calculation of acoustic radiation using equivalent sphere methods among the methods generally used to solve a problem in the domain of acoustic radiation the equivalent sources method offers an interesting alternative it consists in replacing the vibrating surface with a distribution of acoustic sources placed inside the structure the contribution of each source is determined in such a way that the acoustic field radiated by these sources verifies the same boundary conditions on the structure the number of unknowns in the problem is no longer directly linked to the number of mesh points on the structure as with boundary elements methods but to the number of equivalent sources employed in the model the equivalent source method is therefore of major interest if the acoustic radiation of the structure can be approximated with a sufficiently low number of sources this paper proposes its application when the equivalent source is a sphere in this case the number of unknowns is equal to the number of modes in contrast to the one point multipole the sphere has a surface surrounding a closed volume to express the boundary conditions although sphere multipole equivalence has been demonstrated the surface of the sphere allows normalization of the functions used leading to stabilization of the system to be resolved first the main acoustic radiation characteristics of a sphere and of the linear system verified by the modal coefficients of an equivalent sphere are presented the different parameters of the model are then studied position and radius of the equivalent sphere truncation of the series and influence of the spatial sampling mesh in the same vein a second approach is presented it consists of making each point of the structure correspond to a point of the sphere and the vibrating field at the surface of the sphere is deduced from that of the structure by simple geometric projection results can be obtained very quickly as no matrix inversion is required the accuracy of the results depends on the distance between the sphere and the structure finally an experimental validation that uses both methods is presented and shows interesting results when the structure is closed and when its shape is not too far removed from a sphere

accuracy analysis and optimization of the method of auxiliary sources mas for scattering by a circular cylinder this paper presents a rigorous accuracy analysis of the method of auxiliary sources mas when applied to scattering problems a benchmark canonical geometry consisting of a perfectly conducting infinite circular cylinder is chosen for clarity and simplicity for this particular structure it is shown that the mas square matrix can be inverted analytically yielding exact mathematical expressions for the discretization error and the condition number of the pertinent linear system it is also demonstrated that the error increases very abruptly for source locations associated with the characteristic eigenvalues of the scattering geometry precisely as predicted in theory various plots depict comparisons between analytical and computational data for the boundary condition error and all occurring discrepancies are fully explained among several important results of the analysis the fundamental mas question concerning the optimal location of the auxiliary sources is thoroughly investigated and resolved on the grounds of error minimization

algebras with separating almost cyclic coherent auslander reiten components we prove that the class of artin algebras whose auslander reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras moreover the module category homological properties and the representation type of artin algebras with separating families of almost cyclic coherent auslander reiten components are described

geometric characterizations of the representation type of hereditary algebras and of canonical algebras abstract we show that a finite connected quiver q with no oriented cycles is tame if and only if for each dimension vector d and each integral weight of q the moduli space m q d s s of semi stable d dimensional representations of q is just a projective space in order to prove this we show that the tame quivers are precisely those whose weight spaces of semi invariants satisfy a certain log concavity property furthermore we characterize the tame quivers as being those quivers q with the property that for each schur root d of q the field of rational invariants k rep q d gl d is isomorphic to k or k t next we extend this latter description to canonical algebras more precisely we show that a canonical algebra is tame if and only if for each generic root d of and each indecomposable irreducible component c of rep d the field of rational invariants k c gl d is isomorphic to k or k t along the way we establish a general reduction technique for studying fields of rational invariants on schur irreducible components of representation varieties

simulation of scattered fields some guidelines for the equivalent source method abstract three different approaches of the equivalent source method for simulating scattered fields are compared two of them deal with monopole sets the other with multipole expansions in the first monopole approach the sources have fixed positions given by specific rules while in the second one esga the optimal positions are determined via a genetic algorithm the pros and cons of each of these approaches are discussed with the aim of providing practical guidelines for the user it is shown that while both monopole techniques furnish quite good pressure field reconstructions with simple source arrangements esga requires a number of monopoles significantly smaller and with equal number of sources yields a better precision as for the multipole technique the main advantage is that in principle any precision can be reached provided the source order is sufficiently high on the other hand the results point out that the lack of rules for determining the proper multipole order necessary for a desired precision may constitute a handicap for the user

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

two neuron dynamics and adiabatic elimination abstract we consider an effective neuron network obtained from the hopfield model by adiabatic elimination the validity of the slaving procedure is first numerically examined the self interaction of the effective neuron network may lead to non zero attractors far from the origin ui 0 the qualitative structure of the attractors for this two effective neuron model with j12j21 0 or

on the holographic reconstruction of vibroacoustic fields using equivalent sources and inverse boundary element method in using the near field acoustical holography based on the inverse boundary element method bem for the reconstruction of vibroacoustic source parameters an enormous number of measurements required in practice have limited the extended application of this method to obtain the sufficient field data with a small number of actual measured data the regeneration method of the radiated field using the multipoint equivalent sources is attempted in this paper in using the equivalent source method a vibrating source can be represented by distributed spherical sources inside the actual source surface in this paper the radiated field is expressed with a series of spherical hankel functions and spherical harmonics for suppressing the adverse effect of high order spherical functions spatial filtering of coefficients and wave vector components by a regularization scheme is adopted restored field data appended with actual measured data can be used as input for the inverse bem to reconstruct the source field

an experimental comparison of various methods of nearfield acoustic holography abstract an experimental comparison of four different methods of nearfield acoustic holography nah for planar acoustic sources is presented in this study the four nah methods considered in this study are based on 1 spatial fourier transform 2 equivalent sources model 3 boundary element methods and 4 statistically optimized nah two dimensional measurements were obtained at distances ranging from one half to sixteen microphone spacings away from a sound source and the nah methods were used to reconstruct the sound field at the source surface reconstructed particle velocity and acoustic pressure fields presented in this study showed that the equivalent sources model based algorithm along with tikhonov regularization provided the best localization of the sources reconstruction errors were found to be smaller for the equivalent sources model based algorithm and the statistically optimized nah algorithm the effects of hologram distance on the performance of various algorithms are discussed in detail the study also compares the computational time required by each algorithm to calculate the reconstruction four different regularization parameter choice methods were compared the l curve method provided more accurate reconstructions than the generalized cross validation and the morozov discrepancy principle at larger measurement distances the performance of fixed parameter regularization was comparable to that of the l curve method

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

detecting non uniqueness of solutions to biharmonic integral equations through svd we consider the singular values of an integral operator and of a corresponding square matrix derived from the integral operator by means of a quadrature formula and a collocation the integral operator and also the matrix depend on a real parameter which may also enter the singular values of the operator and the matrix when a singular value drops to zero for a certain critical value of the parameter the corresponding homogeneous integral equation or matrix equation has a nontrivial solution based on several examples with biharmonic integral operators we conjecture that the order of approximation of the critical value for the matrix is at least equal to the order of the quadrature formula used it is therefore possible with a reasonable accuracy to detect such critical values for the integral operator simply through a singular value decomposition of the matrix derived by a quadrature and collocation

on algebras of generalized standard semiregular type abstract we study the structure of artin algebras whose auslander reiten quiver consists of generalized standard semiregular components

calculation of sound radiation in infinite domain using a meshless method a meshless method coupling with a variable order infinite acoustic wave envelope element for sound radiation calculation in infinite domain is presented with the aim of accurately calculating the acoustic radiation and improving computational efficiency it is based on using the element free galerkin method in the inner region enclosing the radiator and a variable order infinite acoustic wave envelope element in the outer region for the proper modeling of the pressure amplitude decay the details are provided for the derivation and implementation of this method the factors of influencing the performance of the method which include the shape function constructing the number of integration points the weight functions and the support domain are discussed a hybrid adaptive gauss legendre quadrature is devised to obtain good integration accuracy the suitable radius of the support domain for the acoustic field calculation in free space is also determined by use of numerical experiments a complex structure is designed for simulation to validate the method the results illustrate the accuracy applicability and effectiveness of this method

acoustic source property prediction based on near field measurements in planar coordinate abstract near field acoustical holography nah can be used to predict the acoustical properties of noise sources by starting from measurements of near field pressures in particular the sound pressure particle velocity and intensity can all be estimated on a source plane in the present work an equation relating acoustical source properties and the pressure radiated from a source is derived from the kirchoff helmholtz integral equation and is here referred to as the inverse rayleigh method the inverse rayleigh method reduces to the rayleigh integral when the source is located on an infinite rigid baffle however the same equation can also be used to predict the acoustic properties of a source in a more general environment i e without assuming the presence of an infinite rigid baffle in this article the inverse rayleigh method is described and then its relative accuracy is compared with other procedures that can be used to predict source particle velocity from near field pressure measurements on a planar hologram by comparing the accuracy of the present nah method with other procedures in the case of a large hologram it was found that the inverse rayleigh method is accurate and computationally efficient for predicting the source particle velocity from near field pressure measurements both with and without a rigid baffle

a study of network dynamics the dynamics of a discrete time neural network model are investigated first a numerical survey of network power spectra is reported for networks of varying size with random weight matrices and initial states the steepness of the logistic function and a symmetry measure of the weight matrix are taken as control parameters summary statistics are presented to give gross measures of the model s temporal activity in parameter space second a detailed study of the dynamics of a particular network is described complex dynamical behavior is observed including hopf bifurcations the ruelle takens newhouse route to chaos showing mode locking at rational winding numbers and the destruction of an invariant torus and the period doubling route to chaos

enhanced nearfield acoustic holography for larger distances of reconstructions using fixed parameter tikhonov regularization this paper evaluates the performance of various regularization parameter choice methods applied to different approaches of nearfield acoustic holography when a very nearfield measurement is not possible for a fixed grid resolution the larger the hologram distance the larger the error in the naive nearfield acoustic holography reconstructions these errors can be smoothed out by using an appropriate order of regularization this study shows that by using a fixed manual choice of regularization parameter instead of automated parameter choice methods reasonably accurate reconstructions can be obtained even when the hologram distance is 16 times larger than the grid resolution

diffusion problems using transient discrete source superposition discrete source superposition techniques seek sets of discrete singular source strengths which satisfy the boundary conditions of a particular problem and necessarily the governing differential equation the sum of the fields produced by such sources thus provides an approximation to the required solution in many respects these techniques are a special case of conventional boundary integral equation methods where density distributions of smeared sources are sought in this paper an attempt is made to extend the discrete source superposition technique to transient problems the example addressed is the transient diffusion equation the method developed does seem to have some promise it is found that even coarse spatial discretization can yield quite accurate results and that surprisingly large timesteps can be employed and accuracy maintained further although no direct comparisons are made the absence of spatial integrations indicates that the computational effort per timestep is likely to be less than for conventional bie

the wave superposition method as a robust technique for computing acoustic fields the wave superposition method has recently been advocated koopmann et al a method for computing acoustic fields based on the principle of wave superposition j acoust soc am 86 2433 2438 1989 as a reliable and accurate technique for computing the acoustic fields generated by arbitrary shaped radiators this study examines in depth the robustness and numerical stability of the method the implementation of the method requires the placement of a finite number of point sources on a surface interior to the body of the radiator the magnitude of these point sources can be evaluated in terms of the prescribed velocity distribution on the surface of the radiator once calculated the magnitude of these point sources allow the pressure distribution exterior to the radiator to be evaluated the first improvement made to the robustness of the method is the use of a hybrid combination of monopole and dipole sources this modification allows the inherent problem of nonuniqueness of the method at certa

tame algebras and tits quadratic forms abstract we solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated tits integral quadratic forms and derive some consequences

bayesian approach of nearfield acoustic reconstruction with particle filters this paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the bayesian approach of parameter estimation in particular the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method esm a state space model is formulated in light of the esm the parameters to estimate are amplitudes and locations of the equivalent sources the parameters constitute the state vector which follows a first order markov process with the transition matrix being the identity for every frequency domain data frame filtered estimates of the state vector obtained are assigned weights adaptively the implementation of recursive bayesian filters involves a sequential monte carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function pmf which evolves with iteration the weight update equation governs the evolution of this pmf and depends primarily on the likelihood function and the prior distribution it is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation

cubic spline interpolation based time domain equivalent source method for modeling transient acoustic radiation abstract transient acoustic radiation from an arbitrarily shaped source is modeled using a cubic spline interpolation based time domain equivalent source method in the method the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field the normal acceleration on the source surface and the equivalent sources and the least squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique the proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily shaped sources numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well the experimental results also further verify the validity of the proposed method

the forward projection of harmonic pressure fields using the generalized internal source density method a previously developed generalized internal source density gisd method is extended to address the forward projection of harmonic pressure fields from normal velocity fields on a closed surface of revolution in a fluid the gisd approach is based on decomposing the normal velocity field on the closed surface into a summation of circumferential orders where the pressure field for each order is associated with an internal linear source distribution of ring sources on the axis of revolution of the surface the linear source distributions are formulated as integral equations of the first kind which are then solved using singular value decomposition methods far field pressures are simply related to the fourier transforms of the linear source distributions numerical results are presented to illustrate the forward projection of harmonic fields using the gisd method for both dirichlet and neumann problems the numerical results for spherical and finite cylindrical vibrators illustrate the usefulness of the gisd method over a wide range of frequencies for both acoustic radiation and scattering problems

two sided gluings of tilted algebras we study the class of algebras a satisfying the property all but at most finitely many non isomorphic indecomposable a modules are such that all their predecessors have projective dimension at most one or all their successors have injective dimension at most one such a class includes the tilted algebras d happel c ringel trans amer math soc 274 1982 399 443 the quasi tilted algebras d happel i reiten s smalo mem am math soc 120 1996 575 the shod algebras f u coelho m lanzilotta manuscripta mathematica 100 1999 1 11 the weakly shod f u coelho m lanzilotta preprint 2001 and the left and right glued algebras i assem f u coelho j pure appl algebra 96 3 1994 225 243

constructing constrained invariant sets in multiscale continuum systems we present a method that we name the constrained invariant manifold method a visualization tool to construct stable and unstable invariant sets of a map or flow where the invariant sets are constrained to lie on a slow invariant manifold the construction of stable and unstable sets constrained to an unstable slow manifold is exemplified in a singularly perturbed model arising from a structural mechanical system consisting of a pendulum coupled to a viscoelastic rod additionally we extend the step and stagger method d sweet h nusse and j yorke phys rev lett 86 2261 2001 to calculate a delta pseudoorbit on a chaotic saddle constrained to the slow manifold in order to be able to compute the lyapunov exponents of the saddle

stability and chaos in an inertial two neuron system abstract inertia is added to a continuous time hopfield 1984 effective neuron system we explore the effects on the stability of the fixed points of the system a two neuron system with one or two inertial terms added is shown to exhibit chaos the chaos is confirmed by lyapunov exponents power spectra and phase space plots

a numerical solution for the general radiation problem based on the combined methods of superposition and singular value decomposition in the method of wave superposition the acoustic field due to a complex radiator is expressed in terms of a fredholm integral equation of the first kind called the superposition integral equation in general fredholm integral equations of the first kind are ill posed and therefore difficult to solve numerically in this paper it will be shown that a simple collocation procedure when combined with the singular value decomposition can yield accurate results for the numerical solution of the superposition integral as an example of the application of the method the acoustic radiation from a circular cylinder will be analyzed using this numerical procedure and compared to the exact solution it is shown that for this problem the accuracy of the numerical solution can be judged by evaluating how well the superposition solution approximates the specified boundary condition on the surface of the radiator an example is also given of a problem which has no exact solution in this situation it is suggested without proof that the accuracy of the numerical solution can be judged in a similar manner by evaluating the error in the superposition solution s satisfaction of the boundary condition

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

acoustic analysis of a rectangular cavity with general impedance boundary conditions a fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls the sound pressure is expressed as the combination of a three dimensional fourier cosine series and six supplementary two dimensional expansions introduced to ensure accelerate the uniform and absolute convergence rate of the series representation in the cavity including the boundary surfaces the expansion coefficients are determined using the rayleigh ritz method since the pressure field is constructed adequately smooth throughout the entire solution domain the rayleigh ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions to unify the treatments of arbitrary nonuniform impedance boundary conditions the impedance distribution function on each specified surface is invariantly expressed as a double fourier series expansion so that all the relevant integrals can be calculated analytically the modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions including nonuniform impedance distributions

reply to the comments on reply to the comments on the boundary point method for the calculation of exterior acoustic radiation by s y zhang x z chen journal of sound and vibration 228 4 1999 761 772

computation of sound radiation by a driver in a cabinet using a substitute source approach sound radiation by a driver set in a rigid closed cabinet is modeled analytically using the principle of wave superposition the driver cabinet assembly is replaced by an array of volumeless substitute sources monopoles confined within its surface the role of substitute sources is to reproduce the sound field exterior to the surface as close to the original field as possible the frequency dependent positions and strengths of substitute monopoles are optimized by an iterative search procedure aimed at matching the prescribed surface boundary conditions of the original source the time consuming optimization of monopole positions is carried out at narrowband center frequencies reducing the computational cost without significant loss of accuracy the consistency of computed results is verified by checking the power output through the cabinet surface modeling is done for anechoic and semi anechoic conditions the model has been validated experimentally in a semi anechoic room with satisfactory results using a mid range driver set in a closed box baffle

active control of the acoustic radiation of a vibrating structure using a superposition formulation a new computational approach provides a methodology for specifying how the acoustic power radiated from a complex three dimensional vibrating structure may be controlled the method uses a superposition principle to transform the surface of a vibrating structure into a discrete distribution of acoustic sources interior to the boundary surface of the structure the transformation is carried out by requiring that the interior sources produce the same or nearly the same normal velocities as those prescribed on the surface of the vibrating structure based on this transformation the total time averaged acoustic power output from the vibrating structure can be expressed in terms of the strengths of the equivalent sources to control the radiated acoustic power one or more secondary point sources is then placed on or near the surface of the vibrating structure by using the total power radiated from the vibrating structure and the secondary sources as an objective function for an optimization operation th

numerical errors associated with the method of superposition for computing acoustic fields the method of wave superposition is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources the accuracy of this representation depends upon how well the velocity boundary condition on the surface of the body is approximated the ultimate objective of this study then is to provide some guidelines for improving the accuracy of the surface velocity reconstruction and consequently the accuracy of the superposition solutions in general this is dependent upon the particular surface velocity distribution to be reconstructed as well as other formulation factors such as the acoustic wave number the number and locations of the surface nodes and the number and locations of the point sources velocity interpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources numerical experiments

numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure in a previous paper a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements expanding the acoustic field from each of the elements in a multipole expansion and truncating all but the lowest order terms in the expansion here the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense this alleviates the difficulties typically encountered in enforcing the boundary condition leading to a relatively simple numerical solution with well defined convergence properties the basis functions for the numerical analysis are taken as the acoustic fields of discrete simple dipole and tripole sources located at the geometrical centers of the surface elements the different source types are used to represent the radiation from different kinds of surface elements simple sources for elements in the plane of an infinite baffle dipole sources for very thin structures which deform only in bending and tripole sources for elements associated with parts of a structure enclosing a finite volume the convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through several example problems

source identification system based on the time domain nearfield equivalence source imaging fundamental theory and implementation abstract a nearfield equivalence source imaging nesi technique is proposed to identify locations and strengths of noise sources the nesi is based on the time domain formulation that applies not only to stationary but also a transient noise multichannel inverse filters are designed using the least square optimization tikhonov regularization is called for to mitigate the ill posedness inherent in the underdetermined model matching problem the design parameters such as array aperture microphone spacing focal point spacing and distance of projection have profound impact on the resulting sound image resolution the distance of reconstruction dor is selected according to the condition number of the propagation matrix a windowing design is also suggested to cope with boundary defocusing problem beam pattern is calculated for the inverse filters with window design in addition a modified approach based on focal point points is devised to avoid the singularity problem in reconstructing sound images the multichannel inverse filters are implemented in light of a highly efficient state space minimal realization technique the nesi is applicable to one dimensional 1d linear array two dimensional 2d rectangular array and even other arrays of irregular geometries as indicated by the simulation results the proposed nesi technique proves effective in the identification of noise sources

an equivalent source technique for calculating the sound field inside an enclosure containing scattering objects the equivalent source method has previously been used to calculate the exterior sound field radiated or scattered from bodies in the free field in this paper the method is used to calculate the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound some of the equivalent source positions are chosen to be the same as the first order images of the source inside the enclosure some are positioned within the scattering objects and the remainder are positioned on a spherical surface some distance outside the enclosure the normal velocity on the surfaces of the scattering objects and the enclosure walls is evaluated at a larger number of positions than there are equivalent sources the sum of the squared difference between this velocity and that expected because of the admittance of the boundary is minimized by adjusting the strengths of the equivalent sources the convergence of the method is checked by evaluating the velocity at a larger number of monitoring positions example results are presented for the sound field and frequency response inside a damped rectangular enclosure which compare very well with the conventional modal model the effect of having rigid spheres inside the enclosure are then investigated and it is found that the effect is significant even some distance from the spheres and at frequencies for which the size of the sphere is small compared to a wavelength finally the effect of a nonlocally reacting boundary condition is illustrated by assuming that one of the walls of the enclosure is an elastic plate

sound field separation technique based on equivalent source method and its application in nearfield acoustic holography a technique for separating sound fields using two closely spaced parallel measurement surfaces and based on equivalent source method is proposed the method can separate wave components crossing two measurement surfaces in opposite directions which makes nearfield acoustic holography nah applications in a field where there exist sources on the two sides of the hologram surface in a reverberant field or in a scattered field possible the method is flexible in applications simple in computation and very easy to implement the measurement surfaces can be arbitrarily shaped and they are not restricted to be regular as in the traditional field separation technique and because the method performs field separation calculations directly in the spatial domain not in the wave number domain it avoids the errors and limitations the window effects etc associated with the traditional field separation technique based on the spatial fourier transform method in the paper a theoretical description is first

a method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

a mapping relationship based near field acoustic holography with spherical fundamental solutions for helmholtz equation abstract in the procedure of the near field acoustic holography nah based on the fundamental solutions for helmholtz equation fs the number of fs and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction the current work is motivated to develop a framework for the nah which supplies a guideline to the determination of the number of fs as well as an optimized measurement setup a mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as fs in spherical coordinates thus reconstruction is converted to obtain the coefficients of participant modes on holograms in addition an integral identity is firstly to be derived for the modes on convex surfaces which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space to determine the number of fs adopted in the mapping relationship based nah mrs based nah two approaches are proposed to supply reasonable estimations with criteria of point wise pressure and energy respectively a technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms such as planar cylindrical and spherical holograms which results in an automatic determinations of the number and position of experimental setup for a given tolerance numerical examples are set up to validate the theory and techniques in the mrs based nah reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers worse results for the elongated cylinder with two spherical caps reveal the deficiency of the mrs based nah for irregular models which is largely due to the adopted modes are fs in spherical coordinates the nah framework pursued in the current work provides a new insight to the reconstruction procedure based on the fs in spherical coordinates

chaos in high dimensional neural and gene networks abstract neural and gene networks are often modeled by differential equations if the continuous threshold functions in the differential equations are replaced by step functions the equations become piecewise linear pl equations the flow through the state space is represented schematically by paths and directed graphs on am n dimensional hypercube closed pathways called cycles may reflect periodic orbits with associated fixed points in a chosen poincare section a return map in the poincare section can be constructed by the composition of fractional linear maps the stable and unstable manifolds of the fixed points can be determined analytically these methods allow us to analyze the dynamics in higher dimensional networks as exemplified by a four dimensional network that displays chaotic behavior the three dimensional poincare map is projected to a two dimensional plane this much simpler piecewise linear two dimensional map conserves the important qualitative features of the flow

reconstruction of nonstationary sound fields based on the time domain plane wave superposition method a time domain plane wave superposition method is proposed to reconstruct nonstationary sound fields in this method the sound field is expressed as a superposition of time convolutions between the estimated time wavenumber spectrum of the sound pressure on a virtual source plane and the time domain propagation kernel at each wavenumber by discretizing the time convolutions directly the reconstruction can be carried out iteratively in the time domain thus providing the advantage of continuously reconstructing time dependent pressure signals in the reconstruction process the tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time wavenumber spectrum on the virtual source plane because the double infinite integral of the two dimensional spatial fourier transform is discretized directly in the wavenumber domain in the proposed method it does not need to perform the two dimensional spatial fast fourier transform that is generally used in time domain holography and real time near field acoustic holography and therefore it avoids some errors associated with the two dimensional spatial fast fourier transform in theory and makes possible to use an irregular microphone array the feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers

algebras with cycle finite galois coverings we prove that the finite dimensional algebras over an algebraically closed field which admit cycle finite galois coverings with torsion free galois groups are of tame representation type and derive some consequences

delay dependent stochastic stability of delayed hopfield neural networks with markovian jump parameters in this paper the problem of stochastic stability for a class of time delay hopfield neural networks with markovian jump parameters is investigated the jumping parameters are modeled as a continuous time discrete state markov process without assuming the boundedness monotonicity and differentiability of the activation functions some results for delay dependent stochastic stability criteria for the markovian jumping hopfield neural networks mjdhnns with time delay are developed we establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities

lyapunov exponents and dimensions of chaotic neural networks dynamical properties of a network model composed of n continuous elements with randomly chosen asymmetrical couplings and reduced connectivity are studied the authors calculate numerically lyapunov exponents and dimensions for chaotic and non chaotic states of the network the dependence of the parameters can be described analytically in good agreement with the numerical data

a bifurcation analysis of the four dimensional generalized hopfield neural network abstract a four neuron hopfield neural network with asymmetric weights and self connection is analyzed its stable steady state and periodic attractors are identified and a complete bifurcation diagram is constructed a center manifold reduction is undertaken and by means of normal form theory the characteristics of the limit cycles are obtained the network is seen to have a large memory storage capacity with both fixed point and periodic memories coexisting the onset of chaos as reported previously is considered

characterizations of algebras with small homological dimensions abstract we introduce the class of double tilted algebras containing the class of tilted algebras and prove various characterizations in particular we show that the class of double tilted algebras is the class of all artin algebras whose ar quiver admits a faithful double section with a natural property moreover we prove that the class of double tilted algebras coincides with the class of all artin algebras of global dimension three for which every indecomposable finitely generated module has projective or injective dimension at most one we also describe the structure of the category of finitely generated modules as well as the ar quiver of double tilted algebras

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

on the additive categories of generalized standard almost cyclic coherent auslander reiten components abstract we prove geometric and homological properties of modules in the additive categories of generalized standard almost cyclic coherent components in the auslander reiten quivers of finite dimensional algebras

a characterization of cycle finite generalized double tilted algebras abstract we provide a new characterization of cycle finite generalized double tilted algebras by the existence of a faithful module which is the middle of at most finitely many short chains

on the perpendicular category of a partial tilting module abstract the perpendicular category of a partial tilting module is studied in particular that of a regular module over a hereditary algebra preferably of wild representation type the results are used to establish the existence of a unique preprojective component for a large class of tilted algebras

geometry of directing modules over tame algebras throughout the paper k denotes a fixed algebraically closed field by an algebra we mean a finite dimensional k algebra associative with an identity and by a module a finite dimensional left a module the class of algebras may be divided into two disjoint subclasses one class consists of tame algebras for which the indecomposable modules occur in each dimension in a finite number of discrete and a finite number of one parameter families the second class is formed by the wild algebras whose representation theory is as complicated as the study of finite dimensional vector spaces together with two noncommuting endomorphisms for which the classification up to isomorphism is a well known unsolved problem hence we can realistically hope to describe modules only for tame algebras given an algebra a and a nonnegative vector d in the grothendieck group k a of a it is an interesting task to study the 0 affine variety mod d of a modules of dimension vector d and the action a of the corresponding product g d of general linear groups for example we may ask when the variety mod d is irreducible smooth complete a intersection gorenstein cohen macaulay normal the main aim of this paper is to describe the geometry of module varieties mod d for the dimension vectors d of arbitrary directing moda w x ules over tame algebras recall that following 20 an indecomposable a module m is said to be directing if it does not belong to a cycle m a m a a m a m of nonzero nonisomorphisms between inde1 r composable a modules directing modules have played an important role

a scattering chamber approach for solving finite rough surface scattering problems in this paper a new method is derived for the computation of scattering from a finite rough free surface the free surface is infinite in extent but only a portion of it is rough in order to reduce the amount of numerical computation for such a problem it is desirable to restrict the computations to the interval of roughness even for remote sources and receivers this can be easily done in the case that the rough portion of the surface is only directed into the surrounding fluid medium in this case the use of the appropriate half space green s function will restrict the integral equation to the interval of roughness only however for general deformations this green s function cannot be used the use of truncated integral equations utilizing the free space green s function is discussed an alternate approach is then described a system of boundary conditions is derived for a finite curve containing the interval of roughness and a surrounding contour in the fluid half space the resulting equations are solved using the method of wave field superposition the derived method is also easily generalized to the case that the rough surface under consideration is the upper boundary of a waveguide

sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array a spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in fourier domain it allows successful reconstructions surrounding the array but the accuracy will be degraded at a distance in order to extend the effective reconstruction to the entire cavity a plane wave basis in space domain is used owing to its non decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity the sensitivity to measurement noise the effects of the numbers of plane waves and measurement positions are discussed simulations show that under the same measurement conditions the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency that is the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measur

a boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions this paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions the difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface this process gives rise to a set of uniquely solvable boundary integral equations distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation the modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only this implementation allows direct application of standard quadrature formulas over the entire integration domain that is the collocation points are exactly the positions at which the integration points are located selecting the interior surface is an easy task moreover only a few corresponding interior nodal points are sufficient for the computation numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders comparisons with analytical solutions are made numerical results demonstrate the efficiency and accuracy of the current solution method

the structure and homological properties of generalized standard auslander reiten components abstract we describe the structure and homological properties of arbitrary generalized standard auslander reiten components of artin algebras in particular we prove that for all but finitely many indecomposable modules in such components the euler characteristic is defined and nonnegative further we provide a handy criterion for an infinite auslander reiten component of an artin algebra to be generalized standard we solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of auslander reiten components