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

anomalous scaling of a passive scalar advected by the synthetic compressible flow abstract the field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by a gaussian nonsolenoidal velocity field with finite correlation time in the presence of large scale anisotropy the energy spectrum of the velocity in the inertial range has the form e k k1 e and the correlation time at the wave number k scales as k 2 it is shown that depending on the values of the exponents e and the model exhibits various types of inertial range scaling regimes with nontrivial anomalous exponents explicit asymptotic expressions for the structure functions and other correlation functions are obtained they are represented by superpositions of power laws with nonuniversal amplitudes and universal independent of the anisotropy anomalous exponents calculated to the first order in e and in any space dimension these anomalous exponents are determined by the critical dimensions of tensor composite operators built of the scalar gradients and exhibit a kind of hierarchy related to the degree of anisotropy the less is the rank the less is the dimension and consequently the more important is the contribution to the inertial range behavior the leading terms of the even odd structure functions are given by the scalar vector operators the anomalous exponents depend explicitly on the degree of compressibility

analyzing head related transfer function measurements using surface spherical harmonics a continuous functional representation of a large set of head related transfer function measurements hrtfs is developed the hrtfs are represented as a weighted sum of surface spherical harmonics sshs up to degree 17 a gaussian quadrature method is used to pick out a set of experimentally efficient measurement directions anechoic impulse responses are measured for these directions between a source loudspeaker and the entrance to the ear canal of a head and torso simulator hats three separate ssh analyses are carried out the first forms a ssh representation from the time responses with the variable onset delay caused by interaural differences intact by applying the analysis to each time sample in turn the second ssh model is formed in exactly the same way except using impulse responses in which the variable onset delays have been equalized the final ssh analysis is carried out in the frequency domain by applying the technique on a frequency bin by frequency bin basis to the magnitude and unwrapped phase responses of the hrtfs the accuracy and interpolation performance of each of the computed ssh models is investigated and the usefulness of the ssh technique in analyzing directional hearing and particularly in spatializing sounds is discussed

heat equilibrium distribution in a turbulent flow we consider a shear flow of a scale invariant gaussian random velocity field that does not depend on the coordinates in the direction of the flow we investigate a heat advection coming from a gaussian random homogeneous source we discuss a relaxation at large time of a temperature distribution determined by the forced advection diffusion equation we represent the temperature correlation functions by means of the feynman kac formula jensen inequalities are applied for lower and upper bounds on the correlation functions we show that at finite time there is no velocity dependence of long range temperature correlations low momentum asymptotics in the direction of the flow but the equilibrium heat distribution has large distance correlations low momentum behavior with an index depending on the scaling index of the random flow and of the index of the random forcing if the velocity has correlations growing with the distance a turbulent flow then the large distance correlations depend in a crucial wa

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

applications of ldpc codes to the wiretap channel with the advent of quantum key distribution qkd systems perfect i e information theoretic security can now be achieved for distribution of a cryptographic key qkd systems and similar protocols use classical error correcting codes for both error correction for the honest parties to correct errors and privacy amplification to make an eavesdropper fully ignorant from a coding perspective a good model that corresponds to such a setting is the wire tap channel introduced by wyner in 1975 in this correspondence we study fundamental limits and coding methods for wire tap channels we provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel we also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes in some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity for the special case of a noiseless main channel and binary erasure channel we consider encoder and decoder design for codes achieving secrecy on the wiretap channel we show that it is possible to construct linear time decodable secrecy codes based on low density parity check ldpc codes that achieve secrecy

anomalous scaling of a triple correlation function of a randomly advected passive scalar for a short correlated gaussian velocity field the problem of a passive scalar with the imposed constant gradient is considered it is shown that the scaling of three point correlation function is anomalous in the limit of large dimension of space d anomalous exponent is calculated

renormalization group operator product expansion and anomalous scaling in models of turbulent advection recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field theoretic renormalization group rg and operator product expansion ope in that approach the anomalous scaling is established as a consequence of the existence in the corresponding field theoretic models of an infinite number of dangerous composite fields operators with negative critical dimensions which are identified with the anomalous exponents this allows one to calculate the exponents in a systematic perturbation expansion similar to the e expansion in the theory of critical phenomena the rg and ope approach is presented in a self contained way for the example of a passive scalar field temperature concentration of an impurity etc advected by a self similar gaussian velocity ensemble with vanishing correlation time the so called kraichnan s rapid change model where the anomalous exponents are known up to order o e3 effects of anisotropy compressibility and the correlation time of the velocity field are discussed passive advection by non gaussian velocity field governed by the stochastic navier stokes equation and passively advected vector e g magnetic fields are considered

calculation of acoustical scattering from a cluster of scatterers the problem of determining the field scattered by a cluster of scatterers when they are insonified by a known acoustical field is addressed the problem is formulated by using the t matrix method and the resulting system of linear equations is solved by using the multilevel fast multipole algorithm mlfma and the fast multipole method fast fourier transform fmmfft method and the efficiency of the two methods is compared it was observed that in general the mlfma performs better than the fmmfft algorithm however when the scatterers are distributed uniformly on a rectangular grid the fmmfft algorithm performs as good as the mlfma the accuracy of the methods is evaluated by modeling a spherical scatterer as composed of many small spheres

structure of the three point correlation function of a passive scalar in the presence of a mean gradient the three point correlation function of a passive scalar advected by a random incompressible velocity field in the presence of a mean gradient is investigated by means of phenomenological hopf equations numerical solutions are provided in the case where the velocity is gaussian white in time and with a power law in space v stackrel ensuremath rightarrow r ensuremath v stackrel ensuremath rightarrow 0 2 ensuremath sim r 2 ensuremath ensuremath epsilon and in the model introduced by shraiman and siggia c r acad sci 321 279 1995 anomalous scaling exponents are found in both models the numerics agrees with all the available analytic perturbative results in addition the angular dependence of the correlation function is explicitly determined in the batchelor limit of random advection by a smooth velocity field the exponent is found to remain very close to 1 as found experimentally in this limit the three point correlation function is found to be very well represented away from collinearity by an explicit integral representation

anomalous scaling nonlocality and anisotropy in a model of the passively advected vector field a model of the passive vector quantity advected by the gaussian velocity field with the covariance ensuremath propto ensuremath delta t ensuremath t ensuremath mathbf x ensuremath mathbf x ensuremath ensuremath varepsilon is studied the effects of pressure and large scale anisotropy are discussed the inertial range behavior of the pair correlation function is described by an infinite family of scaling exponents which satisfy exact transcendental equations derived explicitly in d dimensions by means of the functional techniques the exponents are organized in a hierarchical order according to their degree of anisotropy with the spectrum unbounded from above and the leading minimal exponent coming from the isotropic sector this picture extends to higher order correlation functions like in the scalar model the second order structure function appears nonanomalous and is described by the simple dimensional exponent s 2 ensuremath propto r 2 ensuremath ensuremath varepsilon for the higher order structure functions s 2n ensuremath propto r n 2 ensuremath ensuremath varepsilon ensuremath delta n the anomalous scaling behavior is established as a consequence of the existence in the corresponding operator product expansions of dangerous composite operators whose negative critical dimensions determine the anomalous exponents ensuremath delta n l0 a close formal resemblance of the model with the stirred navier stokes equation reveals itself in the mixing of relevant operators and is the main motivation of the paper using the renormalization group the anomalous exponents are calculated in the o ensuremath varepsilon approximation in large d dimensions for the even structure functions up to the twelfth order

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

calculation of the anomalous exponents in the rapid change model of passive scalar advection to order epsilon 3 the field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the gaussian velocity field with zero mean and correlation function approximately equal to delta t t k d epsilon inertial range anomalous exponents identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients are calculated within the epsilon expansion to order epsilon 3 three loop approximation including the exponents in anisotropic sectors the main goal of the paper is to give the complete derivation of this third order result and to present and explain in detail the corresponding calculational techniques the character and convergence properties of the epsilon expansion are discussed the improved inverse epsilon expansion is proposed and the comparison with the existing nonperturbative results is given

secure diversity multiplexing tradeoff of zero forcing transmit scheme at finite snr in this paper we address the finite signal to noise ratio snr diversity multiplexing tradeoff dmt of the multiple input multiple output mimo wiretap channel where a zero forcing zf transmit scheme that intends to send the secret information in the orthogonal space of the eavesdropper channel is used first we introduce the secrecy multiplexing gain at finite snr that generalizes the definition at high snr then we provide upper and lower bounds on the outage probability under secrecy constraint from which secrecy diversity gain estimates of zf are derived through asymptotic analysis we show that the upper bound underestimates the secrecy diversity gain whereas the lower bound is tight at high snr and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the mimo wiretap channel

secure transmission with multiple antennas part ii the mimome wiretap channel the capacity of the gaussian wiretap channel model is analyzed when there are multiple antennas at the sender intended receiver and eavesdropper the associated channel matrices are fixed and known to all the terminals a computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem the converse is based on a sato type argument used in other broadcast settings and the coding theorem is based on gaussian wiretap codebooks at high signal to noise ratio snr the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition and independently coding across the resulting parallel channels the associated capacity is expressed in terms of the corresponding generalized singular values it is shown that a semi blind masked multi input multi output mimo transmission strategy that sends information along directions in which there is gain to the intended receiver and synthetic noise along directions in which there is not can be arbitrarily far from capacity in this regime necessary and sufficient conditions for the secrecy capacity to be zero are provided which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed the resulting scaling laws establish that to prevent secure communication the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly and that the optimum division of antennas between sender and intended receiver is in the ratio of 2 1

fast multipole method for the biharmonic equation in three dimensions the evaluation of sums matrix vector products of the solutions of the three dimensional biharmonic equation can be accelerated using the fast multipole method while memory requirements can also be significantly reduced we develop a complete translation theory for these equations it is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering the translation of a pair of elementary solutions of the laplace equations the extension of the theory to the case of polyharmonic equations in r 3 is also discussed an efficient way of performing the fmm for biharmonic equations using the solution of a complex valued fmm for the laplace equation is presented compared to previous methods presented for the biharmonic equation our method appears more efficient the theory is implemented and numerical tests presented that demonstrate the performance of the method for varying problem sizes and accuracy requirements in our implementation the fmm for the biharmonic equation is faster than direct matrix vector product for a matrix size of 550 for a relative l 2 accuracy e 2 10 4 and n 3550 for e 2 10 1 2

anomalous scaling of passive scalar fields advected by the navier stokes velocity ensemble effects of strong compressibility and large scale anisotropy the field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities the density and the tracer fields advected by a random turbulent velocity field the latter is governed by the navier stokes equation for compressible fluid subject to external random force with the covariance t t k 4 d y where d is the dimension of space and y is an arbitrary exponent the original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models the corresponding renormalization group equations possess infrared attractive fixed points it is shown that various correlation functions of the scalar field its powers and gradients demonstrate anomalous scaling behavior in the inertial convective range already for small values of y the corresponding anomalous exponents identified with scaling critical dimensions of certain composite fields operators in the quantum field terminology can be systematically calculated as series in y the practical calculation is performed in the leading one loop approximation including exponents in anisotropic contributions it should be emphasized that in contrast to gaussian ensembles with finite correlation time the model and the perturbation theory presented here are manifestly galilean covariant the validity of the one loop approximation and comparison with gaussian models are briefly discussed

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

anomalous scaling of a passive scalar in the presence of strong anisotropy field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar quantity straight theta t x advected by the gaussian strongly anisotropic velocity field with the covariance infinity delta t t x x epsilon inertial range anomalous scaling behavior is established and explicit asymptotic expressions for the structure functions s n r identical with are obtained they are represented by superpositions of power laws the corresponding anomalous exponents which depend explicitly on the anisotropy parameters are calculated to the first order in epsilon in any space dimension d in the limit of vanishing anisotropy the exponents are associated with tensor composite operators built of the scalar gradients and exhibit a kind of hierarchy related to the degree of anisotropy the less is the rank the less is the dimension and consequently the more important is the contribution to the inertial range behavior the leading terms of the even odd structure functions are given by the scalar vector operators for the finite anisotropy the exponents cannot be associated with individual operators which are essentially mixed in renormalization but the aforementioned hierarchy survives for all the cases studied the second order structure function s2 is studied in more detail using the renormalization group and zero mode techniques the corresponding exponents and amplitudes are calculated within the perturbation theories in epsilon 1 d and in the anisotropy parameters if the anisotropy of the velocity is strong enough the skewness factor s 3 s 3 2 2 increases going down towards the depth of the inertial range the higher order odd ratios increase even if the anisotropy is weak

anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow a model of the passive vector field advected by the uncorrelated in time gaussian velocity with power like covariance is studied by means of the renormalization group and the operator product expansion the structure functions of the admixture demonstrate essential power like dependence on the external scale in the inertial range the case of an anomalous scaling the method of finding independent tensor invariants in the cases of two and three dimensions is proposed to eliminate linear dependencies between the operators entering into the operator product expansions of the structure functions the constructed operator bases which include the powers of the dissipation operator and the enstrophy operator provide the possibility of calculating the exponents of the anomalous scaling

computation of scattering from clusters of spheres using the fast multipole method a t matrix based method of solution of the multiple scattering problem was presented by the authors j acoust soc am 112 2688 2701 2002 this method can be applied to the computation of relatively small problems since the number of operations required grows with the number of spheres n as o n3 and with the sixth power of the wave number the use of iterative techniques accelerated using the fast multipole method fmm can accelerate this solution as presented by koc and chew j acoust soc am 103 721 734 1998 originally in this study we present a method that combines preconditioned krylov subspace iterative techniques fmm accelerated matrix vector products a novel fmm based preconditioner and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix vector multiplication grows with n as o n logn and with the third power of the wave number we discuss the convergence of the iterative techniques selection of the truncation number errors in the solution and other issues the results of the solution of test problems obtained with the method for n approximately 10 2 10 4 for different wave numbers are presented

recursions for the computation of multipole translation and rotation coefficients for the 3 d helmholtz equation we develop exact expressions for the coefficients of series representations of translations and rotations of local and multipole fundamental solutions of the helmholtz equation in spherical coordinates these expressions are based on the derivation of recurrence relations some of which to our knowledge are presented here for the first time the symmetry and other properties of the coefficients are also examined and based on these efficient procedures for calculating them are presented our expressions are direct and do not use the clebsch gordan coefficients or the wigner 3 j symbols although we compare our results with methods that use these to prove their accuracy for evaluating an nt term truncation of the translated series involving o n t 2 multipoles our expressions require o n t 3 evaluations compared to previous exact expressions that require o n t 5 operations

an approximate capacity distribution for mimo systems in this letter we derive the exact variance of the capacity of a multiple input multiple output mimo system this enables an investigation of the accuracy of a gaussian approximation to the capacity foreshadowed by various central limit theorems we confirm recent results which state that the capacity variance appears to converge to a limit independent of absolute antenna numbers but dependent on the ratio of the numbers of receive to transmit antennas the gaussian approximation itself is surprisingly good even in the worst cases giving satisfactory results

on local isotropy of passive scalars in turbulent shear flows an assessment of local isotropy and universality in high reynolds number turbulent flows is presented the emphasis is on the behaviour of passive scalar fields advected by turbulence but a brief review of the relevant facts is given for the turbulent motion itself experiments suggest that local isotropy is not a natural concept for scalars in shear flows except perhaps at such extreme reynolds numbers that are of no practical relevance on earth yet some type of scaling exists even at moderate reynolds numbers the relation between these two observations is a theme of this paper

the fast multipole method i error analysis and asymptotic complexity this paper is concerned with the application of the fast multipole method fmm to the maxwell equations this application differs in many aspects from other applications such as the n body problem laplace equation and quantum chemistry etc the fmm leads to a significant speed up in cpu time with a major reduction in the amount of computer memory needed when performing matrix vector products this leads to faster resolution of scattering of harmonic plane waves from perfectly conducting obstacles emphasis here is on a rigorous mathematical approach to the problem we focus on the estimation of the error introduced by the fmm and a rigorous analysis of the complexity o n log n of the algorithm we show that error estimates reported previously are not entirely satisfactory and provide sharper and more precise estimates

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

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

the secrecy capacity region of the gaussian mimo multi receiver wiretap channel in this paper we consider the gaussian multiple input multiple output mimo multi receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper we derive the secrecy capacity region of this channel for the most general case we first show that even for the single input single output siso case existing converse techniques for the gaussian scalar broadcast channel cannot be extended to this secrecy context to emphasize the need for a new proof technique our new proof technique makes use of the relationships between the minimum mean square error and the mutual information and equivalently the relationships between the fisher information and the differential entropy using the intuition gained from the converse proof of the siso channel we first prove the secrecy capacity region of the degraded mimo channel in which all receivers have the same number of antennas and the noise covariance matrices can be arranged according to a positive semi definite order we then generalize this result to the aligned case in which all receivers have the same number of antennas however there is no order among the noise covariance matrices we accomplish this task by using the channel enhancement technique finally we find the secrecy capacity region of the general mimo channel by using some limiting arguments on the secrecy capacity region of the aligned mimo channel we show that the capacity achieving coding scheme is a variant of dirty paper coding with gaussian signals

a scalar potential formulation and translation theory for the time harmonic maxwell equations we develop a computational method based on the debye scalar potential representation which efficiently reduces the solution of maxwell s equations to the solution of two scalar helmholtz equations one of the key contributions of this paper is a theory for the translation of maxwell solutions using such a representation since the scalar potential form is not invariant with respect to translations the translation theory is developed by introducing conversion operators which enable the representation of the electric and magnetic vector fields via scalar potentials in an arbitrary reference frame advantages of this representation include the fact that only two helmholtz equations need be solved and moreover the divergence free constraints are satisfied automatically by construction truncation error bounds are also presented the availability of a translation theory and error bounds for this representation can find application in methods such as the fast multipole method for illustration of the use of the representation and translation theory we implemented an algorithm for the simulation of mie scattering off a system of spherical objects of different sizes and dielectric properties using a variant of the t matrix method the resulting system was solved using an iterative method based on gmres the results of the computations agree well with previous computational and experimental results

calculation of the addition coefficients in electromagnetic multisphere scattering theory one of the most intractable problems in electromagnetic multisphere scattering theory is the formulation and evaluation of vector addition coefficients introduced by the addition theorems for vector spherical harmonics this paper presents an efficient approach for the calculation of both scalar and vector translational addition coefficients which is based on fast evaluation of the gaunt coefficients the paper also rederives the analytical expressions for the vector translational addition coefficients and discusses the strengths and limitations of other formulations and numerical techniques found in the literature numerical results from the formulation derived in this paper agree with those of a previously published recursion scheme that completely avoids the use of the gaunt coefficients but the method of direct calculation proposed here reduces the computing time by a factor of 4 6

turbulent compressible fluid renormalization group analysis scaling regimes and anomalous scaling of advected scalar fields we study a model of fully developed turbulence of a compressible fluid based on the stochastic navier stokes equation by means of the field theoretic renormalization group in this approach scaling properties are related to the fixed points of the renormalization group equations previous analysis of this model near the real world space dimension 3 identified a scaling regime n v antonov et al theor math phys 110 305 1997 tmphah0040 577910 1007 bf02630456 the aim of the present paper is to explore the existence of additional regimes which could not be found using the direct perturbative approach of the previous work and to analyze the crossover between different regimes it seems possible to determine them near the special value of space dimension 4 in the framework of double y and expansion where y is the exponent associated with the random force and 4 d is the deviation from the space dimension 4 our calculations show that there exists an additional fixed point that governs scaling behavior turbulent advection of a passive scalar density field by this velocity ensemble is considered as well we demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial convective range the corresponding anomalous exponents identified as scaling dimensions of certain composite fields can be systematically calculated as a series in y and all calculations are performed in the leading one loop approximation

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

the secrecy capacity of the mimo wiretap channel we consider the mimo wiretap channel that is a mimo broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver while the other user is an eavesdropper perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate while insuring that the eavesdropper gets zero bits of information in this paper we compute the perfect secrecy capacity of the multiple antenna mimo broadcast channel where the number of antennas is arbitrary for both the transmitter and the two receivers our technique involves a careful study of a sato like upper bound via the solution of a certain algebraic riccati equation

a broadband fast multipole accelerated boundary element method for the three dimensional helmholtz equation the development of a fast multipole method fmm accelerated iterative solution of the boundary element method bem for the helmholtz equations in three dimensions is described the fmm for the helmholtz equation is significantly different for problems with low and high kd where k is the wavenumber and d the domain size and for large problems the method must be switched between levels of the hierarchy the bem requires several approximate computations numerical quadrature approximations of the boundary shapes using elements and these errors must be balanced against approximations introduced by the fmm and the convergence criterion for iterative solution these different errors must all be chosen in a way that on the one hand excess work is not done and on the other that the error achieved by the overall computation is acceptable details of translation operators for low and high kd choice of representations and bem quadrature schemes all consistent with these approximations are described

anomalous scaling of a passive scalar advected by the navier stokes velocity field two loop approximation the field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non gaussian velocity field with finite correlation time the velocity is governed by the navier stokes equation subject to an external random stirring force with the correlation function proportional to ensuremath delta t ensuremath t ensuremath k 4 ensuremath d ensuremath 2 ensuremath epsilon it is shown that the scalar field is intermittent already for small ensuremath epsilon its structure functions display anomalous scaling behavior and the corresponding exponents can be systematically calculated as series in ensuremath epsilon the practical calculation is accomplished to order ensuremath epsilon 2 two loop approximation including anisotropic sectors as for the well known kraichnan rapid change model the anomalous scaling results from the existence in the model of composite fields operators with negative scaling dimensions identified with the anomalous exponents thus the mechanism of the origin of anomalous scaling appears similar for the gaussian model with zero correlation time and the non gaussian model with finite correlation time it should be emphasized that in contrast to gaussian velocity ensembles with finite correlation time the model and the perturbation theory discussed here are manifestly galilean covariant the relevance of these results for real passive advection and comparison with the gaussian models and experiments are briefly discussed

analysis of radiative scattering for multiple sphere configurations an analysis of radiative scattering for an arbitrary configuration of neighbouring spheres is presented the analysis builds upon the previously developed superposition solution in which the scattered field is expressed as a superposition of vector spherical harmonic expansions written about each sphere in the ensemble the addition theorems for vector spherical harmonics which transform harmonics from one coordinate system into another are rederived and simple recurrence relations for the addition coefficients are developed the relations allow for a very efficient implementation of the order of scattering solution technique for determining the scattered field coefficients for each sphere prediction of the radiative absorption and scattering characteristics of small particles is important to researchers in a number of fields e g atmospheric modelling analysis of radiative transfer from flames and development of nonintrusive laser based optical diagnostic methods computation of the radiative characteristics of spherical particles from lorenz mie theory is practically a trivial matter due to the existence of efficient computer codes bohren huffman 1983 however it is not unusual to encounter situations in which the individual particles while spherical in shape are so close together that the isolated sphere assumption inherent in lorenz mie theory is questionable a common example is soot formed in combustion processes electron micrographs of the individual soot particles reveal them to be agglomerates of a large number of primary spherical particles dobbins

normal and anomalous scaling of the fourth order correlation function of a randomly advected passive scalar for a delta correlated velocity field simultaneous correlation functions of a passive scalar satisfy closed equations we analyze the equation for the four point function to describe a solution completely one has to solve the matching problems at the scale of the source and at the diffusion scale we solve both the matching problems and thus find the dependence of the four point correlation function on the diffusion and pumping scale for large space dimensionality d it is shown that anomalous scaling appears in the first order of 1 d perturbation theory anomalous dimensions are found analytically both for the scalar field and for it s derivatives in particular for the dissipation field

recovery of individual head related transfer functions from a small set of measurementsa head related transfer functions hrtfs vary with individuals and in practice measuring hrtfs with high directional resolution for each individual is tiresome based on a basis functions representation of hrtfs the present work proposes a method for recovering individual hrtfs from a small set of measurements the hrtfs are represented by a combination of a small set of spatial basis functions sbfs with frequency and individual dependent weights the sbfs are derived by applying spatial principal component analysis to a baseline hrtf dataset with high directional resolution the individual weights for any subject outside the dataset are estimated from measurements at a few source directions and then the hrtfs with high directional resolution are recovered by combining the sbfs and the individual weights in an illustrative case the sbfs derived from a baseline dataset that includes 20 subjects are used to recover the hrtf magnitudes for six subjects outside the baseline dataset results show that individual hrtf magnitudes can be recovered from measurements at 73 directions with a mean signal to distortion ratio of 19 db the proposed method is also applicable to recovering head related impulse responses the results of psychoacoustic experiments indicate that in most cases the recovered and measured hrtfs are indistinguishable

anomalous scaling for a passive scalar near the batchelor limit a class of phenomenological hopf equations describing mixing of a passive scalar by random flow close to the batchelor limit i e advection by random strain and vorticity is analyzed in the batchelor limit multipoint correlators of the scalar are constructed explicitly by exploiting the sl n r symmetry of the hopf operator hopf equations close to this integrable limit are solved via singular perturbation theory based on matched asymptotic expansions the solution for the three point correlator exhibits anomalous scaling indicating persistence of the small scale anisotropy for the scalar in addition to the exponent the full configuration dependence of the correlator is obtained s1063 651x 98 08703 0 pacs number s 47 27 2i