investigation of a griffith crack subject to anti plane shear by using the non local theory abstract field equations of the non local elasticity are solved to determine the state of stress in a plate with a griffith crack subject to the anti plane shear then a set of dual integral equations is solved using schmidts method contrary to the classical elasticity solution it is found that no stress singularity is present at the crack tip the significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales

mixed finite element formulations and related limitation principles a general treatment abstract the complete set of variational principles for an elastic structural model with non homogeneous boundary conditions and inelastic strains is presented a general methodology for deriving the approximate mixed formulation and the relevant matrix form is also shown and applied the limitation principles for a structural model with a linear elastic behaviour are derived and it is shown that each principle relating two different approximate formulations depends upon the state variable interpolated in one formulation and not in the other

nonlocal theory solution of two collinear cracks in the functionally graded materials in this paper the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti plane shear loading is investigated by means of nonlocal theory the traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials to make the analysis tractable it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack by use of the fourier transform the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the displacement on the crack surfaces to solve the triple integral equations the displacement on the crack surfaces is expanded in a series of jacobi polynomials unlike the classical elasticity solutions it is found that no stress singularity is present near the crack tips the nonlocal elastic solutions yield a finite hoop stress at the crack tip thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials the magnitude of the finite stress field depends on the crack length the distance between two cracks the parameter describing the functionally graded materials and the lattice parameter of the materials

principal component analysis based on l1 norm maximization a method of principal component analysis pca based on a new l1 norm optimization technique is proposed unlike conventional pca which is based on l2 norm the proposed method is robust to outliers because it utilizes l1 norm which is less sensitive to outliers it is invariant to rotations as well the proposed l1 norm optimization technique is intuitive simple and easy to implement it is also proven to find a locally maximal solution the proposed method is applied to several datasets and the performances are compared with those of other conventional methods

on some theorems in the nonlocal theory of micropolar elasticity abstract this paper is concerned with the linear nonlocal theory of micropolar elasticity we have established a work and energy theorem and a uniqueness theorem without making any definiteness assumptions about the elastic moduli a reciprocity theorem is also established

sparse geometric image representations with bandelets this paper introduces a new class of bases called bandelet bases which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow this geometric flow indicates directions in which the image gray levels have regular variations the image decomposition in a bandelet basis is implemented with a fast subband filtering algorithm bandelet bases lead to optimal approximation rates for geometrically regular images for image compression and noise removal applications the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion comparisons are made with wavelet image compression and noise removal algorithms

fast algorithm for computing discrete cosine transform an efficient method for computing the discrete cosine transform dct is proposed based on direct decomposition of the dct the recursive properties of the dct for an even length input sequence is derived which is a generalization of the radix 2 dct algorithm based on the recursive property a new dct algorithm for an even length sequence is obtained the proposed algorithm is very structural and requires fewer computations when compared with others the regular structure of the proposed algorithm is suitable for fast parallel algorithm and vlsi implementation

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

two parallel symmetry permeable cracks in functionally graded piezoelectric piezomagnetic materials under anti plane shear loading abstract in this paper the behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric piezomagnetic materials subjected to an anti plane shear loading is investigated to make the analysis tractable it is assumed that the material properties c44 e15 e11 q15 d11 and 11 vary exponentially with coordinate parallel to the crack by using the fourier transform the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces these equations are solved using the schmidt method the normalized stress the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions numerical examples are provided to show the effect of the geometry of the interacting crack and the parameter describing the functionally graded materials upon the stress intensity factor of the cracks

why many theories of shock waves are necessary kinetic relations for non conservative systems for a class of nonconservative hyperbolic systems of partial dif ferential equations endowed with a strictly convex mathematical entropy we formulate the initial value problem by supplementing the equations with a ki netic relation prescribing the rate of entropy dissipation across shock waves our condition can be regarded as a generalization to nonconservative systems of a similar concept introduced by abeyaratne knowles and truskinovsky for subsonic phase transitions and by lefloch for nonclassical undercompressive shocks to nonlinear hyperbolic systems the proposed kinetic relation for non conservative systems turns out to be equivalent for the class of systems under consideration at least to dal maso lefloch and murat s definition based on a prescribed family of lipschitz continuous paths in agreement with previous theories the kinetic relation should be derived from a phase plane analysis of traveling solutions associated with an augmented version of the nonconserva tive system we illustrate with several examples that nonconservative systems arising in the applications fit in our framework and for a typical model of turbulent fluid dynamics we provide a detailed analysis of the existence and properties of traveling waves which yields the corresponding kinetic function

uniqueness of initial boundary value problems in nonlocal elasticity abstract in this study we have dealt with the uniqueness of the solutions of a class of initial boundary value problems in linear isotropic homogeneous nonlocal elasticity the proof of uniqueness is based on the positive definiteness of total strain energy after giving the sufficient conditions under which total strain energy is positive definite it has been shown that the solutions of the initial boundary value problems which are considered in this study are unique existence of the solutions of these problems is an a priori assumption

macroscopic theory of multicomponent flows irreversibility and well posed equations abstract a theory of the coupling of n systems of navier stokes equations is presented a set of coupled navier stokes systems contains the macroscopic equations of motion for flows of n different material components or phases six postulates are formulated from which three navier stokes sets are derived for arbitrary n the main postulate concerns the second law of thermodynamics which the present sets satisfy for arbitrary n appropriate averages of velocities and pressures distribute the entropy production of each irreversible interaction process among the interacting components increase of entropy is guaranteed if the interaction terms are suitably constructed from positive definite operators a strictly irreversible mass exchange law expressed in the difference of gibbs free energies of the exchanging components is proposed furthermore the characteristic velocities of each navier stokes set are investigated since their realness is required for well posedness of the equations for both navier stokes sets with multiple pressures the characteristic velocities are proven to be real for arbitrary n the canonical problem of complex characteristics of incompressible multiphase flows with a single pressure is revisited a solution to this problem is found by generalizing the standard algebraic stokes drag law to a positive definite operator acting on the velocity difference in this way effects of forces due to nonuniform velocity fields can be incorporated a generalized drag law is specified by the inclusion of m th order spatial derivatives of the velocity differences between two components m 2 the characteristic polynomial is derived for an arbitrary number of components and its roots the characteristic velocities appear to be real this is rigorously proven for two and three phase flows and conjectured to be true for flows with four or more components the linear stability of the incompressible one dimensional case is also investigated ill posedness of the standard case leads to an infinite growth rate for infinitely short waves in the case of generalized drag this growth rate becomes finite for even and neutral for odd m

directionlets anisotropic multidirectional representation with separable filtering in spite of the success of the standard wavelet transform wt in image processing in recent years the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions one dimensional 1 d discontinuities in images edges and contours that are very important elements in visual perception intersect too many wavelet basis functions and lead to a nonsparse representation to efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions a more complex multidirectional m dir and anisotropic transform is required we present a new lattice based perfect reconstruction and critically sampled anisotropic m dir wt the transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two dimensional wt unlike in the case of some other directional transform constructions e g curvelets contourlets or edgelets the corresponding anisotropic basis functions directionlets have directional vanishing moments along any two directions with rational slopes furthermore we show that this novel transform provides an efficient tool for nonlinear approximation of images achieving the approximation power o n sup 1 55 which while slower than the optimal rate o n sup 2 is much better than o n sup 1 achieved with wavelets but at similar complexity

rotated orthogonal transform rot for motion compensation residual coding discrete cosine transform dct is the orthogonal transform that is most commonly used in image and video compression the motion compensation residual mc residual is also compressed with the dct in most video codecs however the mc residual has different characteristics from a nature image in this paper we develop a new orthogonal transform rotated orthogonal transform rot that can perform better on the mc residual than the dct for coding purposes we derive the proposed rot based on orthogonal constrained l1 norm minimization problem for its sparse property using the dct matrix as the starting point a better orthogonal transform matrix is derived in addition by exploring inter frame dependency and local motion activity transmission of substantial side information is avoided the experiment results confirm that with small computation overhead the rot is adaptive to change of local spatial characteristic of mc residual frame and provides higher compression efficiency for the mc residual than dct especially for high and complex motion videos

a strain difference based nonlocal elasticity model abstract a two component local nonlocal constitutive model for macroscopically inhomogeneous linear elastic materials but constant internal length is proposed in which the stress is the sum of the local stress and a nonlocal type stress expressed in terms of the strain difference field hence identically vanishing in the case of uniform strain attention is focused upon the particular case of piecewise homogeneous material the proposed model is thermodynamically consistent with a suitable free energy potential it constitutes an improved form of the vermeer and brinkgreve a new effective nonlocal strain measure for softening plasticity in chambon r desrues j vardulakis i eds localization and bifurcation theory for soils and rocks balkema rotterdam 1994 pp 89 100 model and can also be considered derivable from the eringen nonlocal elasticity model through a suitable enhancement technique based on the concept of redistribution of the local stress the concept of equivalent distance is introduced to macroscopically account for the further attenuation effects produced by the inhomogeneity upon the long distance interaction forces with the aid of a piecewise homogeneous bar in tension a portion of which degrades progressively till failure it is shown that under a suitable choice of a material constant the solution procedure exhibits no pathological features numerical instability mesh sensitivity in every degraded bar condition including the limit idealized stress free condition of the failed bar

benchmarks in nonlocal elasticity defined by eringen s integral model abstract in this paper we present low residual approximate solutions for nonlocal 1d and 2d elasticity problems defined according to eringen s integral model the benchmarks in the 1d cases are defined by prescribing the stress field while the unknown fields are the strains or the displacements for the 2d cases we define problems with equilibrated tractions and evaluate the approximate displacement field meanwhile a fourier series as well as a set of chebyshev polynomials are used as the basis functions for the main unknown fields we increase the number of the approximation functions to decrease the norm of the residuals and repeat the procedure until reasonable accuracy is obtained for the final solution since the procedure is very time consuming in some benchmark problems we present the calculated coefficients and in some other we give some point wise values for further use the results presented in this paper are particularly useful for the validation and convergence studies when numerical methods are to be used for the solution of the nonlocal elasticity problems

on non local and non homogeneous elastic continua abstract a thermodynamic framework endowed with the concept of non locality residual is adopted to derive non local models of integral type for non homogeneous linear elastic materials two expressions of the free energy are considered the former yields a one component non local stress the latter leads to a two component local non local stress since the stress is expressed as the sum of the classical local stress and of a non local component identically vanishing in the case of constant strains the attenuation effects are accounted for by a symmetric space weight function which guarantees the constant strain requirement as well as the dual constant stress condition everywhere in the body the non local and non homogeneous elastic structural boundary value problem under quasi static loads is addressed in a geometrically linear range the complete set of variational formulations for the structural problem is then provided in a unitary framework the solution uniqueness of the non local structural model is proved and the non local fem is addressed starting from the non local counterpart of the total potential energy numerical applications are provided with reference to a non homogeneous bar in tension using the fredholm integral equation and the non local fem the solutions show no pathological features such as numerical instability and mesh sensitivity for degraded bar conditions

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

the finite element method for the mechanically based model of non local continuum summary in this paper the finite element method fem for the mechanically based non local elastic continuum model is proposed in such a model each volume element of the domain is considered mutually interacting with the others beside classical interactions involved by the cauchy stress field by means of central body forces that are monotonically decreasing with their inter distance and proportional to the product of the interacting volume elements the constitutive relations of the long range interactions involve the product of the relative displacement of the centroids of volume elements by a proper distance decaying function which accounts for the decrement of the long range interactions as long as distance increases in this study the elastic problem involving long range central interactions for isotropic elastic continuum will be solved with the aid of the fem the accuracy of the solution obtained with the proposed fem code is compared with other solutions obtained with galerkins approximation as well as with finite difference method moreover a parametric study regarding the effect of the material length scale in the mechanically based model and in the kroner eringen non local elasticity has been investigated for a plane elasticity problem copyright 2011 john wiley sons ltd

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

variational formulations and a consistent finite element procedure for a class of nonlocal elastic continua the structural boundary value problem in the context of nonlocal integral elasticity and quasi static loads is considered in a geometrically linear range the nonlocal elastic behaviour is described by the so called eringen model in which the nonlocality lies in the constitutive relation the diffusion processes of the nonlocality are governed by an integral relation containing a recently proposed symmetric spatial weight function expressed in terms of an attenuation function a firm variational basis to the nonlocal model is given by providing the complete set of variational formulations composed by ten functionals with different combinations of the state variables in particular the nonlocal counterpart of the classical principles of the total potential energy complementary energy and mixed hu washizu principle and hellinger reissner functional are recovered some examples concerning a piecewise bar in tension are provided by using the fredholm integral equation and the proposed nonlocal fem

image compression with variable block size segmentation high quality variable rate image compression is achieved by segmenting an image into regions of different sizes classifying each region into one of several perceptually distinct categories and using a distinct coding procedure for each category segmentation is performed with a quadtree data structure by isolating the perceptually more important areas of the image into small regions and separately identifying larger random texture blocks since the important regions have been isolated the remaining parts of the image can be coded at a lower rate than would be otherwise possible high quality coding results are achieved at rates between 0 35 and 0 7 b p depending on the nature of the original image and satisfactory results have been obtained at 0 25 b p

combined techniques of singular value decomposition and vector quantization for image coding the combination of singular value decomposition svd and vector quantization vq is proposed as a compression technique to achieve low bit rate and high quality image coding given a codebook consisting of singular vectors two algorithms which find the best fit candidates without involving the complicated svd computation are described simulation results show that the proposed methods are better than the discrete cosine transform dct in terms of energy compaction data rate image quality and decoding complexity

optimal algorithms for l_ 1 subspace signal processing we describe ways to define and calculate l 1 norm signal subspaces that are less sensitive to outlying data than l 2 calculated subspaces we start with the computation of the l 1 maximum projection principal component of a data matrix containing n signal samples of dimension d we show that while the general problem is formally np hard in asymptotically large n d the case of engineering interest of fixed dimension d and asymptotically large sample size n is not in particular for the case where the sample size is less than the fixed dimension we present in explicit form an optimal algorithm of computational cost 2 n for the case n d we present an optimal algorithm of complexity o n d we generalize to multiple l 1 max projection components and present an explicit optimal l 1 subspace calculation algorithm of complexity o n dk k 1 where k is the desired number of l 1 principal components subspace rank we conclude with illustrations of l 1 subspace signal processing in the fields of data dimensionality reduction direction of arrival estimation and image conditioning restoration

on thermoelastostatics of composites with nonlocal properties of constituents i general representations for effective material and field parameters abstract a theory of thermoelastic composites with nonlocal properties of constituents is analyzed for multiphase elastic solids of arbitrary geometry and material symmetry due to their generality one uses the nonlocal integral models because the gradient models are usually derived as approximations of corresponding integral models in the immediate infinitely closed vicinity of the point being considered one explores a simplified theory for linear macroscopically elasticity which differs from the classical local theory in the stress strain constitutive relation only whereas the equilibrium and compatibility equations remain unaltered one obtains the new representation of the effective modulus and compliance through the mechanical influence function which does not explicitly depend as opposed to its local counterpart on the elastic operators of constituents the representations for the effective eigenstrains and eigenstresses through either the mechanical influence functions or transformation influence functions are presented the effective strain energy and potential energy are expressed in terms of only average values of the state variables and the effective properties representations of both the first and second statistical moments of stress and strain fields in the constituents are also performed many of the results were obtained as the straightforward generalizations of their local counterparts because the methods used for obtaining the mentioned results widely exploit the hill s 1963 condition which holds for any compatible strain field and equilibrium stress field not necessarily related to each other by a specific stress strain relation

traveling waves solution of convection diffusion systems whose convection terms are weakly nonconservative application to the modeling of two phase fluid flows the paper is concerned with the derivation of explicit approximate jump conditions for the shock waves solutions of hyperbolic systems in nonconservation form extracted from a known second order convection diffusion system the shock waves are defined as the limit as the diffusion tends to zero of the traveling waves solution of the second order system although no explicit jump conditions may be found for general hyperbolic systems in nonconservation form we derive an asymptotic expansion of the nonexplicit jump relations in the case of two phase fluid flows we indeed observe that the terms in nonconservation form arise from pressure gradient forces which act on droplets and are small in the sense that the a small number appears in front of them we obtain an asymptotic expansion of the nonexplicit jump relations whose first two terms can be computed explicitly

divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects abstract transverse vibrations of elastically rested moving beam like nanostructures accounting for surface effect are of high concern the role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years nevertheless the influence of the surface energy on the mechanical behavior of such elements has not been explained yet in this paper equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic shear deformable beam models subsequently the transverse vibrations of the nanostructure are evaluated using galerkin based assumed mode method the explicit expressions of divergence velocities are obtained analytically and these are successfully verified with the results of a numerical approach the roles of crucial parameters on the first divergence velocity are addressed in some detail additionally the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed

hyperbolic two pressure models for two phase flow abstract for some time it has been known that many of the two phase flow models lead to ill posed cauchy problems because they have complex characteristic values a necessary condition at least in the linear case for the cauchy problem to be well posed is that it be stable in the sense of von neumann for systems of partial differential equations of first order stability in the sense of von neumann is essentially equivalent to the condition that the model be hyperbolic all real characteristic values and complete set of characteristic vectors herein models are developed which have real characteristic values for all physically acceptable states state space and except for a set of measure zero have a complete set of characteristic vectors in state space therefore these models are hyperbolic a e almost everywhere in state space also they are stable in the sense of von neumann a e in state space even without inclusion of viscosity terms the models discussed herein are developed for the case of two phase separated planar flow and include transverse momentum considerations these models are referred to as two pressure models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase the pressure fields are related through momentum considerations numerical results on a steady state problem show good agreement with existing steady state results numerical results on a transient problem agree with a single pressure model until the onset of numerical instability in the single pressure model compared to the single pressure hydrostatic model the two pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non local theory in this paper the dynamic behavior of two parallel symmetric cracks in piezoelectric materials under harmonic anti plane shear waves is investigated by use of the non local theory for permeable crack surface conditions to overcome the mathematical difficulties a one dimensional non local kernel is used instead of a two dimensional one for the problem to obtain the stress occurs near the crack tips by means of the fourier transform the problem can be solved with the help of two pairs of dual integral equations that the unknown variables are the jumps of the displacement along the crack surfaces these equations are solved using the schmidt method numerical examples are provided contrary to the previous results it is found that no stress and electric displacement singularity is present near the crack tip the non local elastic solutions yield a finite hoop stress near the crack tip thus allowing for a fracture criterion based on the maximum stress hypothesis the finite hoop stress at the crack tip depends on the crack length the frequency of the incident wave the distance between two cracks and the lattice parameter of the materials respectively contrary to the impermeable crack surface condition solution it is found that the dynamic electric displacement for the permeable crack surface conditions is much smaller than the results for the impermeable crack surface conditions the results show that the dynamic field will impede or enhance crack propagation in the piezoelectric materials at different stages of the dynamic load

non local theory solution to a rectangular crack in a 3d infinite orthotropic elastic medium abstract the non local theory solution to a rectangular crack in a 3d infinite orthotropic elastic medium is investigated by using the generalized almansi s theorem and the schmidt method in the present paper the problem is formulated through the double fourier transform into three pairs of dual integral equations in which the unknown variables are the displacement jumps across the crack surfaces for solving the dual integral equations the displacement jumps across the crack surfaces are directly expanded as a series of jacobi polynomials numerical examples are provided to illustrate the effects of the geometric shape of the rectangular crack and the lattice parameter on the stress fields near the crack edges different from the classical solutions the present solutions exhibit no stress singularity along the rectangular crack edges in an orthotropic elastic medium thus this allows us to use the maximum stress as a fracture criterion

1 d transforms for the motion compensation residual transforms used in image coding are also commonly used to compress prediction residuals in video coding prediction residuals have different spatial characteristics from images and it is useful to develop transforms that are adapted to prediction residuals in this paper we explore the differences between the characteristics of images and motion compensated prediction residuals by analyzing their local anisotropic characteristics and develop transforms adapted to the local anisotropic characteristics of these residuals the analysis indicates that many regions of motion compensated prediction residuals have 1 d anisotropic characteristics and we propose to use 1 d directional transforms for these regions we present experimental results with one example set of such transforms within the h 264 avc codec and the results indicate that the proposed transforms can improve the compression efficiency of motion compensated prediction residuals over conventional transforms

the behavior of two parallel symmetry permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes in this paper the behavior of two parallel symmetry permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes subjected to an anti plane shear loading is investigated by using schmidt method by using the fourier transform the problem can be solved with the help of two pairs of dual integral equations these equations are solved using the schmidt method this process is quite different from that adopted previously the normalized stress and electrical displacement intensity factors are determined for different geometric and property parameters for permeable crack surface conditions numerical examples are provided to show the effect of the geometry of the interacting cracks the thickness and the materials constants of the piezoelectric layer upon the stress and the electric displacement intensity factor of the cracks contrary to the impermeable crack surface condition solution it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions

a five equation reduced model for compressible two phase flow problems this paper studies an eulerian diffuse interface model for the simulation of compressible multifluid and two phase flow problems we first show how to derive this model from a seven equation two pressure two velocity model of baer nunziato type using an asymptotic analysis in the limit of zero relaxation time we then study the mathematical properties of the system the structure of the waves the expression of the riemann s invariants and the existence of a mathematical entropy we also describe two different numerical approximation schemes for this system the first one relies on a linearized riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations finally we present some numerical experiments and comparisons with the results obtained by the two pressure two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids

nonlocal elasticity and related variational principles abstract the eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied the model is refined by assuming an attenuation function depending on the geodetical distance between material particles such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented a suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model the nonlocal elasticity boundary value problem for infinitesimal displacements and quasi static loads is addressed and the conditions for the solution uniqueness are established three variational principles nonlocal counterparts of classical ones i e the total potential energy the complementary energy and the mixed hu washizu principles are provided the former is used to derive a nonlocal type fem nl fem in which the symmetric global stiffness matrix reflects the nonlocality features of the problem an alternative standard fem based solution method is also provided which consists in an iterative procedure of the type local prediction nonlocal correction in which the nonlocality is simulated by an imposed like correction strain the potentialities of these analysis methods are pointed out their numerical implementations being the object of an ongoing research work

dynamical evolution of volume fractions in multipressure multiphase flow models compared to single pressure models multipressure multiphase flow models require additional closure relations to determine the individual pressures of the different phases these relations are often taken to be evolution equations for the volume fractions we present a rigorous theoretical framework for constructing such equations for compressible multiphase mixtures in terms of submodels for the relative volumetric expansion rates ei of the phases these quantities are essentially the rates at which the phases dynamically expand or contract in response to pressure differences and represent the general tendency of the volume fractions to relax toward values that produce local pressure equilibrium we present a simple provisional model of this type in which ei is proportional to pressure differences divided by the time required for sound waves to traverse an appropriate characteristic length it is shown that the resulting approach to pressure equilibrium is monotonic rather than oscillatory and occurs instantaneously in the incompressible limit

plane stress problems in nonlocal elasticity finite element solutions with a strain difference based formulation abstract an enhanced computational version of the finite element method in the context of nonlocal strain integral elasticity of eringen type is discussed the theoretical bases of the method are illustrated focusing the attention on numerical and computational aspects as well as on the construction of the nonlocal elements matrices two numerical examples of plane stress nonlocal elasticity are presented to show the potentials and the limits of the promoted approach

computation of the coding gain for subband coders a procedure to evaluate the coding gain for 2 d subband systems is explicitly presented the technique operates in the signal domain and requires the knowledge of the input process auto correlation function both the case of uniform subband and pyramid decomposition are considered in the case of a separable input process spectrum the evaluation can be performed by considering appropriately defined 1 d systems thus making the procedure very convenient in terms of computational complexity using a model that has been recently derived for difference images in motion compensated image sequence coders we compare the performance of several filter banks and transform coders in terms of coding gain and asymptotic rate distortion figures the results for intraframe and interframe coding show that uniform subband coders can have a performance superior to that of transform coders pyramidal schemes appear to have a slightly worse performance

fractional step methods for thermohydraulic calculation abstract a method of fractional steps is used to extend a semi implicit finite difference technique for multidimensional two phase flow calculations this extension permits time step size to be chosen independent of convection velocities in one space direction and still resolves multidimensional coupled sonic and phase exchange effects implicitly by forming a simple poisson problem for pressure because pure time splitting by physical phenomena was found unsuited to thermal hydraulics problems a stabilizing corrections method was chosen an application in nuclear reactor safety analysis is demonstrated

hllc type riemann solver with approximated two phase contact for the computation of the baer nunziato two fluid model abstract the computation of compressible two phase flows with the baer nunziato model is addressed only the convective part of the model that exhibits non conservative products is considered and the source terms of the model that represent the exchange between phases are neglected based on the solver proposed by tokareva toro 1 a new hllc type riemann solver is built the key idea of this new solver lies in an approximation of the two phase contact discontinuity of the model thus the riemann invariants of the wave are approximated in the subsonic case a major consequence of this approximation is that the resulting solver can deal with any equation of state it also allows to bypass the resolution of a non linear equation based on those riemann invariants we assess the solver and compare it with others on 1d riemann problems including grid convergence and efficiency studies the ability of the proposed solver to deal with complex equations of state is also investigated finally the different solvers have been compared on challenging 2d test cases due to the presence of both material interfaces and shock waves a shock bubble interaction and underwater explosions when compared with others the present solver appears to be accurate efficient and robust

hyperbolic two pressure models for two phase flow revisited this paper presents correction to a previous paper j comput phys 53 1984 124 on stability analyses of one pressure models for two phase flow it also presents some extensions and generalization of previous work on two pressure models the extensions allow both the slopes to the interfaces and the rates of mass transfer through the interfaces to be non negligible these enlargements of the domain of applicability of the two pressure models introduce extra derivative terms into the models these extra derivative terms do not change the basic character of the model the two pressure models remain stable in the sense of von neumann a e in state space with the more complete modeling of the interface copyright 1988 academic press inc

construction of multi dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data abstract kernels for non local elasticity are in general obtained from phonon dispersion relations however non local elastic kernels are in the form of three dimensional 3d functions whereas the dispersion relations are always in the form of one dimensional 1d frequency versus wave number curves corresponding to a particular wave direction in this paper an approach to build 2d and 3d kernels from 1d phonon dispersion data is presented our particular focus is on isotropic media where we show that kernels can be obtained using fourier bessel transform yielding axisymmetric kernel profiles in reciprocal and real spaces these kernel functions are designed to satisfy the necessary requirements for stable wave propagation uniformity of nonlocal stress and stress regularization the proposed concept is demonstrated by developing some physically meaningful 2d and 3d kernels that will find useful applications in nonlocal mechanics relative merits of the kernels obtained via proposed methods are explored by fitting 1d kernels to dispersion data for argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations a comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity

nonlocal integral elasticity 2d finite element based solutions abstract a finite element based method theorized in the context of nonlocal integral elasticity and founded on a nonlocal total potential energy principle is numerically implemented for solving 2d nonlocal elastic problems the key idea of the method known as nonlocal finite element method nl fem relies on the assumption that the postulated nonlocal elastic behaviour of the material is captured by a finite element endowed with a set of cross stiffness element s matrices able to interpret the nonlocality effects induced in the element itself by the other elements in the mesh an eringen type nonlocal elastic model is assumed with a constitutive stress strain law of convolutive type which governs the nonlocal material behaviour computational issues as the construction of the nonlocal element and global stiffness matrices are treated in detail few examples are presented and the relevant numerical findings discussed both to verify the reliability of the method and to prove its effectiveness

direction adaptive discrete wavelet transform for image compression we propose a direction adaptive dwt da dwt that locally adapts the filtering directions to image content based on directional lifting with the adaptive transform energy compaction is improved for sharp image features a mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions the analysis indicates that the proposed da dwt is more effective than other lifting based approaches experimental results report a gain of up to 2 5 db in psnr over the conventional dwt for typical test images subjectively the reconstruction from the da dwt better represents the structure in the image and is visually more pleasing

variational formulations convergence and stability properties in nonlocal elastoplasticity a thermodynamically consistent formulation of nonlocal plasticity in the framework of the internal variable theories of inelastic behaviors of associative type is presented a family of mixed variational formulations with different combinations of state variables is provided starting from the finite step nonlocal elastoplastic structural problem it is shown that a suitable minimum principles provides a rational basis to exploit the iterative elastic predictor plastic corrector algorithm in terms of the dissipation functional a sufficient condition is proved for the convergence of the iterative elastic predictor plastic corrector algorithm based on a suitable choice of the elastic operator in the prediction phase and a necessary and sufficient condition for the existence of a unique solution if any of the nonlocal problem at hand is then provided the nonlinear stability analysis of the nonlocal problem is carried out following the concept of nonexpansivity proposed in local plasticity

closed form solution for a nonlocal elastic bar in tension a simple mechanical one dimensional problem in the context of nonlocal integral elasticity is solved analytically the nonlocal elastic material behaviour is described by the eringen model whose nonlocality features all reside in the constitutive relation this relation of integral type contains an attenuation function usually assumed symmetric aimed to capture the diffusion process of the nonlocality effects it also exhibits a convolution format the governing equation is a fredholm integral equation of second kind whose analytical treatment even for the usual choice of a symmetric kernel is not easy to develop in the present paper assuming a specific shape for the attenuation function a closed form solution in terms of strains is alternatively obtained by solving a volterra integral equation of second kind the latter can be easily solved with standard techniques at least for the adopted kernel taking also advantage from the symmetry of the solution such a closed form solution is an essential result to validate the effectiveness of numerical procedures aimed to solve more complex mechanical problems in the context of nonlocal elasticity 2002 elsevier science ltd all rights reserved

parallel algorithms for implicit material dynamics schemes procedures are presented for parallelizing implicit schemes for computational material dynamics these procedures are illustrated on an implicit version of the von neumann richtmyer vnr scheme the original vnr scheme a one dimensional scheme for continuum dynamics in the material reference frame has extensions to two and three dimensional and spatial reference frames the vnr codes and codes with similar structure are representative of large classes of codes accounting for large numbers of supercomputer cycles

a critical comparison of nonlocal and gradient enhanced softening continua continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients these gradients may occur for instance in the propagation of waves with high wave numbers and at stress concentrators adding nonlocal or gradient terms to the constitutive modelling may enhance the ability of the models to describe such situations the effect of adding nonlocal or gradient terms and the relation between these enhancements are examined in a continuum damage setting a nonlocal damage model and two different gradient damage models are considered in one of the gradient models higher order deformation gradients enter the equilibrium equations explicitly while in the other model the gradient influence follows in a more implicit way from an additional partial differential equation the latter implicit gradient formulation can be rewritten in the integral format of the nonlocal model and can therefore be regarded as truly nonlocal this is not true for the explicit formulation in which the nonlocality is limited to an infinitesimal volume this fundamental difference between the formulations results in quite different behaviour in wave propagation localisation and at crack tips this is shown for the propagation of waves in the models their localisation properties and the behaviour at a crack tip the responses of the nonlocal model and the implicit gradient model agree remarkably well in these situations while the explicit gradient formulation shows an entirely different and sometimes nonphysical response

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

investigation of anti plane shear behavior of two collinear cracks in the piezoelectric materials by using the non local theory abstract in this paper the interaction between two collinear cracks in the piezoelectric materials under anti plane shear loading was investigated by using the non local theory for impermeable crack face conditions by using the fourier transform the problem can be solved with the help of two pairs of triple integral equations the solutions are obtained by using the schmidt method numerical examples are provided to show the effect of the geometry of the interacting cracks contrary to the previous results it is found that no stress and electric displacement singularity is present near the crack tip

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

mechanically based approach to non local elasticity variational principles abstract the mechanically based approach to non local elastic continuum will be captured through variational calculus based on the assumptions that non adjacent elements of the solid may exchange central body forces monotonically decreasing with their interdistance depending on the relative displacement and on the volume products such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle the constitutive relations between dual variables are introduced defining a proper convex potential energy it is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional moreover the euler lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approach

wave propagation in 1d elastic solids in presence of long range central interactions abstract in this paper wave propagation in non local elastic solids is examined in the framework of the mechanically based non local elasticity theory established by the author in previous papers it is shown that such a model coincides with the well known kroner eringen integral model of non local elasticity in unbounded domains the appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the cauchy stress in fact the long range forces between different volume elements are modelled in the body domain as central body forces applied to the interacting elements it is shown that the shape change of travelling disturbances coalesces with those predicted by the non local integral theory of elasticity in unbounded domains but several differences arise in the case of bounded domains the wave propagation problem has been formulated by means of the hamiltonian functional of the proposed mechanically based model of non local elasticity introducing an additional term to the elastic potential energy that accounts for elastic long range interactions in this way the wave equation may be obtained in a weak formulation and be further used to provide approximate analytical solutions to the governing equation in the context of standing wave analysis an equivalent discrete point spring model similar to lattice type networks has also been introduced to show the mechanical equivalence of the non local elastic model as well as to provide a mechanical scheme suitable for the numerical treatment of pressure waves travelling in non local bounded domains

rectangular rigid stamp on a nonlocal elastic half plane first the solution of the problem of a rectangular rigid stamp uniformly moving on an elastic half plane is given secondly the solution is obtained for a motionless rectangular stamp on a nonlocal elastic half space the finite distribution of the stress under the stamp has been compared with the unbounded stresses of local case

direction adaptive partitioned block transform for color image coding the direction adaptive partitioned block transform da pbt is proposed to exploit the directional features in color images to improve coding performance depending on the directionality in an image block the transform either selects one of the eight directional modes or falls back to the nondirectional mode equivalent to the conventional 2 d dct the selection of a directional mode determines the transform direction that provides directional basis functions the block partitioning that spatially confines the high frequency energy the scanning order that arranges the transform coefficients into a 1 d sequence for efficient entropy coding and the quantization matrix optimized for visual quality the da pbt can be incorporated into image coding using a rate distortion optimized framework for direction selection and can therefore be viewed as a generalization of variable blocksize transforms with the inclusion of directional transforms and nonrectangular partitions as a block transform it can naturally be combined with block based intra or inter prediction to exploit the directionality remaining in the residual experimental results show that the proposed da pbt outperforms the 2 d dct by more than 2 db for test images with directional features it also greatly reduces the ringing and checkerboard artifacts typically observed around directional features in images the da pbt also consistently outperforms a previously proposed directional dct when combined with directional prediction gains are less than additive as similar signal properties are exploited by the prediction and the transform for hybrid video coding significant gains are shown for intra coding but not for encoding the residual after accurate motion compensated prediction

fe formulation of a nonlocal plasticity theory a nonlocal continuum plasticity theory is presented the nonlocal field introduced here is defined as a certain weighted average of the corresponding local field taken over all the material points in the body hereby a quantity with the dimension of length occurs as a material parameter when this so called internal length is equal to zero the local classical plasticity theory is regained in the present model the yield function will depend on a nonlocal field the consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers the integral equations are classified as fredholm equations of the second kind and the existence of a solution will be commented upon after discretization a matrix equation is obtained and an algorithm for finding the solution is proposed for a generalized von mises material a plane boundary value problem is solved with a fe method since the nonlocal quantities are integrals c0 continuous elements are sufficient the solution strategy is split into a displacement estimate for equilibrium and the integration of constitutive equations in the numerical simulations shear band formation is analysed and the results display mesh insensitivity

numerical solutions of one pressure models in multifluid flows flows of a mixture of several fluids can be described by one pressure models their formulation is formally simple and their efficiency has been recognized but from the mathematical viewpoint they present severe peculiarities they are not hyperbolic appear to be ill posed and are in nonconservative form so they show ambiguous products of distributions in case of shock waves a resolution of these ambiguities is proposed it gives jump conditions similar to the classical rankine hugoniot jump conditions of conservative systems this resolution attempts to solve the riemann problem and then the cauchy problem by godunov type schemes following nonconservative techniques initiated by a y le roux and collaborators

low latency secondary transforms for intra inter prediction residual in this paper we present a transform scheme where a secondary transform is applied after the conventional dct for intra as well as inter prediction residues our approach is applicable to any block based video codec that employs transforms along the horizontal and vertical direction separably the secondary transform is applied to the lower k k 4 or 8 frequency coefficients of the output of conventional dct at block with dimensions 8 and larger the proposed transform scheme has low complexity as it is applied only to the top left portion of the dct output especially in the context of large blocks such as 32 32 where an alternate non dct 32 32 transform would have a prohibitive implementation hardware cost the proposed technique is single pass and the choice of whether to use the secondary transform is solely based on the prediction direction for intra residue and on transform unit location in the prediction unit for the inter residue the scheme requires no additional signaling information or r d search our simulation results show that the proposed transform scheme provides significant bd rate improvement over the conventional dct based coding scheme finally we also show how to implement the proposed secondary transforms with low latency in hardware

the mechanically based approach to 3d non local linear elasticity theory long range central interactions abstract this paper presents the generalization to a three dimensional 3d case of a mechanically based approach to non local elasticity theory recently proposed by the authors in a one dimensional 1d case the proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long range forces exerted by non adjacent elements specifically the long range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements measured along the line connecting the centroids further the long range forces are assumed to be proportional to a proper material dependent distance decaying function and to the products of the interacting volumes consistently with the modelling of the long range forces as central body forces the static boundary conditions enforced on the free surface of the solid involve only local stress due to contact forces the proposed 3d formulation is developed both in a mechanical and in a variational context for this the elastic energy functionals of the solid with long range interactions are introduced based on the principle of virtual work to set the proper correspondence between the mechanical and the kinematic variables of the model numerical applications are reported for 2d solids under plane stress conditions

eigenform error estimates of computational material dynamics with shocks 1 1 hooke s law materials abstract eigenform error estimates are sharper than previous a priori error bounds for the von neumann richtmyer vnr scheme theoretical results give insight into the experimental results on the test problems which include shocks the vnr rk4 scheme a runge kutta modification of the original vnr is not only more accurate than the original vnr but also the eigenform error estimates are more accurate for vnr rk4

on the wave structure of two phase flow models we explore the relationship between two common two phase flow models usually denoted as the two fluid and drift flux models they differ in their mathematical description of momentum transfer between the phases in this paper we provide a framework in which these two model formulations are unified the drift flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation which gives the relative velocity between the phases as a function of the flow parameters this closure law is in general highly complex which makes it difficult to analyze the model algebraically to facilitate the analysis we express the quasi linear formulation of the drift flux model as a function of three parameters the derivatives of the slip with respect to the vector of unknown variables the wave structure of this model is investigated using a perturbation technique then we rewrite the drift flux model with a general slip relation such that it is expressed in term