reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

equations for finite difference time domain simulation of sound propagation in moving inhomogeneous media and numerical implementation finite difference time domain fdtd calculations are typically performed with partial differential equations that are first order in time equation sets appropriate for fdtd calculations in a moving inhomogeneous medium with an emphasis on the atmosphere are derived and discussed in this paper two candidate equation sets both derived from linearized equations of fluid dynamics are proposed the first which contains three coupled equations for the sound pressure vector acoustic velocity and acoustic density is obtained without any approximations the second which contains two coupled equations for the sound pressure and vector acoustic velocity is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure it is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere practical fdtd implementation of the second set of equations is discussed results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform high mach number flow and with fast field program calculations of sound propagation in a stratified moving atmosphere

evaluation of diffusion coefficient based on multiple forward solutions abstract this note is concerned with the identification of the unknown diffusion coefficient for a parabolic equation it introduces an iterative algorithm that can be used to recover the unknown function the algorithm assumes an initial guess for the unknown function and obtains a background field it obtains an equation for the error field it then formulates three forward problems for the error field these three formulations share the same unknown function which is the correction to the assumed value of the unknown diffusion coefficient by equating the responses of these three formulations the algorithm obtains two working equations for the unknown function a number of numerical examples are also used to study the performance of the algorithm

sound radiation by a moving line source above an impedance plane with frequency dependent properties abstract an analytic solution for the problem of sound radiation by a harmonic line source moving at a uniform subsonic speed parallel to an impedance plane is proposed the main originality of this work is that the variation of the impedance with the frequency is taken into account compared to the case of a constant impedance the reflection coefficient and the location of its poles in the complex plane are modified a uniform asymptotic expression is then developed for moderate mach numbers and a closed form expression corresponding to a weyl van der pol formula is proposed for a grazing incidence for hard grounds and for low mach numbers unlike previous analytical solutions derived in the literature for a point source the impedance is evaluated at the doppler frequency instead of at the source frequency the analytical solution and asymptotic expressions are then compared satisfactorily to a numerical solution obtained from a time domain solver of the linearized euler equations finally a parametric study is carried out showing that the assumption of a constant impedance is valid if the source mach number remains small typically less than 0 2 and if the source is not too close to the ground

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

minimum relative entropy inversion theory and application to recovering the release history of a groundwater contaminant in this paper we show that given prior information in terms of a lower and upper bound a prior bias and constraints in terms of measured data minimum relative entropy mre yields exact expressions for the posterior probability density function pdf and the expected value of the linear inverse problem in addition we are able to produce any desired confidence intervals in numerical simulations we use the mre approach to recover the release and evolution histories of plume in a one dimensional constant known velocity and dispersivity system for noise free data we find that the reconstructed plume evolution history is indistinguishable from the true history an exact match to the observed data is evident two methods are chosen for dissociating signal from a noisy data set the first uses a modification of mre for uncertain data the second method uses presmoothing by fast fourier transforms and butterworth filters to attempt to remove noise from the signal before the noise free variant of mre inversion is used both methods appear to work very well in recovering the true signal and qualitatively appear superior to that of skaggs and kabala 1994 we also solve for a degenerate case with a very high standard deviation in the noise the recovered model indicates that the mre inverse method did manage to recover the salient features of the source history once the plume source history has been developed future behavior of a plume can then be cast in a probabilistic framework for an example simulation the mre approach not only was able to resolve the source function from noisy data but also was able to correctly predict future behavior

heuristic approximations for sound fields produced by spherical waves incident on locally and non locally reacting planar surfaces the classic weyl van der pol wvdp formula is a well known asymptotic solution for accurately predicting sound fields above a locally reacting ground surface however the form of the wvdp formula is inadequate for predicting sound fields in the vicinity of non locally reacting surfaces a correction term is often required in the formula to provide accurate numerical solutions even with this correction there is a singularity in the diffraction wave term when the source is located directly above or below the receiver this paper explores a heuristic method to remove this singularity and suggests an analytical form comparable to the wvdp formula this improved formula offers a physically interpretable solution and allows for accurate predictions of the total sound field above locally and non locally reacting surfaces for all geometrical configurations

adaptive asymptotic bayesian equalization using a signal space partitioning technique the bayesian solution is known to be optimal for symbol by symbol equalizers however its computational complexity is usually very high the signal space partitioning technique has been proposed to reduce complexity it was shown that the decision boundary of the equalizer consists of a set of hyperplanes the disadvantage of existing approaches is that the number of hyperplanes cannot be controlled in addition a state search process that is not efficient for time varying channels is required to find these hyperplanes in this paper we propose a new algorithm to remedy these problems we propose an approximate bayesian criterion that allows the number of hyperplanes to be arbitrarily set as a consequence a tradeoff can be made between performance and computational complexity in many cases the resulting performance loss is small whereas the computational complexity reduction can be large the proposed equalizer consists of a set of parallel linear discriminant functions and a maximum operation an adaptive method using stochastic gradient descent has been developed to identify the functions the proposed algorithm is thus inherently applicable to time varying channels the computational complexity of this adaptive algorithm is low and suitable for real world implementation

polynomial perceptrons and their applications to fading channel equalization and co channel interference suppression this paper investigates the behaviors of polynomial perceptrons and introduces a fractionally spaced recursive polynomial perceptron with low complexity and fast convergence rate the nonlinear mapping ability of the polynomial perceptron is analyzed it is shown that a polynomial perceptron with degree l spl ges 4 satisfies the stone weierstrass theorem and can approximate any continuous function to within a specified accuracy moreover the nonlinear mapping ability of a polynomial perceptron with degree l is similar to that of the three layer perceptron with one hidden layer for time same number of neurons in the input layer the nonlinear mapping ability of the fractionally spaced recursive polynomial perceptron is also presented applications of polynomial perceptrons for fading channel equalization and co channel interference suppression in a 16 level quadrature amplitude modulation receiver system are considered computer simulations are used to evaluate and compare the performance of polynomial perceptron pp and fractionally spaced bilinear perceptron fsblp with that of the synchronous decision feedback multilayer perceptron sdfmlp fractionally spaced decision feedback multilayer perceptron fsdfmlp and the conventional decision feedback equalizer dfe the results show that the performance of the fractionally spaced bilinear perceptron is clearly superior to that of the other structures

decision feedback equalization using multiple hyperplane partitioning for detecting isi corrupted m ary pam signals a decision feedback equalizer scheme is derived based on multiple hyperplane partitioning of signal space for detecting m ary pulse amplitude modulation symbols transmitted through a noisy intersymbol interference channel the proposed scheme is based on the fact that the optimal bayesian decision boundary separating two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the signal to noise ratio tends to infinity an algorithm is developed to determine these hyperplanes which are then used to partition the observation signal space the resulting detector can closely approximate the optimal bayesian detector at an advantage of considerably reduced detector complexity

full wave modeling of therapeutic ultrasound efficient time domain implementation of the frequency power law attenuation for the simulation of therapeutic ultrasound applications a method including frequency dependent attenuation effects directly in the time domain is highly desirable this paper describes an efficient numerical time domain implementation of the power law attenuation model presented by szabo szabo j acoust soc am 96 491 500 1994 simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time domain fdtd algorithm for nonlinear ultrasound propagation ginter et al j acoust soc am 111 2049 2059 2002 szabo implemented the empirical frequency power law attenuation using a causal convolutional operator directly in the time domain equation though a variety of time domain models has been published in recent years no efficient numerical implementation has been presented so far for frequency power law attenuation models solving a convolutional integral with standard time domain techniques requires enormous computational ef

an inversion method for parabolic equations based on quasireversibility abstract this paper is concerned with a new method to solve a linearized inverse problem for one dimensional parabolic equations the inverse problem seeks to recover the subsurface absorption coefficient function based on the measurements obtained at the boundary the method considers a temporal interval during which time dependent measurements are provided it linearizes the working equation around the system response for a background medium it is then possible to relate the inverse problem of interest to an ill posed boundary value problem for a differential integral equation whose solution is obtained by the method of quasireversibility this approach leads to an iterative method a number of numerical results are presented which indicate that a close estimate of the unknown function can be obtained based on the boundary measurements only

pade approximants for the acoustical characteristics of rigid frame porous media in this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media especially those involving ratios of bessel functions of complex argument can be accurately approximated and greatly simplified by the use of pade approximation techniques in the case of the model of attenborough j acoust soc am 81 93 102 1987 rational approximations are produced for the characteristic impedance propagation constant dynamic compressibility and dynamic density as a function of frequency and the material parameters the model proposed by stinson and champoux j acoust soc am 91 685 695 1992 is approximated via rational approximation for the viscosity correction function

an iterative method for the solution of ill posed parabolic systems this note is concerned with the identification of the unknown initial condition for a parabolic system it introduces an iterative algorithm that can be used to recover the initial condition the algorithm assumes a function for the unknown initial condition and obtains a background field it then obtains the error dynamics the error dynamics is also ill posed in the sense that the initial condition is unknown using the measurements obtained at the boundaries the algorithm introduces two formulations for the error dynamics these two formulations share the same initial condition by equating the responses of these two formulations it is then possible to obtain an equation for the unknown initial condition a number of numerical examples are also used to study the performance of the algorithm

pade approximation in time domain boundary conditions of porous surfaces formulation and implementation of time domain boundary conditions tdbcs at the surface of a reactive porous material are made challenging by the slow decay complexity or noncausal nature of many commonly used models of porous materials in this paper approaches are described that improve computational efficiency and enforce causality one approach involves approximating the known tdbc for the modified zwikker kosten impedance model as a summation of decaying exponential functions a second approach which can be applied to any impedance model involves replacing the characteristic admittance with its pade approximation then approximating fractional derivatives with decaying exponentials a causal and recursive tdbc is formulated

asymptotic bayesian decision feedback equalizer using a set of hyperplanes we present a signal space partitioning technique for realizing the optimal bayesian decision feedback equalizer dfe it is known that when the signal to noise ratio snr tends to infinity the decision boundary of the bayesian dfe is asymptotically piecewise linear and consists of several hyperplanes the proposed technique determines these hyperplanes explicitly and uses them to partition the observation signal space the resulting equalizer is made up of a set of parallel linear discriminant functions and a boolean mapper unlike the existing signal space partitioning technique of kim and moon 1998 which involves complex combinatorial search and optimization in design our design procedure is simple and straightforward and guarantees to achieve the asymptotic bayesian dfe

multidimensional signal space partitioning using a minimal set of hyperplanes for detecting isi corrupted symbols a signal space partitioning technique is presented for detecting symbols transmitted through intersymbol interference channels the decision boundary is piecewise linear and is made up of several hyperplanes the goal here is to minimize the number of hyperplanes for a given performance measure namely the minimum distance between any signal and the decision boundary unlike in voronoi partitioning individual hyperplanes are chosen to separate signal clusters rather than signal pairs the convex regions associated with individual signals which together form the overall decision region generally overlap or coincide among in class signals the technique leads to an asymptotically optimum detector when the target distance is set at half the minimum distance associated with the maximum likelihood sequence detector complexity and performance can be easily traded as the target distance is a flexible design parameter

a uniformly valid far field asymptotic expansion of the green function for two dimensional propagation above a homogeneous impedance plane abstract a generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived the expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance including the limiting cases of zero and infinite impedance the technique used is a rigorous application of the modified steepest descent method of ott 1

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized