continuation of acoustic near fields this paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator this analytic continuation is an extension or extrapolation of the given measured field into a region outside and tangential to the original finite sheet and is based on the green s function the transfer function relating acoustic quantities on the two conformal surfaces the continuation of the measured pressure field is an inverse problem that requires the use or regularization theory especially when noise is present in the data an iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet the results are accurate close to the original boundary and taper decay toward zero with distance away from it the algorithm is tested on numerical and experimental data from a point driven rectangular plate results show the successful extrapolation continuation of this data into an area nearly double that of the original pressure field this algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces

tests of mode coupling theory in two dimensions we analyze the glassy dynamics of binary mixtures of hard disks in two dimensions predictions of the mode coupling theory mct are tested with extensive brownian dynamics simulations measuring the collective particle density correlation functions in the vicinity of the glass transition we verify four predicted mixing effects for instance for large size disparities adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long time dynamics while for small size disparities it leads to a slowing down qualitative features of the nonergodicity parameters and the relaxation which both depend in a nontrivial way on the mixing ratio are found in the simulated correlators studying one system in detail we are able to determine its ideal mct glass transition point as c 0 7948 and test mct predictions quantitatively

on the minimum of the christoffel function abstract we consider the christoffel function n d associated with a measure d on a compact interval and the question where the minimum of the christoffel function is attained sufficient conditions on the coefficients appearing in the continued fraction expansion of the stieltjes transform are obtained for the n th christoffel function to attain its minimum at the boundary points of the underlying interval in contrary to several monotonicity results for christoffel functions in the literature our approach does not require the absolute continuity of the measure with respect to the lebesgue measure

nonequilibrium mode coupling theory for uniformly sheared underdamped systems nonequilibrium mode coupling theory mct for uniformly sheared underdamped systems is developed starting from the microscopic thermostated sllod equation and the corresponding liouville equation special attention is paid to the translational invariance in the sheared frame which requires an appropriate definition of the transient time correlators the derived mct equation satisfies the alignment of the wave vectors and is manifestly translationally invariant isothermal condition is implemented by the introduction of current fluctuation in the dissipative coupling to the thermostat this current fluctuation grows in the ensuremath alpha relaxation regime which generates a pronounced relaxation of the yield stress compared to the overdamped case this result fills the gap between the molecular dynamics simulation and the overdamped mct reported previously the response to a perturbation of the shear rate demonstrates an inertia effect which is not observed in the overdamped case our theory turns out to be a nontrivial extension of the theory by fuchs and cates j rheol 53 957 2009 to underdamped systems since our starting point is identical to that of chong and kim phys rev e 79 021203 2009 the contradictions between fuchs cates and chong kim are resolved

extension of measurement surface in near field acoustic holography in near field acoustic holography when measurements are made over a limited surface there has been recent interest in numerically enlarging the measurement surface tangentially current algorithms use iterative methods to extrapolate the field tangentially outward an algorithm based on the method of superposition is applied here which may be used to either extrapolate the field to enlarge the measurement surface or to interpolate in case there is a hole in the measurement surface where data are not available

3 d sound source reconstruction and field reprediction using the helmholtz integral equation abstract a method for reconstruction of the boundary conditions of an arbitrarily shaped three dimensional 3 d sound source from a finite number of field pressures is presented and the associated field is repredicted by using the helmholtz integral equation to minimize the reconstruction error due to noise in the field pressures a filtering method is proposed and it is verified that numerically singular values which correspond to the higher order modes of the evanescent like components of the source velocities are eliminated for arbitrarily shaped sources with complex boundary conditions the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source our technique can be used in computer aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted

basic theory and properties of statistically optimized near field acoustical holography to avoid the requirement set by standard near field acoustical holography nah to measure an area that fully covers the source a set of so called patch nah methods has been introduced one such method is the statistically optimized nah sonah in this method the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy the present paper gives an overview of the basic theory of sonah including a description of phenomena such as spatial aliasing and wave number domain leakage a revised and generalized mathematical formulation is given covering the calculation of all three components of particle velocity and the use of up to six virtual source planes a set of formulas for the inherent estimation error level of the method is derived and used to visualize the regions of validity of the sonah predictions for some typical microphone array geometries the sensitivity of the inherent error level distribution to changes in the parameters of the sonah algorithm is also investigated

sound field reconstruction using compressed modal equivalent point source method the accuracy resolution and economic cost of near field acoustic holography nah are highly dependent on the number of spatial sampling points generally higher accuracy and resolution require more spatial sampling points which may increase the workload of measurement or the hardware cost compressive sensing cs is able to solve the underdetermined problems by utilizing the sparsity of signals and thus it can be applied to nah to reduce the number of spatial sampling points but at the same time provide a high resolution reconstruction image based on the cs theory this paper proposes a compressed modal equivalent point source method cmesm in the method a sparse basis that is obtained from the eigen decomposition of the power resistance matrix is introduced to compress the equivalent point source strengths and the l1 norm minimization is used to promote sparse solutions both numerical simulation and experimental results demonstrate the validity of the proposed cmesm and show its advantage over the existing methods when the number of spatial sampling points is reduced

molecular mode coupling theory applied to a liquid of diatomic molecules we study the molecular mode coupling theory for a liquid of diatomic molecules the equations for the critical tensorial nonergodicity parameters f m ll q and the critical amplitudes of the beta relaxation h m ll q are solved up to a cutoff l co 2 without any further approximations here l m are indices of spherical harmonics contrary to previous studies where additional approximations were applied we find in agreement with simulations that all molecular degrees of freedom vitrify at a single temperature t c the theoretical results for the nonergodicity parameters and the critical amplitudes are compared with those from simulations the qualitative agreement is good for all molecular degrees of freedom to study the influence of the cutoff on the nonergodicity parameter we also calculate the nonergodicity parameters for an upper cutoff l co 4 in addition we also propose a method for the calculation of the critical nonergodicity parameter from the liquid side of transition

hypergroups of compact type we consider commutative hypergroups with translation operators which are compact on l 2 resp l 1 it will be shown that such hypergroups are necessarily discrete and that in the case of compact translations on l 1 the support of the plancherel measure coincides with the set of all characters and the hypergroup must be symmetric furthermore we will show that a certain type of reiter s condition is fulfilled

extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation a method is presented to suppress grating lobes in beamforming using phase unwrapping and array interpolation when the phase of each cross spectrum is successfully unwrapped the magnitude and phase of the cross spectral matrix may be interpolated for cases where these quantities vary smoothly interpolation is straightforward even above the spatial nyquist frequency two applications are presented localization of a broadband source and characterization of a source with frequency dependent location in both cases grating lobes are suppressed and the source is localized at frequencies up to at least 8 times the spatial nyquist frequency

a generalized internal source density method for the forward and backward projection of harmonic pressure fields from complex bodies a generalized internal source density gisd method is presented to address the forward and backward projection of harmonic pressure fields from complex three dimensional bodies the gisd approach is based on decomposing the field on a closed surface of revolution in the fluid into a summation of circumferential orders where the pressure field for each order is associated with an internal linear distribution of ring sources on the axis of revolution of the surface both dirichlet and neumann boundary value problems may be addressed using the approach in which the axial variation of each ring source distribution is formulated as the solution of a minimum mean square error problem which is subsequently solved using svd methods the resulting linear distributions of ring sources can be simply used to determine the entire pressure and velocity fields of a complex harmonically vibrating body in particular the pressure and or normal velocity on a vibrating body can be readily obtained from the pressure field over a closed surface local intensity and radiated power can thus be simply obtained far field pressures are simply obtained from the axial fourier transforms of the ring source distributions several examples are presented to illustrate the behaviour of the source distributions for spherical geometries the analytical results obtained via the gisd method agree with those obtained via classical methods

a statistical mechanical theory of slow dynamics near the glass transition abstract a statistical mechanical theory of slow dynamics near the glass transition in two kinds of glass forming systems m molecular systems and s suspensions of colloids is presented from a unified point of view based on the tokuyama mori projection operator method the exact diffusion equations for the coherent and the incoherent intermediate scattering functions are first derived whose memory functions are convolutionless in time and contain the correlation effects due to the hydrodynamic interactions in s the analytic expressions of the memory functions are then calculated within the mode coupling theory mct approximation and are shown to coincide with the conventional ones obtained by mct alternative mode coupling equations are thus obtained in m and s separately self diffusion is also discussed alternative equations for the mean square displacement and the non gaussian parameter are also derived within mct approximation all results in both the systems are compared with those obtained by mct

comparison of the tokuyama mori type projection operator method to that of mori type near the glass transition abstract two types of projection operator methods mori type and tokuyama mori type are tested for studying the slow dynamics of a single particle in complex systems near the glass transition from a unified point of view based on the mean field theory recently proposed by the present author the molecular and brownian dynamics simulations and the corresponding solutions of the mode coupling theory developed by employing mori type formalism are compared consistently disagreement is found for the mean square displacements in stage thus validity of both types is fully investigated near the glass transition from a new standpoint

fast fourier transform and singular value decomposition formulations for patch nearfield acoustical holography nearfield acoustical holography nah requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface the latter generally coincident with a vibrator patch nah provides a major simplification by eliminating the need for complete surface pressure scans only a small area needs to be scanned to determine the normal velocity on the corresponding small area concentric patch on the vibrator the theory of patch nah is based on 1 an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and 2 a decomposition of the transfer function pressure to velocity and or pressure to pressure between the two surfaces using the singular value decomposition svd for general shapes and the fast fourier transform fft for planar surfaces inversion of the transfer function is stabilized using tikhonov regularization and the morozov discrepancy principle experimental results show that root mean square errors of the normal velocity reconstruction for a point driven vibrator over 200 2700 hz average less than 20 for two small concentric patch surfaces 0 4 cm apart reconstruction of the active normal acoustic intensity was also successful with less than 30 error over the frequency band

various amenability properties of the l1 algebra of polynomial hypergroups and applications we investigate amenability weak amenability and a t amenability of the l 1 algebra of polynomial hypergroups and derive from these properties some applications for the corresponding orthogonal polynomials

α amenable hypergroups let k denote a locally compact commutative hypergroup l1 k the hypergroup algebra and a real valued hermitian character of k we show that k is amenable if and only if l1 k is left amenable we also consider the amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable

reduction methods of the reconstruction error for large scale implementation of near field acoustical holography new extrapolation methods in real and wave number spaces are proposed to extend near field acoustical holography nah toward a more quantitative technique applicable to the vibration measurement of actual large scale structures the finiteness of the measurement aperture is a serious impediment to such large scale implementation of nah because the measurement aperture sufficiently larger than the vibrating structure of interest is usually needed we should thus investigate how to reduce the reconstruction error when the measurement aperture is restricted to a fraction of the vibrating structure the following practical suggestions are derived from simulations and underwater experiments 1 a wave number space extrapolation method can reduce the reconstruction error to about 25 for the measurement aperture corresponding to 1 16th of the vibrating structure when 10 000 iterations of the extrapolation process are applied 2 a real space extrapolation method can reduce the reconstruction error to negligible degree 10 10 for the measurement aperture corresponding to four times as large as the vibration structure when ten iterations of the extrapolation process are applied 3 the former method may be widely and safely applied but many iterations are necessary the latter method can reduce the reconstruction error very quickly but a wider measurement aperture than that in the former is needed therefore when the measurement aperture cannot be larger than the vibrating structure the former method is recommended while when the measurement aperture is larger than the structure the latter method is recommended summing up the accuracy of our proposed methods which is attributed to the property of data extrapolation method that the data inside the measurement aperture is conserved after adequately extrapolating the data outside the aperture will be relevant to a more quantitative measurement and analysis of real large scale structures

constrained d and d_1 optimal designs for polynomial regression in the common polynomial regression model of degree m we consider the problem of determining the d and d 1 optimal designs subject to certain constraints for the d 1 efficiencies in the models of degree m j m j 1 m k m j 0 k 0 given we present a complete solution of these problems which on the one hand allow a fast computation of the constrained optimal designs and on the other hand give an answer to the question of the existence of a design satisfying all constraints our approach is based on a combination of general equivalence theory with the theory of canonical moments in the case of equal bounds for the d 1 efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials

hypergroups and invariant complemented subspaces abstract let k be a hypergroup with a haar measure the purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of l k and c 0 k the class of left translation invariant w subalgebras of l k and finally the class of non zero left translation invariant c subalgebras of c 0 k in the hypergroup context with the goal of finding some relations between these function spaces among other results we construct two correspondences one between closed weil subhypergroups and certain left translation invariant w subalgebras of l k and another between compact subhypergroups and a specific subclass of the class of left translation invariant c subalgebras of c 0 k by the help of these two characterizations we extract some results about invariant complemented subspaces of l k and c 0 k

connections of activated hopping processes with the breakdown of the stokes einstein relation and with aspects of dynamical heterogeneities we develop an extended version of the mode coupling theory mct for glass transition which incorporates activated hopping processes via the dynamical theory originally formulated to describe diffusion jump processes in crystals the dynamical theory approach adapted here to glass forming liquids treats hopping as arising from vibrational fluctuations in the quasiarrested state where particles are trapped inside their cages and the hopping rate is formulated in terms of the debye waller factors characterizing the structure of the quasiarrested state the resulting expression for the hopping rate takes an activated form and the barrier height for the hopping is self generated in the sense that it is present only in those states where the dynamics exhibits a well defined plateau it is discussed how such a hopping rate can be incorporated into mct so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover we then show that the developed theory accounts for the breakdown of the stokes einstein relation observed in a variety of fragile glass formers it is also demonstrated that characteristic features of dynamical heterogeneities revealed by recent computer simulations are reproduced by the theory more specifically a substantial increase of the non gaussian parameter double peak structure in the probability distribution of particle displacements and the presence of a growing dynamic length scale are predicted by the extended mct developed here which the idealized version of the theory failed to reproduce these results of the theory are demonstrated for a model of the lennard jones system and are compared with related computer simulation results and experimental data

reconstruction of the acoustic field over a limited surface area on a vibrating cylinder the acoustic field on a small region on the surface of a radiating cylindrical shell is reconstructed from measurements of pressure made on a limited nearby surface the boundary element method is applied to compute an operator relating the pressure on a small measurement surface located near the structure to the normal velocity at all points on the structure surface since the inverse problem of the reconstruction of the surface field is ill posed singular value decomposition is applied to invert the operator it is demonstrated that the surface field may be reconstructed over the portion of the structure surface located under the measurement surface

asymptotic laws and preasymptotic correction formulas for the relaxation near glass transition singularities within the mode coupling theory mct for the dynamics of simple liquids the leading corrections to the asymptotic solutions for the relaxation in the vicinity of an ideal glass transition are derived the formulas are used to determine the range of validity of the scaling law description of the mct results for the a and b processes in glass forming systems solutions of the mct equations of motion are calculated for a hard sphere colloidal suspension model and compared with the derived analytical results the leading order formulas are shown to describe the major qualitative features of the bifurcation scenario near the transition and the leadingplus next to leading order formulas are demonstrated to give a quantitative description of the evolution of structural relaxation for the model s1063 651x 97 06005 4

robust designs for polynomial regression by maximizing a minimum of d and d1 efficiencies in the common polynomial regression of degree m we determine the design which maximizes the minimum of the d efficiency in the model of degree m and the d 1 efficiencies in the models of degree m j m k j k 0 given the resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness of fit of the assumed model of degree m by testing the highest coefficients in the polynomials of degree m j m k our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria the optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials

completely monotone solutions of the mode coupling theory for mixtures we establish that a mode coupling approximation for the dynamics of multi component systems obeying smoluchowski dynamics preserves a subtle yet fundamental property the partial density correlation functions are considered as matrices completely monotone i e they can exactly be written as superpositions of decaying exponentials only this statement holds no matter what further approximations are needed to calculate the theory s coupling parameters the long time limit of these functions fulfills a maximum property and an iteration scheme for its numerical determination is given we also show the existence of a unique solution to the equations of motion for which power series both for short times and small frequencies exist the latter except at special points where ergodic to nonergodic transitions occur these transitions are bifurcations that are proven to be of the cuspoid family

associated laguerre and hermite polynomials explicit orthogonality relations are found for the associated laguerre and hermite polynomials one consequence is the construction of the n 1 n pade approximation to a 1 b x a b x where a b x is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity

nonequilibrium mode coupling theory for uniformly sheared systems we develop a nonequilibrium mode coupling theory for uniformly sheared systems starting from microscopic thermostatted sllod equations of motion our theory aims at describing stationary state properties including rheological ones of sheared systems and this is accomplished via two steps first a set of self consistent equations is formulated based on the projection operator formalism and on the mode coupling approach for the transient density correlators which measure the correlations between the density fluctuations in the initial equilibrium state and the ones at later times after the shearing force is turned on the transient time correlation function formalism is then used which combined with the mode coupling approximation expresses stationary state properties in terms of the transient density correlators a detailed comparison of our theory is also presented with the related mode coupling theory which is based on the smoluchowski equation for brownian particles under stationary shearing

orthogonal polynomials with a constant recursion formula and an application to harmonic analysis on calcule la mesure pour laquelle une suite de polynomes avec une formule de recurrence constante est orthogonale

fast wideband acoustical holography patch near field acoustical holography methods like statistically optimized near field acoustical holography and equivalent source method are limited to relatively low frequencies where the average array element spacing is less than half of the acoustic wavelength while beamforming provides useful resolution only at medium to high frequencies with adequate array design both methods can be used with the same array but for holography to provide good low frequency resolution a small measurement distance is needed whereas beamforming requires a larger distance to limit sidelobe issues the wideband holography method of the present paper was developed to overcome that practical conflict only a single measurement is needed at a relatively short distance and a single result is obtained covering the full frequency range the method uses the principles of compressed sensing a sparse sound field representation is assumed with a chosen set of basis functions a measurement is taken with an irregular array and the inverse problem is solved with a method that enforces sparsity in the coefficient vector instead of using regularization based on the 1 norm of the coefficient vector an iterative solution procedure is used that promotes sparsity the iterative method is shown to provide very similar results in most cases and to be computationally much more efficient

fast spherical fourier algorithms spherical fourier series play an important role in many applications a numerically stable fast transform analogous to the fast fourier transform is of great interest for a standard grid of o n2 points on the sphere a direct calculation has computational complexity of o n4 but a simple separation of variables reduces the complexity to o n3 here we improve well known fast algorithms for the discrete spherical fourier transform with a computational complexity of o n2 log2 n furthermore we present for the first time a fast algorithm for scattered data on the sphere for arbitrary o n2 points on the sphere a direct calculation has a computational complexity of o n4 but we present an approximate algorithm with a computational complexity of o n2 log2 n

the problem of vibration field reconstruction statement and general properties abstract the paper addresses the problem of reconstructing the vibration field of a structure or the acoustic field of a bounded fluid from limited data the problem relates to practical situations when there is a need to know the dynamic stress and displacement distribution over the entire structure e g for estimating its remaining service life but the vibration may be measured only on accessible parts of the structure surface in the paper this problem is mathematically formulated and its general properties solvability uniqueness and continuity are studied most attention is paid to the analysis of the error of reconstruction one of the main results obtained is the proof of existence of the optimal vibration model of the structure which renders minimum to the reconstruction error the application of the results to discrete systems is discussed

monotonicity of zeros for a class of polynomials including hypergeometric polynomials we study the monotonicity of zeros in connection with perturbed recurrence coefficients of polynomials satisfying certain three term recurrence relations of frobenius type these recurrence relations are the key ingredient for the tridiagonal approach developed by delsarte and genin to solve the standard linear prediction problem as a particular case we consider the askey para orthogonal polynomials on the unit circle 2 f 1 n a b i 2 a 1 z a b r extending a recent result about the monotonicity of their zeros with respect to the parameter b finally the consequences of our results in the theory of orthogonal polynomials on the real line are discussed

mode coupling theory and the fluctuation dissipation theorem for nonlinear langevin equations with multiplicative noise in this letter we develop a mode coupling theory for a class of nonlinear langevin equations with multiplicative noise using a field theoretic formalism these equations are simplified models of realistic colloidal suspensions we prove that the derived equations are consistent with the fluctuation dissipation theorem we also discuss the generalization of the result given here to real fluids and the possible description of supercooled fluids in the ageing regime we demonstrate that the standard idealized mode coupling theory is not consistent with the fdt in a strict field theoretic sense

nonequilibrium identities and response theory for dissipative particles we derive some nonequilibrium identities such as the integral fluctuation theorem and the jarzynski equality starting from a nonequilibrium state for dissipative classical systems thanks to the existence of the integral fluctuation theorem we can naturally introduce an entropy like quantity for dissipative classical systems in far from equilibrium states we also derive the generalized green kubo formula as a nonlinear response theory for a steady dynamics around a nonequilibrium state we numerically verify the validity of the derived formulas for sheared frictionless granular particles

a study on regularization parameter choice in near field acoustical holography regularization plays an important role in near field acoustical holography nah and choosing the right amount of regularization is crucial in order to get a meaningful solution an automated method such as the l curve or generalized cross validation gcv is often used in nah to choose a regularization parameter these parameter choice methods pcms are attractive since they require no a priori knowledge about the noise however there seems to be no clear understanding of when one pcm is better than the other this paper presents comparisons of three pcms gcv l curve and normalized cumulative periodogram ncp the latter method is new within nah and it is based on the fourier transform of the residual vector the methods are used in connection with three nah methods statistically optimized near field acoustical holography sonah the inverse boundary element method ibem and the equivalent source method esm all combinations of the pcms and the nah methods are investigated using simulated measurements with different types of noise added to the input finally the comparisons are carried out for a practical experiment this aim of this work is to create a better understanding of which mechanisms that affect the performance of the different pcms

reformulation of time convolutionless mode coupling theory near the glass transition abstract the time convolutionless mode coupling theory tmct recently proposed is reformulated under the condition that one of two approximations which have been used to formulate the original tmct in addition to the mct approximations done on a derivation of nonlinear memory function in terms of the intermediate scattering function is not employed because it causes unphysical results for intermediate times the improved tmct equation is then derived consistently under another approximation it is first checked that the ergodic to non ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long time dynamics of both equations coincides with each other however it is emphasized that a difference between them appears in the intermediate time dynamics of physical quantities such a difference is explored numerically in the dynamics of a non gaussian parameter by employing the percus yevick static structure factor to calculate the nonlinear memory function

on monotonicity of zeros of paraorthogonal polynomials on the unit circle abstract the purpose of this note is to establish necessary and sufficient conditions for the monotonicity with respect to a real parameter of zeros of paraorthogonal polynomials on the unit circle it is also provided tractable sufficient conditions and an application example

near field acoustic holography for an axisymmetric geometry a new formulation near field acoustic holography has recently been extended to nonseparable coordinate systems by applying the boundary elements method the formulation currently implemented applies singular value decomposition to treat the presence of evanescent waves in the near field of the structure a new method is introduced for an axisymmetric geometry that is better suited for broadband data than the singular value decomposition algorithm enabling reduced computation time and providing a new expansion for the surface field with a set of functions that can be expressed as real functions independent of frequency and independent of the choice of a measurement surface the method is tested on numerically generated data

compressive sensing based spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity a low frequency sound field within a cylindrical cavity can be well approximated by a sparse set of fourier bessel series in a spherical coordinate system the approximation accuracy can be guaranteed as long as the series coefficients are well estimated by use of spherical microphone arrays sma conventional methods like spherical fourier transform and helmholtz equation least square require a large number of sensors and it is difficult to estimate the high order coefficients in the presence of sensor noise to cope with these issues compressive sensing cs is utilized and compared with the conventional methods in this study the estimate of the high order coefficients from contaminated measurements is examined and the effect of modal behavior is analyzed numerical simulations show that sensors can be significantly saved especially for high order cavity modes due to the low sparsity of coefficients which is also stable as the modal frequency increases and the overall accuracy is also improved the optimal sma configuration for the use of cs is studied a large sma with omni microphone deployed by the fliege sampling scheme is suggested the cs results are finally validated through the good simulated reconstructions of cylindrical cavity modes

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

scaling of plane wave functions in statistically optimized near field acoustic holography statistically optimized near field acoustic holography sonah is a patch holography method meaning that it can be applied in cases where the measurement area covers only part of the source surface the method performs projections directly in the spatial domain avoiding the use of spatial discrete fourier transforms and the associated errors first an inverse problem is solved using regularization for each calculation point a multiplication must then be performed with two transfer vectors one to get the sound pressure and the other to get the particle velocity considering sonah based on sound pressure measurements existing derivations consider only pressure reconstruction when setting up the inverse problem so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem the present paper introduces a scaling of the applied plane wave functions that takes the amplification into account and it is