bluuebunny/crossref_metadata_2025 huggingface dataset:
ON THE SCRAMBLED SET OF THE LOGISTIC MAP WITH DIFFUSION
Authors: ITAYA AKIHIKO , UKAI SEIJI
Published: April 2003

We present a simple example of the infinite-dimensional map which has a scrambled set. It is the "logistic map with diffusion" which is a natural extension of the well known one-dimensional logistic map and derived by a semi-implicit discretization in t of a semilinear parabolic equation obtained by adding the diffusion term to the logistic equation. This map is neither expansive nor invertible even locally and hence outside of existing theories of scrambled and hyperbolic invariant sets. We will establish a sufficient condition for it to become a contractive perturbation of the logistic map and construct a scrambled set with several modifications of the method developed in Refs. 7 and 8.
THE CAUCHY PROBLEM FOR SCHRÖDINGER–DEBYE EQUATIONS
Authors: BIDÉGARAY BRIGITTE
Published: April 2003

In this paper we study the local-in-time Cauchy problem for the Schrödinger–Debye equations. This model occurs in nonlinear optics and describes the non-resonant delayed interaction of an electromagnetic wave with a medium. We extend the study to nonphysical cases such as the three-dimensional case or more general nonlinearities.
EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM
Authors: ELSCHNER JOHANNES , HINDER RAINER , SCHMIDT GUNTHER , PENZEL FRANK
Published: April 2003

This paper is devoted to the analysis of two Helmholtz equations in ℝ2 coupled via quasiperiodic transmission conditions on a set of piecewise smooth interfaces. The solution of this system is quasiperiodic in one direction and satisfies outgoing wave conditions with respect to the other direction. It is shown that Maxwell's equations for the diffraction of a time-harmonic oblique incident plane wave by periodic interfaces can be reduced to problems of this kind. The analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for solutions corresponding to electromagnetic fields with locally finite energy. Special attention is paid to the regularity and leading asymptotics of solutions near the edges of the interface.
APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW
Authors: GALDI GIOVANNI P. , LAYTON WILLIAM J.
Published: April 2003

We present two modifications of continuum models used in large eddy simulation. The first modification is a closure approximation which better attenuates small eddies. The second modification is a change in the boundary conditions for the large eddy model from strict adherence to slip with resistance. For model consistency, the resistance coefficient is a function of the averaging radius so that the model's boundary conditions reduce to a no-slip as the averaging radius decreases to zero.
ON THE 3-D BIPOLAR ISENTROPIC EULER–POISSON MODEL FOR SEMICONDUCTORS AND THE DRIFT-DIFFUSION LIMIT
Authors: LATTANZIO CORRADO
Published: April 2003

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.
FINITE-DIFFERENCE METHODS FOR PROBLEM OF CONJUGATION OF HYPERBOLIC AND PARABOLIC EQUATIONS
Authors: SAMARSKII ALEXANDER A. , KORZYUK VICTOR I. , LEMESHEVSKY SERGEY V. , MATUS PETR P.
Published: April 2003

A problem of conjugation of hyperbolic and parabolic equations in domain with moving boundaries is considered. Existence and uniqueness of a strong solution of the given problem are proved. A priori estimate for operator-difference scheme with non-self-adjoint spatial operator is obtain. Homogeneous difference scheme with constant weights for the conjugation problem is constructed. Moreover, consistency conditions are approximated with the second-order of accuracy with respect to spatial variables. Stability and convergence of the suggested scheme are investigated.
ADVECTION-DIFFUSION MODELS FOR SOLID TUMOUR EVOLUTION IN VIVO AND RELATED FREE BOUNDARY PROBLEM
Authors: DE ANGELIS E. , PREZIOSI L.
Published: April 2003

This paper proposes a multicell model to describe the evolution of tumour growth from the avascular stage to the vascular one through the angiogenic process. The model is able to predict the formation of necrotic regions, the control of mitosis by the presence of an inhibitory factor, the angiogenesis process with proliferation of capillaries just outside the tumour surface with penetration of capillary sprouts inside the tumour, the regression of the capillary network induced by the tumour when angiogenesis is controlled or inhibited, say as an effect of angiostatins, and finally the regression of the tumour size. The three-dimensional model is deduced both in a continuum mechanics framework and by a lattice scheme in order to put in evidence the relation between microscopic phenomena and macroscopic parameters. The evolution problem can be written as a free-boundary problem of mixed hyperbolic–parabolic type coupled with an initial-boundary value problem in a fixed domain.
DIFFUSION OF ELECTRONS BY MULTICHARGED IONS
Authors: LUCQUIN-DESREUX B.
Published: April 2003

Here we consider a magnetized plasma composed of electrons of low mean density and of one species of multicharged ions. Starting with the Vlasov–Fokker–Planck equations for both particles, we derive a diffusion model for the electrons, with explicit transport coefficients which are related to the ions. Finally, we study the kinetic boundary layers in the case of a bounded domain in space variables. For that purpose, we are led to study a Milne problem and to introduce a generalized extrapolation length.
WAVELETS ON THE INTERVAL WITH OPTIMAL LOCALIZATION
Authors: GRIVET-TALOCIA STEFANO , TABACCO ANITA
Published: April 2003

This paper introduces a novel construction of wavelets on the unit interval. With this construction, explicit upper bounds for the length of the modified border wavelets filters can be given. This insures a good localization of the border wavelets when a triangular biorthogonalization scheme is employed. The resulting wavelet bases are then well-suited for the adaptive solution of partial differential equations.
THE CAUCHY PROBLEM IN THE THEORY OF PLATES WITH TRANSVERSE SHEAR DEFORMATION
Authors: CHUDINOVICH IGOR , CONSTANDA CHRISTIAN
Published: April 2003

The Cauchy problem for an infinite plate with transverse shear deformation is studied by means of an area potential and some special initial potentials. This is a fundamental step in the construction of the potential theory for dynamic problems for plates, since such results make it possible to reduce various initial-boundary value problems for the equations of motion to analogous ones for the homogeneous system, which can then be solved by means of retarded potentials.
NUCLEAR COLLISIONS MODELS WITH BOLTZMANN OPERATORS
Authors: DELLACHERIE S. , SENTIS R.
Published: April 2003

We describe a model related to nuclear collisions using Boltzmann operators. An asymptotic analysis is performed concerning the gain operator for the outgoing particles. Some numerical methods related to this model are also described and numerical results are given.
ACCURATE COMPUTATION OF ELECTROGRAMS IN THE LEFT VENTRICULAR WALL
Authors: COLLI-FRANZONE PIERO , PENNACCHIO MICOL , GUERRI LUCIANO
Published: April 2003

An integral representation of electrograms is used for large scale simulations in an anisotropic model of the whole left ventricle. Numerical artifacts, like spurious oscillations or peaks, may appear if the computational grid is not fine enough. To avoid an excessive increase in the number of elements and nodes, we present a numerical procedure based on a combination of: a special refinement of the grid, a sub-element technique, a nonlinear interpolation and a split form of the integral. The numerical simulations show that in this way it is possible to suppress the numerical artifacts thus allowing an accurate computation of electrograms in any point inside or outside the myocardial wall.
LONG TIME BEHAVIOR OF THE TWO-DIMENSIONAL VLASOV EQUATION WITH A STRONG EXTERNAL MAGNETIC FIELD
Authors: FRÉNOD E. , SONNENDRÜCKER E.
Published: April 2003

When charged particles are submitted to a large external magnetic field, their movement in first approximation occurs along the magnetic field lines and obeys a one-dimensional Vlasov equation along these field lines. However, when observing the particles on a sufficiently long time scale, a drift phenomenon perpendicular to the magnetic field lines superposes to this first movement. In this paper, we present a rigorous asymptotic analysis of the two-dimensional Vlasov equation when the magnetic field tends to infinity, the observation time scale increases accordingly. Techniques based on the two-scale convergence and the introduction of a second problem enable us to find an equation verified by the weak limit of the distribution function.
ANALYTICITY, HYPERBOLICITY AND UNIFORM STABILITY OF SEMIGROUPS ARISING IN MODELS OF COMPOSITE BEAMS
Authors: HANSEN SCOTT W. , LASIECKA IRENA
Published: April 2003

We examine the stability properties of a sandwich beam consisting of two outer layers and a thin core. The outer layers are modeled as Euler Bernoulli beams and the inner core provides both elastic and viscous resistance to shearing. We show for both clamped and hinged boundary conditions that (i) if rotational inertia terms are neglected, the model is described by an analytic semigroup, and (ii) if rotational inertia is retained in the outer layers, the model is uniformly exponentially stable.
LACK OF UNIQUENESS IN TRANSPORT EQUATIONS WITH A NONLOCAL NONLINEARITY
Authors: DIEKMANN ODO , GYLLENBERG MATS , THIEME HORST R.
Published: April 2003

By way of examples we show that the initial value problem for transport equations, with coefficients that involve a nonlocal (in space) functional of the solution, may have multiple solutions. We try to expose the essential features of the examples, thus motivating certain assumptions in the theory of physiologically structured population models.
A NONCONFORMING MIXED FINITE ELEMENT METHOD FOR MAXWELL'S EQUATIONS
Authors: DOUGLAS JIM , SANTOS JUAN E. , SHEEN DONGWOO
Published: April 2003

We present a nonconforming mixed finite element scheme for the approximate solution of the time-harmonic Maxwell's equations in a three-dimensional, bounded domain with absorbing boundary conditions on artificial boundaries. The numerical procedures are employed to solve the direct problem in magnetotellurics consisting in determining a scattered electromagnetic field in a model of the earth having bounded conductivity anomalies of arbitrary shapes. A domain-decomposition iterative algorithm which is naturally parallelizable and is based on a hybridization of the mixed method allows the solution of large three-dimensional models. Convergence of the approximation by the mixed method is proved, as well as the convergence of the iteration.
ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO MAXWELL'S EQUATIONS IN BOUNDED DOMAINS WITH APPLICATION TO MAGNETOTELLURICS
Authors: SANTOS JUAN E. , SHEEN DONGWOO
Published: April 2003

We analyze the solution of the time-harmonic Maxwell equations with vanishing electric permittivity in bounded domains and subject to absorbing boundary conditions. The problem arises naturally in magnetotellurics when considering the propagation of electromagnetic waves within the earth's interior. Existence and uniqueness are shown under the assumption that the source functions are square integrable. In this case, the electric and magnetic fields belong to H(curl; Ω). If, in addition, the divergences of the source functions are square integrable and the coefficients are Lipschitz-continuous, a stronger regularity result is obtained. A decomposition of the space of square integrable vector functions and a new compact imbedding result are exploited.
STEADY FLOW OF FLUIDS WITH SHEAR-DEPENDENT VISCOSITY UNDER MIXED BOUNDARY VALUE CONDITIONS IN POLYHEDRAL DOMAINS
Authors: EBMEYER C.
Published: April 2003

In this paper the system of partial differential equations [Formula: see text] is studied, where e is the symmetrized gradient of u, and T has p-structure for some p<2 (e.g. div T is the p-Laplacian and p<2). Mixed boundary value conditions on a three-dimensional polyhedral domain are considered. Ws,p-regularity (s=3/2-ε) of the velocity u and Wr,p′-regularity of the pressure π are proven.
PERIODIC SOLUTIONS OF THE VLASOV–POISSON SYSTEM WITH BOUNDARY CONDITIONS
Authors: BOSTAN M. , POUPAUD F.
Published: April 2003

We study the Vlasov–Poisson system with time periodic boundary conditions. For small data we prove existence of weak periodic solutions in any space dimension. In the one-dimensional case the result is stronger: we obtain existence of mild solution and uniqueness of this solution when the data are smooth. It is necessary to impose a nonvanishing condition for the incoming velocities in order to control the lifetime of particles in the domain.
MODELING WELLS IN POROUS MEDIA FLOW
Authors: FABRIE PIERRE , GALLOUËT THIERRY
Published: April 2003

In this paper, we prove the existence of weak solutions for mathematical models of miscible and immiscible flow through porous medium. An important difficulty comes from the modelization of the wells, which does not allow us to use classical variational formulations of the equations.
THIRD-GRADE FLUIDS IN THE APERTURE DOMAIN
Authors: PASSERINI ARIANNA , CRISTINA M. , THÄTER GUDRUN
Published: April 2003

We analyze steady motions of incompressible second- and third-grade fluids in an aperture domain. Such flows exist due to a pressure drop and provided the flux through the hole is small. We prove that the asymptotic behavior of their velocity field far from the aperture is of order |x|-2, which is the optimal result.
A POSTERIORI ERROR ESTIMATES FOR THE FOKKER–PLANCK AND FERMI PENCIL BEAM EQUATIONS
Authors: ASADZADEH MOHAMMAD
Published: April 2003

We prove a posteriori error estimates for a finite element method for steady-state, energy dependent, Fokker–Planck and Fermi pencil beam equations in two space dimensions and with a forward-peaked scattering (i.e. with velocities varying within the right unit semi-circle). Our estimates are based on a transversal symmetry assumption, together with a strong stability estimate for an associated dual problem combined with the Galerkin orthogonality of the finite element method.
SAINT-VENANT TYPE DECAY RESULTS FOR ILL-POSED ELLIPTIC PROBLEMS
Authors: AMES KAREN A. , PAYNE LAWRENCE E.
Published: April 2003

Differential inequalities play a vital role in the study of ordinary and partial differential equations. In this paper we make use of first-order differential inequalities to investigate the decay of solutions to two ill-posed elliptic problems in a semi-infinite cylindrical domain.
NUMERICAL ANALYSIS OF A POSTERIORI FINITE ELEMENT BOUNDS FOR LINEAR FUNCTIONAL OUTPUTS
Authors: MADAY YVON , PATERA ANTHONY T.
Published: April 2003

We present the numerical analysis of a new a posteriori finite element procedure that provides rigorous, constant-free, lower and upper bounds for linear functional outputs of coercive second-order partial differential equations. We prove that, for a linear finite element space, the bounds converge to the exact result at the optimal rate: [Formula: see text] for sufficiently regular data and output functionals, where H is the diameter of the mesh which provides the solution and adjoint required by our technique.
A σ-ALGEBRA AND A CONCEPT OF LIMIT FOR BODIES
Authors: CAPRIZ G. , MAZZINI G.
Published: April 2003

Recent developments in mechanics of continua (the search for optimal shapes of bodies, homogenization theory, the study of the trabecular structure of bones, the dynamics of immiscible mixtures, etc.) render some of the introductory axioms of continuum mechanics inadequate. Not only does one need to give meaning to the join and meet of two bodies, but also to extend the consequent algebra so as to encompass the result of a countable sequence of operations of join or meet; and one should also be able to define the limit of a sequence of bodies. To achieve this goal we propose here to define a body ab initio through the assignment of a probability measure dπ. We realize that π leaves, generally, too much of the texture of the body unspecified; to make up for this deficiency, we suggest the use of appropriate texture measures, reminescent of Tartar's H-measures.9
AN EXISTENCE RESULT FOR VIBRATIONS WITH UNILATERAL CONSTRAINTS
Authors: PAOLI LAETITIA A.
Published: April 2003

We are motivated by the study of dynamical systems with a finite number of degrees of freedom, subject to unilateral convex constraints without loss of energy at impacts. If we denote the set of constraints by K, the motion is described by [Formula: see text], where ψK is the indicatrix function of K. More generally we consider dynamical systems with a convex potential described by [Formula: see text], where φ is a proper, convex, lower semicontinuous function. We prove that these systems possess a solution whose kinetic energy is conserved through impact in the first case, or more generally, whose energy [Formula: see text] is a continuous function of time in the second case.
CROSS-VALIDATION OF NUMERICAL SCHEMES FOR EXTENDED HYDRODYNAMICAL MODELS OF SEMICONDUCTORS
Authors: ANILE ANGELO MARCELLO , JUNK MICHAEL , ROMANO VITTORIO , RUSSO GIOVANNI
Published: April 2003

The numerical integration of the hydrodynamical model of semiconductors based on extended thermodynamics has been tackled. On account of the mathematical complexity of the system, no theoretical conditions of convergence are available for the existing schemes. Therefore in order to obtain numerical solution it was almost mandatory to resort to a cross-validation comparing the results given by two different methods. The kinetic scheme and the finite difference method represented by a suitable modification of the Nessyahu–Tadmor scheme furnish numerical results for the ballistic diode problem in good agreement even for non-smooth solutions.
THE BOUSSINESQ FORM OF SAINT VENANT'S PRINCIPLE
Authors: ERNST EMIL O.
Published: April 2003

A nonhomogeneous linear elastic solid of general shape is subjected to surface loadings vanishing outside the r-radius sphere centered in a fixed point of its border. In this paper it is proved that the upper limit of the strain energy that might be contained in a fixed part of the body goes to zero at least as rapid as a certain power of r. This result remains valid if the equations of linear elastostatics are replaced by an arbitrary second-order P.D.E. elliptic system.
SOME REMARKS ON AFFINE EVOLUTION EQUATIONS WITH APPLICATIONS TO PARTICLE TRANSPORT THEORY
Authors: BARLETTI LUIGI
Published: April 2003

We consider evolution problems with time-dependent inhomogeneous boundary conditions and discuss their relations with the theory of inhomogeneous evolution equations in Banach spaces. In the second part of the paper the attention is focused on particle transport problems with time-dependent boundary source terms.
A MATHEMATICAL MODEL FOR GRAIN GROWTH IN THIN METALLIC FILMS
Authors: GARCKE HARALD , NESTLER BRITTA
Published: April 2003

We use geometrical arguments based on grain boundary symmetries to introduce crystalline interfacial energies for interfaces in polycrystalline thin films with a cubic lattice. These crystalline energies are incorporated into a multi-phase field model. Our aim is to apply the multi-phase field method to describe the evolution of faceted grain boundary triple junctions in epitaxially growing microstructures. In particular, we are interested in symmetry properties of triple junctions in tricrystalline thin films. Symmetries of triple junctions in tricrystalline films have been studied in experiments by Dahmen and Thangaraj.6,25 In accordance with their experiments, we find in numerical simulations that any two neighboring triple junctions belong to different symmetry classes. We introduce a local equilibrium condition at triple junctions which can be interpreted as a crystalline version of Young's law. The local equilibrium condition at triple junctions is purely determined by the grain boundary energies. In particular no triple junction energies are necessary to explain which triple junctions are possible. All triple junctions observed in the experiments as well as in the simulations fulfil the crystalline version of Young's law. Our approach is also capable of describing grain boundary motion in general polycrystalline thin films.
ASYMPTOTIC BEHAVIOR TO THE 3-D SCHRÖDINGER/HARTREE–POISSON AND WIGNER–POISSON SYSTEMS
Authors: LÓPEZ J. L. , SOLER J.
Published: April 2003

Using an appropriate scaling group for the 3-D Schrödinger–Poisson equation and the equivalence between the Schrödinger formalism and the Wigner representation of quantum mechanics it is proved that, when time goes to infinity, the limit of the rescaled self-consistent potential can be identified as the Coulomb potential. As a consequence, Schrödinger–Poisson and Wigner–Poisson systems are asymptotically simplified and their long-time behavior is explained through the solutions of the corresponding linear limit problems.
A FREE BOUNDARY PROBLEM MODELING A FOAM DRAINAGE
Authors: COLIN THIERRY , FABRIE PIERRE
Published: April 2003

We study a reaction-diffusion problem with a free boundary governing the evolution of a foam. We show that the problem is globaly well-posed and that the solution converges, when the viscosity tends to zero to the solution of an initial-boundary value problem for Burgers equation.
ADAPTIVE FINITE ELEMENT METHODS FOR COMPRESSIBLE TWO-PHASE FLOW
Authors: BURMAN E.
Published: April 2003

We apply the adaptive streamline diffusion method for compressible flow in conservation variables using P1×P0 finite elements to a conservative model of two-phase flow. The adaptive algorithm is based on an a posteriori error estimate involving certain stability factors related to a linearized dual problem. For a model problem we prove that the stability factors are bounded. We compute the stability factors for some numerical examples in one- and two-space dimensions.
ON THE ISOTROPIC DISTRIBUTION OF BEAM DIRECTIONS
Authors: PAPIEŻ LECH , LU XIAOYI , LANGER MARK
Published: April 2003

The notion of an isotropic distribution of beam directions for three-dimensional radiotherapy is discussed. It has been thought that isotropic beam directions minimize the delivery of high dose to tissue outside the target volume. This paper demonstrates that beam arrangements that may be called most isotropic do not necessarily lead to the minimization of the high dose volume lying outside the target. This unexpected finding is related to results on abstract problems of the most symmetric distributions of finite number of points on the surface of the sphere, and optimal packings of circles on the surface of a sphere.
MAXIMUM ENTROPY FOR REDUCED MOMENT PROBLEMS
Authors: JUNK MICHAEL
Published: April 2003

The existence of maximum entropy solutions for a wide class of reduced moment problems on arbitrary open subsets of ℝd is considered. In particular, new results for the case of unbounded domains are obtained. A precise condition is presented under which solvability of the moment problem implies existence of a maximum entropy solution.
PARABOLIC LIMIT AND STABILITY OF THE VLASOV–FOKKER–PLANCK SYSTEM
Authors: POUPAUD F. , SOLER J.
Published: April 2003

In this paper the stability of the Vlasov–Poisson–Fokker–Planck with respect to the variation of its constant parameters, the scaled thermal velocity and the scaled thermal mean free path, is analyzed. For the case in which the scaled thermal velocity is the inverse of the scaled thermal mean free path and the latter tends to zero, a parabolic limit equation is obtained for the mass density. Depending on the space dimension and on the hypothesis for the initial data, the convergence result in L1 is weak and global in time or strong and local in time.
ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM
Authors: MAREMONTI P.
Published: April 2003

We consider the boundary value problem for classical solutions to the Stokes equations. We prove the existence, uniqueness and continuous dependence on the boundary data, which are assumed to be continuous only.
REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS
Authors: BOUCHITTÉ G. , DUBS C. , SEPPECHER P.
Published: April 2003

We consider a class of smooth local nonconvex functionals defined on W2,2(Ω), depending on a small parameter ε and we prove that they converge, as ε tends to 0, to a functional F(u,Ω) with a bulk density depending on the gradient of u and a surface energy concentrated on the jump set of u. This provides a new alternative to the approximation of free discontinuity problems, which applies in particular to the Mumford–Shah model.
NUMERICAL SOLUTION FOR HYDRODYNAMICAL MODELS OF SEMICONDUCTORS
Authors: ROMANO VITTORIO , RUSSO GIOVANNI
Published: April 2003

Numerical solutions of recent hydrodynamical models of semiconductors are computed in one-space dimension. Such models describe charge transport in semiconductor devices. Two models are taken into consideration. The first one has been developed by Blotekjaer, Baccarani et al., and the second one by Anile et al. In both cases the system of equations can be written as a convection-diffusion type system, with a right-hand side describing relaxation effects and interaction with a self-consistent electric field. The numerical scheme is a splitting scheme based on the Nessyahu–Tadmor scheme for the hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results are compared to detailed Monte-Carlo simulation.
DISCRETE VELOCITY MODEL AND IMPLICIT SCHEME FOR THE BGK EQUATION OF RAREFIED GAS DYNAMICS
Authors: MIEUSSENS LUC
Published: April 2003

We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and dissipation of entropy. The discrete velocity model is then discretized in space and time by an explicit finite volume scheme which is proved to satisfy the previous properties. A linearized implicit scheme is then derived to efficiently compute steady-states; this method is then verified with several test cases.
EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE DISCRETIZED CONTACT ELASTO-PLASTIC PROBLEM WITH ISOTROPIC HARDENING
Authors: ROHAN EDUARD
Published: April 2003

A class of quasistatic contact problems for elasto-plastic bodies with isotropic hardening is considered. The problems involve displacements, plastic strains and plastic multipliers. In the framework of multi-valued operator equations, the existence and uniqueness assertions for discretized reduced subproblems are proved using a fundamental theorem on variational inequalities.
A SINGULAR PROBLEM IN INCOMPRESSIBLE NONLINEAR ELASTOSTATICS
Authors: AGUIAR ADAIR R. , FOSDICK ROGER L.
Published: April 2003

This paper represents a contribution to the numerical treatment of problems in incompressible elasticity theory for large deformations. We are especially concerned about the solution of plane problems with corners. A review of the literature on these problems indicates that the behavior of the solution in the vicinity of a corner is given little attention. We investigate the solution of the compressed bonded block problem corresponding to the compression of an incompressible elastic block of rectangular cross-section and infinite transverse length between two opposing bonded rigid surfaces, with the two remaining lateral faces traction-free. We are especially interested in the behavior at a corner where a bonded end is adjacent to a free lateral side. We employ a finite element method based on a reduced and selective integration technique with penalization to construct a numerical solution for this problem. Our computational method converges everywhere except in a small neighborhood of the corner. We appeal to an elementary a priori inequality concerning the angle of shear to show that the numerical calculations in this neighborhood are inaccurate and need a more refined study. Based on the inequality, we offer a conjecture concerning the local shape of the deformed free lateral surface at the corner.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF RADIATING GAS WITH DISCONTINUOUS INITIAL DATA
Authors: NISHIBATA SHINYA
Published: April 2003

A one-dimensional model of radiating gas is obtained from approximating the system of radiating gas with thermo-nonequilibrium. The model system consists of a conservation law and a linear elliptic equation. In this paper, we study the global existence and the time asymptotic behavior of solutions to the model system with discontinuous initial data. Since the first equation is hyperbolic, the solutions contain discontinuities for any positive time. But, the uniqueness of solutions in weak sense holds by imposing the entropy condition. The main concern of this research is to investigate the behavior of the discontinuities contained in the solutions. It is proved that the set of discontinuous points consists of a certain C1-curve. This discrepancy of values at the discontinuities of the solutions is shown to decay to zero exponentially fast as time tends to infinity. This property is utilized in showing that the solutions approach the corresponding smooth traveling waves with the rate t-1/4 in the supremum norm.
EXISTENCE OF SOLUTIONS FOR A CONTINUOUS MULTIGRAIN MODEL FOR POLYMERIZATION
Authors: ANDREUCCI DANIELE , FASANO ANTONIO , RICCI RICCARDO
Published: April 2003

We prove the existence and uniqueness of solutions, for small times, for a mathematical scheme modeling the Ziegler–Natta process of polymerization. The model consists, essentially, of two diffusion problems at two different space scales, one relative to the microscopical catalyst pellets, the other to the macroscopical aggregate of those pellets. The coupling between the two scales is of nonstandard nature.
A LIMIT MODEL IN THE ANALYSIS OF STEEL-CONCRETE BEAMS
Authors: LENCI STEFANO
Published: April 2003

The problem of two bodies joined along their common surface by a thin soft third material having a periodic micro-structure has been considered. After identifying the two natural smallness parameters ε (which measures the thickness and the softness of the intermediate body) and η (which is the period of the micro-structure), the limits of the solution of the elastic problem when ε and η tend to zero successively have been considered. It has been shown that these limits solve suitable elastic (limit) problems, which represent the simplified models of the original configuration. The formulas for computing the equivalent elastic stiffness of the interface are given, and are compared to the usual simplified models employed in the literature. The existence and uniqueness of the solutions of the limit problems have been established, and strong convergence in the norm of the energy is proved. Furthermore, the question of the error estimation between the simplified model and the actual problem has been addressed and a bound on the rate of convergence is computed.
AN ESTIMATE OF THE APPROXIMATION ERROR IN THE FILTERING OF A DISCRETE JUMP PROCESS
Authors: CECI C. , GERARDI A. , TARDELLI P.
Published: April 2003

This paper deals with the filtering of a discrete Markov jump process when only the total number of jumps is observed. By using the recursive structure of the filtering equation, a technique to approximate the filter with a finite-dimensional filter is presented. An explicit bound for the approximation error, both almost surely and in L1, is given.
COMPUTATION OF HIGH FREQUENCY FIELDS NEAR CAUSTICS
Authors: KATSAOUNIS T. , KOSSIORIS G. T. , MAKRAKIS G. N.
Published: April 2003

It is well known that although the usual harmonic ansatz of geometrical optics fails near a caustic, uniform expansions can be found which remain valid in the neighborhood of the caustic, and reduce asymptotically to the usual geometric field far enough from it. Such expansions can be constructed by several methods which make essentially use of the symplectic structure of the phase space. In this paper we efficiently apply the Kravtsov–Ludwig method of relevant functions, in conjunction with Hamiltonian ray tracing to define the topology of the caustics and compute high-frequency scalar wave fields near smooth and cusp caustics. We use an adaptive Runge–Kutta method to successfully retrieve the complete ray field in the case of piecewise smooth refraction indices. We efficiently match the geometric and modified amplitudes of the multi-valued field to obtain numerically the correct asymptotic behavior of the solution. Comparisons of the numerical results with analytical calculations in model problems show excellent accuracy in calculating the modified amplitudes using the Kravtsov–Ludwig formulas.
CONVECTIVE AND RADIATIVE THERMAL TRANSFER WITH MULTIPLE REFLECTIONS: ANALYSIS AND APPROXIMATION BY A FINITE ELEMENT METHOD
Authors: MONNIER J. , VILA J. P.
Published: April 2003

We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and two-dimensional numerical results of thermal exchanges under a car bonnet are presented.
THE HP-VERSION OF THE STREAMLINE DIFFUSION FINITE ELEMENT METHOD IN TWO SPACE DIMENSIONS
Authors: GERDES K. , MELENK J. M. , SCHWAB C. , SCHÖTZAU D.
Published: April 2003

The Streamline Diffusion Finite Element Method (SDFEM) for a two-dimensional convection–diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes", which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such meshes can resolve layer components present in the solutions at robust exponential rates of convergence. We confirm these theoretical results in a series of numerical examples.
A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS
Authors: GOSSE LAURENT
Published: April 2003

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.
ON THE INFLUENCE OF THE DEFORMATION OF THE FORMING SOLID IN THE SOLIDIFICATION OF A SEMI-INFINITE WATER LAYER OF FLUID
Authors: MANSUTTI D. , BALDONI F. , RAJAGOPAL K. R.
Published: April 2003

We use a framework that takes into account the effects of deformation of both the solid and fluid in the solidification process, to study the solidification of a semi-infinite layer of fluid. It is shown that the time required for solidification, and the final location of the interface are significantly different form the predictions of the classical Stefan problem. A detailed numerical solution of the initial-boundary value problem is provided for a variety of values for non-dimensional parameters relevant for freezing water.
TUNING STRATEGIES IN CONSTRAINED SIMULATED ANNEALING FOR NONLINEAR GLOBAL OPTIMIZATION
Authors: WAH BENJAMIN W. , WANG TAO
Published: April 2003

This paper studies various strategies in constrained simulated annealing (CSA), a global optimization algorithm that achieves asymptotic convergence to constrained global minima (CGM) with probability one for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and sufficient condition for discrete constrained local minima (CLM) in the theory of discrete Lagrange multipliers and its extensions to continuous and mixed-integer constrained NLPs. The strategies studied include adaptive neighborhoods, distributions to control sampling, acceptance probabilities, and cooling schedules. We report much better solutions than the best-known solutions in the literature on two sets of continuous benchmarks and their discretized versions.
USING KNOWLEDGE-BASED SYSTEMS WITH HIERARCHICAL ARCHITECTURES TO GUIDE EVOLUTIONARY SEARCH
Authors: JIN XIDONG , REYNOLDS ROBERT G.
Published: April 2003

Regional Knowledge is useful in identifying patterns of relationships between variables, and it is particularly important in solving constrained global optimization problems. However, regional knowledge is generally unavailable prior to the optimization search. The questions here are: 1) Is it possible for an evolutionary system to learn regional knowledge during the search instead of having to acquire it beforehand? and 2) How can this regional knowledge be used to expedite evolutionary search? This paper defines regional schemata to provide an explicit mechanism to support the acquisition, storage and manipulation of regional knowledge. In a Cultural Algorithm framework, the belief space "contains" a set of these regional schemata, arranged in a hierarchical architecture, to enable the knowledge-based evolutionary system to learn regional knowledge during the search and apply the learned knowledge to guide the search. This mechanism can be used to guide the optimization search in a direct way, by "pruning" the infeasible regions and "promoting" the promising regions. Engineering problems with nonlinear constraints are tested and the results are discussed. It shows that the proposed mechanism is potential to solve complicated non-linear constrained optimization problems, and some other hard problems, e.g. the optimization problems with "ridges" in landscapes.
HYBRID SEARCH STRATEGIES FOR HETEROGENEOUS SEARCH SPACES
Authors: GOMES CARLA , SELMAN BART
Published: April 2003

Recently, there has been much interest in enhancing purely combinatorial formalisms with numerical information. For example, planning formalisms can be enriched by taking resource constraints and probabilistic information into account. The Mixed Integer Programming (MIP) paradigm from operations research provides a natural tool for solving optimization problems that combine such numeric and non-numeric information. The MIP approach relies heavily on linear program relaxations and branch-and-bound search. This is in contrast with depth-first or iterative deepening strategies generally used in artificial intelligence. We provide a detailed characterization of the structure of the underlying search spaces as explored by these search strategies. Our analysis shows that much can be gained by combining different search strategies for solving hard MIP problems, thereby leveraging each strategy's strength in terms of the combinatorial and numeric information.
A COLLABORATIVE APPROACH TO COMBINE MULTIPLE LEARNING METHODS
Authors: WEMMERT C. , GANCARSKI P. , KORCZAK J. J.
Published: April 2003

This article deals with the design of a hybrid learning system. This system integrates different kinds of learning methods and gives a set of class hierarchies as the result. The classes in these hierarchies are very similar. The method occurrences compare their results and automatically refine them to try to make them converge towards a unique hierarchy that unifies all the results. Thus, the system decreases the importance of the initial choices made when initializing classification algorithm (the choice of the method and its parameters) and to solve some of the limitations of the methods used such as an imposed number of classes, non-hierarchical result, or the size of the hierarchy found.
STABLE DECISION TREES: USING LOCAL ANARCHY FOR EFFICIENT INCREMENTAL LEARNING
Authors: KALLES DIMITRIOS , PAPAGELIS ATHANASIOS
Published: April 2003

This work deals with stability in incremental induction of decision trees. Stability problems arise when an induction algorithm must revise a decision tree very often and oscillations between similar concepts decrease learning speed. We introduce a heuristic and an algorithm with theoretical and experimental backing to tackle this problem.
NEURULES: IMPROVING THE PERFORMANCE OF SYMBOLIC RULES
Authors: HATZILYGEROUDIS I. , PRENTZAS J.
Published: April 2003

In this paper, we present a method for improving the performance of classical symbolic rules. This is achieved by introducing a type of hybrid rules, called neurules, which integrate neurocomputing into the symbolic framework of production rules. Neurules are produced by converting existing symbolic rules. Each neurule is considered as an adaline unit, where weights are considered as significance factors. Each significance factor represents the significance of the associated condition in drawing the conclusion. A rule is fired when the corresponding adaline output becomes active. This significantly reduces the size of the rule base and, due to a number of heuristics used in the inference process, increases efficiency of the inferences.
EPISODES IN SPACE: QUALITATIVE REPRESENTATION AND REASONING OVER SPATIO-TEMPORAL OBJECTS
Authors: EL-GERESY BAHER A. , ABDELMOTY ALIA I. , JONES CHRISTOPHER B.
Published: April 2003

There is growing interest in many application domains for the temporal treatment and manipulation of spatially referenced objects. Handling the time dimension in spatial databases can greatly enhance and extend their functionality and usability by offering means of understanding the spatial behaviour in time. Few works, to date, have been directed towards the development of formalisms for representation and reasoning in this domain. In this paper, a new approach is presented for the representation and reasoning over spatio-temporal relationships. The approach is simple and aims to satisfy the requirements of coherency, expressiveness and reasoning power. Consistent behaviours of spatial objects in time are denoted episodes. The topology of the domain is defined by decomposing episodes into representative components and relationships are defined between those components. Spatio-temporal reasoning is achieved by composing the relationships between the object components using constraint networks. New composition tables between simple spatio-temporal regions and between regions and volumes are also derived and used in the reasoning process.
ADEQUACY OF LIMITED TESTING FOR KNOWLEDGE BASED SYSTEMS
Authors: MENZIES TIM , CUKIC BOJAN
Published: April 2003

Knowledge-based engineering and computational intelligence are expected to become core technologies in the design and manufacturing for the next generation of space exploration missions. The literature is contradictory on how we are to assess such systems. Studies indicate significant disagreement regarding the amount of testing needed for system assessment. The sizes of standard black-box test suites are impractically large since the black-box approach neglects the internal structure of knowledge-based systems. On the contrary, practical results repeatedly indicate that only a few tests are needed to sample the range of behaviors of a knowledge-based program.

In this paper, we model testing as a search process over the internal state space of the knowledge-based system. When comparing different test suites, the test suite that examines larger portion of the state space is considered more complete. Our goal is to investigate the trade-off between the completeness criterion and the size of test suites. The results of testing experiment on tens of thousands of mutants of real-world knowledge based systems indicate that a very limited gain in completeness can be achieved through prolonged testing. The use of simple (or random) search strategies for testing appears to be as powerful as testing by more thorough search algorithms.
ESTIMATION OF HYBRID REFLECTANCE PROPERTIES AND SHAPE RECONSTRUCTION USING THE LMS METHOD
Authors: LEE MAL-REY , KIM TAE-EUN
Published: April 2003

This paper presents a new method to estimate reflectance properties of non–Lambertian surface by the least-mean-square (LMS) algorithm. In this paper, hybrid reflectance of an object is represented by the Torrance–Sparrow model. We determine reflectance parameters which minimize the sum squared difference of the intensity distribution between the image of a sample sphere and the calculated image. The estimated reflectance parameters provide the range data with intensity distributions. Therefore, we generate three reference images of a range sphere, which has the same diameter as that of the sample, from the same viewpoint with different light directions. Direct matching of the object images to the references can precisely reconstruct the shape of the object. This paper uses a plate diffuse illumination to alleviate the effects of specular spike and highlights. The simulation results show that the proposed method can estimate reflectance properties of the hybrid surface, and also recover the object shape.
RETRIEVAL OF MULTIMEDIA WEB DOCUMENTS AND REMOVAL OF REDUNDANT INFORMATION
Authors: BOURBAKIS N. , MENG W. , ZHANG C. , WU Z. , SALERNO N. J. , BOREK S.
Published: April 2003

This paper describes a search engine for multimedia web documents and a methodology for removing (partially or totally) redundant information from multiple documents in an effort to synthesize new documents. In this paper, a typical multimedia document contains free text and images and additionally has associating well-structured data. An SQL-like query language, WebSSQL, is proposed to retrieve this type of documents. The main differences between WebSSQL and other proposed SQL extensions for retrieving web documents are that WebSSQL is similarity-based and supports conditions on images. This paper also deals with the detection and removal of redundant information (text paragraphs and images) from multiple retrieved documents. Documents reporting the same or related events and stories may contain substantial redundant information. The removal of the redundant information and the synthesis of these documents into a single document can not only save a user's time to acquire the information but also storage space to archive the data. The methodology reported here consists of techniques for analyzing text paragraphs and images as well as a set of similarity criteria used to detect redundant paragraphs and images. Examples are provided to illustrate these techniques.