr . it is showed ( sec . [ sep ] ) that the same holds true for bounds from spatial and time variation of coupling constants . we then predict ( sec . [ satellite ] ) that near - future experiments that aim at testing the ep and measuring a fifth force should observe a large signal , perhaps stronger than previously thought possible . finally , we conclude and summarize our results in sec . [ conclu ] .

the evidence for the accelerated expansion of the universe and the time - dependence of the fine - structure constant suggests the existence of at least one scalar field with a mass of order . if such a field exists , then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the equivalence principle ( ep ) . in this paper , we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity . in our scenario , the mass of the fields depends on the local matter density : the interaction range is typically of order 1 mm on earth ( where the density is high ) and of order au in the solar system ( where the density is low ) . nevertheless , we predict that near - future experiments that will test gravity in space will measure an effective newton s constant different by order unity from that on earth , as well as ep violations stronger than currently allowed by laboratory experiments .

the evidence for the accelerated expansion of the universe and the time - dependence of the fine - structure constant suggests the existence of at least one scalar field with a mass of order . if such a field exists , then it is generally assumed that its coupling to matter must be tuned to unnaturally small values in order to satisfy the tests of the equivalence principle ( ep ) . in this paper , we present an alternative explanation which allows scalar fields to evolve cosmologically while having couplings to matter of order unity . in our scenario , the mass of the fields depends on the local matter density : the interaction range is typically of order 1 mm on earth ( where the density is high ) and of order au in the solar system ( where the density is low ) . all current bounds from tests of general relativity are satisfied . nevertheless , we predict that near - future experiments that will test gravity in space will measure an effective newton s constant different by order unity from that on earth , as well as ep violations stronger than currently allowed by laboratory experiments . such outcomes would constitute a smoking gun for our scenario .

1106.5613

i

we have studied the evolutionary properties and spatial distribution of the stars resolved in izw18 by hst / acs proprietary and archival photometry . to this aim we have analysed both the al07 and the f10 catalogues and found consistent results , independently of the different selection criteria adopted in the two approaches . nonetheless , to be conservative , we have based our conclusions on the al07 most restrictively selected catalogue . the comparison of the cmds resulting from the acs photometry with stellar evolution models ( tracks and isochrones ) indicates that stars of all ages are present in the two bodies . in spite of the impossibility of reaching the oldest ms turn - off in a galaxy 19 mpc away , the extremely low metallicity of izw18 relaxes the age - metallicity degeneracy and makes the red edge of the rgb a signature of the presence of stars up to possibly 13 gyr old . the oldest detectable stars are best visible in the sb and the se portion of the mb , where crowding is less severe , but are present also in the rest of the mb , although measured with larger uncertainties . we have found that the stars are homogeneously distributed over the two bodies , with the younger ones more centrally concentrated , as always found in starburst dwarfs , and the older / fainter ones spread out to the system periphery , also because of selection effects in their detectability . from the maps of the stars spatial distribution ( figure [ map07 ] ) we conclude that old and intermediate age stars are actually distributed homogeneously over the two bodies . * the distance independently estimated from the trgb ( al07 ) and the cepheids ( f10 ) is @xmath101 mpc . * as far as stars are concerned , the sb is completely separated from the mb : no star is detected between the two bodies . if tidal interactions are at work , they do nt appreciably affect the distribution of the stellar populations of the two components . * izw18 contains stars in all the evolutionary phases visible at its distance : massive and intermediate mass stars on the ms , blue and red supergiants , agb and tp - agb stars , carbon stars , rgb stars . hence , it hosts stars of all ages , from a few myr up to possibly 13 gyr . * the mb hosts two bright star forming regions ( nw and se ) , embedded in a common and homogeneous environment of older stars . some stars may have been recently formed on the gas filaments protruding from the nw portion of the mb . * while old and intermediate age stars are present in similar amounts in the mb and in the sb , the youngest stars are only found in the mb and mostly concentrated in its nw region . the se region has also been active recently , but at a lower current rate ; the sb has had definitely less star formation than the mb in the last tens of myr . * of the 34 candidate variable stars studied by f10 , 19 and 15 are in , or around , the mb and the sb respectively . all the confirmed ones are however in the mb : the two ulp cepheids in the nw region ; the classical cepheid and the two lpvs in the se region . * at izw18 s distance , star clusters are not distinguishable from point - like sources . it is thus possible that some of the brightest objects in the main body are actually clusters and not individual stars . comparing their colors with simple stellar population models , we find that the candidate clusters would span ages from a few myr to a hubble time , with the majority of them being younger than @xmath8200 myr . however , the fraction of stellar mass in old ( age@xmath911 gyr ) clusters would be significantly higher than what found in other dwarfs , suggesting that the majority of the candidate old clusters are instead resolved stars . the reddest ( @xmath102 ) brightest objects can not be unresolved clusters and must be supergiants with ages younger than @xmath820 myr . these results show that izw18 is not unique in the sky , but shares the evolutionary properties typical of bcds and , more in general , of late - type dwarfs ( see * ? ? ? * for a review ) . it is not experiencing now its first burst of star formation , but has been forming stars over many gyrs , most likely over the whole hubble time . this implies that its extremely low metallicity can not be explained by a low chemical enrichment due to extremely recent star formation . at best , one may hope that the sfr has been low until relatively recently ( see e.g. * ? ? ? * ) , although the conspicuous presence of stars of all ages does not make this likely . the same problem obviously concerns all the other metal - poor bcds where stars many gyr old have been found , like sbs1415 + 437 @xcite . we recall that no genuinely young galaxy has been found yet by anybody . all the galaxies whose stellar content has been resolved so far contain stars as old as the lookback time allowed by the available instrumentation , whatever their morphological type and metallicity ( see e.g. * ? ? ? * ; * ? ? ? * and references therein ) . hence , since stellar nucleosynthesis has had plenty of time to pollute them , the only ways to explain the low observed metallicity of these galaxies are either to dilute sufficiently their insterstellar medium by accretion of primordial or very metal poor gas , or to remove the stellar nucleosynthesis products through galactic winds triggered by supernova explosions , or both . chemical evolution models of late - type dwarfs and bcds have shown long ago @xcite that infall of metal poor gas alone is not sufficient to reproduce the low metallicity of starburst dwarfs , and that galactic winds must be invoked too . observational evidence for galactic winds has been found for a handful of starburst dwarfs @xcite , and izw18 is indeed one of those where the outflowing ( martin 1996 ) ionized gas associated with the most recent sf activity may indeed have a speed higher than the escape velocity and be able to remove metals from the system . it would be crucial to get detailed information also on the cold gas , see how it is spatially distributed , and what its kinematics is . understanding the chemical and dynamical evolution of izw18 represents a key step to approach the evolution of all dwarf galaxies as well as that of more massive systems which may have formed from the assembly of small objects like it . we thank filippo fraternali and renzo sancisi for interesting conversations on the hi gas properties . financial support for this study was provided by asi through contracts cofis asi - inaf i/016/07/0 and asi - inaf i/009/10/0 . support to the us co - authors was provided by nasa through grants associated with program go-10586 from the space telescope science institute ( stsci ) , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . aloisi , a. , tosi , m. , & greggio , l. 1999 , , 118 , 302 aloisi , a. , van der marel , r. p. , mack , j. , leitherer , c. , sirianni , m. , & tosi , m. 2005 , , 631 , l45 aloisi , a. , et al . 2007 , , 667 , l151 marel , r. p. , mack , j. , leitherer , c. , sirianni , m. , & tosi , m. 2005 , , 631 , l45 annibali , f. , tosi , m. , monelli , m. , sirianni , m. , montegriffo , p. , aloisi , a. , & greggio , l. 2009 , , 138 , 169 annibali , f. , tosi , m. , aloisi , a. & van der marel , r. p. , 2011 , , submitted avni , y. 1976 , , 210 , 642 billett , o. h. , hunter , d. a. , & elmegreen , b. g. 2002 , , 123 , 1454 bomans , d. j. , van eymeren , j. , dettmar , r .- j . , weis , k. , & hopp , u. 2007 , , 51 , 141 cannon , j. m. , skillman , e. d. , garnett , d. r. , & dufour , r. j. 2002 , , 565 , 931 cervio , m. , & luridiana , v. 2004 , , 413 , 145 chandar , r. , leitherer , c. , tremonti , c. a. , calzetti , d. , aloisi , a. , meurer , g. r. , & de mello , d. 2005 , , 628 , 210 cignoni , m. , & tosi , m. 2010 , advances in astronomy , 2010 , davidson , k. , & kinman , t. d. 1985 , , 58 , 321 davidson , k. , kinman , t. d. , & friedman , s. d. 1989 , , 97 , 1591 dufour , r. j. , garnett , d. r. , & shields , g. a. 1988 , , 332 , 752 dufour , r. j. , & hester , j. j. 1990 , , 350 , 149 dufour , r. j. , esteban , c. , & castaneda , h. o. 1996a , , 471 , l87 dufour , r. j. , garnett , d. r. , skillman , e. d. , & shields , g. a. 1996b , from stars to galaxies : the impact of stellar physics on galaxy evolution , 98 , 358 fagotto , f. , bressan , a. , bertelli , g. , & chiosi , c. 1994 , , 104 , 365 fiorentino , g. , et al . 2010 , , 711 , 808 garnett , d. r. , skillman , e. d. , dufour , r. j. , & shields , g. a. 1997 , , 481 , 174 363 , 142 girardi , l. , et al . 2010 , , 724 , 1030 grimes , j. p. , et al . 2009 , , 181 , 272 holtzman , j. a. , burrows , c. j. , casertano , s. , hester , j. j. , trauger , j. t. , watson , a. m. , & worthey , g. 1995 , , 107 , 1065 hunter , d. a. , & thronson , h. a. , jr . 1995 , , 452 , 238 hunter , d. a. , oconnell , r. w. , gallagher , j. s. , & smecker - hane , t. a. 2000 , , 120 , 2383 izotov , y. i. , thuan , t. x. , & lipovetsky , v. a. 1994 , , 435 , 647 izotov , y. i. , & thuan , t. x. 1998 , , 497 , 227 izotov , y. i. , & thuan , t. x. 2004 , , 616 , 768 izotov , y. i. , guseva , n. g. , fricke , k. j. , & papaderos , p. 2009 , , 503 , 61 kunth , d. , lequeux , j. , sargent , w. l. w. , & viallefond , f. 1994 , , 282 , 709 larsen , s. s. , & richtler , t. 2000 , , 354 , 836 legrand , f. 2000 , , 44 , 345 lequeux , j. , peimbert , m. , rayo , j. f. , serrano , a. , & torres - peimbert , s. 1979 , , 80 , 155 lequeux , j. , & viallefond , f. 1980 , , 91 , 269 maz apellniz , j. 2009 , , 699 , 1938 marconi , g. , matteucci , f. , & tosi , m. 1994 , , 270 , 35 marconi , m. , et al . 2010 , , 713 , 615 marigo , p. , & girardi , l. 2007 , , 469 , 239 martin , c. l. 1996 , , 465 , 680 matteucci , f. , & tosi , m. 1985 , , 217 , 391 momany , y. , et al . 2005 , , 439 , 111 olive , k. a. , steigman , g. , & skillman , e. d. 1997 , , 483 , 788 origlia , l. , leitherer , c. , aloisi , a. , greggio , l. , & tosi , m. 2001 , , 122 , 815 pagel , b. e. j. , simonson , e. a. , terlevich , r. j. , & edmunds , m. g. 1992 , , 255 , 325 petrosian , a. r. , boulesteix , j. , comte , g. , kunth , d. , & lecoarer , e. 1997 , , 318 , 390 pilyugin , l. s. 1993 , , 277 , 42 sargent , w. l. w. , & searle , l. 1970 , , 162 , l155 searle , l. , & sargent , w. l. w. 1972 , , 173 , 25 searle , l. , sargent , w. l. w. , & bagnuolo , w. g. 1973 , , 179 , 427 silva - villa , e. , & larsen , s. s. 2011 , , 529 , a25 sirianni , m. , et al . 2005 , , 117 , 1049 skillman , e. d. , & kennicutt , r. c. , jr . 1993 , , 411 , 655 2005 , , 117 , 1049 stasiska , g. , & leitherer , c. 1996 , , 107 , 661 stetson , p. b. 1987 , , 99 , 191 stetson , p. b. 1994 , , 106 , 250 tolstoy , e. , hill , v. , & tosi , m. 2009 , , 47 , 371 tosi , m. , aloisi , a. , mack , j. , & maio , m. 2007 , iau symposium , 235 , 65 tosi , m. 2009 , iau symposium , 258 , 61 van der marel , r. p. , & cioni , m .- r . l. 2001 , , 122 , 1807 van zee , l. , westpfahl , d. , haynes , m. p. , & salzer , j. j. 1998 , , 115 , 1000 zwicky , f. 1966 , , 143 , 192

the evolutionary properties and spatial distribution of i zwicky 18 stellar populations are analyzed by means of hst / acs deep and accurate photometry . the comparison of the resulting colour - magnitude diagrams with stellar evolution models indicates that stars of all ages are present in all the system components , including objects possibly up to 13 gyr old , intermediate age stars and very young ones . the stellar spatial distribution shows that the younger ones are more centrally concentrated , while old and intermediate age stars are distributed homogeneously over the two bodies , although more easily detectable at the system periphery . the oldest stars are best visible in the secondary body ( sb ) and in the south east ( se ) portion of the mb , where crowding is less severe , but are present also in the rest of the mb , although measured with larger uncertainties . the youngest stars are a few myr old , are located predominantly in the mb and mostly concentrated in its nw portion . the se portion of the mb appears to be in a similar , but not as young evolutionary stage as the nw , while the sb stars are older than at least 10 myr . all our results suggest that izw18 is not atypical compared to other bcds .

the evolutionary properties and spatial distribution of i zwicky 18 stellar populations are analyzed by means of hst / acs deep and accurate photometry . the comparison of the resulting colour - magnitude diagrams with stellar evolution models indicates that stars of all ages are present in all the system components , including objects possibly up to 13 gyr old , intermediate age stars and very young ones . the colour - magnitude diagrams show evidence of thermally pulsing asymptotic giant branch and carbon stars . classical and ultra - long period cepheids , as well as long period variables have been measured . about 20 objects could be unresolved star clusters , and are mostly concentrated in the north - west ( nw ) portion of the main body ( mb ) . if interpreted with simple stellar population models , these objects indicate a particularly active star formation over the past hundred myr in izw 18 . the stellar spatial distribution shows that the younger ones are more centrally concentrated , while old and intermediate age stars are distributed homogeneously over the two bodies , although more easily detectable at the system periphery . the oldest stars are best visible in the secondary body ( sb ) and in the south east ( se ) portion of the mb , where crowding is less severe , but are present also in the rest of the mb , although measured with larger uncertainties . the youngest stars are a few myr old , are located predominantly in the mb and mostly concentrated in its nw portion . the se portion of the mb appears to be in a similar , but not as young evolutionary stage as the nw , while the sb stars are older than at least 10 myr . there is then a sequence of decreasing age of the younger stars from the secondary body to the se portion of the mb to the nw portion . all our results suggest that izw18 is not atypical compared to other bcds .

gr-qc0408091

i

laser - beam detectors of gravitational waves are designed to explore the universe in a new type of radiation and from a new perspective . with the already operating instruments , and coming soon online , we are expecting to witness the discovery of fascinating physics involved in powerful sources of cosmic gravitational radiation . the astrophysical aims of the gravitational wave ( g.w . ) science are well understood and comprehensively described in the literature ( for recent reviews , see for example @xcite ) . naturally , g.w . community is focused on the ambitious target of ` reaching for the black holes ' . but what about a more modest goal of looking inside our own planet ? no doubt , black holes are fascinating and scientifically important objects . but it is also necessary to remember that , say , the still poorly understood and unpredictable earthquakes are claiming thousands of human lives per year . is it possible that the cutting - edge technology of g.w . interferometers @xcite may help us with accurate geophysical studies , as a by - product of the continuous search for astrophysical gravitational waves ? this is the major question of the present work , and the answer is positive . we shall show in this paper that a laser - beam detector of gravitational waves is in fact automatically a valuable geophysical device . without collecting , recording and processing environmental information of geophysical origin , a g.w . laser interferometer would simply be incapable of working as a sensitive astrophysical instrument . certainly , we have to make sure that the extraction of geophysical information does not compromise the astrophysical aims of the instrument . a laser - beam detector of gravitational waves is a conceptually simple installation . each arm of the interferometer , typically of the length @xmath2 , consists of two mirrors , and the distance variation between the mirrors is monitored by the laser beam . the mirrors are hanging on wires in supporting towers . each mirror is essentially a mass element of the pendulum placed in the local gravitational field of the earth . the eigen - frequency of the pendulum is normally in the range of @xmath3 . the multi - stage pendulum system shields the mirrors from large uncontrollable displacements of the tops of the supporting towers . this makes the interferometer capable of measuring , in the region of relatively high frequencies of astrophysical interest @xmath0 , the incredibly small variations of distance between the mirrors , at the level of @xmath4 . the expected cause of these variations is the incoming astrophysical gravitational wave . the isolation from noises in the region of relatively high frequencies is only a part of the story . to ensure successful performance of the interferometer as an astrophysical instrument , control systems of the interferometer should also register and compensate for large external interventions of geophysical origin that take place in the region of relatively low frequencies . for example , the tidal half - daily variations of distance beween towers separated by @xmath5 are typically at the level of @xmath6 . this change of distance is 14 orders of magnitude larger than the anticipated astrophysical signal . if this sort of variations were allowed to affect distance between the mirrors , the interferometer would not be in the ` locked ' state , and hence it would not be able to operate as astrophysical instrument . the ` locking ' of the interferometer requires that the distance between the mirrors is maintained unchanged with accuracy of approximately one hundredth of the laser light wavelength , which amounts to @xmath7 and less . this means that the low - frequency variations of distance between the mirrors should be monitored and largely removed by a control system called the adjustment system . a similar monitoring and compensation should be done with respect to low - frequency variations of the angle between the interferometer mirrors . this is being done by a control system called the alighnment system . ideally , in order to reach the astrophysical goals , control systems should keep the interferometer in the working condition for the duration of time exceeding many months . thus , the collected and recorded low - frequency information , which is vital for maintaining the operational state of the laser - beam detector of gravitational waves , inevitably makes the g.w . detector also a geophysical instrument . the time - scales of geophysical processes , some of which are believed to be crucial for global geodynamics , lie in the range from several minutes to several hours . in other words , we will be interested in frequencies , which we call geophysical frequencies , somewhere in the interval @xmath8 . in sec.2 we consider a simple model of g.w . interferometer as a geophysical instrument . it is assumed that the mirrors suspension points can move and the plumb lines of hanging mirrors can vary . these changes arise as a result of the earth surface deformations and variations of local gravitational field caused , for example , by the internal earth dynamics . we derive general formulas for the distance between the mirrors and the angles between the local plumb lines . ideally , these are two variables that are supposed to be monitored by , respectively , the adjustment and alignment systems of the interferometer . in sec.3 we consider a number of interesting geophysical phenomena which inevitably affect the performance of a g.w . the signatures of these phenomena are contained in the outcomes of the adjustment and alignment control systems . the geophysical effects to be studied include tidal perturbations , normal modes of earth oscillations , movements of the inner solid core of earth , etc . we place the main emphasis on the fascinating phenomenon of the inner core oscillations . we estimate the useful geophysical signal accompanying this phenomenon , which will manifest itself in the variation of distance between the mirrors and in the variation of angle between the plumb lines of the hanging mirrors . the guidance for the expected amplitude of the signal is provided by the reported in the literature indications that the inner core oscillations have been actually detected by other , traditional , methods . from the requirement that the signal to noise ratio should be larger than 1 , we define the level of tolerable noise in the proposed measurements . specifically , the tolerable noise allows the detection of the useful signal , if the observation time exceeds 70 , or so , inner core oscillation periods . a useful signal can be detected if the environmental and instrumental noises are smaller than the calculated level of tolerable noise . in sec.4 we consider noises which we find most dangerous . we explicitely show that seismic , atmospheric and instrumental noises should not be capable of preventing the detection of inner core oscillations , even if only marginally . this refers both to distance and angle measurements . there exists , however , a specific problem with the angle measurements , related to the fact that the presently operating alignment systems are subject to a certain degeneracy . they can not tell apart a tilt of the mirror , which we are mostly interested in , and a latteral shift of the mirror , which can be caused by a dull deformational noise . we analyze this difficulty in great detail in sec.5 . since the angular measurements provide an important additional channel of geophysical information , we adress the problem of degeneracy in sec.6 and suggest the ways of its circumvention . the desire to keep the angular channel useful for geophysical applications may require some modest and harmless modifications of the optical scheme of g.w . we discuss at some length a few ideas with regard to such modifications . it appears that , without interfering with the astrophysical program of the instrument , certain geophysical modifications are feasible . in sec.7 we emphasize some conclusions of the paper .

the existing high technology laser - beam detectors of gravitational waves may find very useful applications in an unexpected area - geophysics . to make possible the detection of weak gravitational waves in the region of high frequencies of astrophysical interest , , control systems of laser interferometers must permanently monitor , record and compensate much larger external interventions that take place in the region of low frequencies of geophysical interest , . we specifically identify the low - frequency information contained in distances between the interferometer mirrors ( deformation of earth ) and angles between the mirrors suspensions ( deviations of local gravity vectors and plumb lines ) . we show that the access to the angular information may require some modest amendments to the optical scheme of the interferometers , and we suggest the ways of doing that . the detailed evaluation of environmental and instrumental noises indicates that they will not prevent , even if only marginally , the detection of interesting geophysical phenomena . gravitational - wave instruments seem to be capable of reaching , as a by - product of their continuous operation , very ambitious geophysical goals , such as observation of the earth s inner core oscillations . 0 * * 0 # 1_f

the existing high technology laser - beam detectors of gravitational waves may find very useful applications in an unexpected area - geophysics . to make possible the detection of weak gravitational waves in the region of high frequencies of astrophysical interest , , control systems of laser interferometers must permanently monitor , record and compensate much larger external interventions that take place in the region of low frequencies of geophysical interest , . such phenomena as tidal perturbations of land and gravity , normal mode oscillations of earth , oscillations of the inner core of earth , etc . will inevitably affect the performance of the interferometers and , therefore , the information about them will be stored in the data of control systems . we specifically identify the low - frequency information contained in distances between the interferometer mirrors ( deformation of earth ) and angles between the mirrors suspensions ( deviations of local gravity vectors and plumb lines ) . we show that the access to the angular information may require some modest amendments to the optical scheme of the interferometers , and we suggest the ways of doing that . the detailed evaluation of environmental and instrumental noises indicates that they will not prevent , even if only marginally , the detection of interesting geophysical phenomena . gravitational - wave instruments seem to be capable of reaching , as a by - product of their continuous operation , very ambitious geophysical goals , such as observation of the earth s inner core oscillations . 0 * * 0 # 1_f

1112.1774

i

the main target of the dark energy research over the next few years or so is to distinguish between the @xmath3-cold - dark - matter ( @xmath3cdm ) model and dynamical models with time - varying equations of state @xmath4 . from the observational data of wmap7 combined with baryon acoustic oscillations ( bao ) @xcite and the hubble constant measurement @xcite , komatsu _ et al . _ @xcite derived the bound @xmath5 ( 68 % cl ) for the constant equation of state . adding the supernovae type ia ( sn ia ) data provides tighter constraints on @xmath4 , but still the phantom equation of state ( @xmath6 ) is allowed by the joint data analysis @xcite . this property persists for the time - varying dark energy equation of state with the parametrization such as @xmath7 @xcite , where @xmath8 is the scale factor @xcite . in the framework of general relativity ( gr ) it is generally difficult to construct theoretically consistent models of dark energy which realize @xmath6 . in quintessence @xcite with a slowly varying scalar - field potential , for example , the field equation of state is always larger than @xmath9 . a ghost field with a negative kinetic energy leads to @xmath6 @xcite , but such a field is plagued by a catastrophic instability of the vacuum associated with the spontaneous creation of ghost and photon pairs @xcite . in modified gravitational theories it is possible to realize @xmath6 without having ghosts and laplacian - type instabilities ( see refs . @xcite ) . in @xmath10 gravity , where the lagrangian @xmath11 is a function of the ricci scalar @xmath12 , the dark energy equation of state crosses the cosmological constant boundary ( @xmath13 ) @xcite for the viable models constructed to satisfy cosmological and local gravity constraints @xcite . this is also the case for the brans - dicke theory @xcite with a field potential which accommodates the chameleon mechanism @xcite to suppress the propagation of the fifth force @xcite . in modified gravity models of dark energy based on the chameleon mechanism ( including @xmath10 gravity ) , the effective potential of a scalar degree of freedom needs to be carefully designed to pass cosmological and local gravity constraints @xcite . there is another class of modified gravity models of dark energy in which a nonlinear self - interaction of a scalar degree of freedom @xmath14 can lead to the recovery of gr in a local region through the vainshtein mechanism @xcite . the representative models of this class are those based on the dvali - gabadadze - porrati ( dgp ) braneworld @xcite and the galileon gravity @xcite ( see refs . @xcite for the implementation of the vainshtein mechanism in these models ) . the nonlinear interaction of the form @xmath15 , which appears from the brane - bending mode in the dgp model @xcite , gives rise to the field equation invariant under the galilean shift @xmath16 in the flat spacetime . this was extended to more general field lagrangians satisfying the galilean symmetry in the limit of the minkowski spacetime @xcite . the cosmology based on the covariant galileon or on its modified versions has been studied by many authors @xcite . in refs . @xcite the dynamics of dark energy was investigated in the presence of the full covariant galileon lagrangian . in this model the solutions with different initial conditions converge to a common trajectory ( tracker ) . along the tracker the dark energy equation of state @xmath4 changes as @xmath17 ( radiation era ) @xmath18 @xmath19 ( matter era ) @xmath18 @xmath9 ( de sitter era ) @xcite . there exists a viable parameter space in which the ghosts and laplacian instabilities are absent . however , the joint analysis based on the observational data of sn ia , cmb , and bao shows that the tracker solution is disfavored because of the large deviation of @xmath4 from @xmath9 during the matter era @xcite . the solutions that approach the tracker only at late times are allowed from the combined data analysis @xcite . as an extension of the covariant galileon model , deffayet _ et al . _ @xcite obtained the most general lagrangian in scalar - tensor theories with second - order equations of motion . in four dimensions the corresponding lagrangian is of the form ( [ lagsum ] ) with the four functions ( [ eachlag2])-([eachlag5 ] ) given below . in fact this is equivalent to the lagrangian found by horndeski @xcite more than 3 decades ago @xcite . the conditions for the avoidance of ghosts and laplacian instabilities were recently derived in ref . @xcite in the presence of two perfect fluids ( non - relativistic matter and radiation ) . the covariant galileon corresponds to the choice @xmath20 , @xmath21 , @xmath22 , @xmath23 in eqs . ( [ eachlag2])-([eachlag5 ] ) , where @xmath24 s are dimensionless constants , @xmath25 , @xmath26 is the reduced planck mass , and @xmath27 is a constant having the dimension of mass . kimura and yamamoto @xcite studied the model with the functions @xmath20 , @xmath28 ( @xmath29 ) , @xmath30 , and @xmath31 , in which case the dark energy equation of state during the matter era is given by @xmath0 with @xmath32 . at the background level this is equivalent to the dvali - turner model @xcite , which can be consistent with the observational data for @xmath33 larger than the order of 1 . if we consider the evolution of cosmological perturbations , the lss tends to be anti - correlated with the late - time isw effect . this places the tight bound on the power @xmath33 , as @xmath34 ( 95% cl ) @xcite , in which case the dark energy equation of state is practically indistinguishable from that in the @xmath3cdm model . in ref . @xcite the present authors proposed more general extended galileon models with the functions @xmath35 , @xmath36 , @xmath37 , and @xmath38 , where the masses @xmath39 s are fixed by the hubble parameter at the late - time de sitter solution with @xmath40constant . for the powers @xmath41 , @xmath42 , @xmath43 , @xmath44 , where @xmath45 and @xmath46 are positive constants , there exists a tracker solution characterized by @xmath47constant . during the matter - dominated epoch one has @xmath0 , where @xmath48 , along the tracker . this covers the model of kimura and yamamoto @xcite as a specific case ( @xmath49 , @xmath50 , @xmath51 , @xmath52 ) . in the presence of the nonlinear field self - interactions in @xmath53 and @xmath54 , the degeneracy of the background tracker solution for given values of @xmath45 and @xmath46 is broken by considering the evolution of cosmological perturbations . hence the isw - lss anti - correlation found in refs . @xcite for @xmath55 should not be necessarily present for the models with non - zero values of @xmath56 and @xmath57 . in this paper we first place constraints on the tracker solution in the extended galileon models by using the recent observational data of sn ia , cmb , and bao . the bound on the value @xmath48 is derived from the background cosmic expansion history with / without the cosmic curvature @xmath58 . we then study the evolution of cosmological density perturbations in the presence of non - relativistic matter to break the degeneracy of the tracker solution at the background level . we will show that the lss and the isw effect are either positively or negatively correlated , depending on the parameters @xmath56 and @xmath57 . this information should be useful to distinguish between the extended galileon models with different values of @xmath56 and @xmath57 from observations .

the extended galileon models possess tracker solutions with de sitter attractors along which the dark energy equation of state is constant during the matter - dominated epoch , i.e. , where is a positive constant . we show that , depending on the model parameters , the lss and the isw effect is either positively or negatively correlated .

the extended galileon models possess tracker solutions with de sitter attractors along which the dark energy equation of state is constant during the matter - dominated epoch , i.e. , where is a positive constant . even with this phantom equation of state there are viable parameter spaces in which the ghosts and laplacian instabilities are absent . using the observational data of the supernovae type ia , the cosmic microwave background ( cmb ) , and baryon acoustic oscillations , we place constraints on the tracker solutions at the background level and find that the parameter is constrained to be ( 95 % cl ) in the flat universe . in order to break the degeneracy between the models we also study the evolution of cosmological density perturbations relevant to the large - scale structure ( lss ) and the integrated - sachs - wolfe ( isw ) effect in cmb . we show that , depending on the model parameters , the lss and the isw effect is either positively or negatively correlated . it is then possible to constrain viable parameter spaces further from the observational data of the isw - lss cross - correlation as well as from the matter power spectrum .

1112.1774

c

in this paper we have studied cosmological constraints on the extended galileon models of dark energy . for the functions ( [ gegali ] ) with the powers ( [ power ] ) there exist tracker solutions along which the field equation of state @xmath4 changes as @xmath409 ( radiation era ) @xmath18 @xmath410 ( matter era ) @xmath18 @xmath9 ( de sitter era ) , where @xmath411 . unlike the case of the covariant galileon ( @xmath129 ) , @xmath4 can be close to @xmath9 during the radiation and matter eras for @xmath412 . moreover , even for @xmath6 , there are viable model parameter spaces in which the ghosts and laplacian instabilities are absent . using the recent data of sn ia , cmb , and bao , we placed observational constraints on the background tracker solutions with @xmath159 . in the flat universe we found that the model parameters are constrained to be @xmath2 and @xmath413 ( 95% cl ) from the joint data analysis . the chi - square for the best - fit case ( @xmath414 ) is slightly smaller than that in @xmath3cdm . however the difference of the aic information criteria between the two models is @xmath261 , so that the extended galileon is not particularly favored over the @xmath3cdm . we also carried out the likelihood analysis in the presence of the cosmic curvature @xmath58 and obtained the bounds @xmath415 , @xmath416 , and @xmath417 ( 95% cl ) . the tracker for the covariant galileon ( @xmath129 ) is disfavored from the data , in which case only the late - time tracking solution is allowed observationally @xcite . the background quantities for the tracker are independent of the values of @xmath112 and @xmath113 . this means that the models with different @xmath112 and @xmath113 can not be distinguished from the observational constraints derived from the background cosmic expansion history . in order to break this degeneracy we studied the evolution of cosmological perturbations in the presence of non - relativistic matter for the flat flrw background . as shown in ref . @xcite , for @xmath325 , the matter density perturbation @xmath298 divided by the scale factor @xmath8 is anti - correlated with the effective gravitational potential @xmath343 for the modes relevant to the lss . this leads to the anti - correlation between the lss and the isw effect in cmb , so that the parameter @xmath1 for the tracker is severely constrained to be @xmath418 ( 95% cl ) . for the models with @xmath329 and @xmath330 , however , the correlation between @xmath342 and @xmath343 depends on the values of @xmath112 and @xmath113 . if @xmath49 and @xmath133 ( i.e. @xmath165 ) , for example , @xmath342 and @xmath343 tend to be positively correlated for the model parameters close to the border ( b ) in fig . [ validfig ] ( @xmath335 ) , whereas they show anti - correlations for @xmath112 and @xmath113 close to the border ( a ) ( @xmath334 ) . the typical examples of the positive and negative correlations are plotted in figs . [ pofig ] and [ anfig ] , respectively . the qualitative differences between these two cases can be understood by estimating the effective gravitational coupling @xmath322 and the quantity @xmath339 derived under the quasi - static approximation on sub - horizon scales . as the model parameters approach the border ( a ) in fig . [ validfig ] , @xmath316 gets larger while @xmath322 decreases , so that the anti - correlation between @xmath342 and @xmath343 tends to be stronger . we studied the evolution of perturbations for different values of @xmath1 in the range @xmath406 and found that the basic properties for the isw - lss correlation are similar to those discussed for @xmath165 . we also estimated the growth index @xmath393 of the matter perturbation and found that , for @xmath49 and @xmath406 , it typically varies in the range @xmath408 at the redshifts for @xmath396 . hence it is also possible to distinguish between the extended galileon models and the @xmath3cdm model from the galaxy clustering . however , we expect that the tightest observational bounds on the values @xmath112 and @xmath113 should come from the isw - lss correlation . we leave such observational constraints for future works .

even with this phantom equation of state there are viable parameter spaces in which the ghosts and laplacian instabilities are absent . using the observational data of the supernovae type ia , the cosmic microwave background ( cmb ) , and baryon acoustic oscillations , we place constraints on the tracker solutions at the background level and find that the parameter is constrained to be ( 95 % cl ) in the flat universe . in order to break the degeneracy between the models we also study the evolution of cosmological density perturbations relevant to the large - scale structure ( lss ) and the integrated - sachs - wolfe ( isw ) effect in cmb . it is then possible to constrain viable parameter spaces further from the observational data of the isw - lss cross - correlation as well as from the matter power spectrum .

the extended galileon models possess tracker solutions with de sitter attractors along which the dark energy equation of state is constant during the matter - dominated epoch , i.e. , where is a positive constant . even with this phantom equation of state there are viable parameter spaces in which the ghosts and laplacian instabilities are absent . using the observational data of the supernovae type ia , the cosmic microwave background ( cmb ) , and baryon acoustic oscillations , we place constraints on the tracker solutions at the background level and find that the parameter is constrained to be ( 95 % cl ) in the flat universe . in order to break the degeneracy between the models we also study the evolution of cosmological density perturbations relevant to the large - scale structure ( lss ) and the integrated - sachs - wolfe ( isw ) effect in cmb . we show that , depending on the model parameters , the lss and the isw effect is either positively or negatively correlated . it is then possible to constrain viable parameter spaces further from the observational data of the isw - lss cross - correlation as well as from the matter power spectrum .

1007.1459

i

the formation and evolution of galaxies in the universe is accompanied unavoidably by the emission of radiation . all this radiated energy is still streaming through the universe , although much is now at longer wavelengths due to redshifting and absorption / re - emission by dust . the photons mostly lie in the range @xmath3 0.1 - 1000 @xmath1 m , ultraviolet ( uv ) , optical , and infrared ( ir ) , and produce the second most energetic diffuse background after the cosmic microwave background , thus being essential for understanding the full energy balance of the universe . we will account in this work for the radiation accumulated by star formation processes through most of the life of the universe , plus a contribution from active galactic nuclei ( agns ) to this wavelength range , known as the diffuse extragalactic background light ( ebl ) . the direct measurement of the ebl is a very difficult task subject to high uncertainties . this is mainly due to the contribution of zodiacal light , some orders of magnitude larger than the ebl ( @xcite ; @xcite ) . there are some measurements in the optical ( @xcite ) and in the near - ir ( @xcite ; @xcite ) , but there is not general agreement about the reliability of these data sets ( @xcite ) . in addition , these near - ir data appear to give intensity levels for the ebl in contradiction with the observation of very high energy ( vhe , 30 gev-30 tev ) photons from extragalactic sources ( @xcite ; @xcite ; @xcite ) . little is known about the mid - ir from direct detection due to the higher contamination from zodiacal light at those wavelengths . measurements with the far - infrared absolute spectrometer ( firas ) instrument on board the cosmic background explorer , in the far - ir ( @xcite ; @xcite ) , are thought to be more reliable . other observational approaches set reliable lower limits on the ebl , such as measuring the integrated light from discrete extragalactic sources ( @xcite ; @xcite ) . there are also other authors that focus on studying galaxy properties based on ebl results ( @xcite ) , or on modeling a region of the ebl spectrum ( @xcite ) . on the other hand , there are phenomenological approaches in the literature that predict an overall ebl model ( between 0.1 - 1000 @xmath1 m and for any redshift ) . these are basically of four kinds : 1 . forward evolution , which begins with cosmological initial conditions and follows a forward evolution with time by means of semi - analytical models ( sams ) of galaxy formation , @xcite , @xcite ( hereafter , sgpd10 ) and @xcite ( hereafter , gspd10 ) . backward evolution , which begins with existing galaxy populations and extrapolates them backwards in time , @xcite , @xcite , @xcite ( hereafter , frv08 ) . evolution of the galaxy populations that is inferred over a range of redshifts . the galaxy evolution is inferred here using some quantity derived from observations such as the star formation rate ( sfr ) density of the universe , kneiske et al . ( 2002 ) , @xcite , @xcite . evolution of the galaxy populations that is directly observed over the range of redshifts that contribute significantly to the ebl . the present paper , which we term empirical , belongs in this category . the type ( i ) sgpd10 and gspd10 models discuss the same galaxy formation sam but in different contexts : sgpd10 contains details of the model used in calculating the bolometric luminosity history of the universe and comparison with data , and gspd10 focuses on the derived ebl and @xmath0-ray attenuation . the sgpd10-gspd10 model is based on an updated version of the semi - analytic theoretical approach described in @xcite from the growth of super - massive black holes and their host galaxies within the context of the hierarchical lambda cold dark matter ( @xmath4cdm ) cosmological framework . this is based in part on @xcite , @xcite , and in the simulations summarized by @xcite , and @xcite . we consider that these types of models are complementary to the observational approach taken here . we consider the type ( ii ) frv08 model the most complete observationally - based work of those mentioned above . they base their ebl modeling on galaxy luminosity functions ( lfs ) , quantities which are directly observed and well understood . frv08 exploit a variety of data to build evolutionary schemes according to galaxy morphology . they account for the contribution from early , late - type galaxies and a starburst population to the ebl . they use observed near - ir lfs from the local universe to @xmath5 for describing the early and late - type galaxies . for the starburst population they use an optical and only local lf . different prescriptions are used to extrapolate the evolution of the different morphological types to higher redshifts , and corrections to fit their results to other observational data are applied . type ( iii ) models are not directly based on galaxy data . instead , they are built from some parametrization of the history of the sfr density . this is a quantity derived using several different methods , each of which have different and signitficant uncertainties and biases . the sfr density is combined with uncertain assumptions about the emitted galaxy spectral energy distribution ( sed ) evolution as well . our type ( iv ) ebl estimates ( the first approach in this category ) will be compared in detail with the type ( i ) forward evolution semi - analytical galaxy formation model by sgpd10 and gspd10 , and the type ( ii ) oservationally motivated model by frv08 . the other works mentioned are briefly compared with our ebl calculations in sec . [ discussion ] . our aim in this paper is to develop an ebl model that is as observationally - based and realistic as possible , yet fully reproducible , including a quantitative study of the main uncertainties in the modeling that are directly due to the data . this constrains the range of the background intensity and its implications to @xmath0-ray astronomy . one important application of the ebl for @xmath0-ray astronomy is to recover the unattenuated spectra of extragalactic sources . our goal is to measure the ebl with enough precision that the uncertainties due to the ebl modeling , in these recovered unattenuated spectra , are small compared with other effects such as systematic uncertainties in the @xmath0-ray observations . examples of this are discussed in sec . [ attenuation ] . our model is based on the rest - frame @xmath2-band galaxy lf by @xcite ( hereafter , c10 ) and on multiwavelength galaxy data from the all - wavelength extended groth strip international survey ( aegis , @xcite ; @xcite ) of about 6000 galaxies in the redshift range 0.2 - 1 . these data sets are put together in a very transparent and consistent framework . the c10 lf is used to count galaxies ( and therefore to normalize the total ebl intensity ) at each redshift . the lf as well as our galaxy sample are divided in three magnitude bins according to the absolute rest - frame @xmath2-band magnitude faint , middle , and bright ( defined quantitatively later ) . within every magnitude bin a sed - type is statistically attached to each galaxy in the lf assuming sed - type fractions that are function of redshift within those magnitude bins . this is estimated from fitting our aegis galaxy sample to the 25 galaxy sed templates from the swire library . then , luminosity densities are calculated from these magnitude bins from every galaxy population at all wavelengths , and finally all the light at all redshifts is added up to get the overall ebl spectrum . the results are linked with @xmath0-ray astronomy and with the current understanding on galaxy evolution . the paper is organized as follows : section [ data ] describes the lf , our multiwavelength galaxy catalogue and the galaxy templates . section [ method ] explains our methodology . the results for galaxy sed - type fractions , luminosity densities , sfr densities , ebl buildup , and ebl intensities are given in section [ results ] . section [ attenuation ] shows the attenuation computed from our ebl model for some vhe sources taken from the literature . in section [ discussion ] our results are discussed including a detailed study on the uncertainties from the modeling , a comparison between our observationally - based ebl and that given by theoretical sams of galaxy formation . finally , in section [ summary ] a summary with our main results and conclusions is presented . throughout this paper , a standard @xmath4cdm cosmology is assumed , with matter density @xmath6 , vacuum energy density @xmath7 , and hubble constant @xmath8 km s@xmath9mpc@xmath9 .

the evolving , overall spectrum of the ebl is derived here utilizing a novel method based on observations only . these are based on fitting swire templates to a multiwavelength sample of about 6000 galaxies in the redshift range from 0.2 to 1 from the all - wavelength extended groth strip international survey ( aegis ) . our ebl calculations are compared with those from a semi - analytic model , from another observationally - based model and observational data . the ebl uncertainties in our modeling based directly on the data are quantified , and their consequences for attenuation of very high energy-rays due to pair production on the ebl are discussed . + [ firstpage ] galaxies : evolution galaxies : formation cosmology : observations - diffuse radiation infrared : diffuse background

the extragalactic background light ( ebl ) is of fundamental importance both for understanding the entire process of galaxy evolution and for-ray astronomy , but the overall spectrum of the ebl between 0.1 - 1000 m has never been determined directly from galaxy spectral energy distribution ( sed ) observations over a wide redshift range . the evolving , overall spectrum of the ebl is derived here utilizing a novel method based on observations only . this is achieved from the observed evolution of the rest - frame-band galaxy luminosity function up to redshift 4 ( ) , combined with a determination of galaxy sed - type fractions . these are based on fitting swire templates to a multiwavelength sample of about 6000 galaxies in the redshift range from 0.2 to 1 from the all - wavelength extended groth strip international survey ( aegis ) . the changing fractions of quiescent galaxies , star - forming galaxies , starburst galaxies and active galactic nucleus ( agn ) galaxies in that redshift range are estimated , and two alternative extrapolations of sed - types to higher redshifts are considered . this allows calculation of the evolution of the luminosity densities from the uv to the ir , the evolving star formation rate density of the universe , the evolving contribution to the bolometric ebl from the different galaxy populations including agn galaxies and the buildup of the ebl . our ebl calculations are compared with those from a semi - analytic model , from another observationally - based model and observational data . the ebl uncertainties in our modeling based directly on the data are quantified , and their consequences for attenuation of very high energy-rays due to pair production on the ebl are discussed . it is concluded that the ebl is well constrained from the uv to the mid - ir , but independent efforts from infrared and-ray astronomy are needed in order to reduce the uncertainties in the far - ir . + [ firstpage ] galaxies : evolution galaxies : formation cosmology : observations - diffuse radiation infrared : diffuse background

astro-ph9811208

c

an analysis of the available published and unpublished spectra of the born - again giant sakurai s object from 1996 confirms the extremely rapid evolution of the star previously noted by asplund et al . ( 1997b ) . throughout 1996 sakurai s object cooled significantly by about 1000k , which is also obvious from photometry ( duerbeck et al . 1997 ) ; the cooling has also continued until the present ( 1998 ) . such a cooling is presumably the result of the expansion of the photosphere following the drastically increased luminosity due to the he - shell flash . even more spectacular , the chemical composition of sakurai s object shows definite signs of having been significantly altered within only a few months ( from april to october 1996 ) . again , these changes are most likely interpreted as being caused by the mixing and nuclear reactions which have ensued as a result of the final he - shell flash : ingestion and burning of the h - rich envelope , li - production through the cameron - fowler mechanism , and @xmath0-processing of the light @xmath0-elements ( including sc ) . to our knowledge , sakurai s object represents the fastest case of stellar evolution ever observed when disregarding complete stellar disruptions such as supernovae . sakurai s object shows strong abundance similarities with the rcrb stars , not only a distinct h - deficiency and c - enhancement . in all respects , sakurai s object would be classified as an rcrb star judging from a compositional perspective ( lambert et al . 1998 ) . since sakurai s object also recently has started showing irregular fading episodes typical of the rcrb stars ( liller et al . 1998 ) , sakurai s object indeed seem to have evolved into being an rcrb star . thus , for the first time ever , the `` birth '' of an rcrb star may have been witnessed , which lends strong support for the final flash scenario as a probable channel for forming at least some of the rcrb stars . the exact relation between sakurai s object and the majority and minority classes of the rcrb stars needs , however , to be clarified before one draws any conclusions on how many of the rcrb stars have been formed through a final he - shell flash in a post - agb star on the wd cooling track . further studies of the future evolution of sakurai s object is clearly needed . judging from its rapid metamorphosis already since discovery in 1996 , it is not unlikely that the star will provide astronomers with even more surprises and spectacular changes of appearance in the years to come . in this respect , both a close photometric monitoring of the visual variability and spectroscopic studies of the changes in chemical composition after 1996 are of great importance . the latter will , however , require a brave soul in order to analyse the terrifying richness of atomic and molecular lines , many of which are yet unidentified lines presumably due to @xmath0-elements . as long as the ir excess is not too disturbing ( eyres et al . 1998 ) , it may be advantageous to use high - resolution near - ir spectrum for such abundance analyses . furthermore , we encourage studies on the chemical composition of fgsge , in particular regarding its h - content , and the rcrb star uaqr , which shows very pronounced @xmath0-element enhancements similar to fgsge and sakurai s object ( bond et al . 1979 ) , in order to assess better the relationship between born - again giants and the rcrb stars . finally and most urgently , the theoretical modelling of the final he - shell flash events needs to be extended to a range of stellar masses and initial conditions with a detailed study of the mixing processes and including the relevant nuclear reactions such as cno - cycling , he - burning , li - production and @xmath0-processing , which will likely provide strong constraints on the models . admittedly , such modelling is a herculean task considering the dynamical nature of the event , but is unfortunately required in order to fully understand the rapid evolution of sakurai s object and related stars . we are grateful to g. gonzalez , m. keane , v. klochkova and g. wallerstein for obtaining spectra of sakurai s object . the referee h. duerbeck provided us with useful suggestions . ma acknowledges financial support connected with a post - doctoral fellowship at nordita . dll s research has been supported in part by the u.s . national science foundation ( grant nsf 9618414 ) and the robert a. welch foundation of houston , texas . the financial support tk has received through the estonian science foundation grant 3166 is acknowledged . asplund m. , 1998 , a&a 330 , 641 asplund m. , gustafsson b. , kiselman d. , eriksson k. , 1997a , a&a 318 , 521 asplund m. , gustafsson b. , lambert d.l . , rao n.k . , 1997b , a&a 321 , l17 asplund m. , gustafsson b. , rao n.k . , lambert d.l . , 1998 , a&a 332 , 651 beer h. , voss f. , winters r.r . , 1992 , apjs 80 , 403 blcker t. , schnberner d. , 1997 , a&a 324 , 991 bond h.e , luck r.e . , newman m.j . , 1979 , apj 233 , 205 cameron a.g.w . , fowler w.a . , 1971 , apj 164 , 111 cardelli j.a . , 1994 , science 265 , 209 clayton g.c . , de marco o. , 1997 , aj 114 , 2679 duerbeck h.w . , benetti s. , 1996 , apj 468 , l111 duerbeck h.w . , benetti s. , gautschy a. , et al . , 1997 , aj 114 , 1657 edvardsson b. , andersen j. , gustafsson b. , et al . , 1993 , a&a 275 , 101 eyres s.p.s . , evans a. , geballe t.r . , et al . , 1998 , mnras 298 , l37 gonzalez g. , lambert d.l . , giridhar s. , 1997 , apj 481 , 452 gonzalez g. , lambert d.l . , wallerstein g. , et al . , 1998 , apjs 114 , 133 grevesse n. , sauval a.j . , 1998 , space sci . , in press gustafsson b. , asplund m. , 1996 , in : hydrogen - deficient stars , jeffery c.s . , heber u. ( eds . ) . series vol . gustafsson b. , bell r.a . , eriksson k. , nordlund . , 1975 , a&a 42 , 407 harrison t.e . , 1996 , pasp 108 , 1112 iben i.jr . , macdonald j. , 1995 . in : white dwarfs , koester d. , werner k. ( eds . ) . springer , berlin , p. 48 iben i.jr . , tutukov a.v . , yungelson l.r . , 1996 , apj 456 , 750 jacoby g.h . , de marco o. , sawyer d.g . , 1998 , aj , 116 , 1367 kerber f. , gratl h. , roth m. , 1997 , iac circ . 6601 kimeswenger s. , kerber f. , 1998 , a&a 330 , l41 kipper t. , 1996 , in : hydrogen - deficient stars , jeffery c.s . , heber u. ( eds . ) . series vol . 96 , p. 329 kipper t. , kipper m. , 1993 , a&a 276 , 389 kipper t. , klochkova v.g . , 1997 , a&a 324 , l65 lambert d.l . , rao n.k . , gustafsson b. , asplund m. , 1998 , submitted to a&a langer g.e . , kraft r.p . , anderson k.s . , 1974 , apj 189 , 509 liller w. , janson m. , duerbeck h.w . , van genderen a. , 1998 , iau circ . 6825 ludendorff m.h . , 1922 , an 217 , 167 lundmark k. , 1921 , pasp 33 , 314 malaney r.a . , 1987 , apj 321 , 832 nakano s. , sakurai y. , hazen m. , et al . , 1996 , iau circ . 6322 papousek j. , 1992 , iau circ . 5604 renzini a. , 1979 , in : stars and star systems , westerlund b.e . reidel , dordrecht , p. 155 renzini a. , 1990 , in : confrontation between stellar pulsation and evolution , cacciari c. , clementini g. ( eds . ) . series vol . 11 , p. 549 schnberner d. , 1996 , in : hydrogen - deficient stars , jeffery c.s . , heber u. ( eds . ) . series vol . 96 , p. 433 seitter w.c . , 1987 , messenger 50 , 14 shetrone m.d . , keane m. , 1998 , in : faint blue stars , davis - philip a.g . l. davis press , schenectady , in press van genderen a.m. , gautschy a. , 1995 , a&a 294 , 453

the extraordinarily rapid evolution of the born - again giant sakurai s object following discovery in 1996 has been investigated . the evolution can be traced both in a continued cooling of the stellar surface and dramatic changes in chemical composition on a timescale of a mere few months . sakurai s object thus lends strong support for the suggestion that at least some of the rcrb stars have been formed through a final he - shell flash in a post - agb star .

the extraordinarily rapid evolution of the born - again giant sakurai s object following discovery in 1996 has been investigated . the evolution can be traced both in a continued cooling of the stellar surface and dramatic changes in chemical composition on a timescale of a mere few months . the abundance alterations are the results of the mixing and nuclear reactions which have ensued due to the final he - shell flash which occurred during the descent along the white dwarf cooling track . the observed changes in the h and li abundances can be explained by ingestion and burning of the h - rich envelope and li - production through the cameron - fowler mechanism . the rapidly increasing abundances of the light-elements ( including sc ) is consistent with current-processing by neutrons released from the concomitantly producedc . however , the possibility that the-elements have previously been synthesized during the agb - phase and only mixed to the surface in connection with the final he - shell flash in the pre - white dwarf can not be convincingly ruled out either . since sakurai s object shows substantial abundance similarities with the rcrb stars and has recently undergone rcrb - like visual fading events , the `` birth '' of an rcrb star may have been witnessed for the first time ever . sakurai s object thus lends strong support for the suggestion that at least some of the rcrb stars have been formed through a final he - shell flash in a post - agb star .

hep-th0002012

i

the f - theory vacuum @xcite constructed from an elliptically fibered threefold @xmath2 with section determines an effective theory with @xmath3 supersymmetry in six dimensions . such supersymmetric theories will have fields in hypermultiplets , vector supermultiplets and tensor supermultiplets . ( see , for example , @xcite for a discussion of such theories . ) for any particular f - theory vacuum , the taxonomy of the supermultiplets may be derived from the geometry of @xmath2 as an elliptic fibration via seemingly straightforward methods in the case of the vector and tensor multiplets @xcite . the classification of the hypermultiplet content has always been a little harder to carry out . many methods have been proposed which allow the hypermultiplets to be determined from the geometry in certain cases @xcite . the purpose of this paper is to outline a systematic approach to the problem of determining the gauge symmetry and hypermultiplet content of a given six - dimensional theory obtained from f - theory . ( note that as far as the moduli space of hypermultiplets in concerned , our methods utilize the associated type iia compactification and thus also apply directly to the compactification of m - theory on @xmath2 giving an @xmath4 theory in five dimensions and to the compactification of the type iia string on @xmath2 to yield an @xmath5 theory in four dimensions , provided that the expectation values of certain ramond ramond fields have been tuned appropriately . ) the methods we employ will not be particularly new but we will see that the process of analyzing the gauge group and matter content can be quite a bit more subtle than had previously been appreciated . in particular , the case of monodromy of the fibration leading to non - simply - laced lie algebras requires some care . a particularly awkward case which has caused some confusion is when a @xmath6 monodromy acts on a curve of @xmath0 singularities , i.e. , a curve of @xmath7 fibers in f - theory language . in this paper we resolve this problem in agreement with an observation by intriligator and rajesh in @xcite concerning anomaly cancellation . in section [ s : lcy ] we will show how many features of a lie algebra structure arise naturally from an elliptically fibered threefold . this will allow us to elucidate the method for determining the gauge algebra . in section [ s : hyper ] we discuss exactly how to analyze the hypermultiplet content in the cases where the associated curves and surfaces within the threefold are smooth . we discuss the cases where these curves and surfaces are singular in section [ s : odd ] . this section includes some unexpected rules we are forced to adopt for @xmath1-brane wrapping . although the results of this section are less rigorous than the preceding section , we are able to give precise results in many instances which can be extended to the general case under the fairly conservative assumption that the relevant physics is determined locally from the geometry of the singularities . finally in section [ s : num ] we emphasize the peculiar numerical predictions which arise from anomaly cancellation in the f - theory compactification on @xmath2 .

the f - theory vacuum constructed from an elliptic calabi yau threefold with section yields an effective six - dimensional theory . the lie algebra of the gauge sector of this theory and its representation on the space of massless hypermultiplets are shown to be determined by the intersection theory of the homology of the calabi yau threefold . ( similar statements hold for m - theory and the type iia string compactified on the threefold , where there is also a dependence on the expectation values of the ramond ramond fields . ) yau threefolds with section which arise from anomaly cancellation in six dimensions . 0

the f - theory vacuum constructed from an elliptic calabi yau threefold with section yields an effective six - dimensional theory . the lie algebra of the gauge sector of this theory and its representation on the space of massless hypermultiplets are shown to be determined by the intersection theory of the homology of the calabi yau threefold . ( similar statements hold for m - theory and the type iia string compactified on the threefold , where there is also a dependence on the expectation values of the ramond ramond fields . ) we describe general rules for computing the hypermultiplet spectrum of any f - theory vacuum , including vacua with non - simply - laced gauge groups . the case of monodromy acting on a curve of singularities is shown to be particularly interesting and leads to some unexpected rules for how-branes are allowed to wrap certain-cycles . we also review the peculiar numerical predictions for the geometry of elliptic calabi yau threefolds with section which arise from anomaly cancellation in six dimensions . 0

1005.5626

c

summarizing , we show in this paper how the fermionic representation for spin @xmath0 systems can be generalized to spin systems with @xmath2 . the symmetry group of the spin operator is @xmath15 group for integer spin and @xmath16 group for half - odd - integer spin . different path integral formulations and mean field theories are developed corresponding to different ways of handling the constraints . in 1d , we show that the particle - hole symmetric mean field theory for @xmath3 and @xmath4 spin chains are consistent with haldane s conjecture , and we argue that the difference reflects a fundamental difference between integer and half - odd - integer spin chains . we also study 2d spin-1 afm on triangular lattice where we find two spin liquid states , one is a gapless @xmath7-wave spin liquid and the other is a topological @xmath6 spin liquid state . we propose that the gapless @xmath7-wave spin liquid is a plausible ground state for the material niga@xmath8s@xmath9 . our approach can be applied to any other spin models and provides a new approach to spin liquid states for @xmath2 spin systems . we note that because of limitation in scope we have addressed only a very limited number of issues in the study of spin - liquid states in this paper . within the mean - field theory we have restricted ourselves to spin liquids solutions of hamiltonian ( [ hamiltonian ] ) with spin rotational symmetry ( 1d ) and lattice translational symmetry ( 1d and 2d ) . we note that solutions which break spin rotational symmetry exist in our theory which may serve as ground states of hamiltonian ( [ hamiltonian])@xcite . for example , we show in ref . that state with long - ranged magnetic order exists as lowest energy state of the mean - field theory of the @xmath274-@xmath275 model and anti - ferro nematic order may exist when the bi - quadratic ( @xmath360 ) spin - spin interaction exists in the hamiltonian . for simplicity we only considered the mean field states without breaking the translational symmetry . we note that states that break translational symmetry ( such as dimerized states ) are believed to be ground states of some 1d or 2d spin models.@xcite another very important issue is whether the spin liquid states we find are stable against gauge fluctuations . in 1-d , the gauge fluctuations can be removed by a time - dependent read - newns gauge transformation and thus have no effect to the low energy properties@xcite . the situation is very different in two or higher dimensions where the stability of the mean - field state depends on dimensionality and the ( gauge ) structure of the gauge field fluctuations . for instance , @xmath149 spin liquid is believed to be stable at 2d@xcite and gapless @xmath81 dirac fermionic spin liquids is stable at 2d in the large-@xmath19 limit@xcite . in our case of spin liquid solutions for the @xmath3 heisenberg model , the @xmath81 gauge fluctuation is gapped by the spinon - pairing term via the anderson - higgs mechanism . the ground state is stable against the low energy gauge fluctuations which is described by an effective @xmath149 gauge theory . we note that the emergence of gauge - field structure is a direct consequences of particle number constraints and a reliable answer to the question of stability of spin liquid states can be obtained only if we can handle the particle number constraint reliably . gauge field theory can only handle long distance , low energy gauge fluctuations and a more satisfactory answer to the question of stability of the spin liquid states can be obtained only after the gutzwiller projection wavefunctions are studied carefully . we thank prof . michael ma for the discussion about 1d models . we also thank prof . a. lee and naoto nagaosa for suggesting the @xmath6-ansatz for afm on triangular lattice , and thank mr . cheung chan and dr . xiao - yong feng for helpful discussions . zxl and tkn are supported by rgc grant of hksar and hkust3/crf/09 . yz is supported by national basic research program of china ( 973 program , no.2011cb605903 ) , the national natural science foundation of china(grant no.11074218 ) and the fundamental research funds for the central universities in china .

, different path integral representations and mean field theories can be formulated for spin models . in particular , we construct a lagrangian with restored particle - hole symmetry , and apply the corresponding mean field theory to one dimensional ( 1d ) and antiferromagnetic heisenberg models , with results that agree with haldane s conjecture . for a open chain , we show that majorana fermion edge states exist in our mean field theory . the generalization to spins with arbitrary magnitude is discussed . our approach can be applied to higher dimensional spin systems . as an example two spin liquids with different pairing symmetries are discussed : the gapped-wave spin liquid and the gapless-wave spin liquid .

the fermion representation for spins is generalized to spins with arbitrary magnitudes . the symmetry properties of the representation is analyzed where we find that the particle - hole symmetry in the spinon hilbert space of/2 fermion representation is absent for . as a result , different path integral representations and mean field theories can be formulated for spin models . in particular , we construct a lagrangian with restored particle - hole symmetry , and apply the corresponding mean field theory to one dimensional ( 1d ) and antiferromagnetic heisenberg models , with results that agree with haldane s conjecture . for a open chain , we show that majorana fermion edge states exist in our mean field theory . the generalization to spins with arbitrary magnitude is discussed . our approach can be applied to higher dimensional spin systems . as an example , we study the geometrically frustrated afm on triangular lattice . two spin liquids with different pairing symmetries are discussed : the gapped-wave spin liquid and the gapless-wave spin liquid . we compare our mean field result with the experiment on nigas , which remains disordered at low temperature and was proposed to be in a spin liquid state . our fermionic mean field theory provide a framework to study spin liquids with fermionic spinon excitations .

1404.5882

i

a growing number of neutrino experiments conducted at proton accelerators derive their neutrino beams from horn - focused beams of pions and kaons which result from proton - nucleus collisions in low - z materials . at the neutrinos at the main injector ( numi ) facility at fermilab , hadron production uncertainties in monte carlo ( mc ) simulations generally dominate the uncertainties of the neutrino flux predictions at the level of 1520% , and are a limiting factor in the neutrino and anti - neutrino cross - section measurements being done by many numi - based experiments @xcite . one of the goals of the main injector particle production ( mipp ) experiment was to measure the hadron production yield off of an actual numi target with 120 gev / c protons from the main injector ( mi ) to within 5% in order to verify and validate the monte carlo calculations of the numi flux . here we report a measurement of charged pion yield per 120 gev / c proton - on - target in approximately 120 bins of longitudinal and transverse momentum . the statistical and systematic uncertainties in most bins are between 5 and 10% .

the fixed - target mipp experiment , fermilab e907 , was designed to measure the production of hadrons from the collisions of hadrons of momenta ranging from 5 to 120 gev / c on a variety of nuclei . the data have been analyzed and we present here charged pion yields per proton - on - target determined in bins of longitudinal and transverse momentum between 0.5 and 80 gev / c , with combined statistical and systematic relative uncertainties between 5 and 10% .

the fixed - target mipp experiment , fermilab e907 , was designed to measure the production of hadrons from the collisions of hadrons of momenta ranging from 5 to 120 gev / c on a variety of nuclei . these data will generally improve the simulation of particle detectors and predictions of particle beam fluxes at accelerators . the spectrometer momentum resolution is between 3 and 4% , and particle identification is performed for particles ranging between 0.3 and 80 gev / c using , time - of - flight and cherenkov radiation measurements . mipp collected events of 120 gev main injector protons striking a target used in the numi facility at fermilab . the data have been analyzed and we present here charged pion yields per proton - on - target determined in bins of longitudinal and transverse momentum between 0.5 and 80 gev / c , with combined statistical and systematic relative uncertainties between 5 and 10% .

1303.4289

i

estimation and detection are two main concerns in the course of designing a communication system @xcite . the main goal is to design optimal demodulators at the receiver side providing the detector with the necessary sufficient statistics for its decision on the transmitted symbol at a specific observation interval . furthermore , the optimization of the decision device is also a target , i.e. , its design based on such statistical tests which rely on sufficient statistics and minimize the probability of error . a different setup of optimal designs related to radar and sonar systems is to detect the presence of either a deterministic or random signal in noise with least probability of error or false alarm @xcite . although the two aforementioned setups have conceptual differences , they are usually treated in the same fashion . first , an optimal demodulator is necessary to deliver the sufficient statistics to the decision device . then , the decision device , that optimally uses these sufficient statistics , has to be derived . the optimal design of the decision device is formulated in any case as a hypotheses testing problem . moreover , the optimization of the transmitter is another related problem . in this case , the problem turns to be the design of optimal transmission sets , such that the end performance metric , i.e , the probability of error is minimized . depending on the degree of knowledge about the transmission channel at the receiver side , the detector can be coherent , semi - coherent or noncoherent @xcite . the more information about the transmission channel is available , the better the receiver s performance will be . this justifies the fact that the receivers usually have a built - in channel estimator . in the communication and signal processing literature , the usual channel estimators are the minimum variance unbiased ( mvu ) and the minimum mean square error ( mmse ) estimators @xcite . the combination of these channel estimators with the optimal decision devices is usually considered to address the problem of determining the optimal receiver . current physical layer ( phy ) standards that have attracted a lot of attention both from the mobile industry and the research community are the wireless interoperability for microwave access ( wimax ) , the long term evolution ( lte ) and the digital video broadcasting ( dvb ) either in its terrestrial ( dvb - t ) or its handheld ( dvb - h ) versions @xcite . these standards are orthogonal frequency division multiple access ( ofdma ) based and they can satisfy the need for shorter communication links to provide truly broadband connectivity services . in these systems , either mvu / least squares ( ls ) or mmse channel estimators are used , usually employing some sort of estimate interpolation through the frame if the goal is to track a time - varying channel @xcite . in this paper , we re - examine the validity of the common belief that the mvu and mmse channel estimators are the best choices to be combined with the optimal detectors , delivering an overall optimal receiver , when finite - sample training is used to estimate the channel . to this end , ideas originating from the system identification field are employed . recent results in optimal experiment design indicate that it is better to design the optimal training for the estimation of a certain set of unknown parameters with respect to optimizing the end performance metric rather than the mean square error of the parameter estimator itself @xcite . we will slightly modify this idea and we will examine if the aforementioned channel estimators are the best choices , when the selection of the channel estimator is made with respect to an appropriately defined end performance metric . for illustration purposes , this study is performed on a toy channel model , namely a single input single output ( siso ) flat fading channel with additive white gaussian noise ( awgn ) . the initial focus is on two different mse criteria . these mse criteria serve to demonstrate the dependence of the optimal channel estimators on the end performance metrics . their choice is based on the simplicity of the analysis that they allow . then , using the obtained results , we will examine the case of the error probability as the performance metric of interest . we show that for several performance metrics examined in this paper , the mvu and mmse channel estimators are suboptimal , while we propose ways to obtain better channel estimators . finally , we numerically compare the performances of the derived channel estimators with those of the mvu and mmse channel estimators for all performance metrics in this paper . these comparisons verify that the optimality of the usual channel estimators with respect to common end performance metrics is questionable . this paper is organized as follows : section [ sec : probst ] defines the problem of designing the channel estimator with respect to the end performance metric . section [ sec : prelim ] presents some results and comments that will be useful in the rest of the paper , while it introduces approximations of the performance metrics that the rest of the analysis will be based on . the optimality of the mvu and mmse channel estimators with respect to the minimization of the symbol estimate mse is examined in section [ sec : dmse ] and subsections therein , while uniformly better channel estimators are also proposed . the same analysis as in section [ sec : dmse ] is pursued in section [ sec : emse ] for a differently defined symbol estimate mse and in section [ sec : minpe ] for a rough approximation ( variation ) of the error probability performance metric . section [ sec : sims ] illustrates the validity of the derived results . finally , section [ sec : concl ] concludes the paper .

the fundamental task of a digital receiver is to decide the transmitted symbols in the best possible way , i.e. , with respect to an appropriately defined performance metric . examples of usual performance metrics are the probability of error and the mean square error ( mse ) of a symbol estimator . in a coherent receiver , this paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased ( mvu ) and the minimum mean square error ( mmse ) estimators for these metrics and on proposing better estimators whenever it is necessary . for illustration purposes , this study is performed on a toy channel model , namely a single input single output ( siso ) flat fading channel with additive white gaussian noise ( awgn ) . in this way , this paper highlights the design dependencies of channel estimators on target performance metrics . minimum mean square error ( mmse ) , minimum variance unbiased ( mvu ) , probability of error , single input single output ( siso ) .

the fundamental task of a digital receiver is to decide the transmitted symbols in the best possible way , i.e. , with respect to an appropriately defined performance metric . examples of usual performance metrics are the probability of error and the mean square error ( mse ) of a symbol estimator . in a coherent receiver , the symbol decisions are made based on the use of a channel estimate . this paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased ( mvu ) and the minimum mean square error ( mmse ) estimators for these metrics and on proposing better estimators whenever it is necessary . for illustration purposes , this study is performed on a toy channel model , namely a single input single output ( siso ) flat fading channel with additive white gaussian noise ( awgn ) . in this way , this paper highlights the design dependencies of channel estimators on target performance metrics . minimum mean square error ( mmse ) , minimum variance unbiased ( mvu ) , probability of error , single input single output ( siso ) .

1409.2398

i

in the generalized function matching problem one is given a text @xmath0 and a pattern @xmath1 and the goal is to decide whether there is a match between @xmath1 and @xmath0 , where a single letter of the pattern is allowed to match multiple letters of the text ( we say that @xmath1 gf - matches @xmath0 ) . for example , if the text is @xmath2 and the pattern is @xmath3 , then a generalized function match ( on short , gf - match ) is @xmath4 , but if @xmath5 and @xmath6 , then there is no gf - match . if , moreover , the matching is required to be injective , then we term the problem generalized parameterzied matching ( gpm ) . in @xcite , amir and nor describe applications of gfm in various areas such as software engineering , image searching , dna analysis , poetry and music analysis , or author validation . gfm is also related to areas such as ( un-)avoidable patterns @xcite , word equations @xcite and the ambiguity of morphisms @xcite . gfm has a long history starting from 1979 . ehrenfeucht and rozenberg @xcite show that gfm is np - complete . independently , angluin @xcite studies a more general variant of gfm where the pattern may contain also letters of the text alphabet . angluin s paper received a lot of attention , especially in the learning theory community @xcite ( see @xcite for a survey ) but also in many other areas . recently , a systematic study of the classical complexity of a number of variants of gfm and gpm under various restrictions has been carried out @xcite . it was shown that gfm and gpm remain complete for many natural restrictions . moreover , the study of gfm and its variants within the framework of parameterized complexity has recently been initiated @xcite . in this paper we study the parameterized complexity of the optimization variant of gfm ( called max - gfm ) and its variants , where one is allowed to replace some of the pattern letters with some special symbols `` ? '' , termed wildcards or do nt cares , which can be mapped to an arbitrary substring of the text . the goal is to minimize the number of wildcards used . the problem was first introduced to the pattern matching community by amir and nor @xcite . they show that if the pattern alphabet has constant size , then a polynomial algorithm can be found , but that the problem is complete otherwise . then , in @xcite , it is shown the hardness of the gfm ( without wildcards ) and the hardness of the gfm when the function @xmath7 is required to be an injection ( named gpm ) . more specifically , gfm is hard even if the text alphabet is binary and each letter of the pattern is allowed to map to at most two letters of the text @xcite . in the same paper it is given a @xmath8 approximation algorithm for the optimization variant of gfm where the goal is to search for a pattern @xmath9 that gf - matches @xmath0 and has the smallest hamming distance to @xmath1 . in @xcite the optimization versions of gfm and gpm are proved to be * apx*-hard . [ [ our - results ] ] our results + + + + + + + + + + + before we discuss our results , we give formal definitions of the problems . in the following let @xmath0 be a text over an alphabet @xmath10 and let @xmath11 be a pattern over an alphabet @xmath12 . we say that @xmath1 _ gf - matches _ @xmath0 if there is a function @xmath13 such that @xmath14 . to improve the presentation we will sometimes abuse notation by writing @xmath15 instead of @xmath16 . let @xmath17 be a natural number . we say that a pattern @xmath1 _ @xmath17-gf - matches _ @xmath0 if there is a text @xmath9 over alphabet @xmath18 of hamming distance at most @xmath17 from @xmath1 such that @xmath9 gf - matches @xmath0 . given a text @xmath0 , a pattern @xmath1 , and an integer @xmath17 , decide whether @xmath1 @xmath17-gf - matches @xmath0 . the max - gfm can be seen as the optimization variant of gfm in which we want to replace some of the pattern letters with special wildcard symbols , i.e. , the symbols @xmath19 , which can be mapped to any non - empty substring of the text . we also study the max - gpm problem . the only difference between max - gpm and max - gfm is that for max - gpm the function @xmath7 is required to be injective . the notions of gp - matching and @xmath17-gp - matching are defined in the natural way , e.g. , we say a pattern @xmath1 _ gp - matches _ a text @xmath0 if @xmath1 _ gf - matches _ @xmath0 using an injective function . in this paper we study the parameterized complexity of the two problems using a wide range of parameters : maximum number of occurrences of a letter in the text @xmath20 , maximum number of occurrences of a letter in the pattern @xmath21 , size of the text alphabet @xmath22 , size of the pattern alphabet @xmath23 , the maximum length of a substring of the text that a letter of the pattern alphabet can be mapped to ( i.e. , @xmath24 ) , the number of wildcard letters @xmath25 , and the maximum length of a substring of the text that a wildcard can be mapped to , denoted by @xmath26 . our results are summarized in table [ table : tab2 ] . we verified the completeness of our results using a simple computer program . in particular , the program checks for every of the @xmath27 possible combinations of parameters @xmath28 that the table contains either : i ) a superset of @xmath28 under which max - gfm / gpm is hard ( and thus , max - gfm / gpm is hard if parameterized by @xmath28 ) ; or ii ) a subset of @xmath28 for which max - gfm / gpm is fpt ( and then we have an fpt result for the set of parameters @xmath28 ) . since some of our results do not hold for both max - gfm and max - gpm , we carried out two separate checks , one for max - gfm and one for max - gpm . .parameterized complexity of max - gfm and max - gpm . [ cols="^,^,^,^,^,^,^,^",options="header " , ] the paper is organized as follows . in section [ sec : prel ] we give preliminaries , in section [ sec : fpt ] we present our fixed - parameter algorithms and in section [ sec : hardness ] we show our hardness results .

the generalized function matching ( gfm ) problem has been intensively studied starting with [ ehrenfeucht and rozenberg , 1979 ] . in this paper we study the parameterized complexity of the optimization variant of gfm ( called max - gfm ) , which has been introduced in [ amir and nor , 2007 ] . here , one is allowed to replace some of the pattern letters with some special symbols `` ? '' , termed wildcards or do nt cares , which can be mapped to an arbitrary substring of the text . the goal is to minimize the number of wildcards used . we give a complete classification of the parameterized complexity of max - gfm and its variants under a wide range of parameterizations , such as , the number of occurrences of a letter in the text , the size of the text alphabet , the number of occurrences of a letter in the pattern , the size of the pattern alphabet , the maximum length of a string matched to any pattern letter , the number of wildcards and the maximum size of a string that a wildcard can be mapped to .

the generalized function matching ( gfm ) problem has been intensively studied starting with [ ehrenfeucht and rozenberg , 1979 ] . given a pattern p and a text t , the goal is to find a mapping from the letters of p to non - empty substrings of t , such that applying the mapping to p results in t. very recently , the problem has been investigated within the framework of parameterized complexity [ fernau , schmid , and villanger , 2013 ] . in this paper we study the parameterized complexity of the optimization variant of gfm ( called max - gfm ) , which has been introduced in [ amir and nor , 2007 ] . here , one is allowed to replace some of the pattern letters with some special symbols `` ? '' , termed wildcards or do nt cares , which can be mapped to an arbitrary substring of the text . the goal is to minimize the number of wildcards used . we give a complete classification of the parameterized complexity of max - gfm and its variants under a wide range of parameterizations , such as , the number of occurrences of a letter in the text , the size of the text alphabet , the number of occurrences of a letter in the pattern , the size of the pattern alphabet , the maximum length of a string matched to any pattern letter , the number of wildcards and the maximum size of a string that a wildcard can be mapped to .

1203.2416

c

high - mass protostellar outflows show a variety of morphologies , and their driving mechanism is less clear than for low - mass protostellar outflows . well known energetic outflows like the orion bn / kl and dr 21 outflows show a wide opening angle and complicated shock structures ( see e.g. , * ? ? ? * ; * ? ? ? in contrast , some high - mass protostar drive a relatively collimated outflow analogous to that associated with low - mass protostars @xcite . these tend to be associated with a protostar with spectral types of late o or b , not with the earlier spectral types ( see * ? ? ? * ; * ? ? ? * for review ) . @xcite proposed an evolution scenario of outflows from massive stars . in their scenario , an outflow from a massive star is collimated in their early evolutionary phases . as it grows by accretion , it reaches the main sequence , associated with an ultra compact region . the opening angle of the outflow could then be increased by the ionized wind from the massive star . as mentioned in section 3.1 , the h@xmath3 emission in most of the egos is associated with a collimated outflow . this suggests that they are relatively young , or their masses are not very high , according to the scenario proposed by @xcite . in contrast , ego g35.20 - 0.74 exhibits a large opening angle h@xmath3 outflow . the hourglass shape outflow is unlikely to be a composite of two collimated outflows at different directions , because the shapes , lengths , and intensities of mho 2431c and d are similar ( figure [ fig : g35.20 - 0.74 ] ) . in addition , co interferometric observations also support that it is a single outflow with large opening angle @xcite . the h@xmath3 outflow is likely to be driven by a yso which is associated with an ultra compact region @xcite at the outflow base , and it is the only h@xmath3 outflow with a known region in our sample . our results support the evolution scenario of @xcite . in our sample , two egos are likely to be associated with h@xmath3 outflows from multiple protostars ( ego g19.88 - 0.53 and g35.13 - 0.74 ) . three radio sources are located near the outflow base of ego g19.88 - 0.53 @xcite , and ego g35.13 - 0.74 is associated with a young star cluster mercer 14 @xcite . in this section , we discuss the emission mechanisms of those egos with near - infrared counterparts , based on the 23 egos mentioned in 3 . originally , @xcite suggested that the extended 4.5 @xmath1 emission of egos traces shocked molecular gas in outflows . however , some studies suggest that the 4.5 @xmath1 emission come from scattered light . for example , the appearance of ngc 6334 v is similar to that of egos in the @xmath0 three - color image . in the 2 @xmath1 polarimetric image , ngc 6334 v shows two highly polarized reflection nebulae ( scattered light ) coinciding with the 4.5 @xmath1 emission and the bipolar outflow @xcite . another source , ego g35.20 - 0.74 known as g35.2n , also shows a highly polarized extended reflection nebulae in @xmath4-band @xcite . these two cases suggest that @xmath4-band emission represents scattered emission from embedded ysos , which is consistent with results from @xcite and @xcite . iras 17527 - 2439 has an s - shaped h@xmath3 outflow which may be caused by the precession of a jet @xcite , and its appearance in the @xmath0 image is similar to that of egos . interestingly , the morphologies of the continuum ( @xmath4 and @xmath0 bands ) and h@xmath3 emission of iras 17527 - 2439 are different . the continuum emission in @xmath4 and @xmath0 bands in the direction of the outflow is rotated counterclockwise with respect to the h@xmath3 outflow , suggesting that the continuum emission emerges from the outflow cavity of the yso @xcite . recently , @xcite took spectra of egos at 5 10 @xmath1 wavelength , and found that the 4.5 @xmath1 emission is not due to h@xmath3 lines which would be too faint to contribute the irac 4.5 @xmath1 emission . in our sample , only three of the 12 egos with h@xmath3 outflows show a distribution of the h@xmath3 emission similar to that of the 4.5 @xmath1 emission ( ego g35.68 - 0.18 , g35.83 - 0.20 , and west lobe of ego g19.88 - 0.53 ) . the 4.5 @xmath1 emission of these three egos likely comes from h@xmath3 emission . the @xmath12- and @xmath13-band spectrum of ego g19.88 - 0.53 show h@xmath3 emission @xcite , supporting this idea . in contrast , for the remaining 9 egos with h@xmath3 outflows in our sample , we found that the morphologies of the 4.5 @xmath1 and h@xmath3 emission are different . the peaks of the 4.5 @xmath1 emission are rarely associated with h@xmath3 emission , and the 4.5 @xmath1 emission generally appears close to the bases of the outflows ( embedded ysos ) . the h@xmath3 emission is more extended than the 4.5 @xmath1 emission which is usually weak or not detected at the peak of the h@xmath3 emission . this suggests that the origins of the h@xmath3 and 4.5 @xmath1 emission are different . for those egos with @xmath4-band emission , the morphologies of the extended @xmath4-band emission and the 4.5 @xmath1 emission resemble each other , suggesting the same origin . furthermore , seven of the sources with extended @xmath4-band emission also show extended emission in the @xmath5-band , with flux distributions similar to the @xmath4-band emission . this @xmath5-band emission is not likely to be due to shocked emission , since ( 1 ) the flux distribution is significantly different between h@xmath3 and @xmath4-band emission ; and ( 2 ) shocked emission in the @xmath5-band should be so faint that it is not likely to be observed ( e.g. , * ? ? ? * ; * ? ? ? these observed characteristics can be consistently explained if the extended emission at @xmath5 , @xmath4 , 3.6 , and 4.5 @xmath1 is due to scattered continuum @xcite . indeed , all of these sources are associated with 24 @xmath1 source(s ) , i.e. , a protostar or multiple protostars , which are the sources of the scattered light . in figure [ fig : hk ] , the gradual change in flux distribution with wavelength is consistent with extinction at different wavelengths . in ego g35.20 - 0.74 , the emission in @xmath4-band and 4.5 @xmath1 shows a bipolar distribution about the position of the protostar seen at 24 @xmath1 . this implies that the scattering occurs in an outflow cavity @xcite , as in low - mass protostars ( e.g. , * ? ? ? * ; * ? ? ? * ) . in our 23 ego sample , only three are consistent with the 4.5 @xmath1 emission coming from the h@xmath3 emission , and the rest are likely associated with scattered light from the embedded ysos or mixture of both . throughout , we suggest that the 4.5 @xmath1 emission could result from scattered light or / and h@xmath3 emission . however , the 4.5 @xmath1 emission itself can not tell which emission mechanism dominates , and we need other wavelength observations ( e.g. , narrow h@xmath3- and @xmath4-band ) to distinguish the contributions of these two emission mechanisms .

these egos are potential candidates for high mass protostellar outflows . furthermore , the morphologies of the near - infrared continuum and 4.5 emission are similar to each other for those egos with-band emission , implying that at least a part of the irac - band continuum emission of egos comes from scattered light from the embedded ysos .

the glimpse survey has revealed a number of extended green objects " ( egos ) which display extended emission at 4.5 . these egos are potential candidates for high mass protostellar outflows . we have used high resolution ( ) h 1 - 0 s(1 ) line , , and-band images from the united kingdom infrared telescope to study 34 egos to investigate their nature . we found that 12 egos exhibit h outflows ( two with chains of h knotty structures ; five with extended h bipolar structures ; three with extended h lobes ; two with pairs of h knots ) . in the 12 egos with h outflows , three of them exhibit similar morphologies between the 4.5 and h emission . however , the remaining 9 egos show that the h features are more extended than the continuum features , and the h emission is seldom associated with continuum emission . furthermore , the morphologies of the near - infrared continuum and 4.5 emission are similar to each other for those egos with-band emission , implying that at least a part of the irac - band continuum emission of egos comes from scattered light from the embedded ysos .

0808.1888

i

motivated by problems arising from dna sequencing and the properties of circle graphs of 2-in , 2-out digraphs , arratia , bollobs and sorkin introduced a new family of graph invariants , the interlace polynomials , in @xcite . these invariants may be defined either through recursive elimination of vertices or as sums indexed by subsets of vertices @xcite , much as the tutte polynomial may be defined either through recursive elimination of edges or as a sum indexed by subsets of edges . ellis - monaghan and sarmiento @xcite have shown ( among other results ) that one of the one - variable interlace polynomials , @xmath3 , can be computed in polynomial time for bipartite distance hereditary graphs . their proof depends on the corresponding result for the tutte polynomials of series - parallel graphs , first proved in @xcite , and the fact that bipartite distance hereditary graphs are circle graphs of euler circuits in medial graphs of series - parallel graphs . in this paper we discuss several useful features of interlace polynomials that have been modified to incorporate vertex weights . after defining the weighted interlace polynomials in section 2 , we observe that a simple adjustment of weights makes it unnecessary to have the third term in the fundamental recursion @xmath4 of @xcite . in section 3 we present reduction formulas that can be used to eliminate a vertex that is a twin of another , or pendant on another . these pendant - twin reductions are analogous to the series - parallel reductions of electrical circuit theory , in which two resistors wired in series ( resp . parallel ) are replaced by one resistor with @xmath5 ( resp . @xmath6 ) . the pendant - twin reductions are used to extend the result of ellis - monaghan and sarmiento mentioned above to the two - variable interlace polynomials of looped , non - bipartite distance hereditary graphs . in section 4 we show that if @xmath7 is a looped graph obtained using the composition construction of cunningham @xcite then @xmath1 is equal to the interlace polynomial of a suitably re - weighted version of @xmath8 ; this generalizes results of @xcite that describe the @xmath3 polynomials of simple graphs constructed through substitution . composition has proven useful in the study of circle graphs ( see for instance @xcite ) , so it is not surprising to see it appear in the theory of the interlace polynomials . in section 5 we discuss some elementary properties of the unweighted @xmath3 polynomial , focusing on simple ( unlooped ) graphs . in section 6 we sketch a combinatorial description of the interlace polynomials of trees and forests introduced by anderson , cutler , radcliffe and the present author in @xcite . this combinatorial description bears a striking resemblance to the activities description of the tutte polynomial , and in section 7 we extend it to arbitrary graphs using activities defined with respect to recursive interlace polynomial calculations . we do not know whether or not these activities have a convenient combinatorial description in general . we should observe that the idea of using vertex weights for interlace polynomials has appeared before , though our implementation of the idea is different from those we have seen elsewhere . in @xcite , courcelle introduced a multivariate interlace polynomial that is more complicated than the polynomials we consider here , and involves assigning indeterminates to the vertices of a graph . he used monadic second - order logic to show that it is possible to compute bounded portions of this polynomial ( and the entire unweighted interlace polynomial @xmath9 ) in polynomial time for graphs of bounded clique - width . this technique is quite general but involves large built - in constants , so for pendant - twin reductions and compositions the formulas presented here are considerably more practical . also , blser and hoffmann @xcite use the idea of assigning indeterminates to vertices , along with the adjunction of two types of pendant - twin vertices , to show that evaluating interlace polynomials is generally @xmath10-hard for almost all values of the variables . in @xcite arratia , bollobs and sorkin observe that there is a natural ( so natural it is `` practically a tautology '' ) correspondence between the kauffman bracket of an alternating link diagram and an interlace polynomial of an associated 2-in , 2-out digraph . the situation is clear enough that we do not discuss it in detail , but it is worth mentioning that this correspondence may be extended to arbitrary link diagrams using vertex weights . the well - known relationship between the jones and tutte polynomials is similar , in that an edge - weighted or -signed version of the tutte polynomial conveniently incorporates crossing information when dealing with non - alternating links @xcite .

one novel property is a version of the fundamental three - term formula that lacks the last term . binary computation trees provide a description of that is analogous to the activities description of the tutte polynomial . three other novel properties are weighted pendant - twin reductions , which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged . . keywords .

the interlace polynomials introduced by arratia , bollobs and sorkin extend to invariants of graphs with vertex weights , and these weighted interlace polynomials have several novel properties . one novel property is a version of the fundamental three - term formula that lacks the last term . it follows that interlace polynomial computations can be represented by binary trees rather than mixed binary - ternary trees . binary computation trees provide a description of that is analogous to the activities description of the tutte polynomial . if is a tree or forest then these `` algorithmic activities '' are associated with a certain kind of independent set in . three other novel properties are weighted pendant - twin reductions , which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged . these reductions allow for smaller computation trees as they eliminate some branches . if a graph can be completely analyzed using pendant - twin reductions then its interlace polynomial can be calculated in polynomial time . an intuitively pleasing property is that graphs which can be constructed through graph substitutions have vertex - weighted interlace polynomials which can be obtained through algebraic substitutions . keywords . interlace polynomial , vertex weight , pendant vertex , twin vertex , series , parallel , graph composition , graph substitution , join , computational complexity , tree , tutte polynomial , jones polynomial mathematics subject classification .

1303.4583

i

the atlas and cms collaborations of large hadron collider ( lhc ) have recently discovered a bosonic particle whose mass being around 125 gev @xcite . the data from the lhc is strongly favouring the spin of this bosonic particle to be zero and it is consistent with the higgs boson @xcite , which is necessary to achieve the electroweak symmetry breaking . the atlas and cms groups have analyzed the decay properties of this higgs - like particle into various standard model fields . an indication for the excess of events in the higgs to diphoton channel as compared to that in the standard model ( sm ) has been reported . explicitly , by defining the quantity @xmath9_{\rm observed}}{\left[\sigma(pp\to h)\times { \rm br}(h\to \gamma\gamma ) \right]_{\rm sm } } , \label{e : rgg}\ ] ] where @xmath10 is the higgs boson , the atlas and cms had earlier reported that @xmath11 @xmath12 and @xmath13 @xcite , respectively . the above quoted values for @xmath14 have been recently updated in march 2013 at the conference rencontres de moriond . the atlas group has claimed @xmath15 @xcite , which indicates a slight enhancement in the @xmath16 channel . however , the cms group has reported that @xmath14 could be @xmath17 or @xmath18 , depending on the type of the analysis @xcite . the values quoted by the cms group imply that the discovered higgs boson is consistent with the sm within the uncertainties . we can hope that the future analysis at atlas and cms can resolve the differences in @xmath14 . at this moment , it is worth to analyse by assuming that the discovery made at the lhc favours new physics . new physics has been motivated by several considerations and some of them are gauge hierarchy problem and smallness of neutrino masses . gauge hierarchy problem can be solved by proposing supersymmetry @xcite . in supersymmetric models the higgs boson mass can be around the electroweak scale and it is protected from radiative corrections . the weakly interacting neutrinos are found to have non - zero masses which should not exceed 1 ev . the non - zero masses for neutrinos and upper limits on them have been established by neutrino oscillation experiments @xcite , cosmological observations @xcite and @xmath19-decay experiments @xcite . since the neutrino masses should be smaller than the electroweak scale by at least twelve orders of magnitude , the smallness of their masses indicate a new mechanism for mass generation . to solve both the gauge hierarchy problem and smallness of neutrino masses , bilinear r - parity violating supersymmetric ( brpvs ) model is a viable option . for a review on the brpvs model , this model is a minimal extension of the minimal supersymmetric standard model ( mssm ) . in the brpvs model , additional bilinear terms of the forms @xmath20 and @xmath21 are added to the superpotential and scalar potential respectively . here @xmath22 and @xmath23 are superfields ( scalar components ) of lepton and up - type higgs doublets respectively . the above mentioned bilinear terms violate lepton number and also the r - parity . @xmath0 is a mass parameter and @xmath1 is a mass - square parameter . provided that the @xmath0 and @xmath1 are very small , the masses of neutrinos can be shown to be consistent with the observed neutrino oscillation data @xcite . one may explain the smallness of @xmath0 and @xmath1 by proposing additional symmetries @xcite or by embedding this model in a high scale physics @xcite . the brpvs model has rich phenomenology @xcite . in this work we want to study the affects of recent discoveries at the lhc on the parameter space of the brpvs model . as mentioned above that the brpvs model is an extension of mssm and the additional parameters in it are @xmath0 and @xmath1 . moreover , both @xmath0 and @xmath1 should be very small in order to account for the smallness of neutrino masses . as a result of this , in the brpvs model , the contribution to the higgs boson mass and also to the quantity @xmath14 are dominantly determined by the mssm parameters . in order to have light higgs boson mass @xmath24 125 gev , the stop masses should be considerably high as well as large mixing is needed in the stop sector @xcite . however , parameters in the squark sector do not affect the neutrino masses in the brpvs model . on the other hand , to have @xmath25 it has been shown that relatively light stau masses and large left - right mixing in the stau sector are required @xcite . essentially , this would mean that the soft parameters of slepton masses ( @xmath5 ) , higgsino mass parameter ( @xmath26 ) and the ratio of vacuum expectation values ( vevs ) of the two neutral higgs fields ( @xmath27 ) determine @xmath14 . we will show that cp - odd higgs boson mass ( @xmath6 ) also has a role to play in the enhancement of higgs to diphoton decay rate . shortly below we will explain that the parameters which determine @xmath14 can affect the neutrino masses in the brpvs model . it is to remind that in the singlet extension of mssm , enhancement in @xmath14 can be made not necessarily with light staus @xcite . in the brpvs model , one neutrino state acquires non - zero mass at tree level due to mixing between flavor neutrinos and neutralinos @xcite . the remaining two neutrino states acquire masses at 1-loop level due to mixing between sneutrinos and the three neutral higgs bosons @xcite . explicitly , apart from @xmath0 and @xmath1 , the neutrino masses in this model are dominantly depended on the neutralino parameters ( @xmath28 , @xmath26 , @xmath27 ) , @xmath5 and @xmath6 . from the discussion in the previous paragraph , we can understand that the parameters which determine the neutrino masses in the brpvs model have a role to play in the enhancement of higgs to diphoton decay rate . from this perspective , we can understand that the requirement of @xmath25 can lead to certain allowed values for @xmath0 and @xmath1 , which determine the overall scales of neutrino masses . both the atlas and cms groups of the lhc are yet to confirm whether @xmath25 or not . hence we have also analyzed the case @xmath29 . in either of these cases we will see that the allowed values of @xmath0 and @xmath1 are small , and their smallness can be motivated from a high scale physics . while motivating these parameters from a high scale physics , we can also predict allowed ranges for @xmath5 , @xmath6 and also about other supersymmetric parameters . the paper is organized as follows . in the next section , we give a brief overview of the brpvs model and also describe the neutrino masses in this model . in the same section we will also explain the relevant quantities regarding the higgs boson mass and @xmath14 . in sec . 3 , we describe our results on @xmath0 and @xmath1 which are compatible with neutrino oscillation data and also with @xmath14 . we then motivate these results from a high scale physics . we conclude in sec .

we have studied implications of these discoveries in the bilinear r - parity violating supersymmetric model , whose main motivation is to explain the non - zero masses for neutrinos . the r - parity violating parameters in this model are and , and these parameters determine the scale of neutrino masses . if the enhancement in the higgs to diphoton decay rate is true , then we have found gev and 1 gev in order to be compatible with the neutrino oscillation data . also , in the above mentioned analysis , we can determine the soft masses of sleptons ( ) and cp - odd higgs boson mass ( ) . * implications of higgs to diphoton decay rate in the bilinear r - parity violating supersymmetric model * + raghavendra srikanth hundi + centre for high energy physics , + indian institute of science , + bangalore 560 012 , india . + e - mail : [email protected] + pacs numbers : 12.60.jv , 14.60.pq , 14.80.da

the large hadron collider has recently discovered a higgs - like particle having a mass around 125 gev and also indicated that there is an enhancement in the higgs to diphoton decay rate as compared to that in the standard model . we have studied implications of these discoveries in the bilinear r - parity violating supersymmetric model , whose main motivation is to explain the non - zero masses for neutrinos . the r - parity violating parameters in this model are and , and these parameters determine the scale of neutrino masses . if the enhancement in the higgs to diphoton decay rate is true , then we have found gev and 1 gev in order to be compatible with the neutrino oscillation data . also , in the above mentioned analysis , we can determine the soft masses of sleptons ( ) and cp - odd higgs boson mass ( ) . we have estimated that 300 gev and 700 gev . we have also commented on the allowed values of and , in case there is no enhancement in the higgs to diphoton decay rate . finally , we present a model to explain the smallness of and . * implications of higgs to diphoton decay rate in the bilinear r - parity violating supersymmetric model * + raghavendra srikanth hundi + centre for high energy physics , + indian institute of science , + bangalore 560 012 , india . + e - mail : [email protected] + pacs numbers : 12.60.jv , 14.60.pq , 14.80.da

astro-ph0403344

i

the cosmic microwave background ( cmb ) radiation has played an essential role in shaping our current understanding of the large - scale properties of the universe . the discovery of this radiation in 1965 by penzias and wilson @xcite , and its subsequent interpretation as the relic radiation from a hot , dense phase of the universe @xcite put the hot big bang model on a firm observational footing . the prediction of angular variations in the temperature of the radiation , due to the propagation of photons through an inhomogeneous universe , followed shortly after @xcite , but it was not until 1992 that these were finally detected by the differential microwave radiometers ( dmr ) experiment on the cosmic background explorer ( cobe ) satellite @xcite . the fractional temperature anisotropies are at the level of @xmath1 , consistent with structure formation in cold dark matter ( cdm ) models @xcite , but much smaller than earlier predictions for baryon - dominated universes @xcite . another experiment on cobe , the far infrared absolute spectrophotometer ( firas ) , spectacularly confirmed the black - body spectrum of the cmb and determined the ( isotropic ) temperature to be 2.725k @xcite . in the period since cobe , many experiments have mapped the cmb anisotropies on a range of angular scales from degrees to arcminutes ( see @xcite for a recent review ) , culminating in the first - year release of all - sky data from the wilkinson microwave anisotropy probe ( wmap ) satellite in february 2003 @xcite . the observed modulation in the amplitude of the anisotropies with angular scale is fully consistent with predictions based on coherent , acoustic oscillations @xcite , derived from gravitational instability of initially adiabatic density perturbations in a universe with nearly - flat spatial sections . the amplitude and scale of these acoustic features has allowed many of the key cosmological parameters to be determined with unprecedented precision @xcite , and a strong concordance with other cosmological probes has emerged . in this review we describe the essential physics of the temperature anisotropies of the cmb , and its recently - detected polarization @xcite , and discuss how these are used to constrain cosmological models . for reviews that are similar in spirit , but from the pre - wmap era see e.g. @xcite . we begin in sect . [ adc : sec : fundamentals ] with the fundamentals of cmb physics , presenting the kinetic theory of the cmb in an inhomogeneous universe , and the various physical mechanisms that process initial fluctuations in the distribution of matter and spacetime geometry into temperature anisotropies . section [ adc : sec : params ] discusses the effect of cosmological parameters on the power spectrum of the temperature anisotropies , and the limits to parameter determination from the cmb alone . the physics of cmb polarization is reviewed in sect . [ adc : sec : pol ] , and the additional information that polarization brings over temperature anisotropies alone is considered . finally , in sect . [ adc : sec : highlights ] we describe some of the scientific highlights that have emerged from recent cmb observations , including the detection of cmb polarization , implications for inflation , and the direct signature of dark - energy through correlations between the large - scale anisotropies and tracers of the mass distribution in the local universe . throughout , we illustrate our discussion with computations based on @xmath2cdm cosmologies , with baryon density @xmath3 and cold dark matter density @xmath4 . for flat models we take the dark - energy density parameter to be @xmath5 giving a hubble parameter @xmath6 . we adopt units with @xmath7 throughout , and use a spacetime metric signature @xmath8 .

the linear anisotropies in the temperature of the cosmic microwave background ( cmb ) radiation and its polarization provide a clean picture of fluctuations in the universe some after the big bang . we discuss the simple physics that processes primordial perturbations into the linear temperature and polarization anisotropies . we also describe the role of the cmb in constraining cosmological parameters , and review some of the highlights of the science extracted from recent observations and the implications of this for fundamental physics .

the linear anisotropies in the temperature of the cosmic microwave background ( cmb ) radiation and its polarization provide a clean picture of fluctuations in the universe some after the big bang . simple physics connects these fluctuations with those present in the ultra - high - energy universe , and this makes the cmb anisotropies a powerful tool for constraining the fundamental physics that was responsible for the generation of structure . late - time effects also leave their mark , making the cmb temperature and polarization useful probes of dark energy and the astrophysics of reionization . in this review we discuss the simple physics that processes primordial perturbations into the linear temperature and polarization anisotropies . we also describe the role of the cmb in constraining cosmological parameters , and review some of the highlights of the science extracted from recent observations and the implications of this for fundamental physics .

astro-ph0405587

i

@xmath0 car and the associated clusters tr 16 and tr 14 , contain some of the youngest and most massive stars in the galaxy . these stars presumably trace a sequence in descending order of mass from the enigmatic @xmath0 car , the wolf - rayet star hd 93162 , the o3if ( presumed wolf - rayet precursor ) hd 93129ab , hd 93250 ( o3 v ) , and on through other main sequence stars . an early chandra image was centered on @xmath0 car , and contained tr 16 and part of tr 14 . @xmath0 car itself from this image has been discussed by seward et al . the luminosities and hardness ratios of other stars in the clusters have been discussed by evans et al . ( 2003 , hereafter paper i ) . source variability will be discussed in a future ( in preparation . ) the chandra acis image provides low resolution spectra of sufficiently luminous sources . this paper is a discussion of the spectral properties of these stars . the low resolution spectra supplement grating spectra which can only be obtained for the very brightest x - ray sources . hetg spectra have been obtained for @xmath0 car itself ( e.g. corcoran et al , 2001 ) . a major aim of x - ray studies of this region is to understand the factors that dominate the evolution of the most massive stars in the galaxy . the large number of o stars in this part of the sky justifies the use of less than optimal chandra data ( see section 2 ) . since the surprising discovery of x - rays in o stars with the einstein satellite ( see paper i for background ) , it has been known that at least in some cases , x - ray emission originates in shocks in the strong winds produced by very massive stars . as shown by macfarlane et al . ( 1991 ) , a stellar wind distribution of shocks is expected to produce a unique x - ray emission line signature of very broad , highly asymmetric , blue- shifted x - ray emission line profiles . although chandra hetgs observations do show the expected broadness , the emission lines are found to be essentially symmetric and unshifted ( waldron and cassinelli 2001 ; miller et al . the one exception is the early o - star @xmath1 pup ( cassinelli et al . 2001 ) which shows blue - shifted lines , but the predicted large line asymmetry is minimal . the picture may be further complicated by the possibility that in some cases a binary system may contain two massive stars giving rise to `` colliding wind '' systems . recent investigations ( eg schulz et al . 2003 ) add a further complication in that some hot stars appear to produce x - rays through magnetic processes ( eg . @xmath2 ori c , a , and e ) . tr 14 and tr 16 therefore provide one of the best locations to investigate x - ray production in a broad range of massive stars . general introduction to the clusters tr 14 and tr 16 is provided in paper i. since that paper was submitted , two additional studies on the area have become available which are particularly relevant to our discussion . raassen et al ( 2003 ) have analyzed an xmm - newton high - resolution spectrum of wr 25 . albacete et al ( 2003 ) have discussed the luminosities and low - resolution spectra of other sources in the region , also using xmm - newton data . we will include these papers in our discussion later in this paper . x - rays are particularly good tracers of activity high in the atmospheres of stars . in high mass young stars , the mass loss from the atmosphere is fundamental to the future evolution of these objects . it is also linked to the dynamical and chemical history of the interstellar medium . in this paper ( paper ii ) , we focus on the information that acis - ccd low - resolution spectra provide . we are investigating three areas in particular . first , what insights can the spectra provide to the factors effecting evolution of the most massive sequence of objects ( @xmath0 car , hd 93129ab , wr 25 , and hd 93250 ) ? second , how are the x - ray spectra and intrinsic photospheric stellar parameters ( such as temperature ) or extrinsic parameters ( such as reddening ) related for the o main sequence stars from o3 through o8 ? finally , what are the characteristics of the x - ray spectra for the cool ( less massive ) , presumably pre - main sequence stars ? cool stars " refers to the photospheric temperature of low mass stars , even though their x - ray temperatures are often higher than those of high mass stars . specifically , our analysis consists of fitting the spectra to multi - component models ( where the spectra have enough counts ) , fitting simpler ciao / sherpa models to weaker spectra , intercomparing the spectra themselves in appropriate subgroups , and comparing derived temperatures and hardness ratios . succeeding sections of this paper discuss the following topics . 1 . the sources are identified . strong sources are modeled with a detailed wind model . 3 . weaker sources are fit with models available in the ciao sherpa package . 4 . spectra of sources are intercompared . information which can be obtained from acis low resolution spectra is discussed . results are summarized .

the low resolution x - ray spectra around car covering tr 16 and part of tr 14 have been extracted from a chandra ccd acis image . various analysis techniques have been applied to the spectra based on their count rates . direct comparisons of spectra confirm the consistency of the fitting results and also hardness ratios for cases of unusually large extinction in the clusters . the spectra of the low mass stars are harder than the more massive stars . stars in the sequence evolving from the main sequence ( hd 93250 ) through the system containing the o supergiant ( hd 93129ab ) and then through the wolf - rayet stage ( hd93162 ) , presumably ending in the extreme example of car , share the property of being unusually luminous and hard in x - rays . for these x - ray luminous stars , their high mass and evolutionary status ( from the very last stages of the main sequence and beyond ) , cambridge , ma 02138

the low resolution x - ray spectra around car covering tr 16 and part of tr 14 have been extracted from a chandra ccd acis image . various analysis techniques have been applied to the spectra based on their count rates . the spectra with the greatest number of counts ( hd 93162 = wr 25 , hd 93129ab , and hd 93250 ) have been fit with a wind model , which uses several components with different temperatures and depths in the wind . weaker spectra have been fit with raymond - smith models . the weakest spectra are simply inter - compared with strong spectra . in general , fits produce reasonable parameters based on knowledge of the extinction from optical studies and on the range of temperatures for high and low mass stars . direct comparisons of spectra confirm the consistency of the fitting results and also hardness ratios for cases of unusually large extinction in the clusters . the spectra of the low mass stars are harder than the more massive stars . stars in the sequence evolving from the main sequence ( hd 93250 ) through the system containing the o supergiant ( hd 93129ab ) and then through the wolf - rayet stage ( hd93162 ) , presumably ending in the extreme example of car , share the property of being unusually luminous and hard in x - rays . for these x - ray luminous stars , their high mass and evolutionary status ( from the very last stages of the main sequence and beyond ) is the common feature . their binary status is mixed , and magnetic status is still uncertain . address for correspondence : nancy r. evans smithsonian astrophysical observatory ms 4 , 60 garden st . , cambridge , ma 02138

0704.0150

i

low - dimensional quantum spin systems with competing interactions have become an intriguing subject in the last decades . among many achievements in this area , the phenomenon of the topological quantization of magnetization has attracted much attention both theoretically and experimentally . a general necessary condition for the appearance of the magnetization plateaus has been proposed by oshikawa , yamanaka and affleck ( oya ) @xcite , stating that for the heisenberg antiferromagnetic ( af ) spin chain with a single - ion anisotropy , the magnetization curve may have plateaus at which the magnetization per site @xmath18 is topologically quantized by @xmath19 , where @xmath20 is the spin , and @xmath21 is the period of the ground state determined by the explicit spatial structure of the hamiltonian . as one of fascinating models which potentially possesses the magnetization plateaus , the heisenberg diamond chain , consisting of diamond - shaped topological unit along the chain , as shown in fig . [ chain ] , has also gained much attention both experimentally and theoretically ( e.g. refs . drillon , sakurai , ishii , fujisawa , cucooh1,cucooh2,tks , aaa1,aaa2,aaa3,aaa4,aaa5,faf1,faf2 ) . it has been observed that the compounds , a@xmath16cu@xmath16(po@xmath22)@xmath22 with a = ca , sr@xcite , and bi@xmath22cu@xmath16v@xmath17o@xmath23sakurai can be nicely modeled by the heisenberg diamond chain . another spin-@xmath0 compound cu@xmath16cl@xmath24(h@xmath17o)@xmath17@xmath252h@xmath26c@xmath22so@xmath17 was initially regarded as a model substance for the spin-@xmath0 diamond chain @xcite , but a later experimental research reveals that this compound should be described by a double chain model with very weak bond alternations , and the lattice of the compound is found to be cu@xmath17cl@xmath27@xmath25h@xmath26c@xmath22so@xmath17 @xcite . recently , kikuchi _ _ et al.__@xcite have reported the experimental results on a spin-@xmath0 compound cu@xmath16(co@xmath16)@xmath17(oh)@xmath17 , where local cu@xmath28 ions with spin @xmath29 are arranged along the chain direction , and the diamond - shaped units consist of a one - dimensional ( 1d ) lattice . the @xmath30 magnetization plateau and the double peaks in the magnetic susceptibility as well as the specific heat as functions of temperature have been observed experimentally@xcite , which has been discussed in terms of the spin-@xmath0 heisenberg diamond chain with af couplings @xmath1 , @xmath2 and @xmath31 . on the theoretical aspect , the frustrated diamond spin chain with af interactions @xmath1 , @xmath2 and @xmath31 was studied by a few groups . the first diamond spin chain was explored under a symmetrical condition @xmath32@xcite . owing to the competition of af interactions , the phase diagram in the ground state of the spin-@xmath0 frustrated diamond chain was found to contain different phases , in which the magnetization plateaus at @xmath12 as well as @xmath30 are predicted@xcite . another frustrated diamond chain with ferromagnetic ( f ) interactions @xmath1 , @xmath4 and af interaction @xmath5 was also investigated theoretically , which can be experimentally realized if all angles of the exchange coupling bonds are arranged to be around @xmath33 , a region where it is usually hard to determine safely the coupling constants and even about their signs@xcite . despite of these works , the investigations on the heisenberg diamond spin chain with various competing interactions are still sparse . motivated by the recent experimental observation on the azurite compound cu@xmath34(co@xmath16)@xmath17(oh)@xmath17@xcite , we shall explore systematically the magnetic and thermodynamic properties of the spin-@xmath0 heisenberg diamond chain with various competing interactions in a magnetic field , and attempt to fit into the experimental observation on the azurite in a consistent manner . the density matrix renormalization group ( dmrg ) as well as the transfer matrix renormalization group ( tmrg ) techniques will be invoked to study the ground - state properties and thermodynamics of the model under interest , respectively . the local magnetic moments , spin correlation functions , and static structure factors will be discussed for three cases at zero temperature . it is found that the static structure factor @xmath9 shows peaks in zero magnetic field at wavevectors @xmath10 @xmath35 for different couplings , while in the magnetic fields where the magnetization plateau with @xmath12 remains , the peaks appear only at wavevectors @xmath13 , @xmath14 and @xmath15 , which are found to be couplings - independent . these information could be useful for further neutron studies . the double - peak structures of the susceptibility and specific heat against temperature are obtained , where the peak positions and heights are found to depend on the competition of the couplings . it is uncovered that the xxz anisotropy of f and af couplings leads the system without frustration ( see below ) to display quite different behaviors . in addition , the experimental data of the susceptibility , specific heat and magnetization for the compound cu@xmath16(co@xmath16)@xmath17(oh)@xmath17 are fairly compared with our tmrg results . the rest of this paper is outlined as follows . in sec . ii , we shall introduce the model hamiltonian for the spin-@xmath0 heisenberg diamond chain with three couplings @xmath1 , @xmath2 and @xmath36 , where three particular cases are identified . in sec . iii , the magnetic and thermodynamic properties of a frustrated diamond chain with af interactions @xmath1 , @xmath2 and @xmath3 will be discussed . in sec . iv , the physical properties of another frustrated diamond chain with f interactions @xmath1 , @xmath4 and af interaction @xmath5 will be considered . in sec . v , the magnetism and thermodynamics of a non - frustrated diamond chain with af interactions @xmath1 , @xmath5 and f interaction @xmath4 will be explored , and a comparison to the experimental data on the azurite compound will be made . finally , a brief summary and discussion will be presented in sec .

the density matrix renormalization group ( dmrg ) technique is invoked to study the properties of the system in the ground state , while the transfer matrix renormalization group ( tmrg ) technique is applied to explore the thermodynamic properties . the local magnetic moments , spin correlation functions , and static structure factors are discussed in the ground state for the three cases . it is shown that the static structure factor shows peaks at wavevectors for different couplings in a zero magnetic field , which , however in the magnetic fields where the magnetization plateau with pertains , exhibits the peaks only at , and , which are found to be couplings - independent . the double - peak structures of the susceptibility and specific heat against temperature are obtained , where the peak positions and heights are found to depend on the competition of the couplings . it is also uncovered that the xxz anisotropy of f and af couplings leads the system of case ( c ) to display quite different behaviors . in addition , the experimental data of the susceptibility , specific heat and magnetization for the compound cu(co)(oh) are fairly compared with our tmrg results .

the magnetic and thermodynamic properties of spin- heisenberg diamond chains are investigated in three different cases : ( a ) , , ( frustrated ) ; ( b ) , , ( frustrated ) ; and ( c ) , , ( non - frustrated ) , where the bond coupling stands for an antiferromagnetic ( af ) interaction , and for a ferromagnetic ( f ) interaction . the density matrix renormalization group ( dmrg ) technique is invoked to study the properties of the system in the ground state , while the transfer matrix renormalization group ( tmrg ) technique is applied to explore the thermodynamic properties . the local magnetic moments , spin correlation functions , and static structure factors are discussed in the ground state for the three cases . it is shown that the static structure factor shows peaks at wavevectors for different couplings in a zero magnetic field , which , however in the magnetic fields where the magnetization plateau with pertains , exhibits the peaks only at , and , which are found to be couplings - independent . the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes , where two fitting equations are proposed . it is observed that the six modes are closely related to the low - lying excitations of the system . at finite temperatures , the magnetization , susceptibility and specific heat show various behaviors for different couplings . the double - peak structures of the susceptibility and specific heat against temperature are obtained , where the peak positions and heights are found to depend on the competition of the couplings . it is also uncovered that the xxz anisotropy of f and af couplings leads the system of case ( c ) to display quite different behaviors . in addition , the experimental data of the susceptibility , specific heat and magnetization for the compound cu(co)(oh) are fairly compared with our tmrg results .

0704.0150

i

in this paper , we have numerically studied the magnetic and thermodynamic properties of spin-@xmath0 heisenberg diamond chains with three different cases ( a ) @xmath1 , @xmath2 , @xmath31 ( frustrated ) , ( b ) @xmath1 , @xmath4 , @xmath48 ( frustrated ) , and ( c ) @xmath1 , @xmath5 , @xmath4 ( non - frustrated ) by means of the dmrg and tmrg methods . in the ground states , the local magnetic moment , spin correlation function , and static structure factor are explored . the static structure factor @xmath9 at zero field shows peaks at wave vector @xmath13 , @xmath153 , @xmath14 , @xmath137 , @xmath305 and @xmath124 for different couplings , in which the peaks at @xmath13 , @xmath306 and @xmath15 in the magnetization plateau state with @xmath12 are observed to be couplings independent . the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes , where two fitting equations are proposed . it is seen that the six modes are closely related to the low - lying excitations of the system . at finite temperatures , the magnetization , susceptibility and specific heat are calculated , which show various behaviors for different couplings . the double - peak structure of the susceptibility and specific heat can be procured , whose positions and heights are found to be dependent on competing couplings . it has been shown that the xxz anisotropy of f and af couplings can have remarkable effect on the physical behaviors of the system . in addition , the experimental susceptibility , specific heat and magnetization of the diamond chain compound cu@xmath16(co@xmath16)@xmath17(oh)@xmath17cucooh1 can be nicely fitted by our tmrg results . for the spin-@xmath0 frustrated heisenberg diamond chains with af couplings @xmath239 , @xmath2 and @xmath36 , the magnetization plateau at @xmath12 in the ground state coincides with a perfect fixed sequence of the averaged local magnetic moment such as @xmath68 with @xmath307 , which might be described by trimerized states . on the other hand , the static structure factor @xmath9 shows peaks at wave vectors @xmath308 , @xmath153 ( @xmath124 ) , and @xmath14 ( @xmath15 ) for different external fields and different af couplings . we note that the similar behavior of @xmath309 has been experimentally observed in diamond - typed compound sr@xmath16cu@xmath16(po@xmath22)@xmath22 @xcite . in addition , the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes . it is observed that the six modes are closely related to the low - lying excitations of the present case . at finite temperatures , the magnetization @xmath273 , susceptibility @xmath231 and specific heat @xmath267 demonstrate different behaviors at different af couplings , say , the magnetization plateau at @xmath12 is observed whose width is found to be dependent on the couplings ; the double peak structure is observed for the susceptibility @xmath231 and specific heat @xmath267 as a function of temperature , and the heights and positions of the peaks are found to be dependent on the af couplings . for the spin-@xmath0 frustrated heisenberg diamond chains with f couplings @xmath239 , @xmath36 and af coupling @xmath2 , the magnetization plateau at @xmath12 in the ground state corresponds to a perfect fixed sequence of the averaged local magnetic moment such as @xmath310 with @xmath311 , which could be understood by trimerized states . the static structure factor @xmath9 shows peaks also at wave vectors @xmath13 , @xmath312 ( @xmath124 ) , and @xmath14 ( @xmath15 ) for different external fields and different f couplings @xmath1 , @xmath36 and af coupling @xmath2 , which is expected to be experimentally observed in the related diamond - type compound . in addition , the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes with the fitting equations mentioned above . the six modes are closely related to the low - lying excitations of the system . at finite temperatures , the magnetization @xmath273 , susceptibility @xmath231 and specific heat @xmath267 demonstrate various behaviors for different couplings , namely , the magnetization plateau at @xmath18 = @xmath58 is observed whose width is found to depend on the couplings ; the double - peak structure is also observed for the susceptibility @xmath231 and specific heat @xmath267 , and the heights and positions of the peaks are found dependent on f couplings @xmath1 , @xmath36 and af coupling @xmath2 . for the spin-@xmath0 non - frustrated heisenberg diamond chains with af couplings @xmath1 , @xmath2 and f coupling @xmath36 , the magnetization plateau at @xmath12 in the ground state coincides with a perfect fixed sequence of the averaged local magnetic moment such as @xmath310 with @xmath313 , which could be understood by trimerized states . the static structure factor @xmath9 is observed to exhibit the peaks at wave vectors @xmath13 and @xmath14 ( @xmath15 ) for different external fields and different af couplings @xmath1 , @xmath2 and f coupling @xmath36 , which could be experimentally detected in the related diamond - type compound . in addition , it is found that the zero - field spin correlation function @xmath127 is similar to that of the @xmath29 heisenberg af chain . at finite temperatures , the magnetization @xmath273 , susceptibility @xmath189 and specific heat @xmath267 are found to reveal different behaviors for different couplings , i.e. , the magnetization plateau at @xmath12 is obtained , whose width is found to depend on the couplings ; the double - peak structure is observed for the temperature dependence of the susceptibility @xmath189 and specific heat @xmath267 , where the heights and positions of the peaks depend on different af couplings @xmath1 , @xmath2 and f coupling @xmath314 . the effect of the anisotropy of the af and f interactions on the physical properties of the non - frustrated heisenberg diamond chain is also investigated . for the case of the couplings satisfying @xmath269 , when the anisotropic ratio @xmath315 , it is found that the width of the plateau at @xmath12 , the saturation field , and the susceptibility @xmath231 show the same tendency , but quantitatively different , under the external field @xmath60 along the @xmath271 and @xmath275 directions , while the specific heat @xmath267 for @xmath60 along the @xmath271 direction coincides with that along the @xmath275 direction . for the case of the couplings satisfying @xmath277 , when the anisotropic ratio @xmath316 , it is seen that the width of the plateau at @xmath12 , the saturation field , and the susceptibility @xmath231 exhibit the opposite trends for @xmath60 along the @xmath271 and @xmath275 directions , while the specific heat @xmath267 for @xmath60 along the @xmath271 direction also coincides with that along the @xmath275 direction . for all the three cases , plateau states of @xmath12 are observed during the magnetization , whose static structure factor @xmath9 shows peaks at wavevectors @xmath13 , @xmath14 and @xmath15 . but in absence of the magnetic field , the static structure factor @xmath9 in the ground state displays peaks at @xmath13 , @xmath153 , @xmath14 , @xmath137 , @xmath15 , and @xmath124 for the frustrated case with @xmath1 , @xmath2 , @xmath31 ; peaks at @xmath13 , @xmath153 , @xmath128 , and @xmath124 for the frustrated case with @xmath1 , @xmath4 , @xmath48 ; and a peak at @xmath125 for the non - frustrated case with @xmath1 , @xmath48 , @xmath4 . in addition , the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes , where the fitting equation is proposed . at finite temperatures , the double - peak structure of the susceptibility and specific heat against temperature can be obtained for all the three cases . it is found that the susceptibility shows ferrimagnetic characteristics for the two frustrated cases with some couplings , while no ferrimagnetic behaviors are observed for the non - frustrated case . the compound cu@xmath16(co@xmath16)@xmath17(oh)@xmath17 is regarded as a model substance for the spin-@xmath0 heisenberg diamond chain . the @xmath30 magnetization plateau and the two broad peaks both in the magnetic susceptibility and the specific heat have been observed experimentallycucooh1 . our tmrg calculations with @xmath282 and @xmath283 capture well the main characteristics of the experimental susceptibility , specific heat and magnetization , indicating that the compound cu@xmath16(co@xmath16)@xmath17(oh)@xmath17 may not be a spin frustrated magnet@xcite .

the magnetic and thermodynamic properties of spin- heisenberg diamond chains are investigated in three different cases : ( a ) , , ( frustrated ) ; ( b ) , , ( frustrated ) ; and ( c ) , , ( non - frustrated ) , where the bond coupling stands for an antiferromagnetic ( af ) interaction , and for a ferromagnetic ( f ) interaction . the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes , where two fitting equations are proposed . it is observed that the six modes are closely related to the low - lying excitations of the system . at finite temperatures , the magnetization , susceptibility and specific heat show various behaviors for different couplings .

the magnetic and thermodynamic properties of spin- heisenberg diamond chains are investigated in three different cases : ( a ) , , ( frustrated ) ; ( b ) , , ( frustrated ) ; and ( c ) , , ( non - frustrated ) , where the bond coupling stands for an antiferromagnetic ( af ) interaction , and for a ferromagnetic ( f ) interaction . the density matrix renormalization group ( dmrg ) technique is invoked to study the properties of the system in the ground state , while the transfer matrix renormalization group ( tmrg ) technique is applied to explore the thermodynamic properties . the local magnetic moments , spin correlation functions , and static structure factors are discussed in the ground state for the three cases . it is shown that the static structure factor shows peaks at wavevectors for different couplings in a zero magnetic field , which , however in the magnetic fields where the magnetization plateau with pertains , exhibits the peaks only at , and , which are found to be couplings - independent . the dmrg results of the zero - field static structure factor can be nicely fitted by a linear superposition of six modes , where two fitting equations are proposed . it is observed that the six modes are closely related to the low - lying excitations of the system . at finite temperatures , the magnetization , susceptibility and specific heat show various behaviors for different couplings . the double - peak structures of the susceptibility and specific heat against temperature are obtained , where the peak positions and heights are found to depend on the competition of the couplings . it is also uncovered that the xxz anisotropy of f and af couplings leads the system of case ( c ) to display quite different behaviors . in addition , the experimental data of the susceptibility , specific heat and magnetization for the compound cu(co)(oh) are fairly compared with our tmrg results .

astro-ph9707109

i

the distribution function of neutral hydrogen masses among galaxies and intergalactic clouds ( the mass function or himf ) , and more generally , the neutral hydrogen density in the nearby universe , @xmath9 , are important inputs into models of cosmology and galaxy evolution . different attempts have been made to construct an himf by using optically selected galaxies ( rao & briggs 1993 , hereafter rb , solanes , giovanelli & haynes 1996 ) . these studies are based on the assumption that is always associated with optically bright galaxies . a major concern is whether the himf is complete when it is computed for these galaxies . for example , the population of low surface brightness ( lsb ) galaxies might hypothetically constitute a substantial portion of the population of nearby extragalactic objects ( disney 1976 , mcgaugh 1996 , dalcanton , spergel & summers 1997 , sprayberry et al . the lsb population easily escapes detection optically and would not be included in the samples that are commonly used to evaluate the himf . this would be particularly problematic since lsb galaxies are generally found to be rich in neutral gas ( schombert et al . 1992 , de blok , mcgaugh & van der hulst 1996 ) and could therefore contribute substantially to the neutral gas content . gas rich dwarf galaxies may also play an important part . for example tyson & scalo ( 1988 ) have argued that the majority of these dwarf galaxies remain undetected because only the small portion that is currently undergoing a rapid phase of star formation is presently observed with optical telescopes . a final possible population of gas rich systems that would escape inclusion in optical catalogs is a class of intergalactic clouds without stars . so far , only a few such systems have been discovered , and they are always found to be gravitationally bound to a galaxy or a group of galaxies ( for example the leo ring , schneider 1989 ) . clearly , the himf and the content of the local universe should be measured directly , in such a way that they suffer no bias against gas rich galaxies or intergalactic clouds which are difficult to detect optically . this is possible by means of surveys in the line . several of these surveys have been carried out over the last two decades . the majority were single dish observations using on / off techniques , since these surveys were done in conjunction with observations targeted on cataloged galaxies ( fisher & tully 1981b , giovanelli & haynes 1985 , 1989 ) . some surveys were concentrated on groups of galaxies ( haynes & roberts 1979 , lo & sargent 1979 , fisher & tully 1981a , hoffman , lu & salpeter 1992 ) to specifically search for clouds in the vicinity of known galaxies . other surveys were designed to find signals in voids ( krumm & brosch 1984 , szomoru et al 1996 ) , or to compare voids and superclusters ( weinberg et al . 1991 , szomoru et al . since these surveys are not pointed at randomly chosen regions of sky , they may not provide fair tests of the shape of the himf or an unbiased measure of the average density . a few truly blind surveys have been conducted , the first one in driftscan mode ( shostak 1977 ) and one by observing a series of pointings on lines of constant declination ( kerr & henning 1987 , henning 1992 ) . it is worrisome that this latter survey could not reproduce the himf defined for optically selected galaxies , possibly because the survey was targeted toward large volumes of known voids . another possibility is that the achieved survey sensitivity is not well understood , leading to an underestimation of the true number density of rich galaxies and intergalactic clouds . more recently , several surveys have been made using the arecibo telescope ( sorar 1994 , spitzak 1996 , schneider 1997 ) . surveys are in progress at dwingeloo ( dogs ) and at parkes , where the survey will cover the entire southern sky ( staveley - smith et al . 1996 ) . in this paper we analyze the arecibo strip survey ( sorar 1994 ) , a blind survey for extragalactic covering @xmath0 square degrees of sky , out to a redshift of 7400 @xmath2 . the analysis of the survey results will concentrate specifically on the understanding of the achieved survey sensitivity and the vulnerability to large scale structure . we describe the details of the survey and the optical and 21 cm follow - up observations in section [ observations.sect ] . section [ sensitivity.sect ] gives a detailed analysis of the achieved survey sensitivity . we present the himf in section [ himf.sect ] , the possible influence of large scale structure on the determination of the himf is examined by performing numerical experiments , and the cosmological mass density of at the present time is calculated in this section . in section [ discussion.sect ] we compare our findings with previous estimates of the himf based on 21 cm surveys and optically selected galaxy samples and discuss the implications of our results . section [ conclusions.sect ] summarizes the results . the distances used in this paper are based on a hubble constant @xmath10 .

no free floating clouds without stars are found . the influence of large scale structure on the determination of the himf from the arecibo strip survey is tested by numerical experiments and was not found to affect the resulting himf significantly . the cosmological mass density of at the present time determined from the survey , , is in good agreement with earlier estimates .

the mass function ( himf ) for galaxies in the local universe is constructed from the results of the arecibo strip survey , a blind extragalactic survey in the 21 cm line . the survey consists of two strips covering in total square degrees of sky , with a depth of and was optimized to detect column densities of neutral gas ( ) . the survey yielded 66 significant extragalactic signals of which approximately 50% are cataloged galaxies . no free floating clouds without stars are found . vla follow - up observations of all signals have been used to obtain better measurements of the positions and fluxes and allow an alternate determination of the achieved survey sensitivity . the resulting himf has a shallow faint end slope ( ) , and is consistent with earlier estimates computed for the population of optically selected gas rich galaxies . this implies that there is not a large population of gas rich low luminosity or low surface brightness galaxies that has gone unnoticed by optical surveys . the influence of large scale structure on the determination of the himf from the arecibo strip survey is tested by numerical experiments and was not found to affect the resulting himf significantly . the cosmological mass density of at the present time determined from the survey , , is in good agreement with earlier estimates . we determine lower limits to the average column densities of the galaxies detected in the survey and find that none of the galaxies have , although there are no observational selection criteria against finding lower density systems . eight percent of the signals detected in the original survey originated in groups of galaxies , whose signals chanced to coincide in frequency .

astro-ph9707109

c

we have used the arecibo strip survey in combination with 21 cm follow - up observations with the vla to determine the mass function of gas rich galaxies in the local universe . the resulting himf is in good agreement with earlier estimates based on samples of optically selected galaxies . this implies that there is not a large population of gas rich dwarfs or low surface brightness galaxies , previously undetected by optical surveys . the observed faint end slope of the himf is flat ( @xmath208 ) leaving no room for a large class of gas rich dwarfs . the cosmological mass density of in the local universe is @xmath209 , also consistent with earlier estimates . the neutral gas content is dominated by high mass galaxies with @xmath182 . the observations indicate the existence of a lower limit to the average column density of 19.7 @xmath210 , consistent with theoretical predictions concerning the ionizing extragalactic uv background . bland - hawthorn , j. , freeman , k. c. , quinn , p.j . 1997 , apj , in press bothun , g. b. 1985 , 90 , 1982 bothun , g. b. , beers , t. , mould , j. , huchra , j. 1986 , apj , 308 , 510 briggs , f. h. 1990 , aj , 100 , 999 briggs , f. h. , & rao , s. 1993 , apj , 417 , 494 ( br ) briggs , f. h. , sorar , e. , kraan - korteweg , r. c. , & van driel , w. 1997 , pasa , 14 , 37 cayatte , v. , kotanyl , c. , balkowski , c. , & van gorkom , j. h. 1994 , aj , 107 , 1003 charlton , j. c. , salpeter , e. e. , & linder , s. m. 1994 , apj , 430 , l29 christensen , c. g. 1975 , aj , 80 , 282 corbelli , e. , salpeter , e. e. 1993 , apj , 419 , 104 dalcanton j. j. , spergel , d. n. , & summers , f. j. 1997 , apj , 482 , 659 de blok , w. j. g. , mcgaugh , s. s. , & van der hulst , j. m. 1996 , mnras , 283 , 18 dekel , a. , & silk , j. 1986 , apj , 303 , 39 disney , m. j. 1976 , nature , 263 , 573 disney m. j. , & banks , g. 1997 , pasa , 14 , 69 eder , j. a. , oemler , a. jr . , schombert , j. m. , & dekel , a. 1989 , apj , 340 , 29 efstathiou , g. , ellis , r. s. , & peterson , b. a. 1988 , mnras , 231 , 479 fall , s. m. , & pei , y. c. 1993 , apj , 402 , 479 fisher , j. r. , & tully , r. b. 1975 , a&a , 44 , 151 fisher , j. r. , & tully , r. b. 1981a , apjs , 47 , 139 fisher , j. r. , & tully , r. b. 1981b , apjl , 243 , l23 geller , m. j. , & huchra , j. p. 1989 , science , 246 , 897 giovanelli , r. , & haynes , m. p. 1989 , apjl , 346 , l5 giovanelli , r. , & haynes , m. p. 1985 , aj , 90 , 2445 haynes , m. p , & roberts , m. s. 1979 , apj , 227 , 767 haynes , m. p , & giovanelli , r. 1984 , aj , 89 , 758 henning , p. a. 1992 , apjs , 78 , 365 henning , p. a. 1995 , apj , 450 , 578 hoffman , g. l. , lewis , b. m. , helou , g. , salpeter , e. e. , & williams , b. m. 1989 , apjs , 69 , 65 hoffman , g. l. , lu , n. y. , & salpeter , e. e. 1992 , aj , 104 , 2086 huchtmeier , w. k. , & richter , o. -g . 1989 , a general catalog of observations of galaxies : the reference catalog ( new york : springer - verlag ) kerr , f. j. , & henning , p. a. 1987 , apj , 320 , l99 krumm , n. , & brosch , n. 1984 , aj , 89 , 1461 lanzetta , k. m. , wolfe , a. m. , & turnshek , a. m. 1995 , apj , 440 , 435 lin , h. , kirshner , r. p. , shectman , s. a. , landy , s.d . , oemler , a. , tucker , d. l. , & schechter , p. l. 1996 , 464 , 60 lo , k. y. , & sargent , w. l. w. 1979 , apj , 227 , 756 lo , k. y. , & sargent , w. l. w. , young , k. 1993 , aj , 106 , 507 maloney , p. 1993 , apj , 414 , 41 marzke , r. o. , geller , m. j. , & huchra , j. p. 1994 , aj , 108 , 437 mcgaugh , s. s. 1994 , apj , 426 , 135 mcgaugh , s. s. 1996 , mnras , 280 , 337 mcmahon , p. m. 1993 , ph.d thesis , columbia university mo , h. j. , mcgaugh , s. s. , & bothun , g. d. 1994 , mnras , 267 , 129 quinn , t. , katz , n. , & efstathiou , g. 1996 , mnras , 278 , l49 rao , s. , briggs , f. h. 1993 , apj , 419 , 515 ( rb ) rao , s. , turnshek , a. m. , & briggs , f. h. 1995 , apj , 449 , 488 salpeter , e. e. , & hoffmann , g. l. 1996 , apj , 465 , 595 saunders , w. , rowan - robinson , m. , lawrence , a. , efstathiou , g. , kaiser , n. , ellis , r. s. , & frenk , c. s. 1990 , mnras , 242 , 318 schechter , p. 1976 , apj , 203 , 297 schmidt , m. 1968 , apj , 151 , 393 schneider , s. e. 1989 , apj , 343 , 94 schneider , s. e. 1997 , pasa , 14 , 99 schombert , j. m. , bothun , g. d. , schneider , s. e. , & mcgaugh , s. s. 1992 , aj , 103 , 1107 shostak , g. s. 1977 , a&a , 54 , 919 smette , a. , claeskens , j. -f . , & surdej , j. 1997 , newa , 2 , 53 solanes , j. m. , giovanelli , r. , & haynes , m. 1996 , apj , 461 , 609 sorar , e. 1994 , ph.d . thesis , university of pittsburgh spitzak , j. g. 1996 , ph.d . thesis , university of massachusetts sprayberry , d. , impey , c. d. , irwin , m. j. , & bothun , g. d. 1997 , apj , 482 , 104 staveley - smith , l. , wilson , w. e. , bird , t. s. , disney , m. j. , ekers , r. d. , freeman , k. c. , haynes , r. f. , sinclair , m. w. , vaile , r. a. , webster , r. l. , & wright , a. e. 1996 , pasa , 13 , 243 storrie - lombardi , l. j. , irwin , m. j. , & mcmahon , r. g. 1996 , mnras , 282 , 1330 swaters , r. a. , 1997 , in preparation szomoru , a. , guhathakurta , p. , van gorkom , j. h. , knapen , j. h. , weinberg , d. h. , & fruchter , a. s. 1994 , aj , 108 , 491 szomoru , a. , van gorkom , j. h. , gregg , m. d. , & strauss , m. a. 1996 , aj , 111 , 2150 taylor , c. l. 1997 , apj , 480 , 524 thuan , t. x. , gott , j. r. , & schneider , s. e. 1987 , apjl , 315 , l93 thuan , t. x. , alimi , j - m . , gott , j. r. , & schneider , s. e. 1991 , apj , 370 , 25 tully , r. b. , & fisher , j. r. , 1977 , a&a , 54 , 661 tyson , n. d. , & scalo , j. m. 1988 , apj , 329 , 618 van der hulst , j. m. , skillman , e. d. , smith , t. r. , bothun , g. d. , mcgaugh , s. s. , & de blok , w. j. g. 1993 , aj , 106 , 548 van gorkom , j. h. 1993 , in the environment and evolution of galaxies , ed . j. m. shull and h. a. thronson ( kluwer academic publishers ) , 345 weinberg , d. h. , szomoru , a. , guhathakurta , p. , & van gorkom , j. h. 1991 , apj , 372 , l13

the resulting himf has a shallow faint end slope ( ) , and is consistent with earlier estimates computed for the population of optically selected gas rich galaxies . this implies that there is not a large population of gas rich low luminosity or low surface brightness galaxies that has gone unnoticed by optical surveys .

the mass function ( himf ) for galaxies in the local universe is constructed from the results of the arecibo strip survey , a blind extragalactic survey in the 21 cm line . the survey consists of two strips covering in total square degrees of sky , with a depth of and was optimized to detect column densities of neutral gas ( ) . the survey yielded 66 significant extragalactic signals of which approximately 50% are cataloged galaxies . no free floating clouds without stars are found . vla follow - up observations of all signals have been used to obtain better measurements of the positions and fluxes and allow an alternate determination of the achieved survey sensitivity . the resulting himf has a shallow faint end slope ( ) , and is consistent with earlier estimates computed for the population of optically selected gas rich galaxies . this implies that there is not a large population of gas rich low luminosity or low surface brightness galaxies that has gone unnoticed by optical surveys . the influence of large scale structure on the determination of the himf from the arecibo strip survey is tested by numerical experiments and was not found to affect the resulting himf significantly . the cosmological mass density of at the present time determined from the survey , , is in good agreement with earlier estimates . we determine lower limits to the average column densities of the galaxies detected in the survey and find that none of the galaxies have , although there are no observational selection criteria against finding lower density systems . eight percent of the signals detected in the original survey originated in groups of galaxies , whose signals chanced to coincide in frequency .

1411.1065

i

star formation is one of the main internal driving forces of galaxy evolution , resulting in the chemical enrichment of a galaxy , the heating of the interstellar medium ( ism ) , and indirectly , the production of dust through the winds of dying stars . star formation converts a galaxy s molecular gas into stars through multiple complicated processes including gas accretion and the collapse and cooling of molecular clouds . although the star formation process itself is intricate , the overall conversion of gas into stars can be expressed simply by the schmidt - kennicutt ( sk ) law which directly relates the molecular gas content to the star formation rate ( sfr ) through a power - law equation , @xmath8 , albeit with significant scatter @xcite . the bulk of the present day stellar mass was formed at a peak epoch of star formation , from @xmath9 ( * ? ? ? * and references therein ) . during this era , the buildup of stellar mass was dominated by dusty galaxies referred to as luminous infrared galaxies ( lirgs , @xmath10 ) and ultra luminous infrared galaxies ( ulirgs , @xmath11 ) ( e.g. , * ? ? ? in the past two decades , the spate of far - ir / submillimeter space - based and ground - based telescopes have enabled astronomers to simultaneously study the star formation , through infrared ( ir ) emission , and molecular gas , through co emission , of dusty galaxies out to redshifts of @xmath12 ( * ? ? ? * and references therein ) . the ir luminosity , @xmath1 , is an ideal measure of the sfr for dusty galaxies as it is the integrated emission from the dust , presumably heated by star formation . on galaxy - wide scales , co traces the molecular hydrogen which is difficult to observe directly ; a conversion factor , @xmath13 , is used to relate the co luminosity directly to the h@xmath0 mass ( * ? ? ? * and references therein ) . in the past few years , a `` galaxy main sequence '' has been empirically determined for local and high redshift galaxies ; a tight relationship holds between sfr and stellar mass , and this relationship evolves with redshift ( e.g. , * ? ? ? * ; * ? ? ? galaxies that lie above the main sequence , that is , galaxies that have an enhanced sfr for a given stellar mass , are designated `` starbursts '' in this parameter space , as they are thought to be undergoing a short - lived burst of star formation , likely triggered by a major merger . the rate at which a galaxy can form stars is limited by the amount of molecular gas present . @xcite proposed an extended sk law which relates the specific star formation rate ( @xmath14 ) to the stellar mass surface density , suggesting that the existing stellar population may play a role in regulating the amount of star formation . the authors apply their extended sk law to an analytical model of gas accretion and find that it accurately reproduces the galaxy main sequence . a dichotomy between starbursts and normal star forming galaxies may also be observed by comparing @xmath1 with @xmath2 . first , there may be a `` normal '' rate of star formation measured in undisturbed disk galaxies for a given amount of molecular gas . then , there is an enhanced starburst mode , where a galaxy has a higher @xmath1 than expected for a given @xmath2 , possibly triggered by a major merger funneling gas towards the inner regions of a galaxy ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this dichotomy has a direct effect on the calculation of the h@xmath0 mass , since @xmath13 is proposed to be a factor of @xmath15 lower for starbursting galaxies , due to significant amounts of co residing in the inter - cloud medium . correctly identifying starbursts is critical for calculating accurate gas masses . it now appears that every massive galaxy hosts a supermassive black hole at the center , implying that all galaxies have gone through an active galactic nuclei ( agn ) phase , and some lirgs and ulirgs show signs of concurrent black hole growth and star formation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in the classical picture of galaxy evolution , a starburst is triggered by a major merger , and this phase can be followed by an agn phase , implying that an obscured growing agn may be observable during a galaxy s starburst phase ( e.g. , * ? ? ? if present , an agn can dramatically influence the internal evolution of a galaxy by heating the dust , expelling the gas , and ultimately quenching the star formation through feedback mechanisms ( e.g. , * ? ? ? the effect of an obscured agn on the ism can be probed through ir observations . in the mid - ir , star forming galaxies have prominent pah features arising from photodissociation regions ( pdrs ) , but agn emission can dilute these features , leaving a warm dust power - law continuum @xcite . radiation from the agn can heat the dust in the ism to temperatures @xmath16k , producing a significant contribution ( @xmath17 ) to the far - ir emission ( e.g. , * ? ? ? * ; * ? ? ? the degree of scatter in the relationship between @xmath1 and @xmath2 , often attributed to the two different modes of star formation , is possibly affected by the contribution from an agn to @xmath1 . @xcite observe high @xmath3 in qsos and infer that these ratios might be boosted by an agn contribution to @xmath1 . @xcite build on this study by using hcn as a tracer of star formation in qsos . using iras bright galaxies , the authors determine the median hcn / co ratio for normal star forming galaxies and use this , combined with @xmath3 and @xmath18 , to statistically correct @xmath1 of qsos for an agn contribution . an alternate approach is to use @xmath19 ( 40 - 500@xmath20 m or 42.5 - 11.5@xmath20 m ) instead of @xmath1 ( 8 - 1000@xmath20 m ) , as dust emission in this regime should come primarily from heating by young stars . @xcite conclude that @xmath21 in a sample of 17 qsos is similar to the ratios in local ulirgs ( many of which are known to host obscured agn ) , and @xcite finds high @xmath21 ratios in qsos relative to the iras galaxies . in this paper , we build upon observations in the high redshift and local universe with a study of intermediate redshift galaxies ( @xmath22 ) from the 5 mjy unbiased _ spitzer _ extragalactic survey ( 5muses ; p.i . george helou ) . these galaxies have extensive ir data from the _ spitzer space telescope _ and _ herschel space observatory _ , allowing us to accurately measure @xmath1 and quantify the contribution from an agn . we complement the existing ir data with new co(1 - 0 ) observations from the redshift search receiver , which has a large bandwidth of 38ghz and a resolution of 100km / s , on the large millimeter telescope alfonso serrano , enabling us to explore how much of the scatter in the @xmath23 relation is due to an agn contribution to @xmath1 . we discuss the details of our sample and observations in section 2 , the effect of an agn on the relationships between @xmath1 , pahs , and co(1 - 0 ) emission in section 3 , and summarize our findings in section 4 . throughout this paper , we adopt a flat cosmology with @xmath24kms@xmath25mpc@xmath25 , @xmath26 , and @xmath27 .

the molecular gas , h , that fuels star formation in galaxies is difficult to observe directly . as such , the ratio of to is an observational estimation of the star formation rate compared with the amount of molecular gas available to form stars , which is related to the star formation efficiency and the inverse of the gas consumption timescale . we test what effect an ir luminous agn has on the ratio in a sample of 24 intermediate redshift galaxies from the 5 mjy unbiased _ spitzer _ extragalactic survey ( 5muses ) . we obtain new co(1 - 0 ) observations with the redshift search receiver on the large millimeter telescope .

the molecular gas , h , that fuels star formation in galaxies is difficult to observe directly . as such , the ratio of to is an observational estimation of the star formation rate compared with the amount of molecular gas available to form stars , which is related to the star formation efficiency and the inverse of the gas consumption timescale . we test what effect an ir luminous agn has on the ratio in a sample of 24 intermediate redshift galaxies from the 5 mjy unbiased _ spitzer _ extragalactic survey ( 5muses ) . we obtain new co(1 - 0 ) observations with the redshift search receiver on the large millimeter telescope . we diagnose the presence and strength of an agn using _ spitzer _ irs spectroscopy . we find that removing the agn contribution to results in a mean for our entire sample consistent with the mean derived for a large sample of star forming galaxies from . we also include in our comparison the relative amount of polycyclic aromatic hydrocarbon emission for our sample and a literature sample of local and high redshift ultra luminous infrared galaxies and find a consistent trend between and , such that small dust grain emission decreases with increasing for both local and high redshift dusty galaxies .

1411.1065

r

in the local universe , the sk law is traditionally expressed in terms of surface densities , which necessarily require resolved measurements of star formation and molecular gas @xcite . at higher redshifts , resolved measurements are often not feasible , and global measurements of the sfr and molecular gas are used instead . the ratio of @xmath1 , directly related to a global sfr , and @xmath70 is commonly referred to as a star formation efficiency @xcite . it is essentially the integrated version of the sk law without the uncertain conversion from co to h@xmath0 mass . this quantity is also related to the inverse of the gas depletion timescale which describes how long a galaxy could continue to form stars at the current rate if the gas reservoir is not replenished ( e.g. , * ? ? ? in general , @xmath1 correlates with @xmath70 , although there is significant scatter . @xmath1 is primarily measuring the reradiated light from newly formed stars ( with some contribution from an older stellar population ) , while @xmath70 is measuring the reservoir of molecular gas available to form stars in the future ; hence the dust and gas do not necessarily trace star formation on the same timescales . co emission can also be present between molecular clouds , introducing more scatter in the relationship between @xmath1 and @xmath2 . to account for this scatter , many authors propose two relationships , one for starbursts , undergoing an enhanced @xmath3 , and one for normal star forming galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? if a galaxy undergoes a burst of star formation that also triggers agn growth , this could account for some of the scatter in @xmath3 . initially , as an embedded agn grows more luminous , it heats some of the surrounding dust , but is enshrouded enough that the host galaxy is still visible ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the increase in the amount of warm dust heated by the agn will enhance @xmath1 but may not yet affect @xmath70 , implying an artificially high @xmath3 unless the agn contribution is accounted for ( e.g. , by considering @xmath85 ) . as the agn becomes less enshrouded , the pah and cold dust emission from the host become less prominent because the dust heated by the agn is outshining the dust in star forming regions , and/or because feedback from the agn is quenching the star formation . if the agn is quenching the star formation , this will produce lower @xmath85 values and hence lower @xmath5 , unless feedback from the agn expels co on the same timescales . as yet , no study has attempted to quantify the effect of the agn on @xmath3 individually in galaxies due to the difficulty in measuring the amount of @xmath1 attributable to an agn . the 5muses sample has mid - ir spectra that exhibit both pah features and a strong underlying continuum , allowing us to cleanly separate out the agn luminosity and calculate @xmath85 . figure [ fig : lir_lco ] shows the relationship between @xmath85 and @xmath70 , and the points are colored according to @xmath80 . we overplot the relations between @xmath85 and @xmath70 determined for star forming galaxies ( sfgs , dashed line ; grey region indicates one standard deviation ) and starbursts ( dotted line ) in @xcite . these relations were robustly determined using large samples of normal star forming galaxies and starbursts from @xmath6 , and we are interested in testing how removing the agn component in our galaxies changes their position relative to these relations . the presence of two separate relations is discussed in depth in @xcite , where the authors also present a single relation fitting all available @xmath1 and @xmath103 measurements in the literature . we compare to the separate starburst and sfg relations to investigate any difference in @xmath5 according to ir power source or starburstiness . @xcite determined the relations for sfgs and starbursts using the far - ir luminosity ( fir : @xmath104 m ) as opposed to @xmath1 , so we scale the relationships according to @xmath105 , a ratio determined using the lirg and ulirg templates from @xcite . we overplot the @xmath106 scatter from @xcite as the grey shaded region . we plot the main sequence galaxies ( determined by equation [ eq : ms ] ) as filled circles and starbursts as filled stars . the starbursts on average have a factor of two higher @xmath85 @xmath70 than the main sequence galaxies . we find that both the main sequence and starbursts are consistent with the sfg relationship from @xcite , and there is no strong separation according to ir power source . we can look at this more simply by considering the ratio @xmath107 . in figure [ fig : sfe ] , we plot @xmath107 as a function of @xmath80 . we also include @xmath108 as the unfilled circles and stars . the grey shaded regions illustrate the standard deviation around the average @xmath3 calculated for starbursts and sfgs in @xcite . the standard deviation for the sfg region is 0.33 dex , slightly larger than the standard deviation illustrated in figure [ fig : lir_lco ] . this is due to the fact that the relation between @xmath1 and @xmath2 is non - linear , so the standard deviation relative to the mean @xmath3 is larger . none of our galaxies lie in the starburst region . @xcite find a mean @xmath109 of 44 . we calculate that the mean @xmath108 is 59 , but when we remove the agn contribution to @xmath4 , we calculate a mean @xmath107 of 52 , closer to the mean measured by @xcite . removing the agn component only mildly reduces the scatter about the mean @xmath107 . two galaxies , 5muses-179 and 5muses-275 , lie below the sfg region . the galaxy with the lowest @xmath5 , 5muses-179 , also lies decidedly below the main sequence region in figure [ fig : ms ] , further indicating that its star formation is highly inefficient , and this galaxy could be transitioning to a quiescent phase . we find no relationship between @xmath5 and @xmath80 . for this small sample , the star forming galaxies exhibit less scatter in @xmath5 than the composite galaxies , although both groups have the same average @xmath5 . the agn have a lower average @xmath5 indicating that these galaxies are not converting gas to stars at the same rate as the composite or sf galaxies ; this hints that the star formation might be beginning to quench in these agn sources . it is interesting to note that two galaxies with very high @xmath5 lower limits ( 5muses-249 and 5muses-294 ) show no trace of an agn according to their mid - ir spectra . this could be illustrative of the different timescales that agn signatures , starburst signatures , and enhanced @xmath5 ratios are visible . mid - ir spectroscopy and chandra x - ray observations provide evidence that the majority of local ulirgs and high redshift submillimeter galaxies ( smgs ) , which have a high merger ( and hence , starburst ) fraction and enhanced @xmath3 , are predominately powered by star formation in the mid - ir ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . a non - negligible fraction of lirgs and ulirgs host a mid - ir luminous agn , although optical morphologies of local lirgs reveal that mid - ir agn signatures are predominately found either in isolated disk galaxies or coalesced nuclei at the end of a merger @xcite . we expect , then , that if the agn and starburst phase do not overlap completely , agn should have lower @xmath5 ratios , and figure [ fig : sfe ] shows that they do , for this small sample , once the agn contribution to @xmath4 has been accounted for . also of interest is that we do not observe any dichotomy in @xmath5 either as a function of mid - ir power source or along the main sequence / starburst classification . @xcite observe a clear relationship between the gas depletion timescale and the ssfr in a large , complete , sample of local galaxies as part of the cold gass survey . we compare our sources with the cold gass galaxies in figure [ fig : tdep ] . @xcite calculate the depletion timescale as @xmath110 , but to avoid any uncertainties due to converting @xmath2 to @xmath111 ( see section [ sec : gas ] ) , we simply use the ratio sfr/@xmath112 . we have calculated the sfrs for our galaxies using @xmath85 . figure [ fig : tdep ] also includes the @xmath113 galaxies from @xcite , where we have corrected the sfrs , calculated using the conversion in @xcite , to be on the same scale as ours . the sfrs from @xcite are calculated by fitting the sed from the uv out to 70@xmath20 m . we do not further correct for differing cosmologies as the intrinsic scatter in figure [ fig : tdep ] is larger than any shift introduced in this manner . when looking at just our 5muses sample in figure [ fig : tdep ] , there is no strong correlation between sfr/@xmath2 and ssfr , just as we observed no separation according to ssfr in figure [ fig : sfe ] . however , when we extend the dynamical range of the plot by considering the local galaxies from @xcite and the @xmath113 galaxies from @xcite , there is a strong correlation ( a spearman s rank test gives a correlation coefficient of @xmath114 with a two - sided significance equal to 0.0 ) . our sample lies in the range expected . this suggests that we are not observing any differences between our starburst and main sequence galaxies in figures [ fig : lir_lco ] and [ fig : sfe ] simply because we are not probing a large enough range of @xmath2 and @xmath1 . ir , co , and pah luminosities are all commonly used as tracers of star formation in dusty galaxies . pah emission arises from pdrs surrounding young stars and has been demonstrated locally to be largely cospatial with the molecular clouds traced by co emission @xcite . if star formation is continuously fueled for @xmath115gyr , these tracers should all correlate . for most star forming galaxies , the ratio of @xmath116 is fairly constant , but there is an observed deficit of pah emission relative to @xmath1 in local ulirgs , possibly due to an increase in the hardness of the radiation field caused either by a major merger / starburst or an agn @xcite . this same deficit does not hold for similarly luminous galaxies at high redshift , however , where the majority of ulirgs are observed to have strong pah emission @xcite . @xcite explored the evolution of @xmath117 with redshift for a sample of ulirgs from @xmath118 as well as a sample of local ulirgs . specifically , the authors compare @xmath117 with @xmath1 and find that the deficit in @xmath119 relative to @xmath1 occurs at a higher @xmath1 for high redshift galaxies than is seen in the local universe . galaxies from @xmath9 typically have higher gas fractions than local counterparts @xcite . this increase in molecular gas could be linked to the relative increase in pah emission , since both are largely cospatial . indeed , when @xcite compare @xmath117 with @xmath109 , they find a consistent relationship for both the local and high redshift ulirgs . we now build on the analysis presented in @xcite by extending the parameter space explored to the lower luminosity 5muses sample . the 5muses galaxies combined with the local ulirgs comprise a low redshift sample for comparison with the high redshift ulirgs . we plot @xmath120 vs. @xmath85 for our sample in the left panel of figure [ fig : pah_co ] . we also include the high redshift and local ulirgs from @xcite where we have calculated @xmath85 for all ulirgs by scaling the mid - ir agn strength , determined by decomposing the mid - ir spectra . there is a decreasing trend between the 5muses sample and the local ulirgs , but the high redshift ulirgs are shifted from this relation . in the right panel , we plot @xmath120 vs. @xmath107 . @xmath2 is calculated using the estimated co(1 - 0 ) luminosity for all galaxies ( see * ? ? ? * for conversion details ) . in this panel , most galaxies follow the same decreasing trend , with a few obvious outliers . we overplot the best fit relation for the 5muses sample and the local and high redshift ulirgs . the shaded region indicates one standard deviation above and below the fit . there is a decreasing correlation between @xmath120 and @xmath107 for most galaxies . figure [ fig : pah_co ] suggests that the relative amount of emission from small dust grains is related to @xmath107 for dusty galaxies out to @xmath121 . that is , weaker pah emission is associated with a higher star formation efficiency and faster gas depletion timescales . the decrease in @xmath92 with increasing @xmath1 could indicate that pah emission in general is suppressed for more luminous galaxies . we do not find significantly lower @xmath120 ratios for our agn or composite galaxies as compared to our star forming galaxies , indicating that in our sample , the growing agn is not affecting this ratio . as discussed in @xcite , the pah deficit could be similar to the observed deficit in [ cii ] emission at high @xmath1 in local galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite probe the [ cii ] deficit in local lirgs and find that galaxies with compact mid - ir emission have a [ cii ] deficit , regardless of the mid - ir power source . for our sample , follow - up observations are required to trace the compactness of the galaxies . if our galaxies have extended dust emission , this would explain the similar @xmath7 ratios for the 5muses galaxies and the high redshift ulirgs , since high redshift ulirgs are known to have extended dust emission ( e.g. , * ? ? ? based on the relative strengths of the dust emission and co(1 - 0 ) emission , the 5muses sources , primarily lirgs , seem to be more accurate counterparts for the high redshift ulirgs than the local ulirgs , evidencing the evolution of ism properties with redshift . a morphological comparison of these sources could provide more insight into structure and compactness of the dust and gas emission . the gas fraction is expressed as @xmath122 , where @xmath123 . @xmath124 is a commonly adopted value for normal star forming galaxies , while in starbursts , the conversion @xmath125 has been measured ( * ? ? ? * and references therein ) . we have two observational indicators of starburstiness : @xmath5 and ssfr . to calculate @xmath126 , we explore two scenarios . first , we apply @xmath127 to our entire sample ( top panel of figure [ fig : gas ] ) . none of our galaxies have @xmath5 indicative of a starburst ( figure [ fig : sfe ] ) , so applying the same @xmath13 to the entire sample is a reasonable assumption . second , we use @xmath125 to calculate the gas mass for those galaxies with an ssfr indicative of a starburst ( bottom panel of figure [ fig : gas ] ) . we plot the gas fractions as a function of redshift we also plot gas fractions of normal star forming galaxies from the literature , and we have corrected the individual @xmath13 values used to be 4.6 . the average molecular gas fraction evolves with redshift , and we plot the measured relation , @xmath128 , determined from a stellar mass limited sample with @xmath129 @xcite , similar to the masses of our 5muses sample . our gas fractions ( in both panels ) lie in the range expected when comparing with the best fit line and the points from @xcite and @xcite . our co(1 - 0 ) detection rate is high ( 17 out of 24 sources ) , producing a large range of measured gas fractions . in the top panel , our starburst galaxies are systematically higher than the main sequence galaxies , and the scatter about the @xmath130 line is larger , which suggests that the lower @xmath125 conversion factor might be more appropriate for these sources if we expect similar gas fractions for main sequence and starburst galaxies . theoretically , the conversion factor depends on the geometry of the co and h@xmath0 distribution . when the co emission is extended and not confined to molecular clouds , warm , and has a high surface density , as is the case in mergers , then the lower @xmath13 value is appropriate ( * ? ? ? * and references therein ) . @xcite measure @xmath13 for a sample of high redshift main sequence and starburst galaxies and find an anti - correlation between @xmath13 and ssfr , which they interpret as evidence that the mechanisms responsible for raising a galaxy off the main sequence must also affect the physical conditions within the star forming regions . we also find that the gas fractions reproduce a similar separation between sources as the main sequence criterion , linking @xmath13 with the ssfr . in contrast , neither @xmath5 nor @xmath120 shows any separation between the starburst and main sequence galaxies , likely due to the limited range being probed . these ratios , then , are relatively stable for galaxies of a limited mass and luminosity range . @xcite argue against a bimodal @xmath13 conversion factor , and instead develop a fitting formula for the conversion factor that depends on the metallicity and co line intensity . we currently lack metallicities for our sample , so we can not directly apply the prescribed variable conversion factor . given the continuous relationship between ssfr and sfr/@xmath2 evidenced in figure [ fig : tdep ] , a continuous , rather than bimodal , conversion factor based on galactic environment may be the most appropriate choice and would mean that all galaxies in our sample obey a similar relationship between the molecular gas and the stellar mass .

we also include in our comparison the relative amount of polycyclic aromatic hydrocarbon emission for our sample and a literature sample of local and high redshift ultra luminous infrared galaxies and find a consistent trend between and , such that small dust grain emission decreases with increasing for both local and high redshift dusty galaxies .

the molecular gas , h , that fuels star formation in galaxies is difficult to observe directly . as such , the ratio of to is an observational estimation of the star formation rate compared with the amount of molecular gas available to form stars , which is related to the star formation efficiency and the inverse of the gas consumption timescale . we test what effect an ir luminous agn has on the ratio in a sample of 24 intermediate redshift galaxies from the 5 mjy unbiased _ spitzer _ extragalactic survey ( 5muses ) . we obtain new co(1 - 0 ) observations with the redshift search receiver on the large millimeter telescope . we diagnose the presence and strength of an agn using _ spitzer _ irs spectroscopy . we find that removing the agn contribution to results in a mean for our entire sample consistent with the mean derived for a large sample of star forming galaxies from . we also include in our comparison the relative amount of polycyclic aromatic hydrocarbon emission for our sample and a literature sample of local and high redshift ultra luminous infrared galaxies and find a consistent trend between and , such that small dust grain emission decreases with increasing for both local and high redshift dusty galaxies .

1605.04485

i

the fundamental description of dynamically arrested states of matter is a crucial step towards understanding the properties of very common amorphous solid materials such as glasses and gels @xcite , and of more technologically specialized materials , such as spin glasses @xcite . the main fundamental challenge posed by these materials derives from their inability to reach thermodynamic equilibrium within experimental times , and from the fact that their properties depend on the protocol of preparation , in obvious contrast with materials that have genuinely attained thermodynamic equilibrium . understanding the origin of this behaviour falls outside the realm of classical and statistical thermodynamics , and must unavoidably be addressed from the perspective of a non - equilibrium theory @xcite . in fact , a major challenge for statistical physics is to develop a microscopic theory able to predict the properties of glasses and gels in terms not only of the intermolecular forces and applied external fields , but also in terms of the protocol of preparation of the material . _ first - principles _ theoretical frameworks exist , leading to _ quantitative _ predictions of the dynamic properties of structural glass forming liquids near their dynamical arrest transitions , one of the best - known being mode coupling theory ( mct ) @xcite . however , this theory , as well as the equilibrium version of the self - consistent generalized langevin equation ( scgle ) theory of dynamical arrest @xcite , are meant to describe the dynamics of _ fully equilibrated _ liquids . hence , the phenomenology of the transient time - dependent processes , such as aging , occurring during the amorphous solidification of structural glass formers , falls completely out of the scope of these _ equilibrium _ theories . thus , it is important to attempt their extension to describe these non - stationary non - equilibrium structural relaxation processes , which in the end constitute the most fundamental kinetic fingerprint of glassy behavior . in an attempt to face this challenge , in 2000 latz @xcite proposed a formal non - equilibrium extension of mct which , however , has not yet found a specific quantitative application . in the meanwhile , the scgle theory has recently been extended to describe non - stationary non - equilibrium processes in glass - forming liquids @xcite . the resulting non - equilibrium theory , referred to as the _ non - equilibrium _ self - consistent generalized langevin equation ( ne - scgle ) theory , was derived within the fundamental framework provided by a non - stationary extension @xcite of onsager s theory of linear irreversible thermodynamics @xcite and of time - dependent thermal fluctuations @xcite , with an adequate extension @xcite to allow for the description of memory effects . the ne - scgle theory thus derived , aimed at describing non - equilibrium relaxation phenomena in general @xcite , leads in particular @xcite to a simple and intuitive but generic description of the essential behavior of the non - stationary and non - equilibrium structural relaxation of glass - forming liquids near and beyond its dynamical arrest transition . this was explained in detail in ref . @xcite in the context of a model liquid of soft - sphere particles . the recent comparison @xcite of the predicted scenario with systematic simulation experiments of the equilibration and aging of dense hard - sphere liquids , indicates that the accuracy of these predictions go far beyond the purely qualitative level , thus demonstrating that the ne - scgle theory is a successful pioneering first - principles statistical mechanical approach to the description of these fully non - equilibrium phenomena . as an additional confirmation , let us mention that for model liquids with hard - sphere plus attractive interactions , the ne - scgle theory predicts a still richer and more complex scenario , involving the formation of gels and porous glasses by arrested spinodal decomposition @xcite . as we know , quenching a liquid from supercritical temperatures to a state point inside its gas - liquid spinodal region , normally leads to the full phase separation through a process that starts with the amplification of spatial density fluctuations of certain specific wave - lengths @xcite . under some conditions , however , this process may be interrupted when the denser phase solidifies as an amorphous sponge - like non - equilibrium bicontinuous structure @xcite , typical of physical gels @xcite . this process is referred to as _ arrested _ spinodal decomposition , and has been observed in many colloidal systems , including colloid - polymer mixtures @xcite , mixtures of equally - sized oppositely - charged colloids @xcite , lysozyme protein solutions @xcite , mono- and bi - component suspensions of colloids with dna - mediated attractions @xcite , and thermosensitive nanoemulsions @xcite . from the theoretical side , it was not clear how to extend the classical theory of spinodal decomposition @xcite to include the possibility of dynamic arrest , or how to incorporate the characteristic non - stationarity of spinodal decomposition , in existing theories of glassy behavior @xcite . in refs . @xcite and @xcite it has been shown that the ne - scgle theory provides precisely this missing unifying theoretical framework . recently the ne - scgle theory was extended to multi - component systems @xcite , thus opening the route to the description of more complex non - equilibrium amorphous states of matter . until now , however , the ne - scgle theory faces the limitation of referring only to liquids of particles with radially symmetric pairwise interparticle forces , thus excluding its direct comparison with the results of important real and simulated experiments involving intrinsically non - spherical particles @xcite and , in general , particles with non - radially symmetric interactions . the present work constitutes a first step in the direction of extending the ne - scgle theory to describe the irreversible evolution of the static and dynamic properties of a brownian liquid constituted by particles with non - radially symmetric interactions , in which the orientational degrees of freedom are essential . more concretely , the main purpose of the present paper is to describe the theoretical derivation of the ne - scgle time - evolution equations for the spherical harmonics projections @xmath10 , @xmath11 , and @xmath12 , of the non - equilibrium and non - stationary static structure factor @xmath13 and of the collective and self intermediate scattering functions @xmath14 and @xmath15 . for this , we start from the same general and fundamental framework provided by the non - stationary extension of onsager s theory , developed in ref . @xcite to discuss the spherical case . the result of the present application are eqs . ( [ relsigmadifnonspher13])-([flmsqframenonstats ] ) below , in which @xmath8 is the delay time , and @xmath9 is the evolution ( or `` waiting '' ) time after the occurrence of the instantaneous temperature quench . the solution of these equations describe the non - equilibrium ( translational and rotational ) diffusive processes occurring in a colloidal dispersion after an instantaneous temperature quench , with the most interesting prediction being the aging processes that occur when full equilibration is prevented by conditions of dynamic arrest . although this paper only focuses on the theoretical derivation of the ne - scgle equations , as an illustration of the possible concrete applications of the extended non - equilibrium theory , here we also solve the resulting equations for one particular system and condition . we refer to a liquid of dipolar hard - spheres ( dhs ) with fixed positions and subjected to a sudden temperature quench . this is a simple model of the irreversible evolution of the collective orientational degrees of freedom of a system of strongly interacting magnetic dipoles with fixed but random positions . although this particular application by itself has its own intrinsic relevance in the context of disordered magnetic materials , the main reason to choose it as the illustrative example is that eqs . ( [ relsigmadifnonspher13])-([flmsqframenonstats ] ) describe coupled translational and rotational dynamics , whose particular case @xmath16 coincide with the radially - symmetric case , already discussed in detail in refs . thus , the most novel features are to be expected in the non - equilibrium rotational dynamics illustrated in this exercise . just like in the case of liquids formed by spherical particles , the development of the ne - scgle theory for liquids of non - spherical particles requires the previous development of the _ equilibrium _ version of the corresponding scgle theory . such an equilibrium scgle theory for non - spherical particles , however , was previously developed by elizondo - aguilera et al . @xcite , following to a large extent the work of schilling and collaborators @xcite on the extension of mode coupling theory for this class of systems . thus , we start our discussions in section [ section2 ] with a brief review of the main elements of the non spherical _ equlibrium _ scgle theory and its application to dynamical arrest in systems formed by colloidal interacting particles with non spherical potentials . in section [ nonequilib ] we outline the conceptual basis and the main steps involved in the derivation of the non - equilibrium extension of the scgle theory for glass - forming liquids of non - spherical particles . in the same section we summarize the resulting set of self consistent equations which constitutes this extended theory . in section [ agingspinglass ] , we introduce a simplified model for interacting dipoles randomly distributed in space and apply our equations to investigate the slow orientational dynamics as well as the aging and equilibration processes of the system near its `` spin glass''-like transitions . finally in section [ conclusions ] we summarize our main conclusions .

the non - equilibrium self - consistent generalized langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile of a suddenly - quenched colloidal liquid of particles interacting through non spherically - symmetric pairwise interactions , whose mean value is constrained to remain uniform and isotropic , .

the non - equilibrium self - consistent generalized langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile of a suddenly - quenched colloidal liquid of particles interacting through non spherically - symmetric pairwise interactions , whose mean value is constrained to remain uniform and isotropic , . such self - consistent theory is cast in terms of the time - evolution equation of the covariance of the fluctuations of the spherical harmonics projections of the fourier transform of . the resulting theory describes the non - equilibrium evolution after a sudden temperature quench of both , the static structure factor projections and the two - time correlation function , where is the correlation _ delay _ time and is the _ evolution _ or _ waiting _ time after the quench . as a concrete and illustrative application we use the resulting self - consistent equations to describe the irreversible processes of equilibration or aging of the orientational degrees of freedom of a system of strongly interacting classical dipoles with quenched positional disorder .

astro-ph0111290

c

the conventional picture of uranus and neptune s formation , whereby the ice giants accrete near their present heliocentric distances , has grave problems . numerical simulations have not been able to produce @xmath5 10 m@xmath3 objects in the trans - saturnian region in the lifetime of the solar system without significantly increasing protoplanet radii , or invoking dissipational forces and planetesimal disk densities too large to be consistent with a physically plausible protostellar disk . building on our previous work ( tdl99 ) , we have performed additional n - body simulations of the evolution of the outer solar system starting at the time when the first gas giant forms . at this point , we assume that a number of @xmath5 10 m@xmath3 objects have formed at a heliocentric distance of roughly 5 to 10 au , as is suggested by the oligarchic growth model ( kokubo & ida 1998 , 2000 ) . using a variety of different initial conditions , we find as before that the accretion of jupiter s gas envelope causes the remaining protoplanets to become violently unstable . in most cases they are scattered onto high - eccentricity orbits in the trans - saturnian region . with most of its orbit now crossing the largely pristine trans - saturnian planetesimal disk , a scattered protoplanet experiences dynamical friction and has its eccentricity rapidly damped . as a result , the protoplanets tend to end up on nearly circular , well - spaced orbits on a myr timescale , with semimajor axes comparable to those of saturn , uranus and neptune . of the simulations which initially contain a total of four giant protoplanets and form jupiter from the innermost , the majority produce final orbital configurations similar to that of our outer solar system . such systems are produced though with lower probability even if ones adds an extra protoplanet , or lets the second - innermost protoplanet grow into jupiter . these results strengthen our earlier conclusion that if uranus and neptune shared the same birthplace as the gas giants , they could then readily have been delivered to their present orbits . the role of migration in the formation of uranus and neptune was previously investigated numerically by ipatov ( 1991 ) , based on an idea by zharkov and kozenko ( 1990 ) . ipatov concludes that planetary embryos of a few m@xmath3 may have originated just outside the orbit of saturn , to migrate outward and later grow into uranus and neptune , provided that they did not acquire high eccentricities during this process . in contrast , we find that uranus and neptune could have originated from anywhere in the jupiter - saturn region , and that initially high eccentricities which nearby bodies naturally tend to acquire during jupiter s final growth phase are in fact a powerful mechanism for rapidly transporting them outward . also , the long growth timescales in the outer solar system suggest that uranus and neptune likely already completed most of their growth in the jupiter - saturn region ; even with a `` head start '' of a few earth masses , the formation of uranus- and neptune - mass objects much beyond 10 au within the age of the solar system is unlikely ( levison and stewart 2001 , thommes , duncan and levison 2001 ) can one find any observational support for this model in the present - day solar system ? the high inclinations in the classical kuiper belt point to strong dynamical excitation in the past , and the simulations performed here do produce high inclinations in this region as a natural side effect . however , the simulations all fall short of reproducing the mean debiased inclination of the classical kuiper belt . strong observational support would be provided by the discovery of a fossilized scattered disk in the kuiper belt , and a dynamically colder population beyond . it is tempting to link the trans - neptunian object 2000 cr@xmath106 with a fossilized scattered disk ; its high eccentricity ( 0.8 ) is characteristic of a scattered disk object , but recent observations ( gladman et al 2001 ) have established that its perihelion is at 44 au , far beyond the reach of neptune . however , none of the fossilized disk objects in our simulations acquire semimajor axes as high as that of 2000 cr@xmath106 ( 216 au ) . fig . [ qa_run11 ] shows a plot of perihelion distance versus semimajor axis for set 5 , revealing only one case ( b ) where one or more objects simultaneously acquire a semimajor axis of @xmath5 100 au and a perihelion distance significantly further out than the ( circularized ) outermost protoplanet . all other sets of runs fare even more poorly . 5b is a run in which a protoplanet spends a long time at high eccentricity , and excites particularly high planetesimal inclinations in the disk . a long circularization time may thus be an important ingredient in reproducing both objects like 2000 cr@xmath106 and the high inclinations of the kuiper belt ; we will address this possibility in future work . findings regarding the deuterium to hydrogen ( d / h ) ratios of uranus , neptune and comets are particularly interesting in the context of this model . from infrared observations , feuchtgruber et al ( 1999 ) find that the d / h ratios of the ice giants are lower than those of the oort cloud comets halley ( eberhardt et al 1995 ) , hyakutake ( bockel ' ee - morvan et al . 1998 ) and hale - bopp ( meier et al 1998 ) by a factor of approximately three , a difference large compared to the uncertainties of the measurements . oort cloud comets are thought to have originated primarily in what is today the uranus - neptune region ( duncan , quinn & tremaine 1987 , fernandez 1997 ) , and the notion of a common birthplace is supported by the comets similar d / h ratios . though a sample size of three is clearly very small , this discrepancy between the comets and the ice giants would seem to present a further problem for any scenario in which uranus and neptune form in the trans - saturnian region , since they should then share the chemical composition of the comets . however , this is exactly what one would expect if the ice giants originally formed at a smaller heliocentric distance , where higher temperatures would have made for a lower d / h ratio . an aspect not modeled in any of the simulations is the gravitational interaction of the bodies with a gaseous disk . it has been shown that gas disk tidal forces can cause rapid inward migration of protoplanets ( eg . ward 1997 ) . in fact , the speed of migration may be peaked for objects of @xmath5 10 m@xmath3 , taking place on timescales of @xmath57 years or less . this peak corresponds to the transition between so - called type i migration , where a body s resonant interaction with the gas disk gives rise to a torque imbalance , to type ii migration , where the object opens a gap in the gas disk and is subequently locked to the disk s viscous evolution . tidal migration therefore poses a problem for _ any _ model of giant planet formation : how do they avoid spiralling into the central star as they form ? however , tidal torques may not in fact operate throughout the whole disk . gammie ( 1996 ) develops an accretion disk model which , beyond @xmath5 0.1 au , only transports angular momentum in a relatively thin surface layer . thus the bulk of the disk would have zero viscosity , and objects embedded in it would be subject to neither type i nor type ii orbital decay . also , the disk may be truncated early on by photoevaporation from the central star ( shu , johnstone and hollenbach 1993 ) , or from surrounding stars , as is seen in the orion nebula proplyds ( johnstone , hollenbach and bally 1998 ) . bodies scattered beyond the truncation distance would then be safe from nebula tides , and those near the edge would experience a net positive torque and migrate outward . of course , such a scenario has the added advantage that , as discussed in the above works , it accounts for uranus and neptune having no massive gas envelopes . in constructing the simulations presented here , we have appealed to the oligarchic growth model as a plausible guide for our choice of initial protoplanet masses and orbits . one can of course envision a number of variations . for instance , two gas giants may form on initially widely separated orbits . the waves they raise in the disk will tend to clear the gas between them , and type ii migration will cause their orbital separation to decrease ( kley 2000 ) . if ice giant sized bodies are trapped in between , they will be prevented from accreting more gas , and will be scattered as the stable region between the gas giants shrinks to nothing . also , if future measurements of jupiter constrain its core to be much smaller , or even absent , this will invalidate the assumption that jupiter grew from an ice giant sized nucleus . though the scattering of ice giants could still take place in principal , one would then need to explain how a small body won the gas accretion race against much larger bodies ( if the core is small ) , or how ice giant sized bodies managed to form before the birth of the first gas giant from an unnucleated disk instability ( if there is no core ; eg . boss 2000 ) . alternatively , one could search for a way in which accretion could continue to take place in close proximity to a gas giant , with scattering delayed until ice giant sized bodies form . for such a scenario type i tidal effects , which cause the eccentricity to decay on an even shorter timescale than the semimajor axis ( eg . papaloizou & larwood 2000 ) , may actually be helpful . it may then be the dispersal of the gas which triggers scattering . doing away with any reference to a specific formation process , the most general statement of our results is : _ ice giant sized bodies can be scattered from the jupiter - saturn region by gas giant sized bodies , to ultimately end up on uranus- and neptune - like orbits . _ ewt is grateful for support from the center for integrative planetary science , as well as from the national sciences and engineering research council ( nserc ) during the earlier part of this work . mjd is grateful for support from nserc . hfl is grateful for support from nasa s _ planetary geology & geophysics _ , _ origins of solar systems _ , and _ exobiology _ programs .

the outer giant planets , uranus and neptune , pose a challenge to theories of planet formation . they exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ( and 17 times as massive as the earth , respectively ) very difficult . previously , we proposed a model which addresses this problem : instead of forming in the trans - saturnian region , uranus and neptune underwent most of their growth among proto - jupiter and -saturn , were scattered outward when jupiter acquired its massive gas envelope , and subsequently evolved toward their present orbits . we also find that this mechanism may partly account for the high orbital inclinations observed in the kuiper belt .

the outer giant planets , uranus and neptune , pose a challenge to theories of planet formation . they exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies ( and 17 times as massive as the earth , respectively ) very difficult . previously , we proposed a model which addresses this problem : instead of forming in the trans - saturnian region , uranus and neptune underwent most of their growth among proto - jupiter and -saturn , were scattered outward when jupiter acquired its massive gas envelope , and subsequently evolved toward their present orbits . we present the results of additional numerical simulations , which further demonstrate that the model readily produces analogues to our solar system for a wide range of initial conditions . we also find that this mechanism may partly account for the high orbital inclinations observed in the kuiper belt .

1002.3486

c

the redshift evolution of oxygen and nitrogen abundances in emission - line sdss galaxies has been studied . we have paid particular attention to the construction of our galaxy sample , using the mpa / jhu catalogs of line flux measurements and other derived physical properties for sdss galaxies . we have devised a way to recognize and exclude from consideration not only agns , but also star - forming galaxies with large errors in their line flux measurements . we have found that the requirement that nitrogen abundances , derived with different calibration relations based on different emission lines , agree , can be used as a reliable criterion to select star - forming galaxies with accurate line fluxes measurements . we have derived relations between nitrogen abundances and the abundance - sensitive n@xmath16 , n@xmath16/r@xmath16 , and n@xmath16/r@xmath15 indexes . those relations have been used to determine nitrogen abundances in the sdss galaxies . the small dispersion among the various derived nitrogen abundances for a given galaxy is used as a criterion to select star - forming galaxies with accurate line fluxes measurements . the relations between the electron temperature t@xmath16 and the n@xmath16 , n@xmath16/r@xmath16 , and n@xmath16/r@xmath15 indexes have also been established . those calibrations have been used to estimate the n / o ratio and derive the oxygen abundances o / h from the nitrogen abundances subsamples of star - forming sdss galaxies have been extracted from the mpa / jhu catalogs , using the small nitrogen abundance dispersion criterion described above . the nitrogen and oxygen abundances are estimated for these galaxies . the evolution of the oxygen and nitrogen abundances with redshift and galaxy stellar mass of galaxy are investigated , that of nitrogen abundances for the first time . we have obtained the following main results . + 1 ) the galaxies of highest masses ( those more massive than @xmath3 10@xmath1m@xmath2 ) do not show an appreciable enrichment in both oxygen and nitrogen from @xmath4=0.25 to @xmath4=0.05 . those galaxies have reached their high astration level in such a distant past that their stars have returned their nucleosynthesis products to the interstellar medium before @xmath4=0.25 . + 2 ) the galaxies in the mass range from @xmath3 10@xmath5m@xmath2 to @xmath3 10@xmath1m@xmath2 do not show an oxygen enrichment , but do show some enrichment in nitrogen . those galaxies also formed stars before @xmath4=0.25 , but at a later epoch in comparison to the galaxies of highest masses . their stars have not returned nitrogen to the interstellar medium before @xmath4=0.25 because they have not had enough time to evolve . + 3 ) the galaxies with masses lower than @xmath3 10@xmath7m@xmath2 show enrichment in both oxygen and nitrogen abundances over the redshift period from @xmath4=0.25 to @xmath4=0.05 , i.e. during the last 3 gyr . the oxygen enrichment increases with decreasing galaxy mass , from 10@xmath7m@xmath2 to m@xmath38=10@xmath52m@xmath2 . it reaches a value @xmath10log(o / h ) @xmath3 0.25 at m@xmath38=10@xmath52m@xmath2 and slightly decreases with further decrease of galaxy mass . the nitrogen enrichment increases with decreasing galaxy mass , from @xmath3 10@xmath7m@xmath2 to @xmath3 10@xmath57m@xmath2 . it reaches a value @xmath10log(n / h ) @xmath3 0.65 at @xmath3 10@xmath57m@xmath2 and slightly decreases with further decrease of galaxy mass . significant star formation has occurred in those galaxies during the last 3 gyr . they have converted up to 20% of their total mass to stars over this period . + 4 ) stars with lifetimes of 23 gyr , i.e. in the 1.5 2 m@xmath2 mass range , contribute to the nitrogen production . this is not in agreement with current stellar evolutionary models of intermediate mass stars which predict that stars in the 3 8 m@xmath2 mass range do the job , not stars in the 1.5 2 m@xmath2 mass range . + 5 ) the general picture of the oxygen abundance evolution with redshift and galaxy stellar mass obtained here and in previous work is confirmed and strengthened by consideration of the nitrogen abundance evolution . we are grateful to the referee for his / her constructive comments . thanks the hospitality of the astronomy department of the university of virginia where part of this investigation was carried out . l.s.p . and i.a.z . acknowledge the partial support of the cosmomicrophysics-2 project of the national academy of sciences of ukraine . the authors acknowledge the work of the sdss team . funding for the sdss has been provided by the alfred p. sloan foundation , the participating institutions , the national aeronautics and space administration , the national science foundation , the u.s . department of energy , the japanese monbukagakusho , and the max planck society . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium ( arc ) for the participating institutions . the participating institutions are the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , the korean scientist group , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . llcccc 12+log(n / h ) & log(n@xmath16 ) & 7.649 & 1.454 & 0.257 & 0.148 + 12+log(n / h ) & log(n@xmath16/r@xmath16 ) & 7.918 & 0.877 & 0.058 & 0.038 + 12+log(n / h ) & log(n@xmath16/r@xmath15 ) & 7.526 & 0.521 & 0.062 & 0.014 + & & & & & + t@xmath16 & log(n@xmath16 ) & 0.778 & 0.354 & 0.001 & 0.044 + t@xmath16 & log(n@xmath16/r@xmath16 ) & 0.702 & 0.248 & 0.042 & 0.019 + t@xmath16 & log(n@xmath16/r@xmath15 ) & 0.802 & 0.172 & 0.003 & 0.011 +

the oxygen and nitrogen abundance evolutions with redshift and galaxy stellar mass in emission - line galaxies from the sloan digital sky survey ( sdss ) are investigated . we have devised a criterion to recognize and exclude from consideration active galactic nuclei ( agns ) and star - forming galaxies with large errors in the line flux measurements . to select star - forming galaxies with accurate line fluxes measurements , we require that , for each galaxy , the nitrogen abundances derived with various calibrations based on different emission lines agree . using this selection criterion , subsamples of star - forming sdss galaxies have been extracted from catalogs of the mpa / jhu group . this suggests that stars with lifetimes of 23 gyr , in the 1.52 m mass range , contribute to the nitrogen production . finally , galaxies with masses 10m show enrichment in both oxygen and nitrogen during the last 3 gyr : they have undergone appreciable star formation and have converted up to% of their mass into stars over this period .

the oxygen and nitrogen abundance evolutions with redshift and galaxy stellar mass in emission - line galaxies from the sloan digital sky survey ( sdss ) are investigated . this is the first such study for nitrogen abundances , and it provides an additional constraint for the study of the chemical evolution of galaxies . we have devised a criterion to recognize and exclude from consideration active galactic nuclei ( agns ) and star - forming galaxies with large errors in the line flux measurements . to select star - forming galaxies with accurate line fluxes measurements , we require that , for each galaxy , the nitrogen abundances derived with various calibrations based on different emission lines agree . using this selection criterion , subsamples of star - forming sdss galaxies have been extracted from catalogs of the mpa / jhu group . we found that the galaxies of highest masses , those with masses 10m , have not been enriched in both oxygen and nitrogen over the last 3 gyr : they have formed their stars in the so distant past that these have returned their nucleosynthesis products to the interstellar medium before=0.25 . the galaxies in the mass range from 10m to 10m do not show an appreciable enrichment in oxygen , but do show some enrichment in nitrogen : they also formed their stars before=0.25 but later in comparison to the galaxies of highest masses ; these stars have not returned nitrogen to the interstellar medium before=0.25 because they have not had enough time to evolve . this suggests that stars with lifetimes of 23 gyr , in the 1.52 m mass range , contribute to the nitrogen production . finally , galaxies with masses 10m show enrichment in both oxygen and nitrogen during the last 3 gyr : they have undergone appreciable star formation and have converted up to% of their mass into stars over this period . both oxygen and nitrogen enrichments increase with decreasing galaxy stellar mass in the mass range fromm tom , then slightly decrease with further decrease of galaxy mass .

1503.03605

i

the paper is devoted to the numerical solution of small - strain quasi - static elastoplastic problems . such a problem consists of the constitutive initial value problem ( civp ) and the balance equation representing the principle of virtual work . a broadly exploited and universal numerical / computational concept includes the following steps : * time - discretization of civp leading to an incremental constitutive problem ; * derivation of the constitutive and consistent tangent operators ; * substitution of the constitutive ( stress - strain ) operator into the balance equation leading to the incremental boundary value problem in terms of displacements ; * finite element discretization and derivation of a system of nonlinear equations ; * solving the system using a nonsmooth variant of the newton method . civp satisfies thermodynamical laws and usually involves internal variables such as plastic strains or hardening parameters . several integration schemes for numerical solution of civp were suggested . for their overview , we refer , e.g. , @xcite and references introduced therein . if the implicit or trapezoidal euler method is used then the incremental constitutive problem is solved by the elastic predictor / plastic corrector method . the plastic correction leads to the return - mapping scheme . we distinguish , e.g. , implicit , trapezoidal or midpoint return - mappings depending on a chosen time - discretization ( * ? ? ? * chapter 7 ) . in this paper , we assume that the plastic flow direction is generated by the plastic potential , @xmath3 . if @xmath3 is smooth then the corresponding plastic flow direction is uniquely determined by the derivative of @xmath3 and consequently , the plastic flow rule reads as follows , e.g. ( * ? ? ? * chapter 8) : @xmath4 here , @xmath5 , @xmath6 , @xmath7 , and @xmath8 denotes the plastic strain rate , the plastic multiplier rate , the stress tensor and the hardening thermodynamical forces , respectively . the corresponding return - mapping scheme is relatively straightforward and leads to solving a system of nonlinear equations . a difficulty arises when @xmath3 is _ nonsmooth_. mostly , it happens if the yield surface contains singular points , such as apices or edges . then the function @xmath3 is rather pseudo - potential than potential and its derivative need not exist everywhere . in such a case , the rule ( [ eqn_flow_rule ] ) is usually completed by some additive formulas depending on particular cases of @xmath3 and @xmath7 in an ad - hoc manner . for example , the implementation of the mohr - coulomb model reported in ( * ? ? ? * chapter 6 , 8) employs one , two , or six plastic multipliers @xmath9 , depending on the location of @xmath7 on the yield surface . since the stress tensor @xmath7 is unknown in civp one must blindly guess its right location . moreover , for each tested location , one must usually solve an auxilliary system of nonlinear equations whose solvability is not guaranteed in general . _ these facts are evident drawbacks of the current return - mapping schemes . _ in associative plasticity , it is well - known that the plastic flow rule ( [ eqn_flow_rule ] ) together with a hardening law and loading / unloading conditions can be equivalently replaced by the principle of maximum plastic dissipation within the constitutive model . this alternative formulation of civp does not require special treatment for nonsmooth @xmath3 and enables to solve civp by techniques based on mathematical programming @xcite . in particular , if the implicit or trapezoidal euler method is used then the incremental constitutive problem can be interpreted by a certain kind of the closest - point projection @xcite . for some nonassociative models , civp can be re - formulated using a theory of bipotentials that leads to new numerical schemes @xcite . these alternative definitions of the flow rule enable a variational re - formulation of the initial boundary value elastoplastic problem . consequently , solvability of this problem can be investigated ( see , e.g. , @xcite ) . therefore , the corresponding numerical techniques are usually also correct from the mathematical point of view . on the other hand , such a numerical treatment is not so universal and its implementation is more involved / too complex in comparison with standard procedures of computational inelasticity . the approach pursued in this paper builds on the subdifferental formulation of the plastic flow rule , e.g. ( * ? ? ? * section 6.3.9 ) , @xmath10 for nonsmooth @xmath3 . here , @xmath11 denotes the subdifferential of @xmath3 at @xmath12 with respect to the stress variable . if @xmath3 is convex at least in vicinity of the yield surface then this definition is justified , e.g. , by ( * ? ? ? * corollary 23.7.1 ) and is valid even when @xmath3 is not smooth at @xmath7 . on the first sight , it seems that ( [ inclusion_flow_rule ] ) is not convenient for numerical treatment due to the presence of the multivalued flow direction . the main goal of this paper is to show that the _ opposite is true _ , by demonstrating that the implicit return - mapping scheme based on ( [ inclusion_flow_rule ] ) leads to solving a just one system of nonlinear equations regardless whether the unknown stress tensor lies on the smooth portion of the yield surface or not at least for a wide class of models with nonsmooth plastic pseudo - potentials . using this technique , we eliminate the blind guessing and thus considerably simplify the solution scheme . moreover , the new technique enables to investigate some useful properties of the constitutive operator , like uniqueness or semismoothness , that are not obvious for the current technique . first of all , we illustrate the new technique on a simple 2d projective problem that mimics the structure of an incremental elastoplastic constitutive problem . consider the convex set @xmath13 and define the projection @xmath14 of a point @xmath15 as follows : @xmath16 the scheme of the projection is depicted in figure [ fig_projection ] . clearly , the function @xmath17 is convex in @xmath18 , nondifferentiable at @xmath19 and @xmath20 if @xmath21 then @xmath22 . conversely , if @xmath23 it follows from the karush - kuhn - tucker conditions and ( [ motivation0 ] ) that the projective problem can be written as follows : _ find @xmath24 and the lagrange multiplier @xmath25 : @xmath26 where _ @xmath27 [ -1,1 ] , & w_2^*=0 , \end{array } \right.\ ] ] to find a solution to ( [ motivationb2 ] ) , it is crucial to rewrite the inclusion ( [ motivationb2])@xmath28 as an equation . observe that @xmath29 where @xmath30 denotes a positive part of a function . this crucial transformation will be derived in detail in section [ sec_dp ] on an analogous elastoplastic example . thus ( [ motivationb2 ] ) leads to the following system of equations : @xmath31 since ( [ motivationb3])@xmath28 implies @xmath32 , the system of three nonlinear equations reduces to a single one @xmath33 consequently , @xmath9 can be found in the closed form as @xmath34 from which one can easily compute @xmath35 by ( [ motivationb3])@xmath36 and ( [ motivationb3])@xmath28 . the presented idea is systematically extended on some elastoplastic models . this paper , part i , is focused on isotropic models containing : @xmath0 yield surfaces with one or two apices ( singular points ) laying on the hydrostatic axis ; @xmath1 plastic pseudo - potentials that are independent of the lode angle ; @xmath2 nonlinear isotropic hardening ( optionally ) . such models are usually formulated by the haigh - westergaard coordinates . further , the implicit euler discretization of civp is considered and thus two types of return on the yield surface within the plastic correction are distinguished : @xmath37 return to the smooth portion of the yield surface ; @xmath38 return to the apex ( apices ) . the paper is organized as follows . section [ sec_preliminaries ] contains some preliminaries related to invariants of the stress tensor and semismooth functions . section [ sec_dp ] is devoted to the drucker - prager model including the nonlinear isotropic hardening . although the plastic corrector can not be found in closed form , the new technique enables to a priori decide about the return type and prove existence , uniqueness and semismoothness of the implicit constitutive operator . the consistent tangent operator is also introduced . in section [ sec_jg ] , we derive similar results for the perfect plastic part of the jirsek - grassl model @xcite . in section [ sec_general ] , the new technique is extended on an abstract model written by the haigh - westergaard coordinates . in particular , within the plastic correction , we formulate a unique system of nonlinear equations which is common for the both type of the return . it can lead to a more correct and/or simpler solution scheme in comparison with the current technique . section [ sec_realization ] is devoted to numerical realization of the incremental boundary value elastoplastic problem using the semismooth newton method . in section [ sec_experiments ] , illustrative numerical examples related to a slope stability benchmark are considered . here , limit load is analyzed by an incremental method depending on a mesh type and mesh density for the drucker - prager and jirsek - grassl models . within this paper , second order tensors , matrices and vectors are denoted by bold letters . as usual , small letters are used for vectors and capitals for matrices ( see section [ sec_realization ] ) . further , the fourth order tensors are denoted by capital blackboard letters , e.g. , @xmath39 or @xmath40 . the symbol @xmath41 means the tensor product @xcite . we also use the following notation : @xmath42 and @xmath43 for the space of symmetric , second order tensors .

the paper is devoted to the numerical solution of elastoplastic constitutive initial value problems . an improved form of the implicit return - mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule . the main advantage of this approach is that the treatment of singular points , such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non - linear equations , similarly to smooth yield surfaces . this paper ( part i ) is focused on isotropic models containing : yield surfaces with one or two apices ( singular points ) laying on the hydrostatic axis ; plastic pseudo - potentials that are independent of the lode angle ; nonlinear isotropic hardening ( optionally ) . it is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence , uniqueness and semismoothness of discretized constitutive operators in implicit form . the paper also contains numerical examples related to slope stability with available matlab implementation .

the paper is devoted to the numerical solution of elastoplastic constitutive initial value problems . an improved form of the implicit return - mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule . the main advantage of this approach is that the treatment of singular points , such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non - linear equations , similarly to smooth yield surfaces . this paper ( part i ) is focused on isotropic models containing : yield surfaces with one or two apices ( singular points ) laying on the hydrostatic axis ; plastic pseudo - potentials that are independent of the lode angle ; nonlinear isotropic hardening ( optionally ) . it is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence , uniqueness and semismoothness of discretized constitutive operators in implicit form . further , the semismooth newton method is introduced to solve incremental boundary - value problems . the paper also contains numerical examples related to slope stability with available matlab implementation . keywords : elastoplasticity , nonsmooth yield surface , multivalued flow direction , implicit return - mapping scheme , semismooth newton method , limit analysis

1304.7668

i

this paper deals with multivariate functions estimation . for the proposed estimator we establish local as well as global oracle inequalities and show how to use them for deriving minimax adaptive results . _ model and setup . _ we observe @xmath0 following @xmath1 where @xmath2 , the noise @xmath3 are i.i.d . centered random variables satisfying a tail probability condition ( assumption [ assassumption - on - noise ] ) , and the design points @xmath4 are independent random vectors with common density @xmath5 with respect to the lebesgue measure . the sequences @xmath6 and @xmath7 are assumed to be independent . the density @xmath8 is known , however , in section [ secunknowndensity ] we discuss how to extend our results to the case of unknown design density . in addition , we assume that the function @xmath9 has a single - index structure , that is , there exist unknown @xmath10 and @xmath11 such that @xmath12 a minimal technical assumption about @xmath13 is that it belongs to some hlder ball , yet the knowledge of this ball will not be required for the proposed estimation procedure ; see the discussion after assumption [ asstechnical ] for more details . the paper aims at estimating the entire function @xmath14 on @xmath15 ^ 2 $ ] or its value @xmath16 , @xmath17 ^ 2 $ ] , from the data @xmath18 without any prior knowledge about the nuisance parameters @xmath19 and @xmath20 . the unit square is chosen for notation convenience ; and all the results remain true when @xmath15 ^ 2 $ ] is replaced by an arbitrary bounded interval of @xmath21 . throughout the paper we adopt the following notation . the joint distribution of the sequence @xmath22 will be denoted by @xmath23 , and those of @xmath24 by @xmath25 . in addition , @xmath26 and @xmath27 stand for the marginal distributions of @xmath28 and @xmath3 , respectively . to judge the quality of estimation , we use either the risk determined by the @xmath29 , @xmath30 , on @xmath31 ^ 2 $ ] with @xmath32 : @xmath33 a `` global '' risk ; or the `` pointwise '' risk defined as follows : @xmath34 ^ 2.\ ] ] here @xmath35 is an estimator , that is , an @xmath36-measurable function , and @xmath37 denotes the mathematical expectation with respect to @xmath38 . all the results established in the paper , except the lower bound given in theorem [ thpointwise - adaptation - lower ] , are obtained for @xmath39 . the principal difficulties with the case of arbitrary dimension are commented in remark [ remdifficulties ] . it is noteworthy that the single - index modeling , even if @xmath40 , is a direct generalization of the univariate regression model . therefore , our results , mainly presented in section [ subsecadaptive - estimation ] , generalize in several directions the existing ones obtained for the univariate random design regression ( see the discussion after theorem [ thglobal - adaptation ] ) . let us formulate the principal assumptions used in the sequel . they are imposed on the distributions of the design and noise variables as well as on the approximation property of the link function . [ assassumption - on - noise ] the random variable @xmath41 has a symmetric distribution with density @xmath42 with respect to the lebesgue measure . moreover , there exist @xmath43 , @xmath44 $ ] , and @xmath45 such that @xmath46 the assumption holds , for example , for the gaussian , laplace or , more generally , for the symmetrized weibull distribution . in the following , the functional class @xmath47 is considered as fixed . [ assassumption - on - design ] there exists @xmath48 such that @xmath49 ^ 2 } g(x ) \ge\underline{g}$ ] . the assumption holds obviously if the design points are uniformly distributed on any bounded borel set containing @xmath50 ^ 2 $ ] . the imposed condition is `` fitted '' to the estimation over @xmath51 ^ 2 $ ] that explains the set @xmath52 ^ 2 $ ] . when estimating over a rectangle @xmath53\times[c , e]\in\mathbb{r}^2 $ ] , the infimum should be taken over @xmath54\times[c-5/2,e+5/2 ] $ ] . if @xmath55 from assumption [ asstechnical ] below is known , the above condition can be relaxed to @xmath56\times[c-2,e+2 ] $ ] . we also remark that independently of the values @xmath57 assumption [ assassumption - on - design ] is fulfilled if @xmath58 and @xmath59 for any @xmath60 . [ asstechnical ] there exist @xmath61 and @xmath62 such that @xmath63 the latter assumption guarantees that the link function is smooth . however , it is important to emphasize that @xmath64 and @xmath65 are not supposed to be known a priori . in particular , they are not involved in our estimation procedure . on the other hand , both the parameters restrict the minimal sample size needed to justify the theoretical results involved . set for any @xmath66 @xmath67 in the sequel it will be assumed that @xmath68 , where @xmath69 to finish this section , we remark that all the presented results remain true if one assumes that @xmath70 , that is , is uniformly bounded , and @xmath65 is known . for clarity of presentation , it is assumed that the index vector , where @xmath71 stands for the unite sphere in @xmath72 . however , in section [ secextensions ] it is shown that our results can be extended to the case @xmath73 . the goal of our studies is at least threefold . we first seek an estimation procedure @xmath74 , @xmath75^{2 } $ ] , for @xmath76 which could be applicable to any function @xmath77 satisfying assumption ( [ single - index ] ) . moreover , we would like to bound the risk of this estimator uniformly over the set @xmath78 . more precisely , we want to establish for @xmath74 the so - called local oracle inequality at any point @xmath79^{2 } $ ] the risk of @xmath80 should be bounded as follows : @xmath81 here @xmath82 is completely determined by the function @xmath83 , vector @xmath84 and observations number @xmath85 , while @xmath86 is a constant independent of @xmath77 and @xmath87 . after being established , the local oracle inequality allows deriving minimax adaptive results for the function estimation at a given point . indeed , let @xmath88 , @xmath89 be a collection of functional classes such that @xmath90 . for any @xmath91 define @xmath92 where the infimum is taken over all possible estimators . the quantity @xmath93 is the minimax risk on @xmath94 . in the framework of minimax adaptive estimation , the task is to construct an estimator @xmath95 such that for any @xmath96 the estimator @xmath95 satisfying ( [ eqlocal - adaptation - intro ] ) is called optimally rate adaptive over the collection @xmath97 . subsequently , let ( [ eqlocal - oracle - intro ] ) be proved ; and let for any @xmath98 then one can assert that the estimator @xmath99 is adaptive over @xmath100 . thus , the first step is to prove ( [ eqlocal - oracle - intro ] ) . to the best of our knowledge , such results do not exist in the context of regression with random design not only under the single - index constraint , but also in univariate regression . next , ( [ eqlocal - oracle - intro ] ) is applied to minimax adaptive estimation over hlder classes , @xmath101 ; see section [ subsecadaptive - estimation ] for pertinent definitions . we will find the minimax rate over @xmath102 and prove that @xmath99 achieves it , that is , is optimally rate adaptive . this result is quite surprising because , if @xmath84 is fixed , say , @xmath103 , it is well known that an optimally adaptive estimator does not exist ; see @xcite for the gaussian white noise model , @xcite for density estimation , and @xcite for regression . local oracle inequality ( [ eqlocal - oracle - intro ] ) allows us to bound from above the `` global '' risk as well . indeed , for any @xmath104 , in view of jensen s inequality and fubini s theorem , @xmath105^r\le\mathbb{e}^{(n)}_{f } \| \widehat f - f \|^{r}_r= \|\mathcal r_{r,\cdot}^{(n ) } ( \widehat f , f ) \| _ r^r $ ] and , therefore , @xmath106 inequality ( [ eqglobal - oracle - intro ] ) is called the global oracle inequality , and in the considered framework it supplies new results . as local oracle inequality ( [ eqlocal - oracle - intro ] ) is a powerful tool for deriving minimax adaptive results in pointwise estimation , so inequality ( [ eqglobal - oracle - intro ] ) can be used for constructing adaptive estimators of @xmath14 . we will consider a collection of nikolskii classes @xmath107 ( see definition [ defnikolskii - class ] ) , where @xmath108 and @xmath109 . when considering these classes , we aim at estimating functions with inhomogeneous smoothness . this means that the underlying function can be very regular on some parts of its domain and rather irregular on the other sets . we will compute bounds for @xmath110 and show that , if @xmath111 , the rate of convergence is the minimax rate over @xmath112 . this means that our estimator @xmath99 is optimally rate adaptive over the collection @xmath113 whenever @xmath111 . in the case @xmath114 , we will show that the latter bound differs from the bound on the minimax risk by a logarithmic factor . following the contemporary language , we say that @xmath99 is `` nearly '' the construction of an optimally rate adaptive over the entire range of the nikolskii classes estimator under the single - index constraint ( [ single - index ] ) is an open question . all presented results are completely new . the adaptive estimation under the @xmath115 loss and single - index constraint , except the case @xmath116 in @xcite , was not studied . note , however , that the cited result was obtained under the gaussian errors model and over the hlder classes that do not admit the consideration of functions with inhomogeneous smoothness . it turns out that the adaptation to the unknown @xmath117 and @xmath118 can be viewed as selecting from a special family of kernel estimators in the spirit of that of @xcite , @xcite , @xcite . however , our selection rule is quite different from the aforementioned proposals , and it allows us to solve the problem of minimax adaptive estimation under the @xmath119 losses over a collection of nikolskii classes . it is worth mentioning that the single - index model is particularly popular in econometrics [ see , e.g. , @xcite , @xcite ] . the estimation , nevertheless , is usually performed under smoothness assumptions on the link function . one usually uses the @xmath120 losses , and the available methodology is based on these restrictions . to the best of our knowledge , the only exceptions are @xcite for the minimax estimation under the projection pursuit constraints , and @xcite for adaptation to unknown smoothness and structure . in section [ subsecoracle - approach ] we present our selection rule and establish for it local and global oracle inequalities . section [ subsecadaptive - estimation ] is devoted to the application of these results to minimax adaptive estimation . the proofs of the main results are given in section [ secproofs ] ; section [ secunknowndensity ] discusses an unknown design density , and the proofs of lemmas are moved to the supplementary material [ @xcite ] .

the problem of adaptive multivariate function estimation in the single - index regression model with random design and weak assumptions on the noise is investigated . a novel estimation procedure that adapts simultaneously to the unknown index vector and the smoothness of the link function by selecting from a family of specific kernel estimators is proposed . we establish a pointwise oracle inequality which , in its turn , is used to judge the quality of estimating the entire function ( `` global '' oracle inequality ) . both the results are applied to the problems of pointwise and global adaptive estimation over a collection of hlder and nikolskii functional classes , respectively .

the problem of adaptive multivariate function estimation in the single - index regression model with random design and weak assumptions on the noise is investigated . a novel estimation procedure that adapts simultaneously to the unknown index vector and the smoothness of the link function by selecting from a family of specific kernel estimators is proposed . we establish a pointwise oracle inequality which , in its turn , is used to judge the quality of estimating the entire function ( `` global '' oracle inequality ) . both the results are applied to the problems of pointwise and global adaptive estimation over a collection of hlder and nikolskii functional classes , respectively .

1607.04873

i

consider an @xmath0-variate polynomial of degree at most @xmath1 : @xmath2 where @xmath3 , @xmath4 , @xmath5 , @xmath6 , and where each coefficient @xmath7 is taken from a ground field @xmath8 . a _ determinantal representation _ of @xmath9 is an @xmath10-matrix @xmath11 of the form @xmath12 where each @xmath13 with @xmath14 . we call @xmath15 the _ size _ of the determinantal representation . clearly , since the entries of @xmath11 are affine - linear forms in @xmath16 , @xmath15 must be at least the degree of @xmath9 . determinantal representations of polynomials play a fundamental role in several mathematical areas : from _ algebraic geometry _ it is known that each plane curve ( @xmath17 ) of degree @xmath1 over an algebraically closed field @xmath8 admits a determinantal representation of size @xmath1 @xcite . over non - algebraically closed fields , and especially when restricting to symmetric determinantal representations , the situation is much more subtle @xcite . for larger @xmath0 , only certain hypersurfaces have a determinantal representation of size equal to their degree @xcite . in _ optimisation _ , and notably in the theory of _ hyperbolic polynomials _ @xcite , one is particularly interested in the case where @xmath18 , @xmath19 is symmetric positive definite , and the @xmath20 are symmetric . in this case , the restriction of @xmath9 to any line through 0 has only real roots . for @xmath17 the converse also holds @xcite ; for counterexamples to this converse holding for higher @xmath0 , see @xcite . in _ complexity theory _ a central role is played by valiant s conjecture that the permanent of an @xmath21-matrix does not admit a determinantal representation of size polynomial in @xmath22 @xcite . via the _ geometric complexity theory _ programme @xcite this leads to the study of polynomials in the boundary of the orbit of the @xmath10-determinant under the action of the group @xmath23 permuting matrix entries . recent developments in this field include the study of this boundary for @xmath24 @xcite and the exciting negative result in @xcite that valiant s conjecture can _ not _ be proved using occurrence obstructions proposed earlier in @xcite . our motivation comes from _ scientific computing _ , where determinantal representations of polynomials have recently been proposed for efficiently solving systems of equations @xcite . for this application , it is crucial to have determinantal representations not of a _ single _ polynomial @xmath9 , but rather of all @xmath0-variate polynomials of degree at most @xmath1 . moreover , the representation should be easily computable from the coefficients of @xmath9 . specifically , in @xcite determinantal representations are constructed for the bivariate case ( @xmath17 ) in which the entries of the matrices @xmath25 themselves _ depend affine - linearly _ on the coefficients @xmath7 . this is what we call a _ uniform determinantal representation _ of the generic polynomial @xmath9 of degree @xmath1 in @xmath0 variables ; see section [ sec : problem ] for a precise definition . [ ex : binaryquadric ] the identity @xmath26 exhibits the matrix on the right as a uniform determinantal representation of the generic bivariate quadric . @xmath27 in applications , the matrix @xmath11 is used as input to algorithms in numerical linear algebra that scale unfavourably with @xmath15 , such as a complexity of @xmath28 . consequently , we are led to consider the following fundamental question . what is the minimal size @xmath29 of any uniform determinantal representation of the generic polynomial of degree @xmath1 in @xmath0 variables ? a construction from @xcite shows that for fixed @xmath17 and @xmath30 we have @xmath31 ; this construction is reviewed in section [ sec : first ] . we improve the construction from @xcite by giving a particularly elegant uniform determinantal representations of bivariate polynomials of size @xmath32 in example [ ex:2d ] , and of size @xmath33 in example [ ex:2d1 ] . in view of the obvious lower bound of @xmath1 this is clearly sharp up to a constant factor for @xmath30 , although we do not know where in the interval @xmath34 $ ] the true answer lies . we show in section [ sec : numerics ] how to use these small determinantal representations of bivariate polynomials for solving systems of equations . before that , we focus on the asymptotic behaviour of @xmath29 for fixed @xmath0 and @xmath30 . in this setting , we derive the following result . [ thm : main ] for fixed @xmath35 there exist positive constants @xmath36 ( depending on @xmath0 ) such that for each @xmath37 the smallest size @xmath29 of a uniform determinantal representation of the generic polynomial of degree @xmath1 in @xmath0 variables satisfies @xmath38 . we will also compare our results with previous constructions , most notably with those by quarez ( * ? ? ? 4.4 ) , who proves the existence of a symmetric representation of size @xmath39 . for fixed @xmath0 and @xmath30 , @xcite therefore has the asymptotic rate @xmath40 , meaning that the results of this paper represent a clear improvement . for fixed @xmath1 and @xmath41 , @xcite leads to the asymptotic behavior @xmath42 , which is similar to our bounds ; we will discuss more details in section [ sec : outlook ] . in section [ sec : problem ] we formalise the notion of uniform determinantal representations , study their symmetries , and derive some simple properties . in particular , we relate uniform determinantal representations to spaces of singular @xmath10-matrices . in section [ sec : singular ] we briefly review some of the existing literature on these singular spaces , and we prove that for @xmath43 there are infinitely many equivalence classes of such objects ; this poses an obstruction to a `` brute - force '' approach towards finding lower bounds on @xmath29 . in section [ sec : first ] we present a first construction , of which however the size is of the order of @xmath44 , rather than @xmath45 , for @xmath30 . in section [ sec : second ] we give a more efficient construction and prove theorem [ thm : main ] . in section [ sec : small ] we give upper bounds on @xmath29 for small @xmath0 and @xmath1 and determine @xmath46 and @xmath47 exactly . we extend representations from scalar to matrix polynomials in section [ sec : matpol ] . in section [ sec : numerics ] we give some numerical results that show that for @xmath17 and small @xmath1 we get a competitive method for computing zeros of polynomials systems . finally , in section [ sec : outlook ] we summarise our main conclusions and collect some questions that arise naturally from our work .

motivated by recent developments in this last area , we introduce the notion of a _ uniform determinantal representation _ , not of a single polynomial but rather of all polynomials in a given number of variables and of a given maximal degree . we derive a lower bound on the size of the matrix , and present a construction achieving that lower bound up to a constant factor as the number of variables is fixed and the degree grows . this construction marks an improvement upon a recent construction due to plestenjak

the problem of expressing a specific polynomial as the determinant of a square matrix of affine - linear forms arises from algebraic geometry , optimisation , complexity theory , and scientific computing . motivated by recent developments in this last area , we introduce the notion of a _ uniform determinantal representation _ , not of a single polynomial but rather of all polynomials in a given number of variables and of a given maximal degree . we derive a lower bound on the size of the matrix , and present a construction achieving that lower bound up to a constant factor as the number of variables is fixed and the degree grows . this construction marks an improvement upon a recent construction due to plestenjak hochstenbach , and we investigate the performance of new representations in their root - finding technique for bivariate systems . furthermore , we relate uniform determinantal representations to vector spaces of singular matrices , and we conclude with a number of future research directions . determinantal representation , system of polynomial equations , multiparameter matrix eigenvalue problem , space of singular matrices . 13p15 , 65h04 , 65f15 , 65f50 .

1605.02213

i

consider the problem of _ online learning and optimization _ of affine memoryless models with unknown parameters that follow a markov jump process . by online learning and optimization we mean that the control input of the unknown model is chosen sequentially to minimize the expected total cost or to maximize the expected cumulative reward procured over a time horizon @xmath0 . in this context , the online learning problem is one of exploration and exploitation ; the need of exploring the space of unknown parameters must be balanced by the need of exploiting the knowledge acquired through learning . for online learning problems with deterministic unknown parameters , a commonly used performance measure is the so - called _ regret _ , defined by the difference between the cumulative cost / reward of an online learning policy and that of a decision maker who knows the model completely and sets the input optimally . the regret grows monotonically with the time horizon @xmath0 , and the rate of growth measures the efficiency of online learning policies . the online learning problem considered in this paper is particularly relevant in dynamic pricing problems when the consumers demand is unknown and possibly varying stochastically . the goal of dynamic pricing is to set the price sequentially , using the observations from the previous sales , to match a certain contracted demand . besides applications in dynamic pricing , results are also relevant to the learning and control problem of markov jump linear systems with unknown parameters . in this paper , we study the online learning and optimization problem of markov jump affine models under two different objectives : ( i ) target matching with a quadratic cost and ( ii ) revenue ( profit ) maximization . our goal is to establish fundamental limits on the rate of regret growth for markov jump affine models and develop an online learning policy that achieves the lowest possible regret growth . without markov jump as part of the model , when there is a single state , the problem considered here is the classical problem of control in experiment design studied by anderson and taylor . anderson and taylor proposed a certainty equivalence rule where the input is determined by using the maximum likelihood estimates of system parameters as if they were the true parameters . despite its intuitive appeal , the anderson - taylor rule was shown to be suboptimal for the quadratic regulation problem by lai and robbins in and also for the revenue maximization problem by den boer and zwart in . in fact , there is a non - zero probability that the anderson - taylor rule produces an input which converges to a suboptimal value for both cases ; therefore , this rule results in _ incomplete learning _ and a linear growth of regret . for the scalar model in which the quadratic cost of the regulation problem is to be minimized , lai and robbins showed that a robbins - monro stochastic approximation approach achieves the optimal regret order of @xmath1 . later , lai and wei showed that this regret order is also achievable for a more general linear dynamic system by an adaptive regulator that uses least square estimates of a reparametrized model and ensures convergence via occasional uses of white - noise probing inputs . the result was further generalized by lai @xcite to multivariate linear dynamic systems with a square invertible system matrix . the result presented in this paper can be viewed as a generalization of this line of work to allow both time - varying linear models and time - invariant models with a non - invertible system matrix . the problem considered in this paper also falls into the category of continuum - armed bandit problem where the control input is chosen from a subset of @xmath2 with the goal of minimizing expected cost ( or maximizing expected reward ) that is an unknown continuous function of the input . this problem was introduced by agrawal @xcite who studied the scalar problem and proposed a policy that combines certainty equivalence control with kernel estimator - based learning . agrawal showed that this policy has a regret growth rate of @xmath3 for a uniformly lipschitz expected cost function . later , kleinberg @xcite proved that the optimal growth rate of regret for this problem can not be smaller than @xmath4 and proposed a policy that achieves @xmath5 . kleinberg @xcite also considered the multivariate problem , @xmath6 , and showed that an adaptation of zinkevich s greedy projection algorithm achieves the regret growth rate of @xmath3 if the cost function is smooth and convex on a closed bounded convex input set . within the continuum - armed bandit formulation , the work of cope @xcite is particularly relevant because of its use of stochastic approximation to achieve the order - optimal regret growth of @xmath7 for a different class of cost functions . cope s results ( both the regret lower bound and the kiefer - wolfowitz technique ) , unfortunately , can not be applied here because of the time - varying markov jump affine models treated here . also relevant is the work of rusmevichientong and tsitsiklis on the so - called linearly parameterized bandit problem where the objective is to minimize a linear cost with input selected from the unit sphere . a learning policy developed in is shown to achieve the lower bound of @xmath7 using decoupled exploration and exploitation phases . even though the model considered in this paper is similar to the one in in terms of the observed output being a linear function of the input , in our paper , the unknown model parameters follow a markov jump process and the specific cost functions studied are quadratic ; thus the problem objective is different . there is a considerable amount of work on dynamic pricing problem with the objective of revenue maximization under a demand model uncertainty in different areas such as operations research , statistics , mathematics , and computer science . in , a multi - armed bandit approach with a regret growth rate of @xmath8 was proposed for a nonparametric formulation of the problem . see also where the same problem under a general parametric demand model is considered and a modified version of myopic maximum likelihood based policy is shown to achieve the regret order of @xmath9 , and where a similar result is obtained for a class of parametric demand models . in both and , authors proved that the lower bound for regret growth rate is @xmath7 . besides more general classes of demand models , affine model similar to the one in this paper has been also studied extensively ; . in both and , it is shown that approximate dynamic programming solutions may outperform greedy method numerically . a special case of our formulation of revenue maximization problem without any markov jump characteristics ( with time - invariant model parameters ) is previously investigated by keskin and zeevi . keskin and zeevi proposed a semi - myopic policy that uses orthogonal pricing idea to explore and learn the system . they showed that the lowest possible regret order is @xmath7 for any policy , and their semi - myopic policy achieves this bound up to a logarithmic factor ; @xmath10 . even though the system model is assumed to be time - invariant in most of the literature , there is a considerable amount of work especially in dynamic pricing that deals with time - varying demand models due to unpredictable environmental factors affecting demand ; see for a demand model that evolves according to a discrete state space markov chain in a revenue management with finite inventory problem , and for a dynamic programming formulation of a profit maximization problem with an unknown demand parameter following an autoregressive process . see also for a revenue maximization problem with an affine demand model where the model parameters are time - varying , yet the cumulative change in the model parameters over the time horizon @xmath0 is bounded . since keskin and zeevi measure the regret of a policy by the difference between the cumulative cost of the policy and that of a clairvoyant who knows all the future temporal changes exactly and chooses the optimal action , their characterization of regret is too pessimistic for the markov jump model considered here . some other examples of related work on online learning with time - varying models apart from dynamic pricing are and . in , besbes , gur , and zeevi studied the online learning problem of more general time - varying cost functions where the cumulative temporal changes is restricted to a budget similar to . however , their characterization of regret is also similar to and thus , incomparable with the one in this paper . yin , ion , and krishnamurthy also considered the problem of estimating a randomly evolving optimum of a cost function which follows a markov jump process . their analysis deals with the convergence of the estimate obtained via stochastic approximation to the limit ( stationary ) solution , whereas in this paper , we are concerned about estimating the optimum of the cost function at each time instant given the previous state of the markov chain . moreover , different than our paper , their analysis relies on the availability of the noisy observations of the cost function gradient and they do not characterize regret . the main contribution of this paper is the generalization of online learning of time - invariant affine models to that of markov jump affine models . extending spall s stochastic approximation method @xcite to the optimization problem of an objective function that evolves according to a markov jump process , we propose an online learning policy , referred to as markovian simultaneous perturbations stochastic approximation ( mspsa ) . we show that mspsa achieves the optimal regret order of @xmath11 for two different objective functions studied for the affine model : ( i ) quadratic regulation and ( ii ) the revenue maximization . furthermore , we also show that the control input of mspsa policy converges to the optimal solution both with probability one and in mean square as @xmath12 . therefore , the proposed policy eventually learns the optimal solution . a key implication of our results is that , in comparing with lai s result on the learning problem of a time - invariant affine model with the quadratic regulation objective @xcite , modulating a linear model by a markov jump process introduces substantial learning complexity ; hence , the regret order increases from @xmath1 to @xmath11 . as a special case , we also show that , even in the absence of markovian jump , when the system matrix is full column rank but not invertible , the best regret order is also @xmath11 . it worths noting that adding just one row to a square and invertible matrix can change the worst case regret from @xmath1 to @xmath11 . in the second part of this paper , we study the profit maximization problem with markov jump demand . to this end , we generalize the lower bound obtained by keskin and zeevi for time - invariant demand to markov jump demand , and we show that this bound is achievable by the mspsa policy for a more general case with markov jump characteristics . the results presented here are obtained using several techniques developed in different contexts . the mspsa policy is a generalization of spall s stochastic approximation method to the optimization problem of an objective function following a markov jump process . to show the optimality of mspsa , we use the van trees inequality to lower bound the estimation error , which is the technique used in . lastly , a result on the convergence of non - negative almost supermartingales @xcite is used to obtain the convergence result for mspsa policy .

the problem of online learning and optimization of unknown markov jump affine models is considered . furthermore , by the use of van trees inequality , it is shown that the regret of any policy grows no slower than that of mspsa , making mspsa an order optimal learning policy . online learning , stochastic approximation , stochastic cramer - rao bounds , continuum - armed bandit , sequential decision making .

the problem of online learning and optimization of unknown markov jump affine models is considered . an online learning policy , referred to as markovian simultaneous perturbations stochastic approximation ( mspsa ) , is proposed for two different optimization objectives : ( i ) the quadratic cost minimization of the regulation problem and ( ii ) the revenue ( profit ) maximization problem . it is shown that the regret of mspsa grows at the order of the square root of the learning horizon . furthermore , by the use of van trees inequality , it is shown that the regret of any policy grows no slower than that of mspsa , making mspsa an order optimal learning policy . in addition , it is also shown that the mspsa policy converges to the optimal control input almost surely as well as in the mean square sense . simulation results are presented to illustrate the regret growth rate of mspsa and to show that mspsa can offer significant gain over the greedy certainty equivalent approach . online learning , stochastic approximation , stochastic cramer - rao bounds , continuum - armed bandit , sequential decision making .

1004.3000

i

the old - new interest in the problem of soliton - soliton intertaction and soliton molecules has been increasingly accumulating particularly over the past few years . this is mainly motivated by the application of optical solitons as data carriers in optical fibers @xcite and the realization of matter - wave solitons in bose - einstein condensates @xcite . one major problem limiting the high - bit rate data transfer in optical fibers is the soliton - soliton interaction . on the one hand , soliton - soliton interaction is considered as a problem since it may destroy information coded by solitons sequences . on the other hand , it is part of the problem s solution , since the interaction between solitons leads to the formation of stable soliton molecules which can be used as data carriers with larger `` alphabet '' @xcite . the interaction force between solitons was first studied by karpman and solovev using perturbation analysis @xcite , gordon who used the exact two solitons solution @xcite , and anderson and lisak who employed a variational approach @xcite . it was shown that the force of interaction decays exponentially with the separation between the solitons and depends on the phase difference between them such that in - phase solitons attract and out - of - phase solitons repel . this feature was demonstrated experimentally in matter - wave solitons of attractive bose - einstein condensates @xcite where a variational approach accounted for this repulsion and showed that , in spite of the attractive interatomic interaction , the phase difference between neighboring solitons indeed causes their repulsion @xcite . for shorter separations between the solitons , malomed @xcite used a perturbation approach to show that stationary solutions in the form of bound states of two solitons are possible . however , detailed numerical analysis showed that such bound states are unstable @xcite . stable bound states were then discovered by akhmediev @xcite and a mechanism of creating robust three - dimensional soliton molecules was suggested by crasovan _ recently , soliton molecules were realized experimentally by stratmann _ _ in dispersion - managed optical fibers @xcite and their phase structure was also measured @xcite . perurbative analysis was used to account theoretically for the binding mechanism and the molecule s main features @xcite . quantization of the binding energy was also predicted numerically by komarov _ _ @xcite . in refs.@xcite , a hamiltonian is constructed to describe the interaction dynamics of solitons . the mechanism by which the relative phase between the solitons leads to their force of interaction , and hence the binding mechanism , is understood only qualitatively as follows . for in - phase ( out - of - phase ) solitons , constructive ( destructive ) interference takes place in the overlap region resulting in enhancement ( reduction ) in the intensity . as a result , the attractive intensity - dependent nonlinear interaction causes the solitons to attract ( repel ) @xcite . a more quantitative description is given in refs . @xcite . in view of its above - mentioned importance from the applications and fundamental physics point of views , we address here the problems of soliton - soliton interaction and soliton molecule formation using the exact two solitons solution . this approach has been long pioneered by gordon @xcite where he used the exact two solitons solution of the homogeneous nonlinear schr@xmath0dinger equation to derive a formula for the force of interaction between two solitons , namely @xmath1 where @xmath2 is the solitons separation and @xmath3 is their phase difference . this formula was derived in the limit of large solitons separation and for small difference in the center - of - mass speeds and intensities , which limits its validity to slow collisions . with appropriately constructed hamiltonian , wu _ et al . _ have derived , essentially , a similar formula that gives the force between two identical solitons and reliefs the condition on slow collisions @xcite . here , we present a more comprehensive treatment where we derive the force between two solitons for arbitrary solitons intensities , center - of - mass speeds , and separation . we also generalize gordon s formula to inhomogeneous cases corresponding to matter - wave bright solitons in attractive bose - einstein condensates with time - dependent parabolic potentials @xcite and to optical solitons in graded - index waveguide amplifiers @xcite . many interesting situations can thus be investigated . this includes the various soliton - soliton collision regimes with arbitrary relative speeds , intensities , and phases . most importantly , soliton - soliton interaction at short solitons separations will now be accounted for more quantitatively than before . specifically , soliton molecule formation is clearly shown to arise from the time - dependence of the relative phase which plays the role of the restoring force . in this case , the force between the two solitons is shown to be composed of a part oscillating between attractive and repulsive , which arises from the relative phase , and an attractive part that arises from the nonlinear interaction . the time - dependence of the relative phase results in a natural oscillation of the molecule s bond length around an equilibrium value . the various features of the soliton molecule , including its equilibrium _ bond length _ , _ spring constant _ , _ frequency _ and _ amplitude _ of oscillation , and _ effective mass _ , will be derived in terms of the fundamental parameters of the solitons , namely their intensities and the nonlinear interaction strength . the two solitons solution is derived here using the inverse scattering method @xcite . although the two solitons solution of the homogeneous nonlinear schr@xmath0dinger equation is readily known @xcite , here we not only generalize this solution to inhomogeneous cases , but also present it in a new form that facilitates its analysis . the solution will be given in terms of the four fundamental parameters of each soliton , namely the initial amplitude , center - of - mass position and speed , and phase . the main features of the solution will be shown clearly such as the contribution of the nonlinear interaction to the actual separation and phase difference between solitons where it turns that the separation between the two solitons increases with logarithm of the difference between the amplitudes of the two solitons . furthermore , the general statement that _ a state of two equal solitons with zero relative speed and finite separation does not exist as a stationary state for the homogeneous nonlinear schr@xmath0dinger equation _ , will be transparently and rigorously proved . stability of soliton molecules is an important issue since , in real systems , perturbations caused by various sources such as losses , raman scattering , higher order dispersion , and scattering from local impurities , tend to destroy the molecules . to investigate the stability of the soliton molecules described by our formalism , we have considered three situations . first , we studied the reflection of the molecule from a hard wall and a softer one . while for the hard wall the molecule preserves its molecular structure after reflection , it generally breaks up for the softer ones due to energy losses at the interface . secondly , the scattering of the molecule by a potential barrier was also investigated . we show that the molecular structure is maintained only for some specific heights of the barrier . this suggests a quantization in the binding energy as predicted by komarov _ the oscillation period of the reflected molecule is noticed to be smaller than for the incident one . in addition , the outcome of scattering depends on the phase of the molecule s oscillation at the interface of the barrier . for instance , a dramatic change in the scattering outcome takes place if the _ coalescence _ point of the molecule lies exactly at the interface . in such a case , the otherwise totally transmitting molecule will now split into reflecting and tunneling solitons . thirdly , we have considered the collision between a single soliton with a stationary soliton molecule . the effects of different initial speeds , amplitudes , and phases of the scatterer soliton were studied . it turns out that for slower collisions , it is easier for the scatterer soliton to break up the soliton molecule , while for fast collisions the scatterer soliton expels and then replaces one of the solitons in the molecule . the phase of the scatterer soliton plays also a crucial rule in preserving or breaking the bond of the molecule , which can be used as _ key _ tool to code or uncode data in the molecule . the rest of the paper is organized as follows . in section [ exact_sec ] , we use the inverse - scattering method to derive the two solitons solution of the inhomogeneous nonlinear schr@xmath0dinger equation and present the solution in the above - mentioned appealing form . the main features of the solution will be discussed in subsection [ mainsec ] . the center - of - mass positions and relative phases will be derived in subsections [ com_sec ] and [ phases_sec ] , respectively . the force between solitons will be derived in section [ force_sec ] where gordon s formula will be extracted as a special case in subsection [ gordon_sec ] and our more general formula will be derived in subsection [ our_sec ] . in subsection [ num_sec ] , we compare our formula with the numerical calculation . in section [ molsec ] , we show the possibility of forming soliton molecules , derive their main features in subsection [ formation_sec ] , and investigate their stability in subsection [ stability_sec ] . we end in section [ conc_sec ] with a summary of results and conclusions . the details of the derivation of the two solitons solution and the center - of - mass positions are relegated to appendices a and b , respectively .

the problem of soliton - soliton force is revisited . from the exact two solitons solution of a nonautonomous gross - pitaevskii equation , we derive a generalized formula for the mutual force between two solitons . the force is given for arbitrary solitons amplitude difference , relative speed , phase , and separation . the latter allows for the investigation of soliton molecules formation , dynamics , and stability . we reveal the role of the time - dependent relative phase between the solitons in binding them in a soliton molecule .

the problem of soliton - soliton force is revisited . from the exact two solitons solution of a nonautonomous gross - pitaevskii equation , we derive a generalized formula for the mutual force between two solitons . the force is given for arbitrary solitons amplitude difference , relative speed , phase , and separation . the latter allows for the investigation of soliton molecules formation , dynamics , and stability . we reveal the role of the time - dependent relative phase between the solitons in binding them in a soliton molecule . we derive its equilibrium bond length , spring constant , frequency , effective mass , and binding energy of the molecule . we investigate the molecule s stability against perturbations such as reflection from surfaces , scattering by barriers , and collisions with other solitons .

astro-ph0204192

i

although tremendous progress has been made in recent years in mapping the large - scale gravitational field ( out to scales of @xmath4 km s@xmath1 ) , relatively little data are available to study the velocity field of galaxies in the local neighborhood ( @xmath5 km s@xmath1 ) . the major impediment to constraining the local flow is the lack of a consistent set of distances to nearby galaxies . locally , the deviations from a pure hubble law have been predicted to be large and measurable , as much as 1 magnitude in distance modulus . if gravitational instability has generated all the large scale structure in the universe , then it must also be responsible for the extremely anisotropic local galaxy distribution ( see fig . [ figure : skydist ] ) @xcite . under this assumption , it is possible to predict the velocity field from this distribution . the catalogs from such full sky galaxy redshift surveys as the 1.2 jy iras survey @xcite allow us to estimate the large scale gravity field out to a redshift @xmath6 km s@xmath1 . in the limit of linear perturbations at late times , one expects the peculiar velocity at a point in space to be proportional to the gravity field at that point . [ figure : skydist ] demonstrates that according to linear theory , the local velocity field is expected to show substantial deviations from uniformity , with quadrupole distortions dominating . outflow is directed toward virgo and fornax on opposite sides of the sky , while substantial infall occurs from the poles of the local distribution . such a flow is expected within any gravitational model and would act to depopulate galaxies from the local poles . the bulk of the local galaxy distribution does reside on the positive and zero contours of figure [ figure : skydist ] ( the local supercluster plane ) , while the regions of negative peculiar velocity are deficient but not entirely devoid of galaxies . it is possible that linear theory does not apply on this scale , but in that case one would expect a more chaotic flow of similar amplitude . observations of local deviations from hubble flow do not really support the expectations of fig . [ figure : skydist ] , especially in the southern direction ( see the review by @xcite ) . however , the data are sparse because large spiral galaxies suitable for tully - fisher or cepheid period luminosity analysis are very rare locally , and the sky coverage , particularly in the expected infalling regions , is poor . we have thus set out to provide new distances to a complementary sample of nearby galaxies that were chosen to lie near the maximum predicted infall . according to stellar evolution theory , the tip of the first ascent red giant branch ( trgb ) marks the onset of the core helium flash in low mass stars . observationally , this phenomenon causes a distinct and abrupt termination of the bright end of the red giant branch luminosity function . this discontinuity translates directly into an excellent distance indicator : the bolometric luminosity of the trgb for low mass stars is predicted to vary by only @xmath7 mag for ages ranging from 2 up to 15 gyr @xcite and for metallicities encompassing the entire range represented by galactic globular clusters ( @xmath8 < -0.7 $ ] ) @xcite . the discontinuity is also found empirically to be stable at the @xmath7 mag level in the @xmath2 band for the same set of stellar properties . the trgb method has a strong empirical , as well as physical , basis . distances obtained using the trgb agree with the cepheid period luminosity relation ( where direct comparisons have been made ) at a @xmath95% level , e.g. @xcite an exception is for m33 : @xcite . furthermore , since all visible galaxies must have had a first generation of stars , the trgb method is applicable to populations in all morphological types , including spiral , elliptical , and even irregular galaxies , provided their metallicity is sufficiently low . the trgb method also requires far less telescope time for observations than cepheids since repeat visits are unnecessary , a considerable advantage . a good review of the trgb , its applications and theoretical underpinnings , is given in @xcite . we have used the tip of the red giant branch to obtain distances to a sample of local galaxies ( mostly dwarfs ) in order to derive their peculiar velocities . in 2 we discuss the observations we have made of several galaxies using both the w.m . keck observatory and the _ hubble space telescope _ ( _ hst _ ) . in 3 we present the methods for measuring the trgb that we have employed and include detailed information on the analysis and error propogation . finally , in 4 we present the color magnitude diagrams , luminosity functions , and derived distances for several of the galaxies studied . we discuss the derived peculiar velocities and their implications in paper ii @xcite .

the properties of the velocity field in the local volume ( km s ) have been difficult to constrain due to a lack of a consistent set of galaxy distances . the sparse observations available to date suggest a remarkably quiet flow , with little deviation from a pure hubble law . however , velocity field models based on the distribution of galaxies in the 1.2 jy iras redshift survey , predict a quadrupolar flow pattern locally with strong infall at the poles of the local supergalactic plane . we probe this velocity field and begin to establish a consistent set of galactic distances . we have obtained images of nearby galaxies in the and band from the w.m . keck observatory and in f814w and f555w filters from the _ hubble space telescope_. where these galaxies are well resolved into stars we can use the tip of the red giant branch ( trgb ) as a distance indicator . using a maximum likelihood analysis to quantitatively measure the magnitude of the trgb

the properties of the velocity field in the local volume ( km s ) have been difficult to constrain due to a lack of a consistent set of galaxy distances . the sparse observations available to date suggest a remarkably quiet flow , with little deviation from a pure hubble law . however , velocity field models based on the distribution of galaxies in the 1.2 jy iras redshift survey , predict a quadrupolar flow pattern locally with strong infall at the poles of the local supergalactic plane . we probe this velocity field and begin to establish a consistent set of galactic distances . we have obtained images of nearby galaxies in the and band from the w.m . keck observatory and in f814w and f555w filters from the _ hubble space telescope_. where these galaxies are well resolved into stars we can use the tip of the red giant branch ( trgb ) as a distance indicator . using a maximum likelihood analysis to quantitatively measure the magnitude of the trgb we determine precise distances to seven nearby galaxies : leo i , sextans b , ngc 1313 , ngc 3109 , ugc 03755 , ugc 06456 , and ugc 07577 .

1507.08624

c

in this work , we have studied the quantum analogue of soliton - like scattering phenomena in the anisotropic spin-1/2 heisenberg chain , by utilising the algebraic bethe ansatz . we considered quantum scattering of localized excitations , created from linear combinations of bethe states with gaussian - distributed momenta , constructing wave packets of @xmath1 bound magnons . this construction allows to study scattering phenomena of wave packets containing an arbitrary number of bound magnons . exact methods based on the algebraic bethe ansatz provide a framework to evaluate the time - dependent expectation value of the local magnetization profile , which allows for a spatial tracking of the localized excitations . this explicit unitary time evolution of the initial state relies on the availability of determinant expressions for matrix elements of local spin operators . the algebraic bethe ansatz time evolution of colliding wave packets of bound magnons displays a spatial displacement in the trajectories of the wave packets under scattering , consistent with scattering theory results . for different values of anisotropy , fits on the displacements of the time evolved trajectories are in agreement with analytical results on the displacement from the derivative of the bethe ansatz scattering phase shifts , for several combinations of string lengths . the scattering phase shift can also be measured directly as well for the scattering between two localized single - magnon wave packets , again matching phase shift expressions provided by bethe ansatz . using tebd , scattering displacements from spin - block states have been studied , showing similar scattering features and validating the analytic predictions of the ising limit for the scattering displacement . the experimental realizability of real time tracking of localized excitations in the heisenberg spin chain@xcite might provide an opportunity to study dynamical scattering phenomena of ( bound ) magnons . a possible manifestation of such phenomena might be provided by the soliton - like scattering effects analysed in this work . the results on the scattering displacements can be extended to other bethe ansatz solvable models . finally , the time evolution method relying on matrix element expressions from algebraic bethe ansatz can be used to construct other initial states in spin chains as well and to study their respective relaxation phenomena .

the local magnetization profile shows the trajectories of colliding wave packets of bound magnons , which obtain a spatial displacement upon scattering . analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and bethe ansatz phase shifts , matching time evolution fits on the displacements . the time evolved block decimation ( tebd ) algorithm allows for the study of scattering displacements from spin - block states , showing similar scattering displacement features .

the quantum scattering of magnon bound states in the anisotropic heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models . localized colliding gaussian wave packets of bound magnons are constructed from string solutions of the bethe equations and subsequently evolved in time , relying on an algebraic bethe ansatz based framework for the computation of local expectation values in real space - time . the local magnetization profile shows the trajectories of colliding wave packets of bound magnons , which obtain a spatial displacement upon scattering . analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and bethe ansatz phase shifts , matching time evolution fits on the displacements . the time evolved block decimation ( tebd ) algorithm allows for the study of scattering displacements from spin - block states , showing similar scattering displacement features .

1206.3905

c

the relation between the ratio of infrared ( ir ) and ultraviolet ( uv ) flux densities ( the infrared excess : irx ) and the slope of the uv spectrum ( @xmath0 ) of galaxies plays a fundamental role in the evaluation of the dust attenuation of star forming galaxies especially at high redshifts . m99 first introduced a very useful method to estimate the dust attenuation by using the relation between the fir - to - fuv flux ratio and the uv slope , the irx-@xmath0 relation . however , subsequent studies revealed a dispersion and/or systematic deviation from the original irx-@xmath0 relation of m99 , depending on sample selection . we reexamined the original irx-@xmath0 relation proposed by m99 by measuring the far- and near - uv flux densities of the original sample galaxies used by m99 with imaging data . we summarize our conclusion as follows : 1 . the uv flux densities of the galaxies used in m99 were significantly underestimated because of the small aperture of which was @xmath7 . consequently , the irx values were lower than that in m99 , which lead the irx-@xmath0 relation shifted downward on the plot . 2 . the aperture effect affected not only the irx but also @xmath0 , because the curve of growth of the flux densities is a function of aperture which depends strongly on the wavelength . correcting the aperture effect , we obtained a new irx-@xmath0 relation for uv - selected starburst galaxies for the same sample with m99 . the original relation was obtained based on data . since bands cover only a wavelength range of @xmath1 m , the fir flux calculated from flux does not represent the total ir emission from dust . we used data from which has a much wider wavelength coverage especially toward longer wavelengths , and obtained an appropriate irx-@xmath0 relation for the data with total dust emission . we also estimated the irx-@xmath0 relation of the sample as a function both on the and images . we found that the irx-@xmath0 relation of the central starburst regions of the sample locates significantly below the relation obtained for the whole galaxy regions . this means that the extended dust emission is important to evaluate various global properties of galaxies , though we need to know the behavior of the psfs of akari diffuse map more precisely to evaluate more quantitatively . 6 . in many previous studies , authors use a conventional conversion factor ( bolometric correction : bc ) of @xmath124 to obtain the total ir flux from dust . we examined the bc of dust emission and found that indeed the value was @xmath128 on average . our new relation is consistent with most of the preceding results on the irx-@xmath0 relation for samples selected at optical and uv , though there is a significant scatter around it . we also found that even the quiescent class of ir galaxies follow this new relation , though luminous and ultraluminous ir galaxies distribute completely differently . the irx-@xmath0 relation for the central starburst regions of m99 s sample galaxies is very similar to the relation proposed by @xcite , based on the smc attenuation curve . this may imply interesting property of high-@xmath6 star - forming galaxies . in this work , we constructed a proper formula for a category of galaxies which are luminous in uv and actively forming stars . we found that this formula also applies to various class of moderately star - forming galaxies , like optically selected or non - luminous ir selected ones . this will be a more firm basis than before when one needs to correct dust extinction of high-@xmath6 galaxies . however , we should note the large intrinsic scatter on the irx-@xmath0 plane , especially the ( u)lirg population which does not obey the irx-@xmath0 relation at all . many issues and problems still remain to be solved for understanding this relation . first of all , we thank the anonymous referee for her / his extremely careful and constructive comments and suggestions that improved this article significantly . this work is based on observations with , a jaxa project with the participation of esa . we thank yasuo doi for preparing the fis diffuse map for our sample galaxies , and ko arimatsu for providing the new synthesized psf of the map . we also thank vronique buat , denis burgarella , agnieszka pollo , ryosuke asano , fumiko nagaya , mai fujiwara , daisuke yamasawa , and takashi kozasa for fruitful discussions and comments . we are grateful to takako t. ishii for developing the basis of the photometric software with idl . ttt has been supported by program for improvement of research environment for young researchers from special coordination funds for promoting science and technology . ttt and aki have been also supported by the grant - in - aid for the scientific research fund ( 20740105 , 23340046 , 24111707 : ttt , 19740108 : aki ) commissioned by the ministry of education , culture , sports , science and technology ( mext ) of japan . ttt , fty , ai , and klm have been partially supported from the grand - in - aid for the global coe program `` quest for fundamental principles in the universe : from particles to the solar system and the cosmos '' from the mext . facilities : , , ,

the relation between the ratio of infrared ( ir ) and ultraviolet ( uv ) flux densities ( the infrared excess : irx ) and the slope of the uv spectrum ( ) of galaxies plays a fundamental role in the evaluation of the dust attenuation of star forming galaxies especially at high redshifts . many authors , however , pointed out that there is a significant dispersion and/or deviation from the originally proposed irx- relation depending on sample selection . we reexamined the irx- relation by measuring the far- and near - uv flux densities of the original sample galaxies with and imaging data , and constructed a revised formula . we found that the newly obtained irx values were lower than the original relation because of the significant underestimation of the uv flux densities of the galaxies , caused by the small aperture of , further , since the original relation was based on data which covered a wavelength range of m , using the data from which has wider wavelength coverage toward longer wavelengths , we obtained an appropriate irx- relation with total dust emission ( tir ) : + 0.22 $ ] . this new relation is consistent with most of the preceding results for samples selected at optical and uv , though there is a significant scatter around it . we also found that even the quiescent class of ir galaxies follows this new relation , though luminous and ultraluminous ir galaxies distribute completely differently as well known before .

the relation between the ratio of infrared ( ir ) and ultraviolet ( uv ) flux densities ( the infrared excess : irx ) and the slope of the uv spectrum ( ) of galaxies plays a fundamental role in the evaluation of the dust attenuation of star forming galaxies especially at high redshifts . many authors , however , pointed out that there is a significant dispersion and/or deviation from the originally proposed irx- relation depending on sample selection . we reexamined the irx- relation by measuring the far- and near - uv flux densities of the original sample galaxies with and imaging data , and constructed a revised formula . we found that the newly obtained irx values were lower than the original relation because of the significant underestimation of the uv flux densities of the galaxies , caused by the small aperture of , further , since the original relation was based on data which covered a wavelength range of m , using the data from which has wider wavelength coverage toward longer wavelengths , we obtained an appropriate irx- relation with total dust emission ( tir ) : + 0.22 $ ] . this new relation is consistent with most of the preceding results for samples selected at optical and uv , though there is a significant scatter around it . we also found that even the quiescent class of ir galaxies follows this new relation , though luminous and ultraluminous ir galaxies distribute completely differently as well known before .

hep-th0202139

i

the open @xcite has so far resisted all the attempts to find analytically its solutions corresponding to the true closed string vacuum or lower dimensional d - branes . on the other hand the solutions are known numerically @xcite and provide a good evidence for the sen s tachyon conjectures @xcite . the vacuum ( vsft ) @xcite , designed to describe the physics around the true tachyon vacuum has been conjectured to have purely ghost kinetic term , which then allows for some exact calculations . canonical choice of a ghost kinetic term has been recently proposed by gaiotto , rastelli , sen and zwiebach @xcite based on some earlier results of hata and kawano @xcite . it has been further discussed by okuyama @xcite . generic feature of pure ghost kinetic terms in vsft is that they allow for simple construction of solutions in terms of projectors in the matter part of the algebra . it has been proved that such solutions indeed have the right ratios of tensions to be interpreted as d - branes @xcite . to determine however the absolute normalization turned out to be quite problematic . as we will show , on general grounds one should expect some sort of divergences in the normalization of the action . to deal with the problem , the authors of @xcite added a small term to the kinetic operator proportional to @xmath0 . with this regularization they observed that the numerical solution in the limit of removed regulator approaches a new type of a projector , called butterfly projector the poetic name comes from the shape of the surface which represents these kind of states in the conformal field theory . some properties of these states were also reported in @xcite . for other very recent development in the vsft see @xcite . in this paper we would like to get more insight into the problem of classical solutions and butterfly states in vsft by an extension of the analysis of our earlier work @xcite . the basic idea is to study implications of anomalous symmetries of the witten s vertex for classical solutions of the action . these techniques turn out to be remarkably useful in this new context . they show that in the vacuum one inevitably encounters some sort of singularities . for the regularized version of the theory we obtain infinite set of nontrivial identities which , as we show , are fulfilled for the simplest butterfly state . the identities are so constraining , that among all well defined surface states they uniquely pick up one particular state , which even happens to be a projector . it would be rather interesting if one could derive more identities which would then determine the projector uniquely in the the whole hilbert space , not necessarily in the subspace of surface states . it turns out to be possible to express any well defined surface state as a reparametrization of the vacuum in the form [ ufek ] u_f = e^k , which greatly simplifies calculations of some star products . here @xmath1 stands for some linear combination of the generators @xmath2 , which are known to act as exterior derivatives in the algebra . this fact has been shown in a recent paper @xcite for wedge states . it allowed to determine the star products of wedge states purely algebraically , without thinking much about gluing surfaces and various coordinate systems . particularly interesting class of states is the one of the form _ e^k . if the limit exists , then it gives states which are invariant under the reparametrization @xmath1 , i.e. they are annihilated by @xmath1 . these states are natural candidates for being projectors . for example the simplest butterfly surface state [ butt2 ] e^-l_2 = _ - e^k_2 is a projector . on the other hand the opposite limit [ butt2f ] e^+l_2 = _ + e^k_2 . is not a projector , we call it a ` false butterfly ' state . these kind of states ( [ butt2],[butt2f ] ) can be naturally generalized by replacing @xmath3 with @xmath4 . the paper is organized as follows : in section 2 we study the consequences of the anomalous symmetries of the witten s three vertex for the classical solutions of the ordinary , vacuum and regulated vacuum theories . we derive an infinite set of identities , which as we show are obeyed by the simplest butterfly state . we then show in section 3 , that the butterfly states and their generalization are indeed projectors . we manage also to calculate the star product @xmath5 for arbitrary @xmath6 $ ] . in section 4 we prove the uniqueness of the solution of the set of identities among the surface states . as a corollary we obtain a formula ( [ ufek ] ) . appendices contain some useful formulas for the exponentials of the virasoro operators , conservation laws for butterfly states and some numerical results for illustrative purposes . related work on butterfly states with some small overlaps with our work has been done independently by gaiotto , rastelli , sen and zwiebach and should appear simultaneously in @xcite .

, we show that the identities we derive , are so constraining , that among all surface states they uniquely select the simplest butterfly projector discovered numerically by these authors . the reparametrization symmetries are also used to give a simple proof that the butterfly states and their generalizations are indeed projectors . center for theoretical physics , massachusetts institute of technology , + cambridge , ma 02139 , usa _

the reparametrization symmetries of witten s vertex in ordinary or vacuum string field theories can be used to extract useful information about classical solutions of the equations of motion corresponding to d - branes . it follows , that the vacuum string field theory in general has to be regularized . for the regularization recently considered by gaiotto et al . , we show that the identities we derive , are so constraining , that among all surface states they uniquely select the simplest butterfly projector discovered numerically by these authors . the reparametrization symmetries are also used to give a simple proof that the butterfly states and their generalizations are indeed projectors . mit - lns-02 - 297 + mit - ctp-3249 + hep - th/0202139 anomalous reparametrizations and butterfly states in string field theory + + 0.5 cm _ center for theoretical physics , massachusetts institute of technology , + cambridge , ma 02139 , usa _

hep-th0202139

c

we have seen that the anomalous @xmath120 symmetries , which are just consequences of the overlap equations for the string vertex , yield nontrivial information about the solutions of the ordinary or vacuum theories . in order to obtain finite action solutions in vsft with pure ghost kinetic operator , we generically need infinite normalization of the action . due to the singular nature of projectors it could happen that the normalization turns out to be finite . in any case it shows that some sort of regularization of the string field action is inevitable . solutions of the regularized version of vsft constructed by adding a term @xmath189 to the kinetic operator obey such a constraint , which among all the surface states admits unique solution which is just the simplest butterfly projector . the constraint , up to a single constant , is the same as for the ordinary open ( osft ) . in that case we know however , that we should look for the solution of the full equations of motion outside the family of surface states . the overlap equations encode all the information about the vertices . it would be interesting to see if we could derive more identities based on overlap equations for products of local operators . such identities could then uniquely specify all the coefficients in the solution @xcite , except for a single parameter . in a recent paper @xcite by gaiotto et al . the authors found an intriguing coincidence for the osft solutions . the coefficients in the matter sector agree within few percent with coefficients of a solution of a ghost number zero theory , whose equation of motion in the siegel gauge reads ( l_0 - 1)= - * . even though the solution is given purely in terms of total virasoro operators acting on the vacuum , we can still find our quadratic identities based on @xmath120 s in the matter sector . they happen to be the same as the matter part of such identities in the osft . whether one can disentangle the matter and ghost sectors and add more identities to fully prove the observed pattern remains to be seen . another issue discussed in the paper are the surface states and projectors . we have shown that @xmath120 star algebra derivatives can be useful to calculate some nontrivial star products and to find some projectors . it would be interesting to obtain full classification of all projectors and to clarify their relation to star algebra derivatives in general .

the reparametrization symmetries of witten s vertex in ordinary or vacuum string field theories can be used to extract useful information about classical solutions of the equations of motion corresponding to d - branes . it follows , that the vacuum string field theory in general has to be regularized . for the regularization recently considered by gaiotto et al .

the reparametrization symmetries of witten s vertex in ordinary or vacuum string field theories can be used to extract useful information about classical solutions of the equations of motion corresponding to d - branes . it follows , that the vacuum string field theory in general has to be regularized . for the regularization recently considered by gaiotto et al . , we show that the identities we derive , are so constraining , that among all surface states they uniquely select the simplest butterfly projector discovered numerically by these authors . the reparametrization symmetries are also used to give a simple proof that the butterfly states and their generalizations are indeed projectors . mit - lns-02 - 297 + mit - ctp-3249 + hep - th/0202139 anomalous reparametrizations and butterfly states in string field theory + + 0.5 cm _ center for theoretical physics , massachusetts institute of technology , + cambridge , ma 02139 , usa _

astro-ph0307192

i

bl lacertae objects are active galactic nuclei whose most characteristic distinguishing property is their relatively low - luminosity optical line emission ; in many cases , their optical continua are completely featureless . like many high - polarization quasars , bl lacertae objects have strong and variable polarization in wavebands ranging from optical through radio ; they usually have compact , flat - spectrum radio structure , and point - like optical structure . for some , luminous elliptical host galaxies are observed ( angel and stockman 1980 ; miller 1981 ; kollgaard 1994 ) , though the optical images of many bl lacertae objects remain unresolved , even in high - resolution observations ( e.g. falomo 1996 ) . the radio emission and much of the optical emission is believed to be synchrotron radiation . historically , bl lacertae objects were first detected primarily via radio surveys , and strong radio emission was earlier thought to be characteristic of this type of agn . more recently , large numbers of bl lacertae objects with much weaker radio emission have been discovered by x - ray surveys . the relationship between these so - called `` radio '' and x - ray " bl lacertae objects is not entirely clear ; the most popular current hypotheses are ( 1 ) that they are similar objects whose spectral energy distributions peak in the infrared and x - ray , respectively , with the radio emission in radio bl lacertae objects experiencing a larger intrinsic relativistic enhancement ( giommi & padovani 1994 ; padovani & giommi 1995 ; fossati et al . 1997 ) , and ( 2 ) that they are intrinsically identical objects whose jets are oriented at different characteristic angles to the line of sight , with x - ray bl lacertae objects being viewed further `` off - axis '' ( stocke et al . 1985 ; maraschi et al . 1986 ) . in the broader context of unified schemes , it is usually thought that the `` parent population '' of bl lacertae objects is primarily fr i radio galaxies ( browne 1983 ; wardle , moore & angel 1984 ) . previous vlbi polarization observations of radio bl lacertae objects at 6 cm and 3.6 cm ( gabuzda & cawthorne 1996 , gabuzda et al . 1999 , and references therein ) have revealed a tendency for the electric vector @xmath3 in polarized knots in the vlbi jets to lie nearly along the local jet direction . the degrees of polarization in the jet components of bl lacertae objects have been observed to be as high as @xmath4 , with typical values @xmath5 , indicating that these components are optically thin and that in at least some cases the magnetic field is very highly ordered . assuming the jet components to be optically thin , the observed typical @xmath3 orientation implies that the associated magnetic fields are perpendicular to the direction of the jet . one natural interpretation of this transverse magnetic field structure is that the visible jet components are associated with relativistic shocks that compress an initially tangled magnetic field , enhancing the magnetic field transverse to the compression ( laing 1980 ; hughes , aller and aller 1989 ) . as images for more bl lacertae objects have become available , it has become increasingly clear that there are also a sizeable minority of these sources in which , in contrast , longitudinal magnetic fields dominate in at least some parts of their vlbi jets . lccccc antenna & diameter & t@xmath6 & t@xmath7 & @xmath8 & epoch + & ( m ) & ( k ) & ( k ) & ( k / jy ) + medicina & 32 & 60 & 50 & 0.160 & 1 , 2 + effelsberg & 100 & 60 & 50 & 0.991 & 1 , 2 + wsrt & @xmath925 & 120 & 120 & & 2 + st . croix & 25 & 45 & 35 & 0.102 & 2 + hancock & 25 & 55 & 60 & 0.092 & 2 + haystack & 37 & 75 & 65 & 0.130 & 1 + green bank & 43 & 35 & 40 & 0.227 & 1 , 2 + north liberty & 25 & 45 & 45 & 0.120 & 1 , 2 + phased vla & @xmath1025 & * * & * * & * * & 1 + kitt peak & 25 & 65 & 65 & 0.120 & 1 + owens valle & 25 & 110 & 110 & 0.120 & 1 , 2 + brewster & 25 & 35 & 35 & 0.088 & 2 + mauna kea & 25 & 35 & 35 & 0.090 & 2 + + at 6 cm , the degrees of polarization of the cores of bl lacertae objects ( @xmath11 ) are , on average , higher than those of quasars ( @xmath12 ) . recent 6 cm space vlbi polarization observations of the bl lacertae object 1803 + 784 ( gabuzda 1999 ) indicate that this is due to the fact that the observed core polarizations include a substantial contribution from newly emerging knots , as suggested by gabuzda et al . ( 1994b ) . previous observations have shown the distribution of core @xmath3 orientations at 6 cm to be bimodal , with @xmath3 either aligned with or transverse to the inner jet direction ; there is some evidence that @xmath13 is roughly perpendicular to the jet when the cores are quiescent , and aligns with the jet at epochs when emission from newly emerging shock components dominate the observed `` core '' polarization ( gabuzda et al . 1994b , gabuzda & cawthorne 1996 ) . to elucidate the nature of the characteristic vlbi total intensity ( @xmath0 ) and polarization ( @xmath1 ) structures observed for radio - bright bl lacertae objects , we are engaged in an ongoing project to obtain multi - epoch , multi - frequency vlbi @xmath0 and @xmath1 images for all sources in the complete sample of bl lacertae objects defined by khr and schmidt ( 1990 ) . these sources have 6 cm fluxes of at least 1 jy , radio spectral indices @xmath14 ( @xmath15 ) , rest frame equivalent widths of the strongest emission lines less than 5 , and optical counterparts on the palomar sky survey plates with brightness greater than 20@xmath16 . vlbi @xmath0 and @xmath1 images for most of the sample sources are presented by roberts , gabuzda & wardle ( 1987 ) ; gabuzda , roberts & wardle ( 1989b ) ; gabuzda et al . ( 1992 , 1994b ) ; and gabuzda , pushkarev & cawthorne ( 1999 ) . the ten sets of @xmath0 and @xmath1 images presented here complete our first - epoch images for the 34 sources in the original sample ( one , 1334127 , was subsequently reclassified as a quasar , so that the final number of sources in the complete bl lac sample is 33 ) . these are the first @xmath1 images for these ten sources , and in a number of cases , the first 6 cm @xmath0 images as well .

the results of vlbi total intensity ( ) and linear polarization ( ) observations at cm are presented for ten radio bright bl lacertae objects . these images complete first - epoch polarization observations for the 1-jy sample of northern bl lacertae objects defined by khr and schmidt . estimates of superluminal speeds are presented for several sources , bringing the total number of sources in the sample for which such estimates are available to 16 . second epoch observations currently being reduced should yield speed estimates for vlbi features in essentially all the sources in the sample .

the results of vlbi total intensity ( ) and linear polarization ( ) observations at cm are presented for ten radio bright bl lacertae objects . these images complete first - epoch polarization observations for the 1-jy sample of northern bl lacertae objects defined by khr and schmidt . estimates of superluminal speeds are presented for several sources , bringing the total number of sources in the sample for which such estimates are available to 16 . second epoch observations currently being reduced should yield speed estimates for vlbi features in essentially all the sources in the sample . the jet magnetic fields of these bl lacertae objects are usually transverse to the local jet direction , but a sizeable minority ( about 30% ) have vlbi jet components with longitudinal magnetic fields . this may suggest that the conditions in the vlbi jets of bl lacertae objects are favorable for the formation of relativistic shocks ; alternatively , it may be that the toroidal component of the intrinsic jet magnetic field is characteristically dominant in these sources . bl lacertae objects : general bl lacertae objects : individual : ( 0003066 , 0814 + 425 , 0820 + 225 , 0823 + 033 , 1334127 , 1732 + 389 , 2131021 , 2150 + 173 , 2155152 , 2254 + 074 polarization radio sources : galaxies

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this paper completes analysis of our first - epoch observations of all sources in the complete sample of bl lacertae objects defined by khr & schmidt ( 1990 ) . certain tendencies were present even in the earliest vlbi polarization observations of bl lac objects ; however , without systematic observations of a complete sample of objects , it was not possible to say whether these properties were relevant for radio - loud bl lac objects in general , or only to a handful of the best studied sources . on the whole , our analysis of the complete sample has confirmed the results of these early observations . however , it is also clear that the behaviour shown by the sample sources is not entirely uniform . we summarize our results below . the vlbi core polarizations of bl lacertae objects are appreciable , with values typically ranging from @xmath172 , and occasionally reaching values as high as @xmath173 . gabuzda et al . ( 1994b ) suggested that these relatively high values reflected the dominant contribution of newly emerging jet components . in the case of one source in the sample 1803 + 784 6 cm space vlbi polarization observations directly showed that the polarized flux was dominated by a compact component in the inner vlbi jet , which was unresolved from the core in ground - based observations ( gabuzda 1999 ) . the 6 cm vlbi core polarizations of quasars are much lower , typically @xmath12 ( cawthorne et al . 1993 ) . this suggests that either the cores of quasars are depolarized ( see , e.g. , taylor 1998 , 2000 ) , or that they are considerably less likely to be dominated by emission from compact new jet components . if the vlbi cores of quasars are depolarized , we expect that the observed degrees of polarization of the cores of quasars and bl lac objects will become more similar at higher frequencies ; thus far , there is no clear evidence for this , but more systematic studies are required . thus , it remains a possibility that the vlbi core polarizations of bl lac objects are more often dominated by the contribution of emerging jet components than are the vlbi core polarizations of quasars . the origin of this systematic difference is not obvious . one possibility is that the birth rate for new jet components is higher in bl lacertae objects than in quasars , increasing the probability of observing a bl lac object core harbouring new jet components . there is some evidence from the university of michigan monitoring database that outbursts in bl lacertae objects may be more frequent and well resolved than those in quasars , suggesting that bl lac objects may generate new components more frequently ( m. aller , private communication ) . since the superluminal speeds observed in bl lacertae objects are , on average , slower than those in quasars , it may be that the jet components of bl lacertae objects spend more time in the unresolved core region before becoming detectable as distinct jet knots . another possibility is that highly - polarized jet components close to the core are often long - lived stationary components whose polarization blends with the true core polarization . quasi - simultaneous multi - frequency vlba observations for all sources in the khr & schmidt sample currently being analyzed should help distinguish between these various possibilities . one of the striking tendencies noted in the earliest vlbi polarization results was for the jets of bl lacertae objects to have transverse magnetic fields . our first - epoch images for the complete khr & schmidt sample confirm that this is the predominant behaviour for the sample as a whole : among the 25 sources in which jet polarization was detected , some 6070% have transverse magnetic fields . at the same time , a sizeable minority of about 30% have longitudinal jet magnetic fields . thus far , transverse magnetic fields have usually been interpreted as manifestations of relativistic shocks in the vlbi jets of these sources , while longitudinal fields have been taken to reflect the presence of shear between the jet and the surrounding medium . in this picture , the common presence of transverse magnetic fields reflects the existence of conditions favorable for the formation of transverse shocks ; the jet components with dominant longitudinal fields would be those in which shocks did not form , or did form but were dominated by the effect of shear . though it seems likely that many individual , compact , highly - polarized features with transverse magnetic fields are associated with shocks , this does not necessarily imply that _ all _ the observed transverse jet fields should be identified with shock components . another possibility is that , in at least some cases , we are detecting the toroidal component of an intrinsic helical jet magnetic field ( see , e.g. , gabuzda 1999 ) . if the dominant magnetic field in the jet is helical , the net observed field can be either transverse or longitudinal , depending on the pitch angle of the field and the viewing angle , though it is more likely that the net observed field will be transverse . in addition , a longitudinal field component could develop due to interaction between the edges of the jet and the surrounding medium ( e.g. aaron 1998 , laing et al . 1999 , aloy et al . thus , it could be that the dominant magnetic - field component in the vlbi jets of bl lacertae objects is characteristically toroidal . this could be consistent with the fact that the observed jet magnetic fields are most often transverse , but occasionally longitudinal . the characteristically modest superluminal speeds observed in the khr & schmidt sources suggest that bl lacertae objects differ from quasars in either the characteristic angles of their jets to the line of sight , or the characteristic intrinsic velocities of components in their jets , or both . the observed apparent speed for a vlbi feature has a peak for motion at an angle to the line of sight of about @xmath174 , where @xmath175 is the lorentz factor of the motion . therefore , if the intrinsic velocities in the two types of sources were essentially the same , the bl lacertae objects could , in principle , have smaller apparent velocities if their jets were significantly further from or nearer to the line of sight than the jets in quasars . since bl lacertae objects are obviously highly beamed sources ( kollgaard 1994 , for example ) , it is not reasonable to suppose that their jets could typically be at significantly larger angles to the line of sight than those in quasars . on the other hand , if their jets were significantly _ closer _ to the line of sight than quasar jets , we would expect bl lacertae objects to be significantly more highly beamed than quasars , and there is no evidence for this ( ghisellini et al . thus , the most straightforward interpretation of the more modest superluminal speeds observed in the vlbi jets of bl lacertae objects compared to quasars is that the intrinsic velocities in the bl lac jets are lower . this seems quite natural in the context of unified schemes linking bl lacertae objects with fr i and quasars with fr ii radio galaxies .

the jet magnetic fields of these bl lacertae objects are usually transverse to the local jet direction , but a sizeable minority ( about 30% ) have vlbi jet components with longitudinal magnetic fields . this may suggest that the conditions in the vlbi jets of bl lacertae objects are favorable for the formation of relativistic shocks ; alternatively , it may be that the toroidal component of the intrinsic jet magnetic field is characteristically dominant in these sources .

the results of vlbi total intensity ( ) and linear polarization ( ) observations at cm are presented for ten radio bright bl lacertae objects . these images complete first - epoch polarization observations for the 1-jy sample of northern bl lacertae objects defined by khr and schmidt . estimates of superluminal speeds are presented for several sources , bringing the total number of sources in the sample for which such estimates are available to 16 . second epoch observations currently being reduced should yield speed estimates for vlbi features in essentially all the sources in the sample . the jet magnetic fields of these bl lacertae objects are usually transverse to the local jet direction , but a sizeable minority ( about 30% ) have vlbi jet components with longitudinal magnetic fields . this may suggest that the conditions in the vlbi jets of bl lacertae objects are favorable for the formation of relativistic shocks ; alternatively , it may be that the toroidal component of the intrinsic jet magnetic field is characteristically dominant in these sources . bl lacertae objects : general bl lacertae objects : individual : ( 0003066 , 0814 + 425 , 0820 + 225 , 0823 + 033 , 1334127 , 1732 + 389 , 2131021 , 2150 + 173 , 2155152 , 2254 + 074 polarization radio sources : galaxies

0805.3300

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flavor transformations caused by neutrino mixing depend on the matter background and on the neutrino fluxes themselves : neutrino - neutrino interactions provide a nonlinear term in the equations of motion @xcite that gives rise to collective flavor transformation phenomena . the neutrino density needs to be so large that a typical neutrino - neutrino interaction energy @xmath0 is comparable to the vacuum oscillation frequency @xmath1 . only recently has it been fully appreciated that this condition is sufficient even if a dense background of ordinary matter provides a much larger interaction energy so that naively neutrino - neutrino interactions would seem negligible . following this crucial insight , nonlinear oscillation phenomena in the supernova ( sn ) context have been studied over the past two years in a long series of papers . one striking effect is `` self - maintained coherence '' @xcite . different neutrino modes have different vacuum oscillation frequencies @xmath1 , but with strong neutrino - neutrino interactions they `` stick together '' and oscillate as a single mode characterized by the `` synchronized oscillation frequency '' @xmath2 . this can lead to all modes going through an msw resonance together , the `` collective msw - like transition '' or `` synchronized msw effect '' @xcite . more interesting still are collective phenomena driven by the decrease of the neutrino flux with distance from the source . the adiabatic transition from a dense to a dilute neutrino gas produces step - like spectral features where the spectrum sharply splits into parts of different flavor transformation , so - called `` step - wise spectral swapping '' or `` spectral splits '' . spectral splits can result from a preceding collective msw effect ( `` msw prepared spectral split '' ) or from neutrino - neutrino interactions alone . the latter case depends on an unusual form of non - equilibrium among neutrino flavors where one has an excess of flavor pairs , say @xmath3 , over the other flavors . for neutrinos streaming off a sn core one indeed expects a hierarchy of number fluxes @xmath4 . therefore , one can have collective transformations of the form @xmath5 , where @xmath6 stands for some suitable combination of @xmath0 and @xmath7 neutrinos . these `` collective pair transformations '' do not violate any conservation law and thus can be catalyzed even by a very small mixing angle . @xmath8 can completely swap with @xmath9 whereas the larger @xmath10 converts only to the extent allowed by flavor - lepton conservation , but in a step - like spectral form . both the complete conversion of @xmath8 and the split in the @xmath11 spectrum provide signatures for the inverted neutrino hierarchy even for an extremely small 13-mixing angle @xcite . for non - isotropic enviroments , multi - angle effects may play an important role . the term `` multi - angle effects '' actually refers to two different issues . one is that the weak interaction potential between two relativistic particles is proportional to ( @xmath12 ) , where @xmath13 is their relative angle of propagation . one usually considers an isotropic background of ordinary matter so that @xmath14 averages to zero . the same is true in an isotropic neutrino gas for the neutrino - neutrino term . the second issue is the `` multi - angle instability '' . neutrinos arriving from different points on the source belong to different angular modes , which may decohere kinematically in flavor space @xcite . this effect can be self - induced in the sense that a very small initial anisotropy is enough to trigger an exponential runaway , for example in a gas consisting of equal densities of neutrinos and antineutrinos @xcite . systems consisting of very few angular modes can show a two - stream or multi - stream instability @xcite . on the other hand , numerical studies show that systems consisting of many angular modes and with a sufficient neutrino - antineutrino asymmetry do not show a multi - angle instability but rather show self - maintained coherence among different angular modes @xcite . the sn neutrino flux parameters seem to be such that the multi - angle instability plays no role in practice . based on this assumption , most of the sn studies have used the `` single - angle approximation '' , where all angular modes are assumed to have the same behavior . multi - angle effects related to the ( @xmath12 ) structure of the neutrino - neutrino term are unavoidable for an extended source radiating neutrinos into space because the emitted neutrino flux can not form an isotropic gas . however , these effects also occur , and are easier to study theoretically , in a homogeneous system evolving in time that has a non - isotropic angular distribution of neutrinos . in practice , however , one usually deals with stationary systems where one asks for the spatial variation of a neutrino ensemble as a function of distance from the source . even if the neutrino - neutrino interaction were isotropic , we still would have geometric multi - angle effects because neutrinos reaching a certain point from an extended source have traveled on different trajectories . even the simple case of an infinite radiating plane is not trivial . here the direction perpendicular to the plane is the only direction in which the overall neutrino ensemble can show any spatial variation . even if all neutrinos have the same energy and thus oscillate with the same frequency along their trajectories , the projection on the direction perpendicular to the plane yields different effective oscillation frequencies and thus kinematical decoherence . neutrino - neutrino effects can synchronize different angular modes so that a sufficiently dense neutrino gas will not show this form of multi - angle decoherence . on the contrary , all angular modes will vary with the same oscillation length as a function of distance from the plane . a similar description applies to a spherical source where one asks for the variation of all angular modes along the radial direction . the single - angle treatment of sn neutrino oscillations amounts to the assumption of self - maintained coherence among angular modes , although it has never been explicitly expressed in this form . some authors assumed that all angular modes oscillate as the radial one @xcite . however , in this case the neutrino - neutrino interaction vanishes because of the ( @xmath12 ) factor , so it was necessary to assume a certain average of the neutrino - neutrino interaction strength . other authors represented all angular modes by a single angular mode radiated at @xmath15 relative to the radial direction and then used a neutrino - neutrino interaction strength consistent with this assumption @xcite . this implementation of the single - angle approximation has the advantage that one can use the same numerical code as for multi - angle simulations , simply restricting oneself to a single angular bin . in yet other cases the system was modeled as a homogeneous and isotropic gas that evolves in time , assuming a time variation of the neutrino density that mimics the radial variation in the spherical case . one of our goals is to show that the single - angle treatment can be formulated self - consistently . the assumption that all angular modes evolve the same in flavor space provides a unique concept of what is meant by `` single - angle behavior . '' this is straightforward in the systems described so far where symmetry dictates that the spatial variation is only along a certain direction , effectively reducing the problem to one dimension . we are really motivated , however , by more general geometries where no special direction is singled out by symmetry . in particular , we are interested in the case of coalescing neutron stars that may form the inner engines of short gamma - ray bursts @xcite . the accretion torus or disk formed during neutron star coalescence is a neutrino source comparable to a sn core . however , the torus is less dense and not efficient at producing @xmath16 and @xmath17 . therefore , the torus is a source for a dominant @xmath3 pair flux which is thought to produce an @xmath18 pair plasma , thus powering short gamma - ray bursts . the annihilation cross section for @xmath19 is much larger than that for @xmath20 , so the neutrino flavor composition strongly influences the number of @xmath21 pairs produced . therefore , one may ask if collective pair conversions occur in this environment close enough to the source to modify the energy transfer to the @xmath21 plasma , and hence affect the strength of the gamma ray burst . for coalescing neutron stars one expects a flux hierarchy @xmath22 , which differs from the sn case because the matter leptonizes when neutrons convert to protons , in contrast to the deleptonization of a sn core . the asymmetry between @xmath10 and @xmath8 could be enough to prevent multi - angle decoherence so that similar collective effects as in the sn environment are conceivable . however , even granting this assumption , it is not straightforward how to implement something like a single - angle approximation in this context because it is not obvious how one should picture self - maintained coherence . the purpose of our paper is to formulate the meaning of self - maintained coherence for general source geometries and study its implications . we find that the flavor variation reduces to a quasi one - dimensional problem along the streamlines of the total neutrino flux . the main difference between the general case and the radiating plane or sphere is that the streamlines are typically curved , at least close to the source , so that self - maintained coherence applies to flavor oscillations along these curved streamlines . we begin in sec . [ sec : eoms ] with the general equations of motion for the neutrino matrices in flavor space . in sec . [ sec : synchronized oscillations ] we formulate the collective equations for neutrinos only ( no antineutrinos ) and consider only synchronized oscillations . sec . [ sec : streamlines ] shows the existence of streamlines and gives a prescription for calculating the flavor evolution along them . in sec . [ sec : geometries ] we solve the problem for several geometries . in sec . [ sec : bipolar ] we study the generalization to a mixed system of neutrinos and antineutrinos where collective pair transformations are possible . in sec . [ sec : neutron stars ] we consider an explicit example for a disk source with parameters inspired by numerical simulations of coalescing neutron stars . we summarize our conclusions in sec . [ sec : conclusions ] .

the rich phenomenology of collective neutrino oscillations has been studied only in one - dimensional or spherically symmetric systems . motivated by the non - spherical example of coalescing neutron stars , presumably the central engines of short gamma - ray bursts , we use the liouville equation to formulate the problem for general source geometries . assuming the neutrino ensemble displays self - maintained coherence , the problem once more becomes effectively one - dimensional along the streamlines of the overall neutrino flux . this approach for the first time provides a formal definition of the `` single - angle approximation '' frequently used for supernova neutrinos and allows for a natural generalization to non - spherical geometries .

the rich phenomenology of collective neutrino oscillations has been studied only in one - dimensional or spherically symmetric systems . motivated by the non - spherical example of coalescing neutron stars , presumably the central engines of short gamma - ray bursts , we use the liouville equation to formulate the problem for general source geometries . assuming the neutrino ensemble displays self - maintained coherence , the problem once more becomes effectively one - dimensional along the streamlines of the overall neutrino flux . this approach for the first time provides a formal definition of the `` single - angle approximation '' frequently used for supernova neutrinos and allows for a natural generalization to non - spherical geometries . we study the explicit example of a disk - shaped source as a proxy for coalescing neutron stars .

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the vast majority of the @xmath52000 known white dwarfs ( mccook and sion 1998 ) are isolated stars discovered at optical wavelengths by virtue of their photometric colours or proper motions . in either case , there is a strong bias against detecting any white dwarfs in unresolved binary systems . a companion star of type k or earlier will completely dominate the optical spectrum of the white dwarf , effectively rendering it invisible . indeed , sirius b , the first white dwarf to be discovered , would never have been resolved from the a1 dwarf sirius were it not for the close proximity of the system to earth ( 2.64pc ) . prior to the rosat and extreme ultraviolet explorer ( euve ) surveys , a small number of unresolved white dwarf / main sequence binaries had been discovered serendiptously . for example , the white dwarf in the v471 tauri system was found as a result of an eclipse by its active k2v companion . in addition , a number of white dwarfs have been accidently discovered during various far - ultraviolet ( far - uv ) observations of the normal stellar companions by the international ultraviolet explorer ( iue ) , e.g. @xmath6 cap ( bhm - vitense 1980 ) , 56 peg ( schindler et al . 1982 ) and 4 @xmath7@xmath8 ori ( johnson and ake 1986 ) , although shipman and geczi ( 1989 ) systematically studied the then existing iue archive for white dwarf companions to g , k and m stars , and found no further examples . now , however , the extreme ultraviolet ( euv ) surveys of the rosat wide field camera ( wfc , pounds et al . 1993 , pye et al . 1995 ) and euve ( bowyer et al . 1994 , 1996 ) have provided evidence for the existence of a substantial sample of these previously unknown white dwarfs , through the detection of euv radiation . sixteen new systems have been discovered in this way , including @xmath3 crateris ( a2iv@xmath2wd , fleming et al . 1991 ) , kw aur c ( f4v@xmath2da , hodgkin et al . 1993 ) , hd18131 ( k0iv@xmath2da , vennes et al . 1995 ) , re j0357@xmath2283 ( k2v@xmath2da jeffries , burleigh and robb 1996 ) , and the latest two , re j0702@xmath2129 ( k0ve@xmath2da , vennes et al . 1997 ) , and hr2875 ( b5v@xmath2wd , vennes , berghoefer and christian 1997 , burleigh and barstow 1998 ) . detailed studies of groups of these objects have been undertaken by barstow et al . ( 1994 ) and burleigh , barstow and fleming ( 1997 , paper i ) . positive identifications have been made in each case through follow - up observations in the far - uv with iue , since for companions later than @xmath0a5 the hot white dwarf is easily visible at these wavelengths ( the companion to the b5v star hr2875 was identified through an euve spectrum , since the b star still dominates the spectrum at far - uv wavelengths ) . it is well established that over half of all stars are members of binary or multiple systems , yet the overwhelming majority of catalogued white dwarfs are isolated objects . the new population of optically hidden white dwarfs emerging from the euv surveys has profound implications , therefore , for our knowledge of the white dwarf luminosity function , space density and formation rate ( e.g. fleming , liebert and green 1986 ) . observations of white dwarfs in detached binary systems also allow us to place constraints on their evolutionary models ( e.g. de kool and ritter 1993 ) . in this paper we report the results of a continuing search for more of these binaries in the rosat wfc catalogue , during the final year of iue operations . we have discovered one new unresolved white dwarf@xmath2main sequence star binary ( re j0500@xmath1362 ) . in the cases where no white dwarf was detected , a number of the target stars show evidence for chromospheric activity . we also present an analysis of the previously known white dwarf@xmath2active star system hd27483 ( bhm - vitense 1993 ) . we show that the white dwarf is contributing to the euv flux and should be included in the growing list of euv - emitting optically - hidden hot white dwarfs in binary systems .

the rosat wide field camera ( wfc ) survey of the extreme ultraviolet ( euv ) has provided us with evidence for the existence of a previously unidentified sample of hot white dwarfs in unresolved , detached binary systems . these stars are invisible at optical wavelengths due to the close proximity of their much more luminous companions ( spectral type k or earlier ) . however , for companions of spectral typea5 or later the white dwarfs are easily visible at far - ultraviolet ( far - uv ) wavelengths , and can be identified in spectra taken by iue . we report the results of our continuing search during the final year of iue operations . some of these objects show evidence for chromospheric and coronal activity . finally , we present an analysis of the previously known wdactive f6v binary hd27483 ( bhm - vitense 1993 ) , and show that , at t,000k , the white dwarf may be contributing significantly to the observed euv flux .

the rosat wide field camera ( wfc ) survey of the extreme ultraviolet ( euv ) has provided us with evidence for the existence of a previously unidentified sample of hot white dwarfs in unresolved , detached binary systems . these stars are invisible at optical wavelengths due to the close proximity of their much more luminous companions ( spectral type k or earlier ) . however , for companions of spectral typea5 or later the white dwarfs are easily visible at far - ultraviolet ( far - uv ) wavelengths , and can be identified in spectra taken by iue . sixteen such systems have been discovered in this way through rosat , euve and iue observations , including four identified by us in paper i ( burleigh , barstow and fleming 1997 ) . in this paper we report the results of our continuing search during the final year of iue operations . one new system , re j0500 ( daf6/7v ) , has been identified . this star appears to lie at a distance of betweenpc , making it one of the most distant white dwarfs , if not the most distant , to be detected in the euv surveys . the very low line - of - sight neutral hydrogen volume density to this object could place a lower limit on the length of the cma interstellar tunnel of diffuse gas , which stretches away from the local bubble in a similar direction to re j0500 . in this paper we also analyse a number of the stars observed where no white dwarf companion was found . some of these objects show evidence for chromospheric and coronal activity . finally , we present an analysis of the previously known wdactive f6v binary hd27483 ( bhm - vitense 1993 ) , and show that , at t,000k , the white dwarf may be contributing significantly to the observed euv flux . if so , it is one of the coolest such stars to be detected in the euv surveys . -1_td-1 _ stars : binaries stars : white dwarfs x - ray : stars ultra - violet : stars ism : general .

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c

the field of this euv source ( see figure 1 ) was surveyed by mason et al . ( 1995 ) during the wfc optical identification programme . no evidence of activity was found in the cores of ca ii h & k in the spectrum of a @xmath013th magnitude star located at the centre of the source error box . various stars were also examined outside the error box , but none could plausibly account for the euv emission . the field was also examined on 1995 september 29/30 with the 2.3 m steward observatory telescope on kitt peak , as part of a programme to search for the optical counterparts to unidentified sources in the rosat wfc 2re catalogue . a spectrum ( figure 2 ) of the central star in the source error box was obtained with the boller and chivens spectrometer and 800@xmath121200 blue sensitive ccd . a 2.5 " slit and 600 lines / mm grating blazed at 3658 were used , and the data were reduced with standard iraf routines . again , there was no evidence for activity . one untested proposition was that this central object could be hiding a hot white dwarf companion . therefore , the star was added to our iue target list for observations during 1995/96 , and a faint , @xmath418th magnitude hot white dwarf companion was discovered ( figure 3 ) . by comparing the relative line strengths and widths of the primary s optical spectrum with spectra in the atlas of jacoby , hunter and christian ( 1984 ) , we conclude that it most closely resembles an f6/7v . it should be noted that the spectrum appears to be deficient in flux at the blue end , below @xmath04500 . as the star was observed at a relatively high air mass ( sec [email protected] ) , this deficiency in counts was probably caused by differential atmospheric dispersion . the spectral identification is strengthened when the iue lwp spectrum ( lwp31729 , figure 4 ) is compared to spectra in the iue spectral atlas ( wu et al . the data are very noisy , and have been binned up as a consequence , but most closely match stars in the range f5v@xmath1g0v . there also appears to be a slight excess of flux in the iue swp spectrum , at wavelengths @xmath51850 , above the level expected from the white dwarf ( figure 3 ) . if the excess is real , then it must attributable to the primary . as @xmath013th magnitude mid - late g and k stars are not bright enough to be detected by iue in this region of the spectrum , this also indicates that the companion is probably a late f. taking the guide star catalogue magnitude of [email protected] , the system lies between 755 ( f7v ) and 870 ( f6v ) parsecs away , although if we consider possible errors on the gsc magnitude ( @xmath230.3 mags ) , and that the absolute magnitudes may be in error by up to @xmath230.5 magnitudes , the system could be as close as 520 parsecs or as distant as 1250 parsecs . is this a true binary or a chance alignment ? given that the source of the euv radiation is almost certainly the hot white dwarf , we can calculate the probability of a random 13th magnitude star also falling within the iue aperture . according to allen ( 1973 ) , the number of stars per square degree at the galactic latitude of re j0500@xmath1364 , brighter than v@xmath913 , is 87.1 . the iue large aperture is a 10``@xmath1220 '' oval , hence we calculate a probability of @xmath41/250 of a chance alignment . ( note that the point spread function of the stellar image of the 13th magnitude star on the digitised sky survey plate is @xmath015 " in radius , see figure 1 ) . assuming this is indeed a true binary , then we believe re j0500@xmath1364 to be one of the most distant white dwarfs , if not the most distant , to be identified in the euv surveys ( for a comparison , see the distance estimates for the white dwarfs detected by the rosat pspc by fleming et al . 1996 , and those detected by euve by vennes et al . . a model fit to the iue spectrum at log [email protected] gives t@xmath938,260k and [email protected]@xmath15 , corresponding to a distance of 830 parsecs . a fit at log [email protected] corresponds to the minimum distance estimate to the system , but gives a higher mass , [email protected]@xmath15 and higher temperature , t@xmath945,000k ( and brings the star into the regime where its atmosphere may be contaminated by elements heavier then he ) . the inferred v magnitude from these models is 17.9 , making this one of the faintest white dwarfs to be detected by rosat . the faintest , re j0616@xmath1649 ( [email protected] ) , is a rare magnetic da ( jordan 1997 ) , but there are few other hot white dwarfs detected fainter than 17th magnitude . this source is not included in the rosat pspc all - sky survey bright source catalogue ( voges et al . 1996 ) , but it has been observed and detected in x - rays during a pointed observation by the rosat high resolution imager ( hri ) . the target was observed as part of programme to identify possible isolated neutron star candidates in the rosat surveys ( pi wang ) . using the point source search programme ( pss ) within the starlink asterix x - ray analysis package ( see pye et al . 1995 ) to analyse the hri image , the position of the x - ray source was found to be coincident with the wfc and euve detections ( figure 1 ) , and has a flux of [email protected] counts per 1000 sec@xmath24 . the source shows no evidence for time variability . although the hri has very limited spectral response ( the spectral properties of the hri are known to vary with detector position and time in an ill - defined manner ) , it is possible to obtain a crude hardness ratio . in this case , the hri data can then be used to test whether there is any hard x - ray emission from the f6/7v companion star , since no emission is expected from the white dwarf photosphere above 0.4 kev . figure 5 shows the hri data plotted as a function of pulse height distribution . the exact energy of each channel varies temporarily and spatially , but channels 1 to 5 are roughly equivalent to the soft ( [email protected] kev ) pspc band , and channels 6@xmath116 are equivalent to the hard ( [email protected] kev ) band . as with the pspc , a hardness ratio can be defined by ( hard@xmath1soft)/(hard@xmath2soft ) . in this case , the hardness ratio @[email protected] confirming , as can be readily seen in figure 5 , that this is a very soft source . we conclude that all of the euv and soft x - ray emission originates from the hot white dwarf . unfortunately , there is no reliable detector matrix for the hri , and it did not prove possible to use the x - ray count rate in the subsequent analysis . therefore , since this left only the two rosat wfc data points to try to constrain the interstellar hydrogen column density and white dwarf atmospheric parameters , we assumed that the white dwarf photosphere was essentially pure hydrogen ( a reasonable assumption for t@xmath1040,000k , and for many hot das t@xmath1050,000k ) , and allowed only the neutral hydrogen column density to vary in the subsequent fitting of the euv data . we found that the wfc s2 photometric data point is well matched by a model fit at log [email protected] , although the s1 flux was predicted to be slightly lower than observed . the hydrogen column density given by this model is n@[email protected]@xmath1210@xmath26 atoms @xmath27 . at 830 parsecs distance , this translates into a neutral hydrogen line - of - sight volume density of only 0.0029 atoms @xmath28 , well below the average local volume density within @xmath080pc of the sun of 0.05 atoms @xmath28 ( warwick et al . if the system is closer ( 530 parsecs ) and the log [email protected] model is applied , then the h column density is higher ( n@[email protected]@xmath1210@xmath13 atoms @xmath27 ) and the line - of - sight volume density is also higher at 0.0146 atoms @xmath28 . again , though , this is well below the average local volume density . notably , this system ( galactic co - ordinates [email protected]@xmath29 , b@[email protected]@xmath29 ) lies in a similar direction to the known exceptionally low column densities towards the b1 giant @xmath3 cma ( l@xmath9226@xmath29 , b@xmath9@xmath114@xmath29 , welsh 1991 ) , and in particular to two other rosat - discovered hot white dwarfs , re j0457@xmath1281 and re j0503@xmath1289 ( [email protected]@xmath29 , b@[email protected]@xmath29 , barstow et al . 1993 ) . at @xmath4200pc distance , @xmath3 cma is known to exist in a rareified `` interstellar tunnel '' of very low neutral gas density , which is itself an extension of the region surrounding the sun called the local bubble ( welsh 1991 ) . the features of the bubble were first mapped out by frisch and york ( 1983 ) , and welsh ( 1991 ) speculates that the @xmath3 cma tunnel may extend for _ at least _ 300pc in that direction away from the sun . welsh ( 1991 ) also estimates the tunnel to be about 50pc in diameter ; the white dwarfs re j0457@xmath1281 and re j0503@xmath1289 ( which are much closer at @xmath490pc ) may then possibly exist in a southward extension of this tunnel , or more likely lie in the foreground , within the local bubble itself . table 8 details the known column densities and volume densities to these three stars , and also to @xmath30 cma ( b2 ii , [email protected]@xmath29 , b@[email protected]@xmath29 ) , the brightest euv source in the sky ( cassinelli et al . 1995 ) , which lies in a similar direction . the line - of - sight neutral hydrogen volume density we measure for re0500@xmath1364 compares favourably with the average volume density to these four stars ( 0.0030 atoms @xmath28 ) . this suggets that re j0500@xmath1364 might also lie within the @xmath3 cma extension of the local bubble . if re j0500@xmath1364 really does lie as far as @xmath0500 or more parsecs away , then it presents a possible lower limit to the size of any neutral gas - free corridor stretching away from the local bubble in that direction . the region is bounded on three sides by several ob associations : the orion nebula ( 450pc away ) , the cma ob1 association ( 800pc distant ) , and the gum nebula ( 290pc away ) . welsh ( 1991 ) hypothesises that this tunnel may have been evacuated by a number of supernova explosions in the last few @xmath1210@xmath31 years . the injection of driven , heated , rarefied gas into an older ( @xmath010@xmath32 years old ) low density cavity in the local interstellar medium would produce the large region of very low density neutral gas that we now see . the hyades system hd27483 consists of two active f6v stars orbiting each other with a period of 3.05 days . although an euv source was detected originating from the direction of this system in the rosat wfc all sky survey in 1990 , the hot white dwarf component was identified independently and serendipitously by bhm - vitense ( 1993 ) during an iue swp observation as part of a survey of hyades f stars ( bhm - vitense 1995 ) . bhm - vitense ( 1993 ) derived atmospheric parameters for the white dwarf of 23000@xmath231000k and [email protected]@xmath15 . however , in the analysis of the white dwarf spectrum the author utilised the unblanketed models of wesemael et al . ( 1980 ) , assuming log [email protected] , to fit the far - uv spectrum at just two points . since the white dwarf might be hot enough to be contributing to the observed euv flux , it could be argued that the system should be included on the list of euv - detected hidden white dwarfs , and thus we have decided to re - analyse the far - uv and rosat data here , in the same manner as the other recently discovered systems . the rosat wfc source re j0420@xmath2138 , associated with hd27483 , was listed in the original bright source catalogue ( pounds et al . 1993 ) , with a count rate of [email protected] counts ksec@xmath24 ( it was not detected in s2 ) , but was not subsequently detected in the reprocessed 2re survey ( pye et al . the significance of the s1 detection in the 2re survey was 4.2 ; sources had to exceed a significance of 5.5 in a combination of both bands to be included in the catalogue . even so , at t@xmath423,000k the white dwarf may be contributing to this small euv flux , despite the fact that the two f star companions are known to be active themselves . there is significant contamination in the iue swp spectrum ( see figure 6 ) at the long wavelength end from the two f6v star companions , but this falls to zero by 1600 . therefore , we were able to use the continuum flux up to this point . bhm - vitense estimated a distance of 47.6 parsecs to this system . we can further constrain this figure with the recently published _ hipparcos _ parallaxes ( esa 1997 ) , where the measured value for hd27483 is [email protected] , corresponding to a distance of [email protected]@[email protected] parsecs . the spectral model which best matches this distance has log [email protected] and t@xmath922,000 , and the corresponding stellar mass is [email protected]@xmath15 . the white dwarf age is then 1.4@xmath1210@xmath34 years , in comparison with the age of the hyades cluster , @xmath07@xmath1210@xmath34 years ( bhm - vitense 1993 ) . given that the white dwarf might have a higher mass than is the average for these stars ( @xmath40.6m@xmath15 , marsh et al . 1997 ) , we can estimate its progenitor mass and place a possible lower limit on the maximum mass for white dwarf progenitor stars in the hyades cluster . from wood ( 1992 ) : @xmath35@xmath9aexp(b@xmath12@xmath36 ) where [email protected]@xmath15 and [email protected]@xmath15@xmath24 . we find , for @[email protected]@xmath15 , @[email protected]@xmath15 . the main sequence lifetime of a 6.7m@xmath15 star is in fact significantly shorter than 560 million years ( the difference between the hyades age and the white dwarf cooling age , e.g. schaller et al . 1992 ) . this suggests that the white dwarf is , in reality , probably lower in mass than 0.94m@xmath15 . however , in order to unambiguously and tightly constrain the fundamental parameters of this star , we will need to obtain a spectrum of the h lyman series with an instrument such as the forthcoming _ fuse _ mission ( see also section 6 ) . the wfc source is coincident with a rosat pspc x - ray source , with a total count rate of [email protected] counts ksec@xmath24 , including a detection in the upper band . this confirms that at least one of the two f6v companion stars is active , as the hard x - rays could not have originated from the white dwarf . the rosat data points can not be matched with any of the white dwarf models ( which assume a homogeneous atmospheric mixture of h and he ) . this implies that the active star(s ) must be providing a significant fraction of the euv flux , since little or no heavy element contamination is expected in the white dwarf photosphere in this cool temperature regime . it is even possible that there is no flux at all from the white dwarf at these wavelengths . the contribution of the white dwarf to the s1 count rate can , however , be estimated . another hot wd@xmath2ms binary , v471 tauri , is detected by rosat in the hyades cluster ( barstow et al . 1992 ) . after subtracting the contribution from the active k2v companion , marsh et al . ( 1997 ) use the wfc count rates to estimate the h column density to this system ( 8.52@xmath1210@xmath26 atoms @xmath27 ) . adopting the same column density to hd27483 , assuming a pure h atmosphere , and using the parameters derived from the log [email protected] model , the white dwarf is predicted to contribute 5.4 counts ksec@xmath24 to the s1 flux ( i.e. @xmath41/3 of the 15 counts ksec@xmath24 detected ) . how is this count rate affected by uncertainties in the h column density ? in fact , from euve spectra , dupuis et al . ( 1997 ) derived a much lower h column density to v471 tauri of 1.5@xmath1210@xmath26 . using this value , in the log [email protected] model , the white dwarf contributes 7.6 counts ksec@xmath24 to the s1 flux ( i.e. @xmath41/2 of the observed flux ) . this hot degenerate companion to hd27483 could itself , then , be regarded as a real euv source . at t@xmath422,000k , this would make it one of the coolest white dwarfs to be detected in the euv surveys . the combined x - ray luminosity of the two f6v stars in the hd27483 system can also be estimated , by subtracting the contribution of the white dwarf to the rosat pspc lower band flux . the pspc count rates are 98@xmath2314 counts ksec@xmath24 in the softer [email protected] band , and 33@xmath239 counts ksec@xmath24 in the harder [email protected] band ( voges et al . 1996 ) . in the log [email protected] model , assuming a column density of 8.52@xmath1210@xmath26 atoms @xmath27 , the white dwarf flux in the [email protected] band is found to be 36.0 counts ksec@xmath24 . eliminating this from the total pspc lower band rate and following the method detailed by fleming et al . ( 1995 ) , we find l@[email protected]@xmath1210@xmath37 ergs sec@xmath24 , and l@xmath21/l@[email protected]@xmath1210@xmath38 . this unclassified star was only observed by the swp camera ( swp56333 ) , and there was no flux visible above the background . if bd@xmath249@xmath29646 is a g or k star , then we probably would not detect it in this waveband anyway . no emission features are visible in the uv spectrum , but the euv source is coincident with a rosat pspc hard x - ray source , and the possibility must remain that bd@xmath249@xmath29646 is coronally active . alternatively , the euv / x - ray source might be another object in the field , or it is possible that the target was missed altogether in the iue observation . as with the wd@xmath2ms binary re j0500@xmath1364 ( discussed above ) , the field of this wfc source was originally observed in 1995 with the 2.3 m steward observatory telescope at kitt peak , as part of a programme to try to identify the remaining optical counterparts to unknown euv sources in the rosat wfc catalogues . in the absence of any plausible euv source , the 15th magnitude g - type central star in the error box may be hiding a hot white dwarf companion . the far - uv spectra obtained with iue ( swp56272 and lwp31800 ) were very noisy and showed no evidence for a hot white dwarf . there was some flux above the background longwards of @xmath02700 in the lwp spectrum , which may have been due to a g star , but it is possible that the target was missed altogether , and this flux was due to scattered solar light which effects the lwp camera sporadically . at [email protected] this star is unlikely to be the source of the euv flux : a 15th magnitude main sequence mid - g star would require l@xmath19/l@[email protected] to produce the count rate seen in the wfc s2 filter ( 45 counts ksec@xmath24 ) , far in excess of the saturation level for coronal emission ( l@xmath19/l@xmath20@xmath010@xmath39 , mathioudakis et al . 1995 ) . prior to the publication of the 2re catalogue ( pye et al . 1995 ) , the 9th magnitude f6v star sao150508 was not thought to be active , although there are no published optical observations which might offer evidence one way or another . the iue spectra ( swp 56195 and lwp31700 , figure 7 ) show no evidence for a hot white dwarf companion . sao150508 is , however , coincident with a rosat pspc x - ray source . therefore , estimates of the x - ray and euv luminosities , assuming sao150508 is active and the true source of the euv and x - ray flux , are presented in table 7 . there is no evidence in the literature that the 8th magnitude g2v star hd36869 is active . the iue spectra ( swp56169 and lwp 31701 , figure 8) also show no evidence for activity , although the star is coincident with a rosat pspc source . given that 8th magnitude stars are comparatively rare , it is still possible that hd36869 is coronally active , and thus we provide estimates of the x - ray and euv luminosities in table 7 . gl216b ( k2v ) is part of a nearby ( @xmath48 parsecs ) triple system , and was chosen as a candidate white dwarf binary on the basis of the s2/s1 count rate ratio . the iue spectra ( swp56194 & lwp31699 , figure 9 ) show no evidence for a hot white dwarf . however , mg ii 2798 is visible in emission ( with a line flux of [email protected]@xmath1210@xmath40 ergs @xmath27 s@xmath24 above the continuum ) . the emission feature in the swp spectrum at @xmath01720 is probably spurious , since it does not coincide with any commonly seen line . from observations made in the optical , de strobel et al . ( 1989 ) concluded that this is a young , active star . if it is the only source of the euv flux , then we determine l@xmath19/l@[email protected]@xmath1210@xmath41 . active stars have a characteristic euv to mg ii flux ratio . for example , jewell ( 1993 ) shows that the [email protected] kev euv flux is 1@xmath110 @xmath12 the mgii flux . for gl216b , though , the euv to mg ii flux ratio is only @xmath40.8 . schmitt et al . ( 1990 ) observed the entire gl216 system in an einstein hri pointing , and found that the nearby f7v star gl216a was 8 times brighter in x - rays than gl216b . thus hodgkin and pye ( 1994 ) concluded that all of the euv radiation in fact comes from gl216a . however , we only targeted gl216b with iue since this is the object associated with the euv source in the 2re catalogue , and at the time of the observation we were unaware of hodgkin and pye s conclusion . the low euv to mg ii flux ratio for gl216b does , though , support these earlier conclusions that the major source of the euv radiation is actually gl216a . estimates of the x - ray and euv luminosities are given in table 7 assuming a ) all the flux comes from gl216a and b ) all the flux comes from gl216b . this g5v star was not known to be active prior to the rosat survey , but subsequently it has been studied in detail by jeffries and jewell ( 1993 ) and is almost certainly the euv source . it is also an x - ray source , and measurements of the x - ray and euv luminosities are given in table 7 . no obvious emission features are visible in the iue lwp and swp spectra ( figure 10 ) ; the feature longwards of 1800 in the swp spectrum is probably spurious , as there is no commonly seen line at this wavelength . there are no references in the literature to this being an active star . however , mg ii is clearly seen in emission at 2800 in the iue lwp spectrum ( figure 11 ) , and there is a suggestion of civ in emission at 1550 in the short wavelength region . measurements of the x - ray and euv luminosities are given in table 7 using the g0 classification given by simbad , and assuming the star is on the main sequence . the euv to mg ii flux ratio ( @xmath48.0 ) strongly suggests that this star is active and the true source of the euv radiation . note that the ratios l@xmath19/l@xmath20 and l@xmath42/l@xmath20 are significantly larger than for any of the other stars in this sample , approaching the saturated level for coronal emission ( @xmath010@xmath39 ) . this suggests that the star may be rapidly rotating . no references are given in the literature to this being an active star . there is clearly no white dwarf visible in the iue swp spectrum ( figure 12 ) , and the emission line at @xmath01800 is probably spurious , perhaps due to a cosmic ray hit . the euv source is not coincident with an x - ray source . the star needs to be examined optically to search for any evidence of chromospheric activity . again , this star was not known to be active prior to the rosat survey . the iue lwp spectrum ( figure 13 ) reveals mg ii in emission at 2800 . measurements of the euv and x - ray luminosities ( this star is also a pspc source ) are given in table 7 , assuming the k0 spectral type given by simbad , and that the star is on the main sequence . the euv to mg ii flux ratio ( @xmath48.25 ) strongly suggests that this star is active and the true source of the euv radiation . with s1 and s2 count rates of 52@xmath237 and 83@xmath239 counts ksec@xmath24 , this is a relatively bright euv source in comparison with most of the targets in this paper . the soft x - ray and euv photometric colours are also characteristic of a hot white dwarf , and it is not detected in the pspc hard band . therefore , it was selected as a potential hidden white dwarf binary . the [email protected] star in the centre of the field , hd70907 ( f3iv / v ) , was observed in both the iue swp and lwp cameras ( figure 14 ) . there is no evidence for a white dwarf companion or emission features indicative of an active star . a nearby v@xmath411 star was also observed and again there was no evidence for a white dwarf , although , in the absence of any flux in the lwp camera that could be attributed to a stellar source , it seems possible that the star was not in the lwp slit . mason et al . ( 1995 ) report that this fainter object is indeed active , although they give no indication of the size of any emission features seen in the optical . they also do not give a spectral type for this star , and thus we have not been able to determine the euv and x - ray luminosities . whether this star is active enough to be the true euv source remains unclear , and the suspicion remains that there is indeed an unresolved hot white dwarf hiding in this field . it is highly unusual to detect an a star in euv or x - ray surveys ( fleming et al . observations by the einstein and exosat observatories failed to find any convincing detections other than the nearby quadruple a star system castor ( pallavicini et al . therefore hr4646 , an am star coincident with rosat wfc 2re and pspc sources , was selected as a potential hidden white dwarf binary . it should be noted that am stars do not possess significant magnetic fields and they are slow rotators , but they almost always appear to lie in close binary systems ( abt 1961 ) , and indeed margoni , munari and stagni ( 1992 ) found that hr4646 is a spectroscopic binary with a period of 1.27 days . the iue swp spectrum ( figure 15 ) shows no evidence for a hot white dwarf companion . it is extremely likely , therefore , that hr4646 has a coronally active cooler companion ( f5 or later ) .

this star appears to lie at a distance of betweenpc , making it one of the most distant white dwarfs , if not the most distant , to be detected in the euv surveys . if so , it is one of the coolest such stars to be detected in the euv surveys .

the rosat wide field camera ( wfc ) survey of the extreme ultraviolet ( euv ) has provided us with evidence for the existence of a previously unidentified sample of hot white dwarfs in unresolved , detached binary systems . these stars are invisible at optical wavelengths due to the close proximity of their much more luminous companions ( spectral type k or earlier ) . however , for companions of spectral typea5 or later the white dwarfs are easily visible at far - ultraviolet ( far - uv ) wavelengths , and can be identified in spectra taken by iue . sixteen such systems have been discovered in this way through rosat , euve and iue observations , including four identified by us in paper i ( burleigh , barstow and fleming 1997 ) . in this paper we report the results of our continuing search during the final year of iue operations . one new system , re j0500 ( daf6/7v ) , has been identified . this star appears to lie at a distance of betweenpc , making it one of the most distant white dwarfs , if not the most distant , to be detected in the euv surveys . the very low line - of - sight neutral hydrogen volume density to this object could place a lower limit on the length of the cma interstellar tunnel of diffuse gas , which stretches away from the local bubble in a similar direction to re j0500 . in this paper we also analyse a number of the stars observed where no white dwarf companion was found . some of these objects show evidence for chromospheric and coronal activity . finally , we present an analysis of the previously known wdactive f6v binary hd27483 ( bhm - vitense 1993 ) , and show that , at t,000k , the white dwarf may be contributing significantly to the observed euv flux . if so , it is one of the coolest such stars to be detected in the euv surveys . -1_td-1 _ stars : binaries stars : white dwarfs x - ray : stars ultra - violet : stars ism : general .