simulated head related transfer function of the phyllostomid bat phyllostomus discolor this paper presents a calculation of the head related transfer function hrtf for the frontal hemisphere of the phyllostomid bat phyllostomus discolor using an acoustic field simulation tool based on the boundary element method from the calculated hrtf results binaural interaural intensity differences iids are derived the results region of highest sensitivity hrtf patterns and iid patterns are shown to be in good agreement with earlier experimental measurements on other specimens of the same bat species i e the differences are within the interspecies variability range next it is argued that the proposed simulation method offers distinct advantages over acoustic measurements on real bat specimens to illustrate this it is shown how computer manipulation of the virtual morphology model allows a more detailed comprehension of bat spatial hearing by investigating the effects of different head parts on the hrtf from this analysis it is concluded that for this species the pinna has a significant

vertical normal modes of human ears individual variation and frequency estimation from pinna anthropometry beyond the first peak of head related transfer functions or pinna related transfer functions prtfs human pinnae are known to have two normal modes with vertical resonance patterns involving two or three pressure anti nodes in cavum cymba and fossa however little is known about individual variations in these modes and there is no established model for estimating their center frequencies from anthropometry here with geometries of 38 pinnae measured prtfs were calculated and vertical modes visualized by numerical simulation most pinnae were found to have both cavum fossa and cavum cymba modes with opposite phase anti nodes in cavum and either fossa or cymba respectively nevertheless in both modes fossa involvement varied substantially across pinnae dependent on scaphoid fossa depth and cymba shallowness linear regression models were evaluated in mode frequency estimation with 3322 measures derived from 31 pinna landmarks the cavum fossa normal mode frequency was best estimated correlat

convergence of nonconforming multigrid methods without full elliptic regularity we consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity we prove that there is a bound 1 for the contraction number of the w cycle algorithm which is independent of mesh level provided that the number of smoothing steps is sufficiently large we also show that the symmetric variable v cycle algorithm is an optimal preconditioner

on the tensor product of weakly compact operators the identity operator on an infinite dimensional hilbert space shows that neither the projective nor the injective tensor product of two weakly compact operators will be weakly compact in general see holub h1 remark p 10 there are however conditions ensuring this along the studies of diestel and faires df and saksman and tylli st we will add some more proposition 1 due to saksman and tylli deals with the tensor product of a compact and a weakly compact operator answering a question of theirs we consider in proposition 2 the tensor product of two weakly compact operators on spaces with the dunford pettis property having treated the case of absolutely p summing operators in proposition 3 we show in proposition 4 that the injective tensor product of two weakly compact operators on pisier spaces is weakly compact our results concern only the projective and the injective tensor product for the elementary properties of weakly compact operators to be used here we refer to ds vi 4 p 482 5

higher order weakly over penalized symmetric interior penalty methods in this paper we study higher order weakly over penalized symmetric interior penalty methods for second order elliptic boundary value problems in two dimensions we derive h p error estimates in both the energy norm and the l 2 norm and present numerical results that corroborate the theoretical results

grothendieck s theorem past and present probably the most famous of grothendieck s contributions to banach space theory is the result that he himself described as the fundamental theorem in the metric theory of tensor products that is now commonly referred to as grothendieck s theorem gt in short or sometimes as grothendieck s inequality this had a major impact first in banach space theory roughly after 1968 then later on in c algebra theory roughly after 1978 more recently in this millennium a new version of gt has been successfully developed in the framework of operator spaces or non commutative banach spaces in addition gt independently surfaced in several quite unrelated fields in connection with bell s inequality in quantum mechanics in graph theory where the grothendieck constant of a graph has been introduced and in computer science where the grothendieck inequality is invoked to replace certain np hard problems by others that can be treated by semidefinite programming and hence solved in polynomial time in this expository paper we present a review of all these topics starting from the original gt we concentrate on the more recent developments and merely outline those of the first banach space period since detailed accounts of that are already available for instance the author s 1986 cbms notes

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

finite difference computation of head related transfer function for human hearing modeling the head related transfer function hrtf is a key to many applications in spatial audio to understand and predict the effects of head geometry and the surrounding environment on the hrtf a three dimensional finite difference time domain model 3d fdtd has been developed to simulate acoustic wave interaction with a human head a perfectly matched layer pml is used to absorb outgoing waves at the truncated boundary of an unbounded medium an external source is utilized to reduce the computational domain size through the scattered field total field formulation this numerical model has been validated by analytical solutions for a spherical head model the 3d fdtd code is then used as a computational tool to predict the hrtf for various scenarios in particular a simplified spherical head model is compared to a realistic head model up to about 7 khz the hrtf is also computed for a realistic head model in the presence of a wall it is demonstrated that this 3d fdtd model can be a useful tool for spatial audio applications

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

a 3 d enlarged cell technique ect for the conformal fdtd method in this paper we present an enlarged cell technique ect to avoid the time step reduction encountered in the conformal finite difference time domain cfdtd method due to small irregular cells truncated by metallic boundaries we focus our efforts on the discussion of the accuracy and stability of the ect and its comparison with other conformal methods especially the one called the uniformly stable conformal usc method we also provide a simplified ect which is much easier to implement in the ect a stability criterion is first constructed to identify instable irregular cells i e those having so small an area to cause instability those instable cells are then enlarged into their adjacent cells to obtain a large stable area careful treatment is performed on the communication between the intruding and intruded cells in terms of electromotive force by keeping the total electromotive force conservative this technique is verified by several 3 d numerical experiments results show that the ect is second order accurate and numerically stable at the regular courant time step limit

residual based a posteriori error estimate for a nonconforming reissner mindlin plate finite element reliable and efficient residual based a posteriori error estimates are established for the nonconforming finite element method for the reissner mindlin plate due to arnold and falk siam j numer anal 26 1989 pp 1276 1290 the error is estimated by a computable error estimator from above and below up to multiplicative constants that depend neither on the mesh size nor on the plate s thickness the error is controlled in norms that are known to converge to zero in a quasi optimal way

road traffic noise shielding by vegetation belts of limited depth abstract road traffic noise propagation through a vegetation belt of limited depth 15 m containing periodically arranged trees along a road is numerically assessed by means of 3d finite difference time domain fdtd calculations the computational cost is reduced by only modeling a representative strip of the planting scheme and assuming periodic extension by applying mirror planes with increasing tree stem diameter and decreasing spacing traffic noise insertion loss is predicted to be more pronounced for each planting scheme considered simple cubic rectangular triangular and face centered cubic for rectangular schemes the spacing parallel to the road axis is predicted to be the determining parameter for the acoustic performance significant noise reduction is predicted to occur for a tree spacing of less than 3 m and a tree stem diameter of more than 0 11 m this positive effect comes on top of the increase in ground effect near 3 dba for a light vehicle at 70 km h when compared to sound propagation over grassland the noise reducing effect of the forest floor and the optimized tree belt arrangement are found to be of similar importance in the calculations performed the effect of shrubs with typical above ground biomass is estimated to be at maximum 2 dba in the uniform scattering approach applied for a light vehicle at 70 km h downward scattering from tree crowns is predicted to be smaller than 1 dba for a light vehicle at 70 km h for various distributions of scattering elements representing the tree crown the effect of the presence of tree stems shrubs and tree crowns is predicted to be approximately additive inducing some pseudo randomness in stem center location tree diameter and omitting a limited number of rows with trees seem to hardly affect the insertion loss these predictions suggest that practically achievable vegetation belts can compete to the noise reducing performance of a classical thin noise barrier on grassland with a height of 1 1 5 m in a non refracting atmosphere

locking free reissner mindlin elements without reduced integration abstract in a recent paper of arnold et al d n arnold f brezzi l d marini a family of discontinuous galerkin finite elements for the reissner mindlin plate j sci comput 22 2005 25 45 the ideas of discontinuous galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the reissner mindlin plate problem by following their basic approach but making different choices of finite element spaces we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator which has been a central feature of many locking free methods for k 2 all the methods use piecewise polynomials of degree k to approximate the transverse displacement and possibly subsets of piecewise polynomials of degree k 1 to approximate both the rotation and shear stress vectors the approximation spaces for the rotation and the shear stress are always identical the methods vary in the amount of interelement continuity required in terms of smallest number of degrees of freedom the simplest method approximates the transverse displacement with continuous piecewise quadratics and both the rotation and shear stress with rotated linear brezzi douglas marini elements

on mixed finite element methods for the reissner mindlin plate model in this paper we analyze the convergence of mixed finite element approximations to the solution of the reissner mindlin plate problem we show that several known elements fall into our analysis thus providing a unified approach we also introduce a low order triangular element which is optimalorder convergent uniformly in the plate thickness

range dependence of the response of a spherical head model the head related transfer function hrtf varies with range as well as with azimuth and elevation to better understand its close range behavior a theoretical and experimental investigation of the hrtf for an ideal rigid sphere was performed an algorithm was developed for computing the variation in sound pressure at the surface of the sphere as a function of direction and range to the sound source the impulse response was also measured experimentally the results may be summarized as follows first the experimental measurements were in close agreement with the theoretical solution second the variation of low frequency interaural level difference with range is significant for ranges smaller than about five times the sphere radius third the impulse response reveals the source of the ripples observed in the magnitude response and provides direct evidence that the interaural time difference is not a strong function of range fourth the time delay is well approximated by well known ray tracing formula due to woodworth and schlosberg finally except for this time delay the hrtf for the ideal sphere appears to be minimum phase permitting exact recovery of the impulse response from the magnitude response in the frequency domain

an fdtd algorithm with perfectly matched layers for general dispersive media a three dimensional 3 d finite difference time domain fdtd algorithm with perfectly matched layer pml absorbing boundary condition abc is presented for general inhomogeneous dispersive conductive media the modified time domain maxwell s equations for dispersive media are expressed in terms of coordinate stretching variables we extend the recursive convolution rc and piecewise linear recursive convolution plrc approaches to arbitrary dispersive media in a more general form the algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media i e lorentz medium unmagnetized plasma and debye medium excellent agreement between the fdtd results and analytical solutions is obtained for all testing cases with both rc and plrc approaches we demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine like objects cylinders and spheres buried in a dispersive half space and the mapping of a curved interface because of their generality the algorithm and computer program can be used to model biological materials artificial dielectrics optical materials and other dispersive media

a staggered grid finite difference method with perfectly matched layers for poroelastic wave equations a particle velocity strain finite difference fd method with a perfectly matched layer pml absorbing boundary condition is developed for the simulation of elastic wave propagation in multidimensional heterogeneous poroelastic media instead of the widely used second order differential equations a first order hyperbolic leap frog system is obtained from biot s equations to achieve a high accuracy the first order hyperbolic system is discretized on a staggered grid both in time and space the perfectly matched layer is used at the computational edge to absorb the outgoing waves the performance of the pml is investigated by calculating the reflection from the boundary the numerical method is validated by analytical solutions this fd algorithm is used to study the interaction of elastic waves with a buried land mine three cases are simulated for a mine like object buried in sand in purely dry sand and in mud the results show that the wave responses are significantly different in these cases the target can be detected by using acoustic measurements after processing

locally conformal method for acoustic finite difference time domain modeling of rigid surfaces the finite difference time domain method is a simple but powerful numerical method for simulating full wave acoustic propagation and scattering however the method can demand a large amount of computational resources traditionally continuously curved boundaries are represented in a stair step fashion and thus accurately modeling scattering from a boundary will require a finer discretization than would otherwise be necessary for modeling propagation in a homogeneous medium however a fine discretization might not be practical due to limited computational resources a locally conformal technique is presented here for modeling acoustic scattering from continuously curved rigid boundaries this technique is low cost simple to implement and gives better results for the same grid discretization than the traditional stair step representation these improvements can be traded for a coarser discretization which reduces the computational burden the improved accuracy of this technique is demonstrated for a spherical scatterer

a new error analysis for discontinuous finite element methods for linear elliptic problems the standard a priori error analysis of discontinuous galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm in this paper a new error analysis of discontinuous galerkin methods is developed using only the h k weak formulation of a boundary value problem of order 2k this is accomplished by replacing the galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in h k

computing interaural differences through finite element modeling of idealized human heads acoustical interaural differences were computed for a succession of idealized shapes approximating the human head related anatomy sphere ellipsoid and ellipsoid with neck and torso calculations were done as a function of frequency 100 2500 hz and for source azimuths from 10 to 90 degrees using finite element models the computations were compared to free field measurements made with a manikin compared to a spherical head the ellipsoid produced greater large scale variation with frequency in both interaural time differences and interaural level differences resulting in better agreement with the measurements adding a torso represented either as a large plate or as a rectangular box below the neck further improved the agreement by adding smaller scale frequency variation the comparisons permitted conjectures about the relationship between details of interaural differences and gross features of the human anatomy such as the height of the head and length of the neck

a low order nonconforming finite element for reissner mindlin plates we propose a locking free element for plate bending problems based on the use of nonconforming piecewise linear functions for both rotations and deflections we prove optimal error estimates with respect to both the meshsize and the analytical solution regularity

computation of the head related transfer function via the fast multipole accelerated boundary element method and its spherical harmonic representation the head related transfer function hrtf is computed using the fast multipole accelerated boundary element method for efficiency the hrtf is computed using the reciprocity principle by placing a source at the ear and computing its field analysis is presented to modify the boundary value problem accordingly to compute the hrtf corresponding to different ranges via a single computation a compact and accurate representation of the hrtf termed the spherical spectrum is developed computations are reduced to a two stage process the computation of the spherical spectrum and a subsequent evaluation of the hrtf this representation allows easy interpolation and range extrapolation of hrtfs hrtf computations are performed for the range of audible frequencies up to 20khz for several models including a sphere human head models the neumann ku 100 fritz and the knowles kemar kemar manikins and head and torso model the kemar manikin comparisons between the different cases are provided comparis

perfectly matched layers for elastic waves in cylindrical and spherical coordinates the perfectly matched layer pml for elastic waves in cylindrical and spherical coordinates is developed using an improved scheme of complex coordinates as is known for electromagnetic waves berenger s original pml scheme does not apply to cylindrical and spherical coordinates the straightforward extension of the complex coordinates for elastic waves to cylindrical and spherical coordinates requires extra unknowns for time domain solutions wasting computer memory and computation time the main idea of the improved scheme in this work is the use of integrated complex variables it is shown that for three dimensional cylindrical and spherical coordinates this improved pml scheme requires no more unknowns than in cartesian coordinates the number of unknowns can be further reduced through the use of symmetry in the partial differential equations the pml scheme allows an arbitrary inhomogeneity in the medium and is suitable for numerical solutions of wave equations by finite difference finite element

weakly over penalized discontinuous galerkin schemes for reissner mindlin plates without the shear variable this paper introduces a new locking free formulation that combines the discontinuous galerkin methods with weakly over penalized techniques for reissner mindlin plates we derive optimal a priori error estimates in both the energy norm and l 2 l2 norm for polynomials of degree k 2 k 2 and we extend the results concerning the energy norm to higher order polynomial degrees numerical tests confirm our theoretical predictions

boundary element method calculation of individual head related transfer function ii impedance effects and comparisons to real measurements following previous work by the author involving the calculation of an individual head related transfer function hrtf using a boundary element method bem approach impedance conditions are now included to take account of the acoustic properties of human hair in addition comparisons are made here between calculations and measured values for the hrtf of a specific individual numerous works have been published regarding the measurement of hrtfs but rarely are several methods compared for the same individual the results presented in the work compare two different measurement techniques and a computational bem for acquiring an individual hrtf impedance effects have been incorporated in the bem model for hair based on measured data providing a final set for comparison measurement results show significant variations for the same individual computational results show good agreement within the range of experimental variations definite trends are observed for many directions while the limitations of the methods are also highlighted for others the effects of incorporating hair impedance are shown to provide an improvement in the correlation of computational results indicating an affect of hair impedance on the hrtf

a finite element method with discontinuous rotations for the mindlin reissner plate model we present a continuous discontinuous finite element method for the mindlin reissner plate model based on continuous polynomials of degree k 2 for the transverse displacements and discontinuous polynomials of degree k 1 for the rotations we prove a priori convergence estimates uniformly in the thickness of the plate and thus show that locking is avoided we also derive a posteriori error estimates based on duality together with corresponding adaptive procedures for controlling linear functionals of the error finally we present some numerical results