bluuebunny/crossref_metadata_2025 huggingface dataset:
Modeling Cortical Sulci with Active Ribbons
Authors: Le Goualher George , Barillot Christian , Bizais Yves
Published: October 2003

We propose a method for the 3D segmentation and representation of cortical folds with a special emphasis on the cortical sulci. These cortical structures are represented using "active ribbons". Active ribbons are built from active surfaces, which represent the median surface of a particular sulcus filled by CSF. Sulci modeling is obtained from MRI acquisitions (usually T1 images). The segmentation is performed using an automatic labeling procedure to separate gyri from sulci based on curvature analysis of the different iso-intensity surfaces of the original MRI volume. The outer parts of the sulci are used to initialize the convergence of the active ribbon from the outer parts of the brain to the interior. This procedure has two advantages: first, it permits the labeling of voxels belonging to sulci on the external part of the brain as well as on the inside (which is often the hardest point) and secondly, this segmentation allows 3D visualization of the sulci in the MRI volumetric environment as well as showing the sophisticated shapes of the cortical structures by means of isolated surfaces. Active ribbons can be used to study the complicated shape of the cortical anatomy, to model the variability of these structures in shape and position, to assist nonlinear registrations of human brains by locally controlling the warping procedure, to map brain neurophysiological functions into morphology or even to select the trajectory of an intra-sulci (virtual) endoscope.
On the Geometry and Shape of Brain Sub-Manifolds
Authors: Joshi Sarang C. , Miller Michael I. , Grenander Ulf
Published: October 2003

This paper develops mathematical representations for neuro-anatomically significant substructures of the brain and their variability in a population. The focus of the paper is on the neuro-anatomical variation of the geometry and the "shape" of two-dimensional surfaces in the brain. As examples, we focus on the cortical and hippocampal surfaces in an ensemble of Macaque monkeys and human MRI brains. The "shapes" of the substructures are quantified via the construction of templates; the variations are represented by defining probabilistic deformations of the template. Methods for empirically estimating probability measures on these deformations are developed by representing the deformations as Gaussian random vector fields on the embedded sub-manifolds. The Gaussian random vector fields are constructed as quadratic mean limits using complete orthonormal bases on the sub-manifolds. The complete orthonormal bases are generated using modes of vibrations of the geometries of the brain sub-manifolds. The covariances are empirically estimated from an ensemble of brain data. Principal component analysis is presented for characterizing the "eigen-shape" of the hippocampus in an ensemble of MRI-MPRAGE whole brain images. Clustering based on eigen-shape is presented for two sub-populations of normal and schizophrenic.
Automatic MRI Database Exploration and Applications
Authors: Guimond Alexandre , Subsol Gérard , Thirion Jean-Philippe
Published: October 2003

The design of representative models of the human body is of great interest to medical doctors. Qualitative information about the characteristics of the brain is widely available, but due to the volume of information that needs to be analyzed and the complexity of its structure, rarely is there quantification according to a standard model. To address this problem, we propose in this paper an automatic method to retrieve corresponding structures from a database of medical images. This procedure being local and fast, will permit navigation through large databases in a practical amount of time. We present as examples of applications the building of an average volume of interest and preliminary results of classification according to morphology.
Utilizing Segmented MRI Data in Image-Guided Surgery
Authors: Grimson W. E. L. , Ettinger G. J. , Kapur T. , Leventon M. E. , Wells III W. M. , Kikinis R.
Published: October 2003

While the role and utility of Magnetic Resonance Images as a diagnostic tool are well established in current clinical practice, there are a number of emerging medical arenas in which MRI can play an equally important role. In this article, we consider the problem of image-guided surgery, and provide an overview of a series of techniques that we have recently developed in order to automatically utilize MRI-based anatomical reconstructions for surgical guidance and navigation.
Preface
Authors: Miguet Serge , Montanvert Annick , Wang P. S. P.
Published: October 2003

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.
Statistical Thermodynamics Models for Multicomponent Isothermal Diphasic Equilibria
Authors: James François , Sepúlveda Mauricio , Valentin Patrick
Published: October 2003

We propose in this paper a whole family of models for isothermal diphasic equilibrium, which generalize the classical Langmuir isotherm. The main tool to obtain these models is a fine modeling of each phase, which states various constraints on the equilibrium. By writing down the Gibbs conditions of thermodynamical equilibrium for both phases, we are led to a constrained minimization problem, which is solved through the Lagrange multipliers. If one of the phases is an ideal solution, we can solve explicitly the equations, and obtain an analytic model. In the most general case, we have implicit formulas, and the models are computed numerically. The models of multicomponent isotherm we obtain in this paper are designed for chromatography, but can be adapted mutatis mutandis to other cases.
Existence and Uniqueness of Solutions in Strain Space of Elastoplastic Problems with Isotropic Hardening
Authors: Hlaváček Ivan , Whiteman John R.
Published: October 2003

The flow theory of elasto-plastic bodies with isotropic strain hardening is formulated in strain space by means of a time-dependent variational inequality. Using concepts of subdifferential and multivalued maximal monotone operators, we prove the existence and uniqueness of a solution of the quasistatic problem in ℝn, (n = 2,3), with mixed boundary conditions.
Nonlinear Chaotic Systems Identification from Observed Time Series
Authors: Anosov O. L. , Butkovskii O. Ya. , Kravtsov Yu. A.
Published: October 2003

Minimax procedure for nonlinear dynamic inverse problems solution is described using two adjacent moving time windows. The identification problem is solved for the discrete dynamic models (maps) and for continuous models (differential equations) (Kalmann–Bucy integrated models). We illustrate the efficiency of the identification procedure on the logistic map and Roessler system in chaotic regime, in the presence of moderate additive noise.
Asymptotic Analysis of the Drift-Diffusion Equations and Hamilton–Jacobi Equations
Authors: Montarnal Ph. , Perthame B.
Published: October 2003

We study the asymptotic behavior of the semiconductor drift-diffusion (DD) equations with a vanishing diffusion term. In order to obtain a closed limit problem, we need to introduce two new variables involving the logarithm of the electronic concentration. We show that the limit problem is a coupled system of Hamilton–Jacobi equations and variational inequalities. In the mono-dimensional case, we show that this limit problem has a unique solution, which allows us to prove the convergence of the DD model for vanishing viscosities. Our method, which is an extension of previous asymptotic studies, sheds new light on the convergence of the electronic concentration, improves some necessary mathematical hypotheses and provides an original approach to the problem, well suited for numerical purposes.
Dimensional Reduction for Helmholtz's Equation on an Unbounded Domain
Authors: Liu Kang-Man
Published: October 2003

The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain Ωd := ℝn × (-d,d) by replacing them with systems of equations in ℝn are investigated. Basic tool to analyze dimensional reduction technique for problems on an unbounded domain Ωd is the use of Fourier transformation. The error estimates between the exact solution and the dimensionally reduced solution in some Hilbert space are obtained when d and N are given. The rates of convergence depend on the smoothness of the data on the faces.
On Large-Scale Vortical Structures in (Incompressible) Fluids with Thermal Expansion
Authors: Berezin Y. A. , Hutter K.
Published: October 2003

This paper extends the analysis of Ref. 1 to non-Boussinesq fluids whose thermal equation of state depends negligibly on pressure but non-negligibly on temperature. It is demonstrated that these fluids are more stable than the Boussinesq fluids under the same conditions. We study the effect of the helicity on the stability of the Bénard problem and demonstrate that there is no separatrix that divides the instability regimes into two classes. Here, the phenomenon of inverse energy cascade is present at all values of helicities.
Continuous Dependence on the Initial-Time Geometry in Generalized Heat Conduction
Authors: Payne L. E. , Song J. C.
Published: October 2003

In this paper we investigate continuous dependence on the initial-time geometry for solutions of a generalized heat conduction system. Assuming the initial data to be measured on a surface t = εF(x), for |F| < 1, and assigned at t = 0, we examine the effects of this error in the initial-time geometry on the solution both forward and backward in time.
Position Controllability of a Deformable Body in Ideal Fluid
Authors: Mahalov A. , Nikitin S.
Published: October 2003

In this paper we formulate the position controllability problem for the movement of a flexible body in ideal fluid. We derive generic conditions under which the movement of a deformable body is position-controllable. The general theory developed in this paper is illustrated with an example of steering of a flexible domain in ideal irrotational 3-D flow.
Nonlinear Elliptic Equations with L1 Data as Limit of Bilateral Problems
Authors: Orsina Luigi
Published: October 2003

In this paper we prove that entropy solutions for nonlinear elliptic equations with L1 data can be obtained as limit as n tends to infinity of the sequence {un} of solutions of the bilateral problems with obstacles n and -n associated to the same equations.
Conservative and Entropy Schemes for Boltzmann Collision Operator of Polyatomic Gases
Authors: Buet C.
Published: October 2003

We propose two discrete velocity models derived from the Boltzmann equation of Larsen–Borgnakke type for polyatomic gases. These two models are natural extensions of previously discussed discrete velocity models used for monoatomic gases. These two models have the same properties as the continuous one, which are conservation of mass, momentum and energy, discrete Maxwellians as equilibrium states and H-theorems.
A New Finite Element Scheme for the Boussinesq Equations
Authors: Ambrosi D.
Published: October 2003

In this paper we consider the Boussinesq equations to simulate the motion of water waves with a moderate curvature of the free surface. The mathematical model describing the wave dynamics is introduced together with a short description of its derivation, posing emphasis on the related assumptions. The discrete representation of the Boussinesq equations is faced with numerical difficulties of two kinds: the nonsymmetric character of the (nonlinear) advection–propagation operator and the presence of third-order differential terms accounting for dispersion phenomena. In this paper it is shown how it is possible to use a finite element Taylor–Galerkin method to discretize the equations, ensuring high order accuracy both in time and space and obtaining a numerical solution free of spurious oscillations.
On Microstructural Inertia
Authors: Capriz Gianfranco , Giovine Pasquale
Published: October 2003

Microstructural inertia may be modified by the presence of a powerless term which derives from the partial indetermination of the kinetic coenergy of the microstructure.
Analysis of a Linear–Linear Finite Element for the Reissner–Mindlin Plate Model
Authors: Arnold Douglas N. , Falk Richard S.
Published: October 2003

An analysis is presented for a recently proposed finite element method for the Reissner–Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual "locking problem" by interpolating the shear stress into a rotated space of lowest order Raviart-Thomas elements. When the plate thickness t = O(h), it is proved that the method gives optimal order error estimates uniform in t. However, the analysis suggests and numerical calculations confirm that the method can produce poor approximations for moderate sized values of the plate thickness. Indeed, for t fixed, the method does not converge as the mesh size h tends to zero.
Solution of a Kinetic Stochastic Equation Modeling a Spray in a Turbulent Gas Flow
Authors: Clouet J. F. , Domelevo K.
Published: October 2003

This paper studies the modeling of the effect of turbulence on spray. The spray satisfies a kinetic equation. The use of the method of characteristics gives under certain assumptions the solution of the problem. When the gas velocity is modeled by using a white-noise, the solution of the problem satisfies a kinetic stochastic equation and may be written in terms of a Wiener chaos expansion.
A Wavelet-Based Adaptive Finite Element Method for Advection-Diffusion Equations
Authors: Canuto C. , Cravero I.
Published: October 2003

We propose a wavelet-based procedure for adapting a finite element mesh to the structure of the solution. After a finite element solution is computed on a given unstructured mesh, it is wavelet-analyzed on a superimposed regular dyadic grid; the analysis leads to an adapted distribution of grid points, which defines the new unstructured mesh via a Delaunay triangulation. Several examples of discretizations of steady convection-diffusion problems in the convection-dominated regime indicate the feasibility of our approach.
High Frequency Vibrations in a Stiff Problem
Authors: Lobo Miguel , Pérez Eugenia
Published: October 2003

The stiff problem here considered models the vibrations of a body consisting of two materials, one of them very stiff with respect to the other. We study the asymptotic behavior of the eigenvalues and eigenfunctions of the corresponding spectral problem, when the stiffness constant of only one of the materials tends to 0. We show that the associated operator has a discrete spectrum "converging", in a certain sense, towards a continuous spectrum in [0,∞) corresponding to an operator. We also provide information on the structure of the eigenfunctions associated with the high frequencies.
Analysis of a Nonconvex Problem Related to Signal Selective Smoothing
Authors: Chipot M. , March R. , Rosati M. , Caffarelli G. Vergara
Published: October 2003

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.
On Mixed Elements for Acoustic Fluid-Structure Interactions
Authors: Wang Xiaodong , Bathe Klaus-Jürgen
Published: October 2003

In this paper we investigate the performance of some mixed finite elements used in the displacement/pressure (u/p) and displacement-pressure-vorticity moment (u-p-Λ) formulations for acoustic fluid-structure interactions. In particular, we show that certain elements pass a numerical inf-sup test and are valuable for general applications. Also considered are macroelements that are based on simple four-node elements.
A Nonlocal Thermodynamic Theory of Superconductivity
Authors: Fabrizio M. , Gentili G. , Lazzari B.
Published: October 2003

We show, on the basis of thermodynamic principles, some shortcoming of the London theory of superconductivity. Successively we change it by neglecting one of the classic London equations. The remaining one is sufficient to account for superconductivity and yields a new nonlocal theory.
Global Existence for Two Laser Models
Authors: Ducomet B.
Published: October 2003

We compare two one-dimensional models giving a simplified description for some nonlinear regimes in laser physics. For these two models, we prove the existence of a global solution, and, for one of them, the existence of a global attractor.
A Quasi Trefftz-Type Spectral Method for Initial Value Problems with Moving Boundaries
Authors: Lifits S. A. , Reutskiy S. Yu. , Tirozzi B.
Published: October 2003

A quasi Trefftz-type spectral method is a new technique for numerical solving boundary value and initial value problems in domains with complex geometry. QTSM combines the properties of the boundary methods with the spectral approach. In the present paper QTSM is applied to the problems with moving boundaries. The problems with a known boundary motion law as well as the Stefan problems are considered. The method is tested on several one- and two-dimensional problems with exact analytic solution. A high accuracy of the calculations is achieved.
Some Remarks on Non-Newtonian Fluids Including Nonconvex Perturbations of the Bingham and Powell–Eyring Model for Viscoplastic Fluids
Authors: Fuchs Martin , Seregin Gregory
Published: October 2003

We consider quasi-static flows of certain viscoplastic materials for which the velocity field v can be found as a minimizer of the functional [Formula: see text] in classes of functions u : ℝn ⊃ Ω → ℝn satisfying div u = 0 and also the appropriate boundary conditions. The density ω is characteristic for the material under consideration and ℰv denotes the symmetric gradient of v. In case of a Bingham fluid we have for example ω(ℰv) = η|ℰv|2 + g|ℰv| with positive constants η and g. We also consider various perturbations of ω which are not assumed to be convex so that we have to study the relaxed variational problem. Our main result states that in all cases the symmetric derivative of the velocity field is a locally bounded function.
Waxy Crude Oils: Some Aspects of their Dynamics
Authors: Farina A.
Published: October 2003

Waxy crude oils are highly non-Newtonian fluids known to cause pipelining difficulties because their rheological properties are strongly affected by paraffin crystallization. On the basis of experimental data, a physical model has been developed to describe the behavior of these crudes. The corresponding mathematical problem has been studied in planar geometry proving the existence and uniqueness of a classical solution. A condition on the pressure gradient has been found ensuring that the system do not come to a complete stop in finite time.
Generalized Invariant Sets for the Boltzmann Equation
Authors: Goudon T.
Published: October 2003

We are interested in the initial value problem for the Boltzmann equation, when the initial data u0 belongs to a set B0 = {δ0m1 (0,x,v) ≤ u0(x,v) ≤ C0m2 (0,x,v)} where m1, m2 are traveling Maxwellians. We consider soft or Maxwell's interactions with cutoff (7/3 < s ≤ 5) and C0 smaller than a bound depending on the coefficients of m2. We obtain global existence of solutions remaining in a "generalized invariant set" Bt ⊂ B∞, characterized by these particular states.
Pointwise Balances and the Construction of Stress Fields in Dielectrics
Authors: DeSimone A. , Podio-Guidugli P.
Published: October 2003

We study the problem of deriving a pointwise version of the force-balance law for a dielectric solid. Our analysis hinges on an explicit treatment of self forces, those which a body part may exert on itself.
On a Right-Inverse for the Divergence Operator in Spaces of Continuous Piecewise Polynomials
Authors: Boillat E.
Published: October 2003

This paper is concerned with the norm of a right-inverse for the divergence operator between spaces of piecewise polynomials on triangular elements. More specifically, one tries to construct a right-inverse acting from the space W of continuous piecewise polynomials of degree p into the space V of R2-valued piecewise polynomials of degree p+1. Our results are as follows. Assume that we are dealing with a quasiuniform family of triangulations {Mh} satisfying two additional hypotheses: Mh can be transformed into a quadriangular mesh by grouping its element two by two and Mh has no boundary vertex shared by only one or exactly three elements. In that context, one proves that the divergence has a right-inverse with an operator norm growing at most like [Formula: see text] when both W and V are equipped with the H1-norm and at most like [Formula: see text] if W is equipped with the L2-norm only. An application of the first of these two results is the approximation of the thermoelasticity equations by the p-version of the finite element methods. One also shows how the second result can be used in the context of higher-order Hood–Taylor method for Stokes problem.
On Geometrical Rigidity of Surfaces.
Authors: Choi Daniel
Published: October 2003

In this paper we first present a panorama about geometrical rigidity and inextensional displacements (also called infinitesimal bendings) for surfaces with kinematic boundary conditions and for surfaces with edges (in the sense of folds or junctions). This theory is fundamental for thin linear elastic shells, as it rules their asymptotic behavior when the thickness tends to zero. This behavior enlights some difficulties encountered in numerical studies of very thin elastic shells. Our approach is based on the introduction of a nonclassical space denoted by R(S) and related to inextensional displacements. It permits us to obtain new results concerning developable surfaces and hyperbolic surfaces, with one or two edges (most of them assumed to keep constant angle), including a theorem of rigid edge when the edge is an asymptotic line of the surface. By applying these results, we are able to exhibit a new example of sensitive problem for a shell with hyperbolic mean surface and with two edges keeping constant angle. In the Appendix, we give a nonclassical variant of Goursat problem for hyperbolic linear partial differential equations system, used in the proof of a rigidity result.
An Analysis of the Marshak Conditions for Matching Boltzmann and Euler Equations
Authors: Arnold Anton , Giering Ulrich
Published: October 2003

Domain decomposition methods based on matching the Boltzmann and Euler equations without overlapping are an important simulation technique in rarefied gas dynamics and semiconductor device modeling. Many existing codes use the Marshak boundary conditions (i.e. imposing continuity of the fluxes) at the interface between the two modeling regimes to implicitly determine the boundary data for the compressible Euler equations.

In this paper we investigate the solvability of the Marshak conditions in the four different flow situations sub-/supersonic in-/outflow in one spacial dimension and for selected cases in 2D and 3D.
A Global Existence Theorem for Large Eddy Simulation Turbulence Model
Authors: Coletti Paolo
Published: October 2003

In this work we show the existence and uniqueness in Sobolev spaces of the solution of Large Eddy Simulation turbulence model for any time provided that initial data and external forces are regular and small enough. We also show that if external forces are time-periodic or time-independent, then the solution is time-periodic or time-independent.
The Parameter Dependence of the Coefficient in a Model for Constant-Pressure Steam Injection in Soil
Authors: Gilding Brian H. , Li Shuanhu
Published: October 2003

In a recently proposed model for the injection of steam into an air-filled soil, an equation which defines an unknown coefficient in terms of the parameters in the model arises. The paper examines this equation. It is shown that the coefficient is well-defined. Furthermore, quantitative and qualitative properties of the dependence of the coefficient on the parameters in the model are derived. A crucial role in the analysis is played by the Mills ratio for the normal probability distribution. By the bye, bounds for the Mills ratio, which to the best of the authors' knowledge are new, are obtained.
Numerical Simulation of Scattering Problems with Fourier-Integral Operators
Authors: de la Bourdonnaye Armel , Tolentino Marc
Published: October 2003

In this paper, we present a general method for approximating oscillatory integrals arising in some scattering problems. In particular, a microlocal basis is used to approximate wave functions, by discretizing their wavefront. Then, we exhibit a result concerning the approximation of the scattering operator, which allows one to retain only interactions between coefficients for which the product of the supports is near the wavefront of the kernel of the operator. Finally, we give an estimate of the algorithmic complexity of the method presented in the paper.
Spatial Behavior for Nonlinear Heat Equations
Authors: Quintanilla R.
Published: October 2003

In this paper we investigate spatial decay and growth estimates for the solutions of the nonlinear heat equation in a three-dimensional cylinder with homogeneous Dirichlet conditions prescribed on the lateral surface for all time. We derive two Phragmen–Lindelöf type growth–decay estimates. Two methods are used in our approximation. One of them involves a measure on the cross-sections and the other uses the "energy" contained in the part of the cylinder beyond a cross-section. For suitable volumetric heat capacity and thermal conductivitythe second-order approximation combined with comparison arguments allow us to improve the decay estimates. We also sketch the application of the first-order method in the case where the solid is a cone. Spatial estimates for the backward nonlinear equation are presented in the last section.
Micromagnetics and Numerical Analysis
Authors: Graziano L. , Romano A.
Published: October 2003

The structure of domain walls in ferromagnetic crystals is investigated by means of micromagnetics. Moreover, the numerical integration of one-dimensional micromagnetic equations in domain walls is carried out in order to obtain approximate expressions of the energy associated to these regions.
Comparison of Matched Asymptotics, Multiple Scalings and Averages in Homogenization of Periodic Structures
Authors: Leguillon Dominique
Published: October 2003

Historically, homogenization of periodic structures has been first investigated by the method of multiple scalings expansions. More recently, an interpretation has been given in terms of averages and effective moduli. Both approaches involve a slow variable at the macroscopic scale, and a fast one at the microscopic level. The periodicity of the solutions with respect to the second variable is a strong assumption made prior to any analysis. Although involving similar calculations, the two approaches differ and it is not so obvious to link them together. The matched asymptotic expansions presented here allow to give a common explanation to the two already mentioned approaches. The first one corresponds to an outer expansion while the second one describes the leading term of an inner expansion. Moreover, no a priori assumption is made, the periodicity of the solutions occurs as a consequence of the structure of the inner problems. The next term (involving a quadratic dependence on the local variable) of the inner expansion can be derived in the same way. The same matched asymptotics process can be used to define homogenized boundary conditions as well as boundary layers. These layers come from a mismatch between the general form of the solution within the domain and the boundary conditions which occur to be a perturbation of the periodicity. Indeed, it is not easy to give an exact definition of the boundary conditions in the original problem, the inner expansion defined on the enlarged domain allows one to give a precise framework for these conditions. They split into two parts, a macroscopic one defined on the smooth (homogenized) boundary and a microscopic periodic fluctuation taking into account the exact shape of the boundary.
On Sensitive Vector Poisson and Stokes Problems
Authors: Guermond J.-L. , Quartapelle L.
Published: October 2003

Lions/Sanchez-Palencia's theory of sensitive boundary value problems is extended from the scalar biharmonic equation to the vector Poisson equation and the Stokes problem associated with the bilinear form (∇ × u, ∇ × v) + (∇ · u, ∇ · v). For both problems the specification of completely natural conditions for the vector unknown on a part of the boundary leads to a variational formulation admitting a unique solution which is however sensitive to abitrarily small smooth perturbations of the data, as shown in the present paper.
The Optimal Shape of a Hanging Heavy Body
Authors: Bacci Adolfo
Published: October 2003

We consider a heavy body hanging from a fixed point. The weight of the body is known but not its shape. The aim is to find the optimal shape of the body that minimizes the stress concentrations. The body is assumed to be plane and composed of a linearly elastic homogeneous isotropic material. The result is that the optimal boundary, chosen in the class of epitrochoids having the same area, is the epicycloidal cardioid having only one cusp at the hanging point. In technical application, the above results suggest adopting economical shapes in the construction of cylindrical solids, suspended to cables.
The Drift–Diffusion Limit for Electron–Phonon Interaction in Semiconductors
Authors: Markowich Peter A. , Schmeiser Christian
Published: October 2003

A scattering operator modeling the interaction of electrons with phonons of given constant energy in semiconductors is analyzed by means of an expansion in terms of spherical harmonics. An application is the derivation of the drift–diffusion limit of the corresponding Boltzmann equation for the transport of electrons in a semiconductor crystal.
Uncoupled ω–ψ Formulation for Plane Flows in Multiply Connected Domains
Authors: Guermond J.-L. , Quartapelle L.
Published: October 2003

This work deals with the numerical solution of the unsteady Navier–Stokes equations in the vorticity and stream function representation for problems in multiply connected two-dimensional regions. A particular decomposition of the stream function space is proposed which leads to an uncoupled variational formulation of the equations linearized and discretized in time, thus extending to transient problems the celebrated method proposed by Glowinski and Pironneau for the biharmonic problem. Numerical results calculated by a mixed finite element implementation of the new uncoupled method are presented.
A Contribution to the Bounds on Real Effective Moduli of Two-Phase Composite Materials
Authors: Tokarzewski Stanisław , Telega Józef Joachim
Published: October 2003

Effective transport coefficients of two-phase composite materials λe(x) can be represented by power expansions of four Stieltjes functions: λe(x)/λ1, λ2(x)/λe, λe(y)/λ2, λ1(y)/λe, where x = (λ2/λ1) - 1 and y = -x/(x + 1), while λ1 and λ2 denote the real moduli of a matrix and inclusions respectively.5 By constructing Padé approximants to power expansions of these functions, we derive an infinite set of fundamental inequalities identifying real-valued Milton's bounds20 as a lower and upper estimations of λe(x). From coefficients of a power expansion of λe(x) not exactly known, but only within the limits, the infinite set of new bounds on λe(x) has been derived. Due to Schulgasser inequality21 some improvement of existing bounds20 is proposed. For an illustration of the results achieved, the improved bounds on the effective conductivity λe(x) of a regular array of spheres are evaluated.
Two-Phase Problem for Two-Dimensional Water Waves of Finite Depth
Authors: Iguchi Tatsuo
Published: October 2003

We consider the two-phase problem for two-dimensional and irrotational motion of incompressible ideal fluids in the case that the fluids are separated into the lower and the upper parts by an almost horizontal interface and that there is an almost flat bottom below the lower fluid. It is proved that the Cauchy problem is well-posed, locally in time, in a Sobolev space of finite smoothness, if the surface tension is taken into account and the initial data are suitably close to the equilibrium rest state. The main part of the proof is the reduction of the problem to a quasi-linear system of integro-differential equations for the function defining the interface and the horizontal component of the velocity of the lower fluid on the interface.
RKH Space Methods for Low Level Monitoring and Control of Nonlinear Systems II. A Vector-Case Example: The Lorenz System
Authors: Cover Alan , Reneke James , Lenhart Suzanne , Protopopescu Vladimir
Published: October 2003

By using techniques from the theory of reproducing kernel Hilbert (RKH) spaces, we continue the exploration of the stochastic linearization method for possibly unknown and/or noise corrupted nonlinear systems. The aim of this paper is twofold:

(a) the stochastic linearization formalism is explicitly extended to the vector case; and

(b) as an illustration, the performance of the stochastic linearization for monitoring and control is assessed in the case of the Lorenz system for which the dynamic behavior is known independently.
Homogenization of the Torsion Problem and the Neumann Problem in Nonregular Periodically Perforated Domains
Authors: Briane Marc
Published: October 2003

This paper is devoted to the homogenization of the torsion problem (or stiff problem) and the Neumann problem (or soft problem) for second-order elliptic but not necessarily symmetric linear operators set in a bounded open subset Ω of ℝN. More precisely, we study the asymptotic behavior of the equations [Formula: see text] in Ω with ε → 0, where Sε is a closed subset of Ω, which represents the set of the inclusions for the stiff problem or the holes for the soft one, and Ωε = Ω \ Sε. The stiff problem corresponds to δ → + ∞ and ν = 0, the soft one to δ → 0 and ν = 1. We prove a homogenization result in the periodic case without assuming any regularity on the set Sε and thus generalizing the result of Cioranescu and Saint Jean Paulin.7
Sentinels for the Identification of an Unknown Boundary
Authors: Bodart O. , Demeestere P.
Published: October 2003

A method for the identification of a part of the boundary in a diffusion problem is proposed. It is based on sentinels. A linearization scheme is used and the local convergence is proved. The method defines and proves the existence of approximate sentinels for the linearized system and builds a fixed point algorithm. To prove the existence of the linearized sentinels, the problem is reformulated as an approximate control problem and solved by a convex analysis method. The contraction property of the fixed point method follows straightforward from the definition of approximate the sentinels. Finally numerical examples are presented.
Traveling Waves Solutions of a Convective–Dispersive System Modeling Two-Phase Fluid Flows
Authors: Bedjaoui Nabil
Published: October 2003

In this paper we are interested in the existence of traveling waves for a convective dispersive system modeling a stratified two-phase fluid flow in horizontal ducts. We prove the existence of a class of nonconstant solitary waves and periodic traveling waves.
Bogolubov and Kinetic Theory: The Bogolubov Equations
Authors: Cohen E. G. D.
Published: October 2003

A short survey is given of Bogolubov's fundamental contributions to the kinetic theory of classical neutral gases and plasmas. This work is then placed in the context of later developments, showing its influence till the present day.
A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model
Authors: Jüngel Ansgar , Pietra Paola
Published: October 2003

A discretization scheme based on exponential fitting mixed finite elements is developed for the quasi-hydrodynamic (or nonlinear drift–diffusion) model for semiconductors. The diffusion terms are nonlinear and of degenerate type. The presented two-dimensional scheme maintains the good features already shown by the mixed finite elements methods in the discretization of the standard isothermal drift–diffusion equations (mainly, current conservation and good approximation of sharp shapes). Moreover, it deals with the possible formation of vacuum sets. Several numerical tests show the robustness of the method and illustrate the most important novelties of the model.
Magnetostatic and Electrostatic Problems in Inhomogeneous Anisotropic Media with Irregular Boundary and Mixed Boundary Conditions
Authors: Fernandes Paolo , Gilardi Gianni
Published: October 2003

Magnetostatic and electrostatic problems with mixed boundary conditions are studied. The medium can have a nonsmooth boundary and very irregular physical properties due to inhomogeneity and anisotropy. The topological assumptions are general enough to meet the requirements of the engineering applications. Necessary and sufficient conditions for solvability are found and the set of the solutions is characterized. Moreover, uniqueness is recovered by means of a finite number of supplementary conditions which are equivalent to prescribing a finite number of suitably chosen fluxes or potentials. A functional framework in which other important problems of electromagnetics naturally fit is developed.
Uniform Time Bounds on the Amplitude of Nonlinear Plane Air Waves in the Presence of Viscosity
Authors: Marzocchi Alfredo
Published: October 2003

Asymptotic behavior in time for a model of nonlinear plane air waves when a viscosity term is present is investigated. The existence of a uniform bound of several norms is established, and in particular the continuity of the solution, which implies the nonexistence of shock waves.
Method of Variational Imbedding for the Inverse Problem of Boundary-Layer Thickness Identification
Authors: Christov Christo I. , Marinov Tchavdar T.
Published: October 2003

The inverse problem of identification of boundary-layer thickness is replaced by the higher-order boundary value problem for the Euler–Lagrange equations for minimization of the quadratic functional of the original system (Method of Variational Imbedding – MVI). The imbedding problem is correct in the sense of Hadamard and consists of an explicit differential equation for the boundary-layer thickness. The existence and uniqueness of solution of the linearized imbedding problem is demonstrated and a difference scheme of splitting type is proposed for its numerical solution. The performance of the technique is demonstrated for three different boundary-layer problems: the Blasius problem, flow in the vicinity of plane stagnation point and the flow in the leading stagnation point on a circular cylinder. Comparisons with the self-similar solutions where available are quantitatively very good.
Some Estimates on the Boltzmann Collision Operator
Authors: Struckmeier Jens
Published: October 2003

The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L∞-norm of the gain term can be bounded in terms of the L1- and L∞-norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L∞-norm of the density function and the loss term of the Boltzmann collision operator.
Completeness of Root Functions for Thermal Conduction in a Strip with Piecewise Continuous Coefficients
Authors: Titeux I. , Yakubov Y.
Published: October 2003

We consider the boundary layer problem associated with the steady thermal conduction problem in a thin laminated plate. Two cases of boundary conditions, Dirichlet and Neumann, are treated in the paper. Transmission conditions across the interfaces should be added since the plate is laminated. The study of the structure of the solution in the matching region of the layer with the basis solution in the plate leads to consideration of an eigenvalue problem for a second-order operator pencil with piecewise continuous coefficients and the corresponding boundary and transmission conditions. Twofold completeness of root functions of the latter problem is proved. The boundary layer term can then be expressed as a combination of these functions.
L2 Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects
Authors: Castella F.
Published: October 2003

We study a system of infinitely many coupled Schrödinger equations with self-consistent Coulomb potential as the initial data has only a regularity of L2-type. We first establish Strichartz' inequalities in the framework of vector-valued wave functions (density matrices). This allows us to prove a well-posedness result, and strong smoothing effects. Also, we state blow-up (resp. decay) estimates for the solution as time goes to zero (resp. infinity).
A Decomposition of the Electromagnetic Field — Application to the Darwin Model
Authors: Ciarlet P. , Sonnendrücker E.
Published: October 2003

In many cases, the numerical resolution of Maxwell's equations is very expensive in terms of computational cost. The Darwin model, an approximation of Maxwell's equations obtained by neglecting the divergence free part of the displacement current, can be used to compute the solution more economically. However, this model requires the electric field to be decomposed into two parts for which no straightforward boundary conditions can be derived. In this paper, we consider the case of a computational domain which is not simply connected. With the help of a functional framework, a decomposition of the fields is derived. It is then used to characterize mathematically the solutions of the Darwin model on such a domain.
Stochastic Analysis of the Failure of Multi-Component High-Temperature Materials
Authors: Axelrad D. R.
Published: October 2003

The main objective of this study is the stochastic formulation of the last stage in short time creep tests of high temperature materials, which ends in the fracture of a material specimen. It is shown that Markov jump processes provide a good approximation to the actual strain-time functions representing the phenomenological behavior of this class of materials.
Incompletely Parabolic Systems from Friedrichs Theory Point of View
Authors: Caussignac Ph.
Published: October 2003

An incompletely parabolic system of partial differential equations consist of one parabolic subsystem coupled to a hyperbolic subsystem. For the initial-boundary value problem, it has been shown, by requiring that a solution remains bounded at any time by the data, that boundary conditions which make both subsystems well-posed render the global system well-posed too. In this paper, we establish the same type of result with the help of the notion of semi-admissible boundary conditions in the theory of Friedrichs positive systems of differential equations. Our aim is not to obtain the same results of existence and uniqueness as those for the Cauchy problem, but rather to find a way to establish boundary conditions on the subsystems which can be used for the global system too. The theory is illustrated by the two examples of the compressible Navier–Stokes equations and of the hydrodynamic model for semiconductor devices, both in two space dimensions.
The Level Set Method for Etching and Deposition
Authors: Adalsteinsson D. , Evans L. C. , Ishii H.
Published: October 2003

We provide a rigorous interpretation of the level set approach to certain nonlocal geometric motions modelling etching effects in manufacture. The shadowing of certain parts of a surface by other parts gives rise to a nonlocal Hamilton–Jacobi type PDE, with a multivalued Hamiltonian. We also show that deposition effects do not fall within the conventional level set framework, and accordingly must be reinterpreted for numerical implementation.
Quasi Trefftz Spectral Method for Stokes Problem
Authors: Lifits S. A. , Reutskiy S. Yu. , Pontrelli G. , Tirozzi B.
Published: October 2003

A new numerical Quasi Trefftz Spectral Method (QTSM) which was earlier suggested for solving boundary value and initial value problems with elliptic operators is applied to linear stationary hydrodynamic problems. The primitive variables [Formula: see text] are used. The method has been found to work well for different problems, including free boundary ones. The problem of the Stefan type in the domain with moving boundary is also considered. The possibilities of further developments of QTSM are discussed.
An Orientation-Sensitive Vassiliev Invariant for Virtual Knots
Authors: Sawollek Jörg
Published: October 2003

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, it is shown that the zeroth order Vassiliev invariant coming from the Conway polynomial cannot distinguish a virtual link from its inverse and that it vanishes for virtual knots.
Stallings Twists Which Can be Realized by Plumbing and Deplumbing Hopf Bands
Authors: Yamamoto Ryosuke
Published: October 2003

We define a type of Stallings twists, which represents a "complexity" of the twist, and show that the Stallings twists of a certain type on a fiber surface for a fibered link in S3 can be realized by plumbing one Hopf band and deplumbing another Hopf band. Using this technique, we construct stable Hopf plumbings which are not Hopf plumbings with an arbitrary high first Betti number.
Fractality of Globular Protein Aggregates: From the Molecular to the Microscopic Level
Authors: Aymard P. , Durand D. , Nicolai T. , Gimel J. C.
Published: October 2003

This paper presents a theoretical approach of scattering by fractal aggregates based on a model with four parameters. It assumes that the aggregates are fractal and polydisperse with a number distribution which has a power law dependence on the molar mass. In addition the extemal cut-offs for the number distribution and the fractal structure are supposed to be stretched exponential functions.

β-lactoglobulin aggregates formed after heat-induced denaturation were studied by light and neutron scattering techniques over a range of wave vectors covering more than 4 decades. The results demonstrate clearly that the aggregates have a fractal structure at larger length scales and their number distribution is self similar. Their local structures depend on the pH and the ionic strength of the solutions and can be either globular at pH 7 or rigid rodlike at pH2 with a persistent length which increases with decreasing ionic strength. The explicit analysis of the dynamic light scattering data allows one to characterise precisely the mass distribution. The calculated structure factors are in good agreement with the experimental data.