interaction of diffusion and boundary conditions on considere le systeme d equations paraboliques u t d u f u x d u n e x u 0 x ou u r n r n n 3 est un ouvert borne de frontiere lisse d diag d 1 d n e diag e 1 e n chaque d j 0 est constant e j r est continu e j 0 j 1 2 n et e 0 est constant pour f e fixe on etudie comment le flot defini ci dessus depend des parametres d

a wavelet based model of one dimensional periodic structure for wave propagation analysis in this paper a wavelet based method is developed for wave propagation analysis of a generic multi coupled one dimensional periodic structure ps the formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite element fe or other numerical methods here unlike its conventional definition the dynamic stiffness matrix is obtained in the wavelet domain through a daubechies wavelet transform the proposed numerical scheme enables both time and frequency domain analysis of pss under arbitrary loading conditions this is in contrast to the existing fourier transform based analysis that is restricted to frequencydomain study here the dispersion characteristics of pss especially the band gap features are studied in addition the method is implemented to simulate time domain wave response under impulse loading conditions the two examples considered are periodically simply supported beam and periodic frame structures in all cases the responses obtained using the present periodic formulation are compared with the response simulated using the fe model without the periodicity assumption and they show an exact match this validates the accuracy of the periodic assumption to obtain the timeand frequency domain wave responses up to a high frequency range apart from this the proposed method drastically reduces the computational cost and can be implemented for homogenization of pss

systems of p laplacian differential inclusions with large diffusion abstract in this paper we consider coupled systems of p laplacian differential inclusions and we prove under suitable conditions that a homogenization process occurs when diffusion parameters become arbitrarily large in fact we obtain that the attractors are continuous at infinity on l 2 l 2 topology with respect to the diffusion coefficients and the limit set is the attractor of an ordinary differential problem

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

variable rate vector quantization for medical image compression three techniques for variable rate vector quantizer design are applied to medical images the first two are extensions of an algorithm for optimal pruning in tree structured classification and regression due to breiman et al the code design algorithms find subtrees of a given tree structured vector quantizer tsvq each one optimal in that it has the lowest average distortion of all subtrees of the tsvq with the same or lesser average rate since the resulting subtrees have variable depth natural variable rate coders result the third technique is a joint optimization of a vector quantizer and a noiseless variable rate code this technique is relatively complex but it has the potential to yield the highest performance of all three techniques

nesting inertial manifolds for reaction and diffusion equations with large diffusivity we study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations a priori we review both local and global dynamics of the system in scales of banach spaces of hilbert type and we prove the existence of a universal compact attractor for the equations extensions yield the existence of a family of nesting inertial manifolds dependent on the diffusion of the system of equations it is introduced an upper semicontinuity notion in large diffusivity for inertial manifolds the limit inertial manifold whose dimension is strictly less than those of the infinite dimensional system of semilinear evolution equations is obtained

interaction of localized large diffusion and boundary conditions abstract in this paper we derive the limiting pdes for parabolic problems where localized large diffusion touches the boundary of the domain hence the limit problem reflects the interaction of large diffusion and boundary conditions the limit problem is a pde coupled with a system of odes through some nonlocal terms we study the well posedness and dissipativity of the nonstandard limit problem as well as the continuity of the dynamics as diffusion becomes large

a matrix methodology for spectral analysis of wave propagation in multiple connected timoshenko beams the dynamics of the timoshenko beam is recast such that the description requires information only at the end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the timoshenko beam irrespective of the length of the element the frequency domain response is converted to the time domain response using the fast fourier algorithm fft examples of its use in wave propagation studies are given

convergence in competition models with small diffusion coefficients abstract it is well known that for reaction diffusion 2 species lotka volterra competition models with spatially independent reaction terms global stability of an equilibrium for the reaction system implies global stability for the reaction diffusion system this is not in general true for spatially inhomogeneous models we show here that for an important range of such models for small enough diffusion coefficients global convergence to an equilibrium holds for the reaction diffusion system if for each point in space the reaction system has a globally attracting hyperbolic equilibrium this work is planned as an initial step towards understanding the connection between the asymptotics of reaction diffusion systems with small diffusion coefficients and that of the corresponding reaction systems

on parameter estimation for normal mixtures based on fuzzy clustering algorithms described here are three approaches to estimate the parameters of a mixture of normal distributions one approach is based on a modification of the expectation maximization algorithm to compute maximum likelihood estimates another makes use of the fuzzy c means clustering algorithms and the third is based on the penalized fuzzy c means clustering algorithms the accuracy and computational efficiency of algorithms of these three types to estimate parameters of normal mixtures are compared with samples drawn from univariate normal mixtures of two classes

wavelet methods for pdes some recent developments abstract this paper is concerned with recent developments of wavelet schemes for the numerical treatment of operator equations with special emphasis on two issues adaptive solution concepts and nontrivial domain geometries after describing a general multiresolution framework the key features of wavelet bases are highlighted namely locality norm equivalences and cancellation properties assuming first that wavelet bases with these properties are available on the relevant problem domains the relevance of these features for a wide class of stationary problems is explained in subsequent sections the main issues are preconditioning and the efficient adaptive application of wavelet representations of the involved operators we indicate then how these ingredients combined with concepts from nonlinear or best n term approximation culminate in an adaptive wavelet scheme for elliptic selfadjoint problems covering boundary value problems as well as boundary integral equations these schemes can be shown to exhibit convergence rates that are in a certain sense asymptotically optimal we conclude this section with some brief remarks on data structures and implementation interrelations with regularity in a certain scale of besov spaces and strategies of extending such schemes to unsymmetric or indefinite problems we address then the adaptive evaluation of nonlinear functionals of wavelet expansions as a central task arising in connection with nonlinear problems wavelet bases on nontrivial domains are discussed next the main issues are the development of fourier free construction principles and criteria for the validity of norm equivalences finally we indicate possible combinations of wavelet concepts with conventional discretizations such as finite element or finite volume schemes in connection with convection dominated and hyperbolic problems

wavelet galerkin solutions for one dimensional partial differential equations in this paper we describe how wavelets may be used to solve partial differential equations these problems are currently solved by techniques such as finite differences finite elements and multi grid the wavelet method however offers several advantages over traditional methods wavelets have the ability to represent functions at different levels of resolution thereby providing a logical means of developing a hierarchy of solutions furthermore compactly supported wavelets such as those due to daubechies1 are localized in space which means that the solution can be refined in regions of high gradient e g stress concentrations without having to regenerate the mesh for the entire problem in order to demonstrate the wavelet technique we consider the one dimensional counterpart of helmholtz s equation by comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed dirichlet boundary conditions are then imposed using the capacitance matrix method described by proskurowski and widlund2 and others the convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method at least for problems with simple geometries

a virtual image cryptosystem based upon vector quantization we propose a new image cryptosystem to protect image data it encrypts the original image into another virtual image since both original and virtual images are significant our new cryptosystem can confuse illegal users besides the camouflage this new cryptosystem has three other benefits first our cryptosystem is secure even if the illegal users know that our virtual image is a camouflage second this cryptosystem can compress image data finally our method is more efficient than a method that encrypts the entire image directly

upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions the motivations to study the problem considered in this paper come from the theory of composite materials where the heat diffusion properties can change from one part of the domain to another mathematically this leads to a nonlinear second order parabolic equation for which the diffusion coefficient becomes large in a subdomain 0 the equation is supplemented by a nonlinear boundary condition on and an initial condition the authors determine the form of the limit problem the so called shadow system which involves an evolution equation for the averages of the density over 0 the main results include global in time existence of solutions and upper semicontinuity of the associated global attractors when the system approaches the shadow system

wavelets and the numerical solution of partial differential equations we present a new numerical method for the solution of partial differential equations in nonseparable domains the method uses a wavelet galerkin solver with a nontrivial adaptation of the standard capacitance matrix method the numerical solutions exhibit spectral convergence with regard to the order of the compactly supported daubechies wavelet basis furthermore the rate of convergence is found to be independent of the geometry we solve the helmholtz equation since for variations in the parameter the solutions have qualitative properties that well illustrate the applications of our method

an invisible hybrid color image system using spread vector quantization neural networks with penalized fcm in this paper an invisible hybrid color image hiding scheme based on spread vector quantization vq neural network with penalized fuzzy c means pfcm clustering technology named spfnn is proposed the goal is to offer safe exchange of a color stego image in the internet in the proposed scheme the secret color image is first compressed by a spread unsupervised neural network with pfcm based on interpolative vq ivq then the block cipher data encryption standard des and the rivest shamir and adleman rsa algorithms are hired to provide the mechanism of a hybrid cryptosystem for secure communication and convenient environment in the internet in the spfnn the penalized fuzzy clustering technology is embedded in a two dimensional hopfield neural network in order to generate optimal solutions for ivq then we encrypted color ivq indices and sorted the codebooks of secret color image information and embedded them into the frequency domain of the cover color image by the hadamard transform ht our proposed method has two benefits comparing with other data hiding techniques one is the high security and convenience offered by the hybrid des and rsa cryptosystems to exchange color image data in the internet the other benefit is that excellent results can be obtained using our proposed color image compression scheme spfnn method

modeling and simulation of an impact test using wavelets analytical solutions and finite elements an instrumented falling weight impact test is thoroughly investigated in two cases that of a rebound and that of a rupture in the sample first the force signal is analyzed with four methods the continuous wavelet transform with different wavelets derivatives of a gaussian and morlet s the gabor transform the wigner ville transform and the classical fourier analysis it is shown how a proper use of the time frequency methods allows to precisely detect the discontinuities in the signal the moment of rupture if any and the frequencies that are excited at the impact in a second part modal and stress analyses are carried out both by an analytical method and by finite element computations the results confirm those obtained in the first part and agree with experimental findings c 2001 elsevier science ltd all rights reserved

on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

hermitian plane wavelet finite element method wave propagation and load identification abstract the two dimensional hermitian interpolation wavelet is constructed by using the tensor product of the modified hermitian wavelets expanded at each coordinate then the two dimensional hermitian interpolation wavelet is substituted into finite element formulations to address the wave propagation and load identification problems hermitian wavelet finite element can be used to describe the wave propagation and to reveal the rule of the wave propagation in plane the wave propagation response is used to solve the load identification inverse problem results show that the identified load value is similar to the applied load when the location of the response node is close to the applied load position the proposed method can accurately identify the location waveform and amplitude of the applied load

polygonal approximation using a competitive hopfield neural network abstract polygonal approximation plays an important role in pattern recognition and computer vision in this paper a parallel method using a competitive hopfield neural network chnn is proposed for polygonal approximation based on the chnn the polygonal approximation is regarded as a minimization of a criterion function which is defined as the arc to chord deviation between the curve and the polygon the chnn differs from the original hopfield network in that a competitive winner take all mechanism is imposed the winner take all mechanism adeptly precludes the necessity of determining the values for the weighting factors in the energy function in maintaining a feasible result the proposed method is compared to several existing methods by the approximation error norms l2 and l with the result that promising approximation polygons are obtained

evolution of a semilinear parabolic system for migration and selection in population genetics abstract the semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated the population occupies a finite habitat of arbitrary dimensionality and shape i e a bounded open domain in rd the selection coefficients depend on position and may depend on the gene frequencies the drift and diffusion coefficients may depend on position sufficient conditions are given for the global loss of an allele and for its protection from loss a sufficient condition for the existence of at least one internal equilibrium is also offered and the profile of any internal equilibrium in the zero migration limit is obtained

sideways heat equation and wavelets the sideways heat equation is considered as a model ill posed problem the aim of this paper is to indicate a possibility of a new approach for solving this problem based on an application of wavelet basis decomposition of measured data the meyer wavelets are applied to formulate a regularized solution which is convergent to the exact one when a data error tends to zero

alternating wavelet time finite element method modeling and analysis of nonlinear wave propagation in one and two dimensional waveguides abstract in this paper a novel method named the alternating wavelet time finite element method awt fem is proposed for studying elastic wave propagation in nonlinear structures an alternating iterative procedure between the time domain and a wavelet domain combined with the spectral finite element method sfem is employed to solve wave equations with general nonlinearities the advantages of the proposed method are 1 the potential to provide high fidelity results for impacts with high frequency content through the use of the spectral finite element method 2 nonlinear structures with physically realistic boundary conditions can easily be studied by circumventing wrap around issues associated with fourier based methods 3 the parallel computing compatible framework and the semi analytical nature of sfem make it more computationally efficient for nonlinear systems modeled with structural components simulations using the proposed method are conducted to demonstrate its applicability to study nonlinear wave propagation in one dimensional and two dimensional systems

asymptotic behavior of strongly monotone time periodic dynamical processes with symmetry given a strongly monotone discrete time dynamical system tn x x n z in an open and order convex subset x of a separable strongly ordered banach space v and a compact connected metrizable group g whose action on x is monotone and commutes with t we prove under some reasonable additional hypotheses that the limit set x of every stable point x x consists of symmetric points only i e g w w for all w x and g g moreover the set of all unstable points is contained in a union of at most countably many lipschitz manifolds of codimension one in v where each manifold is invariant under t and the action of g this result is applied to the time periodic spatially independent irreducible cooperative system of n reaction diffusion equations u t d t u f t u for t x r1 rn with spatially periodic boundary conditions in rn and with an initial distribution u0 which is continuous and satisfies the boundary conditions if u0 is stable then u0 contains spatially constant functions only and the dynamics on u0 is given by the irreducible cooperative system of n odes dudt f t u for t r1 here t is the poincare map if n 1 then u0 is a single fixed point of t if n 2 then v0 is a single fixed point of t for each v0 u0

a dynamical approximation for stochastic partial differential equations random invariant manifolds provide geometric structures for understanding stochastic dynamics in this paper a dynamical approximation estimate is derived for a class of stochastic partial differential equations by showing that the random invariant manifold is almost surely asymptotically complete the asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold under suitable conditions as an application stationary states invariant measures are considered for a class of stochastic hyperbolic partial differential equations

two time scales in spatially structured models of population dynamics a semigroup approach abstract the aim of this work is to provide a unified approach to the treatment of a class of spatially structured population dynamics models whose evolution processes occur at two different time scales in the setting of the c 0 semigroup theory we will consider a general formulation of some semilinear evolution problems defined on a banach space in which the two time scales are represented by a parameter e 0 small enough that mathematically gives rise to a singular perturbation problem applying the so called aggregation of variables method a simplified model called the aggregated model is constructed a nontrivial mathematical task consists of comparing the asymptotic behaviour of solutions to both problems when e 0 under the assumption that the aggregated model has a compact attractor applications of the method to a class of two time reaction diffusion models of spatially structured population dynamics and to models with discrete spatial structure are given

introduction to wavelets in engineering the aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications the paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet based numerical algorithms in particular we provide extensive details of the derivation of mallat s transform and daubechies wavelet coefficients since these are fundamental to gaining an insight into the properties of wavelets the potential benefits of using wavelets are highlighted by presenting results of our research in one and two dimensional data analysis and in wavelet solutions of partial differential equations

wave propagation in multiply connected deep waveguides the longitudinal dynamics of a deep waveguide segment is recast such that the description requires information only at its end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the waveguide segment irrespective of its length by combining these results with a previously presented spectral formulation for the flexural dynamics of a deep timoshenko beam a spectral formulation for the dynamics of multiply connected waveguides forming frames is obtained examples of its use in analyzing wave propagation in connected structures are given and compared with results from a two dimensional finite element analysis

towards a method for solving partial differential equations by using wavelet packet bases abstract in this paper we present a new methodology based on the wavelet packet concept in order to define an adaptive method for the approximation of partial differential equations the wavelet packet framework allows us to define the notion of a minimal basis that has proven to be an efficient procedure for data compression the purpose here is to take benefit of this compression to represent accurately and economically the solution of a time dependent pde the time discretization is a standard multistep scheme the spacial discretization is defined by inferring a reduced basis for the solution at the new time step from the knowledge of the previous ones

preconditioned chebyshev collocation methods and triangular finite elements this paper analyzes triangular finite elements for the preconditioning of chebyshev collocation solutions of elliptic boundary value problems results are given for scalar model problems and for both stokes and navier stokes equations

a spectral multiscale method for wave propagation analysis atomistic continuum coupled simulation in this paper we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis the problem of non physical wave reflection which occurs due to the change in system description across the interface between two scales can be satisfactorily overcome by the proposed method we propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equation in the laplace domain to eliminate the spurious interfacial reflection we use laplace transform based spectral finite element method to model the macroscale which provides the optimum approximations for required dynamic responses of the outer atoms of the simulated microscale region very accurately this new method shows excellent agreement between the proposed multiscale model and the full molecular dynamics md results numerical experiments of wave propagation in a 1d harmonic lattice a 1d lattice with lennard jones potential a 2d square bravais lattice and a 2d triangular lattice with microcrack demonstrate the accuracy and the robustness of the method in addition under certain conditions this method can simulate complex dynamics of crystalline solids involving different spatial and or temporal scales with sufficient accuracy and efficiency c 2014 elsevier b v all rights reserved

wavelet and fourier methods for solving the sideways heat equation we consider an inverse heat conduction problem the sideways heat equation which is a model of a problem where one wants to determine the temperature on both sides of a thick wall but where one side is inaccessible to measurements mathematically it is formulated as a cauchy problem for the heat equation in a quarter plane with data given along the line x 1 where the solution is wanted for 0 leq x 1 the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data we consider stabilizations based on replacing the time derivative in the heat equation by wavelet based approximations or a fourier based approximation the resulting problem is an initial value problem for an ordinary differential equation which can be solved by standard numerical methods e g a runge kutta method we discuss the numerical implementation of fourier and wavelet methods for solving the sideways heat equation theory predicts that the fourier method and a method based on meyer wavelets will give equally good results our numerical experiments indicate that also a method based on daubechies wavelets gives comparable accuracy as test problems we take model equations with constant and variable coefficients we also solve a problem from an industrial application with actual measured data

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

flow invariance for solutions to nonlinear nonautonomous partial differential delay equations we investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations u t b t u t f t ut t s us where b t is a family of nonlinear multivalued accretive operators with d b t possibly depending on t and the operators f t being defined and lipschitz continuous possibly only on thin subsets of the initial history space e the results are applied to population dynamics models we also study the asymptotic behavior of solutions to this equation our analysis will be based on the evolution operator associated to the equation in the initial history space e

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a spectrally formulated plate element for wave propagation analysis in anisotropic material a new spectrally formulated plate element is developed to study wave propagation in composite structures the element is based on the classical lamination plate theory recently developed method based on singular value decomposition svd is used in the element formulation along with this a new strategy based on the method of solving polynomial eigenvalue problem pep is proposed in this paper which significantly reduces human intervention and thus human error in the element formulation the developed element has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation of plate in frequency wavenumber domain as the interpolating functions due to this the mass distribution is modeled exactly and as a result a single element captures the exact frequency response of a regular structure and it suffices to model a plate of any dimension thus the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis the fast fourier transform fft and fourier series are used for inversion to time space domain this element is used to model plate with ply drops and to capture the propagation of lamb waves

general templates for n noded bar elements based on reduced representations and numerical dispersion reduction by optimized finite elements abstract various kinds of finite elements are proposed and employed for one dimensional wave field simulations each of which has their own capabilities and disadvantages this paper deals with structural similarities and differences that arise at the element level by the use of reduced forms of mass and stiffness matrices general parameterized forms are then developed for mass and stiffness matrices of n noded elements elements with n nodes with arbitrary arrangement optimization for the free parameters will deliver elements with better performance and less numerical dispersion error two of such elements are developed and compared for their ability in dispersion error remission

evolution of a semilinear parabolic system for migration and selection without dominance the semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated the population occupies a finite habitat of arbitrary dimensionality and shape i e a bounded open domain in r d the selection coefficients depend on position the drift and diffusion coefficients may depend on position the primary focus of this paper is the dependence of the evolution of the gene frequencies on the strength of selection relative to that of migration it is proved that if migration is sufficiently strong i e is sufficiently small and the migration operator is in divergence form then the allele with the greatest spatially averaged selection coefficient is ultimately fixed the stability of each vertex i e an equilibrium with exactly one allele present is completely specified the stability of each edge equilibrium i e one with exactly two alleles present is fully described when either i migration is sufficiently weak i e is sufficiently large or ii the equilibrium has just appeared as increases the existence of unexpected complex phenomena is established even if there are only three alleles and migration is homogeneous and isotropic corresponding to the laplacian i as increases arbitrarily many changes of stability of the edge equilibria and corresponding appearance of an internal equilibrium can occur and ii the conditions for protection or loss of an allele can both depend nonmonotonically on neither of these phenomena can occur in the diallelic case

asymptotic properties in parabolic problems dominated by a p laplacian operator with localized large diffusion abstract this paper is concerned with upper semicontinuity of the family of attractors associated with nonlinear reaction diffusion equations with principal part governed by a degenerate p laplacian in which the diffusion d blows up in localized regions inside the domain

a wavelet based method for the forced vibration analysis of piecewise linear single and multi dof systems with application to cracked beam dynamics abstract the present investigation outlines a method based on the wavelet transform to analyze the vibration response of discrete piecewise linear oscillators representative of beams with breathing cracks the displacement and force variables in the governing differential equation are approximated using daubechies compactly supported wavelets an iterative scheme is developed to arrive at the optimum transform coefficients which are back transformed to obtain the time domain response a time integration scheme solving a linear complementarity problem at every time step is devised to validate the proposed wavelet based method applicability of the proposed solution technique is demonstrated by considering several test cases involving a cracked cantilever beam modeled as a bilinear sdof system subjected to a harmonic excitation in particular the presence of higher order harmonics originating from the piecewise linear behavior is confirmed in all the test cases parametric study involving the variations in the crack depth and crack location is performed to bring out their effect on the relative strengths of higher order harmonics versatility of the method is demonstrated by considering the cases such as mixed frequency excitation and an mdof oscillator with multiple bilinear springs in addition to purporting the wavelet based method as a viable alternative to analyze the response of piecewise linear oscillators the proposed method can be easily extended to solve inverse problems unlike the other direct time integration schemes

a two codebook combination and three phase block matching based image hiding scheme with high embedding capacity image hiding is a technique that embeds the important images into a cover image such that the important images are imperceptible and can be securely transmitted to the receiver in such research the common goals are to enlarge the embedding capacity as much as possible since the visual quality of the cover image is degraded slightly and to keep high visual quality of the important images when they are extracted from the stego image in this paper we propose an image hiding method based on the two codebook combination the three phase block matching procedure and the modulus substitution the proposed method can achieve these benefits 1 multiple relatively large important images can be embedded into a relatively small cover image 2 the quality of the stego image after embedding the secret data is not distorted significantly 3 the important images have an acceptable visual quality after they are extracted the experimental results also show that the proposed method is more flexible than previous methods

on a wavelet based method for the numerical simulation of wave propagation a wavelet based method for the numerical simulation of acoustic and elastic wave propagation is developed using a displacement velocity formulation and treating spatial derivatives with linear operators the wave equations are rewritten as a system of equations whose evolution in time is controlled by first order derivatives the linear operators for spatial derivatives are implemented in wavelet bases using an operator projection technique with nonstandard forms of wavelet transform using a semigroup approach the discretized solution in time can be represented in an explicit recursive form based on taylor expansion of exponential functions of operator matrices the boundary conditions are implemented by augmenting the system of equations with equivalent force terms at the boundaries the wavelet based method is applied to the acoustic wave equation with rigid boundary conditions at both ends in 1 d domain and to the elastic wave equation with a traction free boundary conditions at a free surface in 2 d spatial media the method can be applied directly to media with plane surfaces and surface topography can be included with the aid of distortion of the grid describing the properties of the medium the numerical results are compared with analytic solutions based on the cagniard technique and show high accuracy the wavelet based approach is also demonstrated for complex media including highly varying topography or stochastic heterogeneity with rapid variations in physical parameters these examples indicate the value of the approach as an accurate and stable tool for the simulation of wave propagation in general complex media

interpolative vector quantization of color images interpolative vector quantization has been devised to alleviate the visible block structure of coded images plus the sensitive codebook problems produced by a simple vector quantizer in addition the problem of selecting color components for color picture vector quantization is discussed computer simulations demonstrate the success of this coding technique for color image compression at approximately 0 3 b pel some background information on vector quantization is provided

spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1 d waveguides in this paper a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1 d connected waveguides first the partial differential wave equation is converted to simultaneous ordinary differential equations odes using daubechies wavelet approximation in time these odes are then solved using finite element fe technique by deriving the exact interpolating function in the transformed domain spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional fe the localized nature of the compactly supported daubechies wavelet allows easy imposition of initial boundary values this circumvents several disadvantages of the conventional spectral element formulation using fast fourier transforms fft particularly in the study of transient dynamics the proposed method is used to study longitudinal and flexural wave propagation in rods beams and frame structures numerical experiments are performed to show the advantages over fft based spectral element methods the efficiency of the spectral formulation for impact force identification is also demonstrated

delay partial differential equations with some large diffusion it is often the case in infinite dimensional dynamical systems that a certain unbounded operator depends upon a parameter v its eigenvalues and eigenfunctions will also depend upon v in many cases see for example l 7 there is a finite number of eigenvalues of the unbounded operator that stay bounded as the parameter varies the remaining eigenvalues blow up at a certain rate in this case one expects the dynamics to be dictated by a system of ordinary differential equations this is indeed the case in several applications and its proof strongly uses the invariant manifold theory in the cases considered in this paper we study the dynamics of infinite dimensional dynamical systems for which a countable number of eigenvalues of the unbounded operator converges to the eigenvalues of an unbounded operator in a lower dimensional domain whereas the remaining blow up this is the case for example in parabolic equations in thin domains studied by hale and raugel s we will not be able to address the general case of thin domains but only the case of a thin straight channel however the property that allows this theory to work is present in the general case that is there is a sequence of eigenvalues that stay bounded and a sequence of eigenvalues that blow up see also arrieta 9 the theory of invariant manifolds will no longer work in this case since it is centered around the existence of backward solutions which cannot be expected in this situation the main tools in this work are a converse theorem on existence of compact attractors and an eigenvalue problem a physical interpretation of a parabolic problem in a thin straight channel is that there is a very high diffusion in one of the directions from which our intuition would say that in that direction spatial changes will not be observed the same interpretation can be given to a damped wave problem in a thin straight channel the wave speed can be interpreted as being very large in one direction this would intuitively imply that there would be no spatial changes for the amplitude of the wave in that direction we also consider the problem called shadow systems where the diffusion is very large for some of the substances in the reaction and not so large for the remaining substances in this

large diffusivity and asymptotic behavior in parabolic systems abstract for systems of reaction diffusion equations with neumann boundary conditions it is shown that the solutions are asymptotic to the solutions of an ordinary differential equation if the diffusivity is large the methods apply also to reaction diffusion systems with time delays

well posed p laplacian problems with large diffusion abstract in this work we study the asymptotic behavior of p laplacian parabolic problems of the form u t d p u u p 2 u b u in a bounded smooth domain in r n and under neumann boundary conditions when the diffusion coefficient d becomes large we prove under suitable assumptions that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity

rate of convergence of attractors for singularly perturbed semilinear problems abstract we exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation we estimate the convergence of attractors in the hausdorff metric by rate of convergence of resolvent operators application to spatial homogenization and large diffusion except in a neighborhood of a point will be considered