stability and accuracy of finite element methods for flow acoustics i general theory and application to one dimensional propagation the dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar helmholtz equation and on the galbrun equation are examined the current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions a general two dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh and results are presented for the particular case of one dimensional acoustic propagation in which the wave direction is aligned with the mean flow the magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes quadratic helmholtz elements in particular are shown to be much less effective for downstream as opposed to upstream propagation even when the effect of wave shortening or elongation due to the mean flow is taken into account these trends are also observed in solutions obtained for simple test problems on finite meshes a similar analysis of two dimensional propagation is presented in an accompanying article

extension of the eulerian lagrangian description to nonlinear perturbations in an arbitrary inviscid flow abstract a new theoretical formulation is proposed to describe the propagation of large amplitude perturbations in an arbitrary flow of inviscid fluid this formulation relies on the mixed eulerian lagrangian description for which exact nonlinear equations are derived using properties of hamiltonian formalism generalized expressions are found for the acoustic pseudo energy density and flux they verify a conservative energy balance all these expressions only depend on the reference flow variables and the displacement vector of the fluid particles due to the perturbation when the small perturbation assumption is added the linear expressions from the literature are retrieved

on the stability of equilibria to weakly coupled parabolic systems in unbounded domains abstract we investigate weakly coupled semilinear parabolic systems in unbounded domains of r 2 or r 3 with general nonlinearities we present several sufficient conditions on the nonlinearities which ensure the stability of the zero solution with respect to h 2 perturbations in addition various examples are discussed to illustrate the scope of application of our results

decay of heat semigroups in l and applications to nonlinear parabolic problems in unbounded domains we characterize all domains of rn such that the heat semigroup decays in l l or l l1 as t namely we prove that this property is equivalent to the poincare inequality and that it is also equivalent to the solvability of u f in l for all f l in particular under mild regularity assumptions on these properties are equivalent to the geometric condition that has finite inradius next we give applications of this linear result to the study of two nonlinear parabolic problems in unbounded domains first we consider the quenching problem for singular parabolic equations we prove that the solution in quenches in finite time no matter how small the nonlinearity is if and only if does not fulfill the poincare inequality second for the semilinear heat equation with a power nonlinearity we prove roughly speaking that the trivial solution is stable in l or in l1 if and only if has finite inradius

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

existence and monotone scheme for time periodic nonquasimonotone reaction diffusion systems application to autocatalytic chemistry abstract the article considers time periodic reaction diffusion systems the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions dirichlet and robin boundary conditions are included the existence of periodic solutions is shown under appropriate conditions monotone approximating sequences closing in on the solutions from above and below are constructed application to autocatalysis in chemistry is given

global existence and asymptotic stability of equilibria to reaction diffusion systems in this paper we study weakly coupled reaction diffusion systems in unbounded domains of or where the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions such systems are more complicated than those in many previous publications and little is known about them a comparison principle and global existence and boundedness theorems for solutions to these systems are established sufficient conditions on the nonlinearities ensuring the positively ljapunov stability of the zero solution with respect to h2 perturbations are also obtained as samples of applications these results are applied to an autocatalytic chemical model and a concrete problem whose nonlinearities are nonquasimonotone our results are novel in particular we present a solution to an open problem posed by escher and yin 2005 j nonlinear anal theory methods appl 60 1065 84

lagrangian speckle model and tissue motion estimation theory ultrasonography it is known that when a tissue is subjected to movements such as rotation shearing scaling etc changes in speckle patterns that result act as a noise source often responsible for most of the displacement estimate variance from a modeling point of view these changes can be thought of as resulting from two mechanisms one is the motion of the speckles and the other the alterations of their morphology in this paper the authors propose a new tissue motion estimator to counteract these speckle decorrelation effects the estimator is based on a lagrangian description of the speckle motion this description allows the authors to follow local characteristics of the speckle field as if they were a material property this method leads to an analytical description of the decorrelation in a way which enables the derivation of an appropriate inverse filter for speckle restoration the filter is appropriate for linear geometrical transformation of the scattering function lt i e a constant strain region of interest roi as the lt itself is a parameter of the filter a tissue motion estimator can be formulated as a nonlinear minimization problem seeking the best match between the pre tissue motion image and a restored speckle post motion image the method is tested using simulated radio frequency rf images of tissue undergoing axial shear

comparison of a finite element model with a multiple scales solution for sound propagation in varying ducts with swirling flows a multiple scales ms solution is proposed to study sound propagation in slowly varying ducts with mean swirling flows instead of the standard linearized euler equations the ms method is applied to the so called galbrun s equation this equation is based on an eulerian lagrangian description and corresponds to a wave equation written only in terms of the lagrangian perturbation of the displacement this yields simpler differential equations to solve for the ms model as well as simpler boundary conditions in this paper galbrun s equation is also solved by a mixed pressure displacement finite element method fem the proposed fem model has already been tested in authors previous papers this model is quite general and is extended here to arbitrary mean flows including compressibility and swirling flow effects some ms and fem solutions are then compared in order to validate both models

bayesian estimation of motion vector fields a stochastic approach to the estimation of 2d motion vector fields from time varying images is presented the formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models two motion models are proposed a globally smooth model based on vector markov random fields and a piecewise smooth model derived from coupled vector binary markov random fields two estimation criteria are studied in the maximum a posteriori probability map estimation the a posteriori probability of motion given data is maximized whereas in the minimum expected cost mec estimation the expectation of a certain cost function is minimized both algorithms generate sample fields by means of stochastic relaxation implemented via the gibbs sampler two versions are developed one for a discrete state space and the other for a continuous state space the map estimation is incorporated into a hierarchical environment to deal efficiently with large displacements

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

finite element method to study harmonic aeroacoustics problems the analysis of aeroacoustics propagation is required to solve many practical problems as an alternative to euler s linearized equations an equation was established by galbrun in 1931 it assumes the flow verifies euler s equations and the perturbation is small and adiabatic it is a linear second order vectorial equation based on the displacement galbrun s equation derives from a lagrangian density and provides conservative expressions of the aeroacoustics intensity and energy density a caa method dealing with the numerical resolution of galbrun s equation using the finite element method fem is presented the exact solution for the propagation of acoustic modes inside an axisymmetric straight lined duct in the presence of a shear flow is known and compared with the fem solution comparisons are found to be in good agreement and validate a first step in the development of a caa method based on the fem and galbrun s equation the fem is then applied to an axisymmetric duct including a varying cross

theoretical investigation of hydrodynamic surface mode in a lined duct with sheared flow and comparison with experiment abstract a spectral collocation method is used to solve the linearized euler equations in a duct with shear flow and lined walls in order to identify a possible hydrodynamic instability observed in published experiments this method is first checked against a reference test case in a cylindrical duct then a theoretical test case in a plane bi dimensional duct with no slip flow is considered the briggs bers stability criterion is proved to be valid and it shows that the hydrodynamic instability does correspond to a right running amplified wave eigenmode analyses are then performed on the experimental configuration an unstable hydrodynamic surface mode is found with an axial wavenumber and velocity eigenfunctions which are in good agreement with the experimental ones acoustic energy calculations show that the hydrodynamic instability paradoxically carries noticeable levels of acoustic energy in the upstream direction finally the influence of mach number and frequency is investigated

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

parabolic systems in unbounded domains i existence and dynamics abstract in this paper we investigate the existence uniqueness and asymptotic behavior of a solution for a class of coupled nonlinear parabolic equations in a general unbounded domain that includes the whole space r n the exterior of a bounded domain and a half space in r n the asymptotic behavior of the solution is with respect to a pair of quasi solutions of the corresponding elliptic system and when these two quasi solutions coincide the solution of the parabolic system converges to a unique solution of the elliptic system

a mixed finite element method for acoustic wave propagation in moving fluids based on an eulerian lagrangian description a nonstandard wave equation established by galbrun in 1931 is used to study sound propagation in nonuniform flows galbrun s equation describes exactly the same physical phenomenon as the linearized euler s equations lee but is derived from an eulerian lagrangian description and written only in term of the lagrangian perturbation of the displacement this equation has interesting properties and may be a good alternative to the lee only acoustic displacement is involved even in nonhomentropic cases it provides exact expressions of acoustic intensity and energy and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly in this paper galbrun s equation is solved using a finite element method in the axisymmetric case with standard finite elements the direct displacement based variational formulation gives some corrupted results instead a mixed finite element satisfying the inf sup condition is proposed to avoid this problem a first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow obtained from pridmore brown s equation a second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple scale method which is an adaptation for the incompressible case of rienstra s recent work

maximum likelihood approach to strain imaging using ultrasound a maximum likelihood ml strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems concepts from continuum mechanics signal analysis and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images the model includes three dimensional 3 d object motion described by affine transformations rayleigh scattering from random media and 3 d system response functions the likelihood function for these waveforms is derived to express the fisher information matrix and variance bounds for displacement and strain estimation the ml estimator is a generalized cross correlator for pre and post compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection experiments involving soft tissuelike media show the ml estimator approaches the cramer rao error bound for small scaling deformations at 5 mhz and 1 2 compression the predicted