a superconvergent ldg hybridizable galerkin method for second order elliptic problems we identify and study an ldg hybridizable galerkin method which is not an ldg method for second order elliptic problems in several space dimensions with remarkable convergence properties unlike all other known discontinuous galerkin methods using polynomials of degree k 0 for both the potential as well as the flux the order of convergence in l 2 of both unknowns is k 1 moreover both the approximate potential as well as its numerical trace superconverge in l 2 like norms to suitably chosen projections of the potential with order k 2 this allows the application of element by element postprocessing of the approximate solution which provides an approximation of the potential converging with order k 2 in l 2 the method can be thought to be in between the hybridized version of the raviart thomas and that of the brezzi douglas marini mixed methods

estimates of effective frequency selectivity based on the detection of a tone added to complex maskers in experiment 1 the validity of parameters associated with the roex p r auditory filter shape was examined for three different types of maskers a a noise masker b a random 12 tone masker whose frequencies varied on a burst by burst basis multiple burst different mbd and c a random 12 tone masker whose frequencies were the same across bursts multiple burst same mbs first the power spectrum model of masking was used to estimate auditory filter shapes for four observers second the resulting auditory filter shapes were used in a computer simulation that provided an estimate of internal noise for each observer third relative weights across frequency were estimated for each observer and each masker type for the noise masker these analyses provided predictions and relative weights that were consistent across the three analyses for the mbd and mbs maskers there was little consistency neither the estimated internal noise nor the estimated relative weights reliably supported a single f

rate of quantum ergodicity in euclidean billiards for a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit in this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the wigner function in the case of ergodic systems of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value this is studied numerically for three euclidean billiards stadium cosine and cardioid billiard using up to 6000 eigenfunctions we find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing ball modes or scarred eigenfunctions we give a detailed discussion and explanation of these effects using a simple but powerful model for the rate of quantum ergodicity in momentum space we observe a slower decay we also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a gaussian distribution

the decision process in forward masked intensity discrimination evidence from molecular analyses in a two interval forced choice intensity discrimination task presenting a fixed increment the level of the forward masker in interval 1 and interval 2 was sampled independently from the same normal distribution on each trial mean and standard deviation of the distribution were varied correlational analyses of the trial by trial data revealed different decision strategies depending on the relation between mean masker level and standard level if the two levels were identical listeners tended to select the interval containing the higher level masker behaving like an energy detector at the output of a temporal window of integration for mean masker level higher than the standard level most listeners showed a negative correlation between the masker level in a given interval and the probability of selecting this interval indicating a strategy of comparing the masker loudness and the target loudness in each of the two observation intervals and voting for the interval where the loudness difference was s

frequency and intensity difference limens for harmonics within complex tones a two interval two alternative forced choice task was used to estimate frequency difference limens dls for individual harmonics within complex tones and dls for the periodicity i e number of periods per s of the whole complexes for complex tones with equal amplitude harmonics the dls for the lowest harmonics were small less than one percent the dls increased rather abruptly around the fifth to seventh harmonic the highest harmonic in each complex was also well discriminated and the discriminability of a single high harmonic was markedly improved by increasing its level relative to the other components the dl for a complex tone was generally smaller than the frequency dl of its most discriminable component the dl for a complex was found to be predictable from the dls of the harmonics comprising the complex using a formula derived by goldstein j acoust soc am 54 1496 1516 1973 from his optimum processor theory for the formation of the pitch of complex tones the dl for a complex i

enhancement of temporal cues to pitch in cochlear implants effects on pitch ranking the abilities to hear changes in pitch for sung vowels and understand speech using an experimental sound coding strategy etone that enhanced coding of temporal fundamental frequency f0 information were tested in six cochlear implant users and compared with performance using their clinical ace strategy in addition rate and modulation rate pitch difference limens dls were measured using synthetic stimuli with f0s below 300 hz to determine psychophysical abilities of each subject and to provide experience in attending to rate cues for the judgment of pitch sung vowel pitch ranking tests for stimuli separated by three semitones presented across an f0 range of one octave 139 277 hz showed a significant benefit for the experimental strategy compared to ace average d prime d values for etone d 1 05 were approximately three time larger than for ace d 0 35 similar scores for both strategies in the speech recognition tests showed that coding of segmental speech information by the exper

high order discontinuous element based schemes for the inviscid shallow water equations spectral multidomain penalty and discontinuous galerkin methods two commonly used types of high order accuracyelement based schemes collocationbased spectral multidomain penalty methods smpm and nodal discontinuous galerkin methods dgm are compared in the framework of the inviscid shallow water equations differences and similarities in formulation are identified with the primary difference being the dissipative term in the rusanov form of the numerical flux for the dgm that provides additional numerical stability however it should be emphasized that to arrive at this equivalence between smpm and dgm requires making specific choices in the construction of both methods these choices are addressed in general both methods offer a multitude of choices in the penalty terms used to introduce boundary conditions and stabilize the numerical solution the resulting specialized class of smpm and dgm are then applied to a suite of six commonly considered geophysical flow test cases three linear and three non linear we also include results for a classical continuous galerkin i e spectral element method for comparison both the analysis and numerical experiments show that the smpm and dgm are essentially identical both methods can be shown to be equivalent for very special choices of quadrature rules and riemann solvers in the dgm along with special choices in the type of penalty term in the smpm although we only focus our studies on the inviscid shallow water equations the results presented should be applicable to other systems of nonlinear hyperbolic equations such as the compressible euler equations and extendable to the compressible and incompressible navier stokes equations where viscous terms are included

imex hdg dg a coupled implicit hybridized discontinuous galerkin and explicit discontinuous galerkin approach for shallow water systems abstract we propose imex hdg dg schemes for planar and spherical shallow water systems of interest is subcritical flow where the speed of the gravity wave is faster than that of nonlinear advection in order to simulate these flows efficiently we split the governing system into a stiff part describing the gravity wave and a non stiff part associated with nonlinear advection the former is discretized implicitly with the hdg method while an explicit runge kutta dg discretization is employed for the latter the proposed imex hdg dg framework 1 facilitates high order solutions both in time and space 2 avoids overly small time step sizes 3 requires only one linear system solve per time stage 4 relative to dg generates smaller and sparser linear systems while promoting further parallelism and 5 suppresses the fast modes in the system with a large time step size numerical results for various test cases demonstrate that our methods are beneficial for applications where non stiff terms are accurately treated while stiff terms are less accurately handled

separating the regular and irregular energy levels and their statistics in a hamiltonian system with mixed classical dynamics we look at the high lying eigenstates from the 10001 to the 13000 in the robnik billiard defined as a quadratic conformal map of the unit disk with the shape parameter lambda 0 15 all the 3000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which in comparison with the classical phase space enabled a clear cut classification of energy levels into regular and irregular this is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties we calculate the fractional measure of regular levels as rho 1 0 365 or 0 01 which is in remarkable agreement with the classical estimate rho 1 0 360 or 0 001 this finding confirms the percival s 1973 classification scheme the assumption in berry robnik 1984 theory and the rigorous result by lazutkin 1981 1991 the regular levels obey the poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally brody like statistics with beta 0 286 or 0 001 this is due to the strong localization of irregular eigenstates in the classically chaotic regions therefore in the entire spectrum we see that the berry robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the berry robnik brody distribution

models of auditory masking a molecular psychophysical approach gilkey et al j acoust soc am 78 1207 1219 1985 measured hit proportions and false alarm proportions for detecting a 500 hz tone at each of four starting phase angles in each of 25 reproducible noise samples in the present paper their results are modeled by fitting the general form of the electrical analog model of jeffress j acoust soc am 48 480 488 1967 to the diotic data the best fitting configurations of this model do not correspond to energy detectors or to envelope detectors a detector composed of a 50 hz wide single tuned filter followed by a half wave rectifier and an integrator with an integration time of 100 to 200 ms fits the data of all four subjects relatively well linear combinations of the outputs of several detectors that differ in center frequency or integration window provide even better fits to the data these linear combinations assign negative weights to some frequencies or to some time intervals suggesting that a subject s decision is based on a comparison of

distribution and fluctuation properties of transition probabilities in a system between integrability and chaos the authors study the statistical properties of transition probabilities or generalized intensities equal to the squared matrix elements of operators having a classical limit they first generalize the shnirelman theorem to include semiclassically integrable states and use this to generalize the feingold peres formula for the average value of generalized intensities they perform an unfolding procedure to separate the smooth mean part of the intensities as a function of frequency from its fluctuating part by applying the generalized feingold peres formula this formula relates the mean value of squared matrix elements to the power spectrum of the given observable over classical trajectories their approach is illustrated numerically by analysing the dipole transition probabilities in a family of billiards between integrability and chaos the average values of the intensities as a function of frequency are excellently described by the generalized feingold peres formula

dyson s coulomb gas on a circle and intermediate eigenvalue statistics dyson s two dimensional coulomb gas on the unit circle with inverse temperature beta is investigated with the help of a metropolis algorithm theoretical predictions for energy and specific heat are verified the connection with the theory of ensembles of random unitary matrices with orthogonal unitary or symplectic symmetry corresponding to beta 1 2 4 is investigated in detail new approximation formulae for the spacing distribution and the so called delta statistics are proposed and found to be useful not only in the three cases mentioned but also for all beta between 0 and 4

classical dynamics of a family of billiards with analytic boundaries the classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated the author gives the stability analysis of major periodic orbits present the poincare maps demonstrate the mixing properties by following the evolution of a small element in phase space show the existence of homoclinic points and calculate the lyapunov exponent and the kolmogorov entropy h it turns out that the system becomes strongly chaotic positive h for sufficiently large deformations of the unit disc the system shows a generic stochastic transition the computations suggest that the system is mixing if the boundary is not convex

tangent map for classical billiards in magnetic fields a charged particle is moving inside a planar billiard embedded in a uniform constant magnetic field which is directed perpendicular to the plane the stability of classical trajectories is studied by the area preserving tangent map which is derived for any billiard shape having a smooth convex boundary as an example two generic billiards are considered here namely the ellipse and the stadium classical trajectories of which are well known to be regular or chaotic respectively for an uncharged particle lyapunov exponents and poincare sections are studied as a function of the field strength and of the billiard deformation regular motion is restored by increasing the magnetic field and or the deformation

adaptive discontinuous evolution galerkin method for dry atmospheric flow we present a new adaptive genuinely multidimensional method within the framework of the discontinuous galerkin method the discontinuous evolution galerkin deg method couples a discontinuous galerkin formulation with approximate evolution operators the latter are constructed using the bicharacteristics of multidimensional hyperbolic systems such that all of the infinitely many directions of wave propagation are considered explicitly in order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection time integration is realized by the imex type approximation using the semi implicit second order backward differentiation formula bdf2 moreover in order to approximate efficiently small scale phenomena adaptive mesh refinement using the space filling curves via the amatos function library is employed four standard meteorological test cases are used to validate the new discontinuous evolution galerkin method for dry atmospheric convection comparisons with the rusanov flux a standard one dimensional approximate riemann solver used for the flux integration demonstrate better stability and accuracy as well as the reliability of the new multidimensional deg method

dominance region for pitch effects of duration and dichotic presentation the dominance region dr for pitch was determined for 16 and 200 ms complex tones containing the first seven harmonics of a fundamental frequency f0 of 250 hz a tone was presented with one of the harmonics mistuned upwards or downwards by 3 followed 500 ms later by a perfectly harmonic tone of the same duration listeners adjusted the f0 of the harmonic tone so that its pitch matched that of the mistuned complex in experiment 1 stimuli were presented monaurally the dr was significantly higher in harmonic number for the short than for the long duration the overall sum of the pitch shifts produced by all harmonics was significantly larger for the short than for the long duration presumably due to stronger perceptual fusion for the former in experiment 2 the mistuned harmonic was presented only contralaterally to the remainder of the complex a similar shift in the dr with duration was observed although the pitch shifts were smaller than for monaural presentation there was no significant effect of duration on the overall pitch shifts the results are discussed in terms of pattern recognition and autocorrelation models of pitch perception and a role of attention in pitch matching is suggested

different auditory filter bandwidth estimates based on profile analysis notched noise and hybrid tasks auditory filter bandwidths were estimated in three experiments the first experiment was a profile analysis experiment the stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 hz the standard stimulus was the sum of equal amplitude tones and the signal stimulus had a power spectrum that varied up down up down the number of components ranged from four to 60 interval by interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal the second experiment was a notched noise experiment in which the 1000 hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 hz detection thresholds were estimated both in the presence of and in the absence of level randomization in the third hybrid experiment a 1000 hz tone was to be detected and the masker was composed of equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz for this experiment thr

the bakerian lecture 1987 quantum chaology bounded or driven classical systems often exhibit chaos exponential instability that persists but their quantum counterparts do not nevertheless there are new regimes of quantum behaviour that emerge in the semiclassical limit and depend on whether the classical orbits are regular or chaotic and this motivates the following definition definition quantum chaology is the study of semiclassical but nonclassical behaviour characteristic of systems whose classical motion exhibits chaos this is illustrated by the statistics of energy levels on scales comparable with the mean level spacing of order h n for n freedoms these fall into universality classes for classically chaotic systems the statistics are those of random matrices real symmetric or complex hermitian depending on the presence or absence of time reversal symmetry for classically regular ones the statistics are poisson on larger scales of order h i e classically small but semiclassically large universality breaks down these phenomena are being explained by representing spectra in terms of classical closed orbits universal spectral behaviour has its origin in very long orbits non universal behaviour depends only on short ones

eigenvalue correlations in the circular ensembles dyson 1972 introduced two types of brownian motion ensembles of random matrices for studying approximate symmetries in complex quantum systems the magnitude of symmetry breaking plays the role of a fictitious time t or 0 the authors study the eigenvalue correlations in the circular type ensembles which serve as models for the evolution operators of quantum maps with chaotic classical limits in two cases involving time reversal symmetry breaking they evaluate explicitly the eigenangle density correlation functions of all orders for all t and for all values of the matrix dimensionality n the general case is described by a hierarchic set of relations among the correlation functions as a function of t the transition in the correlations is found to be rapid for large n discontinuous for n to infinity as a function of a local parameter lambda which measures the mean square symmetry admixing matrix element in units of the local average spacing the transition is found to be smooth the same lambda dependent results were found earlier for the gaussian type ensembles which serve as models for the hamiltonian operators of autonomous chaotic systems

an evaluation of models for diotic and dichotic detection in reproducible noises several psychophysical models for masked detection were evaluated using reproducible noises the data were hit and false alarm rates from three psychophysical studies of detection of 500 hz tones in reproducible noise under diotic n0s0 and dichotic n0s conditions with four stimulus bandwidths 50 100 115 and 2900 hz diotic data were best predicted by an energy based multiple detector model that linearly combined stimulus energies at the outputs of several critical band filters the tone plus noise trials in the dichotic data were best predicted by models that linearly combined either the average values or the standard deviations of interaural time and level differences however these models offered no predictions for noise alone responses the decision variables of more complicated temporal models including the models of dau et al 1996a j acoust soc am 99 3615 3622 and breebaart et al 2001a j acoust soc am 110 1074 1088 were weakly correlated with subjects responses comparisons of the dependencies of each model on envelope and fine structure cues to those in the data suggested that dependence upon both envelope and fine structure as well as an interaction between them is required to predict the detection results

binaural detection with narrowband and wideband reproducible noise maskers iv models using interaural time level and envelope differences the addition of out of phase tones to in phase noises results in dynamic interaural level difference ild and interaural time difference itd cues for the dichotic tone in noise detection task several models have been used to predict listeners detection performance based on ild itd or different combinations of the two cues the models can be tested using detection performance from an ensemble of reproducible noise maskers previous models cannot predict listeners detection performance for reproducible noise maskers without fitting the data here two models were tested for narrowband and wideband reproducible noise experiments one model was a linear combination of ild and itd that included the generally ignored correlation between the two cues the other model was based on a newly proposed cue the slope of the interaural envelope difference sied predictions from both models explained a significant portion of listeners performance for detection of a 500 hz tone in wideband noise predictions based on the sied approached the predictable variance in the wideband condition the sied represented a nonlinear combination of ild and itd with the latter cue dominating listeners did not use a common strategy cue to detect tones in the narrowband condition and may use different single frequencies or different combinations of frequency channels

asymptotic preserving imex finite volume schemes for low mach number euler equations with gravitation in this paper we will present and analyze a new class of the imex finite volume schemes for the euler equations with a gravity source term we will in particular concentrate on a singular limit of weakly compressible flows when the mach number m1 in order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non stiff nonlinear part that models nonlinear advection effects for time discretization we use a special class of the so called globally stiffly accurate imex schemes and approximate the stiff linear operator implicitly and the non stiff nonlinear operator explicitly for spatial discretization the finite volume approximation is used with the central and rusanov laxfriedrichs numerical fluxes for the linear and nonlinear subsystem respectively in the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small mach number we also analyze experimentally convergence rates in the singular limit when the mach number tends to zero

reduced contribution of a nonsimultaneous mistuned harmonic to residue pitch the role of harmonic number listeners adjusted a matching sound so that its pitch equaled that of a subsequent 90 ms complex tone 12 harmonics of a 155 hz f0 whose mistuned harmonic 3 was presented either simultaneously with or after the other harmonics the third or the fourth harmonic was mistuned for both harmonics pitch shifts were significantly smaller when the mistuned harmonic was presented after rather than simultaneously with the remainder of the target complex and when the component corresponding to the mistuned harmonic was absent as opposed to present from the matching sound presenting the mistuned component after the remainder of the complex generally reduced the pitch shifts more for the third than for the fourth harmonic the nonsimultaneous presentation reduced shifts by a factor of 2 8 third and 1 7 fourth in the presence and 6 4 third and 1 9 fourth in the absence of the nominally mistuned harmonic from the matching sound the results are discussed in terms of an analytical listening and matching strategy that results in larger pitch shifts for a nonsimultaneous mistuned harmonic that has an octave or double octave relationship to the f0 than for one that does not without it necessarily being temporally integrated into the residue pitch of the complex

a note on the level spacings distribution of the hamiltonians in the transition region between integrability and chaos it is well known that there is no strict universality of the spectral fluctuations of quantum hamiltonians whose classical counterparts undergo the transition from integrability to complete chaos the author discusses the level spacings distribution p s and explains why the semiclassical formulae of berry and robnik cannot be correct for small s there is no global universality of p s for nearly integrable systems but the approach to the integrability as the perturbation parameter in goes to zero can be universal this is reflected in the fact that the slope of dp ds at s 0 for small in is universally inversely proportional to in the author gives two models in terms of two dimensional random matrices one of them being based on maximum entropy considerations the author also points out the connection to the statistics of zeros of random functions and discusses the numerical evidence

higher order level correlations in integrable quantum systems the author studies the second third and fourth cumulants of the distribution of the number of energy levels in an interval containing levels on an average the distribution function which also depends on the distance n measured in units of average level spacings above the ground state can be obtained either from the exact quantum levels or from the semiclassical approximation to the level density either of the two methods yields the same values for the cumulants in two limits the cumulants have been obtained analytically first for small the functional dependence of the cumulants is obtained using generalisations of berry s semiclassical sum rule for the two point function one finds that in this limit the first four cumulants are equal to the average number of levels in the interval second larger values of the functional dependence can be obtained by taking into account only the slowly oscillating contributions to the cumulants of the semiclassical level density for the second cumulant he obtains an analytical expression when 1

energy conserving discontinuous galerkin spectral element method for the vlasov poisson system abstract we propose a new energy conserving spectral element discontinuous galerkin method for the approximation of the vlasov poisson system in arbitrary dimension using cartesian grids the method is derived from the one proposed in 4 with two modifications energy conservation is obtained by a suitable projection operator acting on the solution of the poisson problem rather than by solving multiple poisson problems and all the integrals appearing in the finite element formulation are approximated with gauss lobatto quadrature thereby yielding a spectral element formulation the resulting method has the following properties exact energy conservation up to errors introduced by the time discretization stability thanks to the use of upwind numerical fluxes high order accuracy and high locality for the time discretization we consider both runge kutta methods and exponential integrators and show results for 1d and 2d cases 2d and 4d in phase space respectively

survey of the eigenfunctions of a billiard system between integrability and chaos we study numerically the eigenfunctions and their wigner phase space distributions of the two dimensional billiard system defined by the quadratic conformal image of the unit disk as introduced by robnik 1983 this system is a generic kam system and displays a transition from integrability to almost ergodicity as the billiard shape changes we clearly identify two classes of states the regular ones associated with integrable regions and the irregular states supported on classically chaotic regions whilst the mixed type states were not found in support of percival s conjecture 1973 we confirm the existence of extremely intense scars in the classically chaotic regions and demonstrate their association with classical periodic orbits three classes of scars are revealed one orbit scars many orbit one family scars of statistically similar orbits in the homoclinic neighbourhood and many orbit many family scars we argue that it is impossible to find an a priori semiclassical theory of individual eigenstates but do not deny the usefulness of general semiclassical arguments in analysing the collective and statistical properties of eigenstates

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

neutrino billiards time reversal symmetry breaking without magnetic fields a dirac hamiltonian describing massless spin half particles neutrinos moving in the plane r x y under the action of a 4 scalar not electric potential v r is in position representation h i h c v r z where x y and z are the pauli matrices acts on two component column spinor wavefunctions r 1 2 and has eigen values ck n does not possess time reversal symmetry t if v r describes a hard wall bounding a finite domain d billiards this is equivalent to a novel boundary condition for 2 1 t breaking is interpreted semiclassically as a difference of between the phases accumulated by waves travelling in opposite senses round closed geo desics in d with odd numbers of reflections the semiclassical large k asymptotics of the eigenvalue counting function spectral staircase n k are shown to have the weyl leading term ak 2 4 where a is the area of d but zero perimeter correction the dirac equation is transformed to an integral equation round the boundary of d and forms the basis of a numerical method for computing the k n when d is the unit disc geodesics are integrable and the eigenvalues which satisfy j l k n j l 1 k n are locally poisson distributed when d is an africa shape cubic conformal map of the unit disc the eigenvalues are locally distributed according to the statistics of the gaussian unitary ensemble of random matrix theory as predicted on the basis of t breaking and lack of geometric symmetry

analysis of adaptive mesh refinement for imex discontinuous galerkin solutions of the compressible euler equations with application to atmospheric simulations the resolutions of interests in atmospheric simulations require prohibitively large computational resources adaptive mesh refinement amr tries to mitigate this problem by putting high resolution in crucial areas of the domain we investigate the performance of a tree based amr algorithm for the high order discontinuous galerkin method on quadrilateral grids with non conforming elements we perform a detailed analysis of the cost of amr by comparing this to uniform reference simulations of two standard atmospheric test cases density current and rising thermal bubble the analysis shows up to 15 times speed up of the amr simulations with the cost of mesh adaptation below 1 of the total runtime we pay particular attention to the implicit explicit imex time integration methods and show that the ark2 method is more robust with respect to dynamically adapting meshes than bdf2 preliminary analysis of preconditioning reveals that it can be an important factor in the amr overhead the compiler optimizations provide significant runtime reduction and positively affect the effectiveness of amr allowing for speed ups greater than it would follow from the simple performance model

zeta function of the bessel operator on the negative real axis we investigate the pole structure of the zeta function zeta anu s sigma k lambda k s built out of the eigenvalues lambda k of a bessel operator anu subject to dirichlet boundary conditions at one end of the domain this leads us to the study of zeta anu on the negative real axis where most of the singularities occur

statistics of energy levels without time reversal symmetry aharonov bohm chaotic billiards a planar domain d contains a single line of magnetic flux phi switching on phi breaks time reversal symmetry t for quantal particles with charge q moving in d whilst preserving the geometry of classical billiard trajectories bouncing off the boundary delta d if delta d is such that these classical trajectories are chaotic the authors predict that t breaking will cause the local statistics of quantal energy levels to change their universality class from that of the gaussian orthogonal ensemble goe of random matrix theory to that of the gaussian unitary ensemble gue in the semiclassical limit this transition is abrupt for statistics involving the first n levels gue behaviour requires that the quantum flux alpha identical to q phi h 0 13n 14 the special flux alpha 1 2 corresponds to false t breaking and for this case goe statistics are predicted these predictions are confirmed by numerical computation of spectral statistics for a classically chaotic billiard without symmetry for which delta d is a cubic conformal image of the unit disc

a molecular description of profile analysis decision weights and internal noise systematic inefficiencies and internal noise in a spectral profile discrimination task were investigated listeners detected a 1000 hz sinusoid added in phase to the central component of a complex consisting of 11 equal intensity sinusoids parameters for a channel model that employs decision weights and internal noise were estimated with molecular psychophysical techniques maximum likelihood predictions of the model were generally within a few decibels of observed thresholds the degree to which an assumption of ideal weights leads to overestimation of internal noise was also assessed

the diagonal approximation for non time reversal symmetric systems we present a simple heuristic justification for the diagonal approximation in the periodic orbit theory of long range spectral statistics for chaotic systems without time reversal symmetry for ergodic systems this extends the validity of the approximation beyond the time where it is supported by more elementary arguments to times of the order of the heisenberg time this is in agreement with eigenvalue correlations in the gaussian unitary ensemble of random matrix theory for diffusive systems the same argument suggests that the diagonal approximation breaks down on a time scale consistent with that expected on the basis of the scaling theory of localization

statistics of nodal lines and points in chaotic quantum billiards perimeter corrections fluctuations curvature for real time reversal symmetric quantum billiards the mean length l of nodal line is calculated for the nth mode n 1 with wavenumber k using a gaussian random wave model adapted locally to satisfy dirichlet or neumann boundary conditions the leading term is of order k i e n and the first perimeter correction dominated by an unanticipated long range boundary effect is of order log k i e log n with the same sign negative for both boundary conditions the leading order state to state fluctuations l are of order log k for the curvature of nodal lines and 2 are of order k but 3 and higher moments diverge for complex e g aharonov bohm billiards the mean number n of nodal points phase singularities in the mode has a leading term of order k2 i e n the perimeter correction again a long range effect is of order klog k i e nlog n and positive notwithstanding nodal depletion near the boundary and the fluctuations n are of order k log k generalizations of the results for mixed robin boundary conditions are stated

number variance for arithmetic hyperbolic surfaces we prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range in fact it is close to having a poisson behavior this fact was discovered numerically by schmit bogomolny georgeot and giannoni it has its origin in the high degeneracy of the length spectrum first observed by selberg

quantising a generic family of billiards with analytic boundaries a generic family of plane billiards has been discovered recently the shape of the boundary is given by the quadratic conformal image of the unit circle and is thus real analytic for small deformations of the unit disc the billiard is a typical kam system but becomes ergodic or even mixing when the curvature of the boundary vanishes at some point the kolmogorov entropy has been calculated and it increases with the deformation of the boundary the author studies aspects of the quantum chaos for this billiard he solves numerically the eigenvalue problem for the laplace operator with dirichlet s boundary condition he examines the spectrum and inspects the avoided crossings at which mixing of nearby states occurs the variation of the nodal structure and of the localisation properties of the eigenfunctions is studied in analysing the level spacing distribution he finds a continuous transition from the poisson distribution towards the wigner distribution the exponent in the level repulsion law varies continuously along with a generic perturbation for small perturbations it seems to be proportional to the square root of the perturbation parameter

sensitivity of the eigenfunctions and the level curvature distribution in quantum billiards in searching for the manifestations of the sensitivity of the eigenfunctions in quantum billiards with dirichlet boundary conditions with respect to the boundary data the normal derivative we have performed instead various numerical tests for the robnik billiard a quadratic conformal map of the unit disk for 600 shape parameter values where we have looked at the sensitivity of the energy levels with respect to the shape parameter we show the energy level flow diagrams for three stretches of fifty consecutive odd eigenstates each with index 1000 to 2000 in particular we have calculated the unfolded and normalized level curvature distribution and found that it continuously changes from a delta distribution for the integrable case circle to a broad distribution in the classically ergodic regime for some shape parameters the agreement with the goe von oppen formula is very good whereas we have also cases where the deviation from goe is significant and of physical origin in the intermediate case of mixed classical dynamics we have a semiclassical formula in the spirit of the berry robnik 1984 surmise here the agreement with theory is not good partially due to the localization phenomena which are expected to disappear in the semiclassical limit we stress that even for classically ergodic systems there is no global universality for the curvature distribution not even in the semiclassical limit

a discontinuous galerkin method for the shallow water equations in spherical triangular coordinates a global model of the atmosphere is presented governed by the shallow water equations and discretized by a runge kutta discontinuous galerkin method on an unstructured triangular grid the shallow water equations on the sphere a two dimensional surface in r 3 are locally represented in terms of spherical triangular coordinates the appropriate local coordinate mappings on triangles on every triangular grid element this leads to a two dimensional representation of tangential momentum and therefore only two discrete momentum equations the discontinuous galerkin method consists of an integral formulation which requires both area elements and line element faces integrals here we use a rusanov numerical flux to resolve the discontinuous fluxes at the element faces a strong stability preserving third order runge kutta method is applied for the time discretization the polynomial space of order k on each curved triangle of the grid is characterized by a lagrange basis and requires high order quadature rules for the integration over elements and element faces for the presented method no mass matrix inversion is necessary except in a preprocessing step the validation of the atmospheric model has been done considering standard tests from williamson et al d l williamson j b drake j j hack r jakob p n swarztrauber a standard test set for numerical approximations to the shallow water equations in spherical geometry j comput phys 102 1992 211 224 unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream a convergence rate of o dx k 1 was observed in the model experiments furthermore a numerical experiment is presented for which the third order time integration method limits the model error thus the time step dt is restricted by both the cfl condition and accuracy demands conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k

psychometric functions for pure tone frequency discrimination the form of the psychometric function pf for auditory frequency discrimination is of theoretical interest and practical importance in this study pfs for pure tone frequency discrimination were measured for several standard frequencies 200 8000 hz and levels 35 85 db sound pressure level spl in normal hearing listeners the proportion correct data were fitted using a cumulative gaussian function of the sensitivity index d computed as a power transformation of the frequency difference f the exponent of the power function corresponded to the slope of the pf on log d log f coordinates the influence of attentional lapses on pf slope estimates was investigated when attentional lapses were not taken into account the estimated pf slopes on log d log f coordinates were found to be significantly lower than 1 suggesting a nonlinear relationship between d and f however when lapse rate was included as a free parameter in the fits pf slopes were found not to differ significantly from 1 consistent with a linear relationship between d and f this was the case across the wide ranges of frequencies and levels tested in this study therefore spectral and temporal models of frequency discrimination must account for a linear relationship between d and f across a wide range of frequencies and levels

numerical accuracy of bogomolny s semiclassical quantization scheme in quantum billiards we use the semiclassical quantization scheme of bogomolny to calculate eigenvalues of the limacon quantum billiard corresponding to a conformal map of the circle billiard we use the entire billiard boundary as the chosen surface of section and use a finite approximation for the transfer operator in coordinate space computation of the eigenvalues of this matrix combined with a quantization condition determines a set of semiclassical eigenvalues which are compared with those obtained by solving the schrodinger equation the classical dynamics of this billiard system undergoes a smooth transition from integrable circle to completely chaotic motion thus providing a test of bogomolny s semiclassical method in coordinate space in terms of the morphology of the wavefunction we analyse the results for billiards which exhibit both soft and hard chaos

spectral zeta functions for aharonov bohm quantum billiards this is a study of the sum zeta s alpha identical to ej 1infinity ej alpha s over the eigenvalues ej alpha of schrodinger s equation in a billiard domain d with reflecting walls threaded by a single line of magnetic flux alpha for integer s zeta s alpha is calculated by generalising a green function technique of itzykson et al ibid vol 19 l111 5 1986 based on a conformal transformation between d and the unit disc when the transformation is generated by a polynomial of finite degree an explicit formula enables zeta 2 alpha to be easily computed with high accuracy in conjunction with a semiclassical approximation the exact values of zeta 2 alpha can be used to calculate the ground state e1 alpha for a non integrable billiard with an error of about one per cent

a conservative discontinuous galerkin semi implicit formulation for the navier stokes equations in nonhydrostatic mesoscale modeling a discontinuous galerkin dg finite element formulation is proposed for the solution of the compressible navier stokes equations for a vertically stratified fluid which are of interest in mesoscale nonhydrostatic atmospheric modeling the resulting scheme naturally ensures conservation of mass momentum and energy a semi implicit time integration approach is adopted to improve the efficiency of the scheme with respect to the explicit runge kutta time integration strategies usually employed in the context of dg formulations a method is also presented to reformulate the resulting linear system as a pseudo helmholtz problem in doing this we obtain a dg discretization closely related to those proposed for the solution of elliptic problems and we show how to take advantage of the numerical integration rules required in all dg methods for the area and flux integrals to increase the efficiency of the solution algorithm the resulting numerical formulation is then validated on a collection of classical two dimensional test cases including density driven flows and mountain wave simulations the performance analysis shows that the semi implicit method is indeed superior to explicit methods and that the pseudo helmholtz formulation yields further efficiency improvements

predictions of diotic tone in noise detection based on a nonlinear optimal combination of energy envelope and fine structure cues tone in noise detection has been studied for decades however it is not completely understood what cue or cues are used by listeners for this task model predictions based on energy in the critical band are generally more successful than those based on temporal cues except when the energy cue is not available nevertheless neither energy nor temporal cues can explain the predictable variance for all listeners in this study it was hypothesized that better predictions of listeners detection performance could be obtained using a nonlinear combination of energy and temporal cues even when the energy cue was not available the combination of different cues was achieved using the logarithmic likelihood ratio test lrt an optimal detector in signal detection theory a nonlinear lrt based combination of cues was proposed given that the cues have gaussian distributions and the covariance matrices of cue values from noise alone and tone plus noise conditions are different predictions of listeners detection performance for three different sets of reproducible noises were computed with the proposed model results showed that predictions for hit rates approached the predictable variance for all three datasets even when an energy cue was not available

relative dominance of individual partials in determining the pitch of complex tones these experiments were conducted to determine the dominance of each partial in determining the residue pitch of a complex tone subjects were required to make pitch matches to a complex tone which had one partial slightly mistuned from its correct harmonic value the shift in residue pitch was measured as a function of the frequency shift of the harmonic for each harmonic in turn for mistunings up to 2 3 the shift in residue pitch was approximately a linear function of the shift in the harmonic but for greater mistunings the shift in residue pitch was reduced the degree to which a given harmonic can influence residue pitch gives a measure of the dominance of that harmonic the dominant harmonics were always contained within the lowest six harmonics for fundamental frequencies of 100 200 and 400 hz but there were marked individual differences in the exact distribution of dominance across harmonics the level of a harmonic relative to adjacent harmonics can have a significant effect on its dominance the implications of the results for theories of pitch perception are discussed

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

interaural fluctuations and the detection of interaural incoherence iv the effect of compression on stimulus statistics the purpose of this experiment was to determine whether the normalized interaural cross correlation cc model or a model based on interaural phase and level differences can better describe incoherence detection data the ability to detect interaural incoherence in three sets of reproducible dichotic noises was tested in six listeners the first set contained noises with a constrained value of the cc and the cc including signal compression the second set contained noises with a constrained value of the cc including signal compression the third set contained noises with constrained values in the fluctuations in the interaural differences modeling showed that neither the cc model nor the model using the interaural differences could account for the data in any set examination of the statistical properties of the stimuli showed that including compression before the calculation of the interaural cc causes a substantial correlation of this metric to the fluctuations in the interaural phase difference this finding implies that it may be more difficult to discriminate between the common types of binaural models than previously thought

on some gaussian ensembles of hermitian matrices a gaussian ensemble of hermitian matrices with an arbitrary ratio of their symmetric and anti symmetric parts is studied similarly a gaussian ensemble of hermitian quaternion matrices with an arbitrary ratio of their self dual and anti self dual parts is studied analytical expressions for the correlation and cluster functions as well as their limits when the order of the matrices is large are derived for both ensembles

a semi lagrangian discontinuous galerkin method for scalar advection by incompressible flows a new conservative semi lagrangian formulation is proposed for the discretization of the scalar advection equation in flux form the approach combines the accuracy and conservation properties of the discontinuous galerkin dg method with the computational efficiency and robustness of semi lagrangian sl techniques unconditional stability in the von neumann sense is proved for the proposed discretization in the one dimensional case a monotonization technique is then introduced based on the flux corrected transport approach this yields a multi dimensional monotonic scheme for the piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion than standard dg methods the accuracy and stability of the method are further demonstrated by two dimensional tracer advection tests in the case of incompressible flows the comparison with results obtained by standard sl and dg methods highlights several advantages of the new technique

relative estimates of combination weights decision criteria and internal noise based on correlation coefficients a means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent normally distributed random variables xi s the first theorem presents the correlation between the binary response variables signal versus no signal and the component xi the second theorem presents a parallel result for the case that additive internal noise is present thus in psychophysical experiments the relative combination weights may be obtained by correlating the observers responses and the input random variables third three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered

a class of implicit explicit two step runge kutta methods this work develops new implicit explicit time integrators based on two step runge kutta methods the class of schemes of interest is characterized by linear invariant preservation and high stage orders theoretical consistency stability and stiff convergence analyses are performed to reveal the excellent properties of these methods the new framework offers extreme flexibility in the construction of partitioned integrators since no coupling conditions are necessary practical schemes of orders three four and six are constructed and are used to solve several test problems numerical results confirm the theoretical findings

improved energy level statistics for a family of billiards with analytic boundaries the energy level statistics of a family of classically chaotic billiards with analytic boundaries is studied numerically with a high chi 2 confidence level for the final results which go substantially beyond the quality of existing similar results the hypothesis of bohigas et al 1984 is strongly supported by the results showing that the level statistics of classically ergodic systems in the semiclassical limit can indeed be described by the gaussian orthogonal ensemble of the random matrix theories contrary to some doubts which have been recently raised e g by wilkinson et al 1991 nevertheless some small deviation of the numerical results compared with the gaussian orthogonal ensemble is observed and shown but it is believed to be still a deficiency of the statistical significance rather than of the model

distribution of the spacing between two adjacent avoided crossings we consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system the distribution of the spacing in the parameter between two adjacent avoided crossings is investigated using a random matrix model we find that the distribution of these spacings is well fitted by a power law distribution for small spacings the powers are 2 and 3 for the gaussian orthogonal ensemble and gaussian unitary ensemble respectively we also find that the distributions decay exponentially for large spacings the distributions in concrete quantum chaotic systems agree with those of the random matrix model

a semi implicit semi lagrangian p adaptive discontinuous galerkin method for the shallow water equations a semi implicit and semi lagrangian discontinuous galerkin method for the shallow water equations is proposed for applications to geophysical scale flows a non conservative formulation of the advection equation is employed in order to achieve a more treatable form of the linear system to be solved at each time step the method is equipped with a simple p adaptivity criterion that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution numerical results show that the method captures well the main features of gravity and inertial gravity waves as well as reproducing correct solutions in nonlinear test cases with analytic solutions the accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high courant numbers and with automatic choice of the local approximation degree

upwind methods for the baernunziato equations and higher order reconstruction using artificial viscosity this article is devoted to the numerical discretisation of the hyperbolic two phase flow model of baer and nunziato a special attention is paid on the discretisation of intercell flux functions in the framework of finite volume and discontinuous galerkin approaches where care has to be taken to efficiently approximate the non conservative products inherent to the model equations various upwind approximate riemann solvers have been tested on a bench of discontinuous test cases new discretisation schemes are proposed in a discontinuous galerkin framework following the criterion of abgrall and the path conservative formalism a stabilisation technique based on artificial viscosity is applied to the high order discontinuous galerkin method and compared against classical tvd muscl finite volume flux reconstruction

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

time reversal symmetry breaking and the statistical properties of quantum systems the breaking of the generalized time reversal symmetry of a quantum chaotic system corresponds to a transition from orthogonal to unitary ensembles of random matrices investigating this transition for the circular ensembles applicable for time dependent periodic systems the authors demonstrate and explain that there exists a relevant difference of the transition rate in comparison with the gaussian ensembles appropriate for quantum conservative systems the above supposition is supported by a numerical study of the eigenvalues and eigenvectors of the periodically kicked top

sum rules for zeros of bessel functions and an application to spherical aharonov bohm quantum bags the authors study the sum zeta h s sigma jej s over the eigenvalues ej of the schrodinger equation in a spherical domain with dirichlet walls threaded by a line of magnetic flux rather than using green function techniques they tackle the mathematically non trivial problem of finding exact sum rules for the zeros of bessel functions jv which are extremely helpful when seeking numerical approximations to ground state energies these results are particularly valuable if v is neither an integer nor half an odd integer

on the relative influence of individual harmonics on pitch judgment spectral weighting functions were estimated in a pitch comparison task to assess the relative influence of individual harmonics on listeners pitch judgment the stimuli were quasi harmonic complex tones composed of the first 12 components with fundamental frequencies ranging from 100 to 800 hz on each stimulus presentation the frequency of each harmonic was randomly jittered by a small amount the perceptual weight for each harmonic was calculated as the correlation coefficient between the binary responses of the listener and the frequency jitters for that harmonic although in general the present results conform to previous ones showing the predominant role of several low ranked harmonics discrepancies exist in details contrary to some previous reports that the dominant harmonics were of fixed harmonic ranks regardless of their frequencies the current results showed that the dominant harmonics were best described as close to a fixed absolute frequency of 600 hz

effect of duration on the frequency discrimination of individual partials in a complex tone and on the discrimination of fundamental frequency thresholds for the discrimination of fundamental frequency fodls and frequency difference limens fdls for individual partials within a complex tone f0 250 hz harmonics 1 7 were measured for stimulus durations of 200 50 and 16 ms the fdls increased with decreasing duration although the results differed across subjects the effect of duration generally decreased as the harmonic number increased from 1 to 4 then increased as the harmonic number increased to 6 and finally decreased for the seventh harmonic for each duration fodls were smaller than the smallest fdl for any individual harmonic indicating that information is combined across harmonics in the discrimination of fo fodls predicted from the fdls corresponded well with observed fodls for the 200 and 16 ms durations but were significantly larger than observed fodls for the 50 ms duration a supplementary pitch matching experiment using two subjects indicated that the contribution of the seventh harmonic to the pitch of the 16 ms complex tone was smaller than would be predicted from the fdl for that harmonic the results are consistent with the idea that the dominant region shifts upward with decreasing duration but that the weight assigned to individual harmonics is not always adjusted in an optimal way

molecular analysis of the effect of relative tone level on multitone pattern discrimination molecular psychophysics attempts to model the observer s response to stimuli as they vary from trial to trial the approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern various factors affecting decision weights have been examined but one largely ignored is the relative level of tones in the pattern in the present study listeners detected a level increment in a sequence of 5 100 ms 2 0 khz tone bursts alternating in level between 40 and 80db spl the level increment was made largest on the 40 db tones yet despite this all four highly practiced listeners gave near exclusive weight to the 80 db tones the effect was the same when the tones were replaced by bursts of broadband gaussian noise alternating in level it was reduced only when the level differences were made 10db and it was entirely reversed only when the low level tones alternated with louder bursts of ga

spectral zeta functions for q bessel equations explicit formulae for the zeta functions of the zeros of hahn exton and jackson s q bessel functions are derived they can be regarded as spectral sum rules for some discrete quantum billiards

semi implicit formulations of the navier stokes equations application to nonhydrostatic atmospheric modeling we present semi implicit implicit explicit formulations of the compressible navier stokes equations nse for applications in nonhydrostatic atmospheric modeling the compressible nse in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the schur complement form of the linear implicit problem we present results for five different forms of the compressible nse and describe in detail how to formulate the semi implicit time integration method for these equations finally we compare all five equations and compare the semi implicit formulations of these equations both using the schur and no schur forms against an explicit runge kutta method our simulations show that if efficiency is the main criterion it matters which form of the governing equations you choose furthermore the semi implicit formulations are faster than the explicit runge kutta method for all the tests studied especially if the schur form is used while we have used the spectral element method for discretizing the spatial operators the semi implicit formulations that we derive are directly applicable to all other numerical methods we show results for our five semi implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling including inertia gravity waves density current i e kelvin helmholtz instabilities and mountain test cases the latter test case requires the implementation of nonreflecting boundary conditions therefore we show results for all five semi implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling no flux reflecting and nonreflecting boundary conditions nrbcs it is shown that the nrbcs exert a strong impact on the accuracy and efficiency of the models

discrete symmetries and spectral statistics we calculate the 2 point spectral statistics associated with a given irreducible representation i e symmetry class for time reversal invariant systems possessing discrete symmetries using semiclassical periodic orbit theory when the representation in question is real or pseudo real our results conform to those of the gaussian orthogonal ensemble goe of random matrices when it is complex we find instead gaussian unitary ensemble gue behaviour this provides a direct semiclassical explanation for the recent observation by leyvraz et al 1996 of gue correlations in the desymmetrized spectra of certain symmetric billiards in the absence of any time reversal invariance breaking e g magnetic fields

comparison between adaptive and uniform discontinuous galerkin simulations in dry 2d bubble experiments adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution however it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result this question is investigated for a specific example of dry atmospheric convection namely the simulation of warm air bubbles for this purpose a novel numerical model is developed that is tailored towards this specific application the compressible euler equations are solved with a discontinuous galerkin method time integration is done with an imex method and the dynamic grid adaptivity uses space filling curves via the amatos function library so far the model is able to simulate dry flow in two dimensional geometry without subgrid scale modeling the model is tested with three standard test cases an error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution for the rising warm air bubble the additional error by using adaptivity is smaller than 1 of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine resolution grid correspondingly the adaptive simulation is almost two times faster than the uniform simulation furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same cpu time

zeta functions of nearly circular domains we study the zeta functions of negative integer powers of eigenvalues of the laplacian on two dimensional domains which are close to the unit disc d for closed form expressions are obtained which describe when the technique developed is applied to derive an asymptotic expansion for zeta functions of regular n sided polygons in the limit

persistent current flux correlations calculated by quantum chaology we consider classically chaotic systems with the topology of a ring threaded by quantum flux 4 using semiclassical asymptotics we calculate the rwaveraged autocorrelation function c 4 of slopes of the energy levels persistent currents normalized by the mean level spacing for flux values differing by 4 our result furnishes the uniform approximation here w the rms winding number of the classical periodic orbits whose period is connected by heisenberg s relation to the mean level spacing is a large semiclassical parameter of order l li d for a system with d freedoms

semiclassical quantization of billiards with mixed boundary conditions the semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived the parametric dependence of the spectrum on the boundary condition is shown to be a very useful diagnostic tool in the semiclassical analysis of the spectrum of billiards it is also used to check in detail some recently proposed parametric spectral statistics the methods are illustrated in the analysis of the spectrum of the sinai billiard and its parametric dependence on the boundary condition on the dispersing arc

continuous and discontinuous galerkin methods for a scalable three dimensional nonhydrostatic atmospheric model limited area mode this paper describes a unified element based galerkin ebg framework for a three dimensional nonhydrostatic model for the atmosphere in general ebg methods possess high order accuracy geometric flexibility excellent dispersion properties and good scalability our nonhydrostatic model based on the compressible euler equations is appropriate for both limited area and global atmospheric simulations both a continuous galerkin cg or spectral element and discontinuous galerkin dg model are considered using hexahedral elements the formulation is suitable for both global and limited area atmospheric modeling although we restrict our attention to 3d limited area phenomena in this study global atmospheric simulations will be presented in a follow up paper domain decomposition and communication algorithms used by both our cg and dg models are presented the communication volume and exchange algorithms for cg and dg are compared and contrasted numerical verification of the model was performed using two test cases flow past a 3d mountain and buoyant convection of a bubble in a neutral atmosphere these tests indicate that both cg and dg can simulate the necessary physics of dry atmospheric dynamics scalability of both methods is shown up to 8192 cpu cores with near ideal scaling for dg up to 32 768 cores

the quantum perturbed cat map and symmetry we investigate a class of quantum symmetries of the perturbed cat map which exist only for a subset of possible values of planck s constant the effect of these symmetries is to change the spectral statistics along this positive density subset the symmetries are shown to be related to some simple classical symmetries of the map