A two-dimensional Landau-Lifshitz model in studying thin film micromagnetics.
A variational method to study the Zakharov equation.
A variational problem modelling behavior of unorthodox silicon crystals
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical mechanical...
A Variational Problem Modelling Behavior of Unorthodox Silicon Crystals
Controlling growth at crystalline surfaces requires a detailed and quantitative understanding of the thermodynamic and kinetic parameters governing mass transport. Many of these parameters can be determined by analyzing the isothermal wandering of steps at a vicinal [“step-terrace”] type surface [for a recent review see [4]]. In the case of orthodox crystals one finds that these meanderings develop larger amplitudes as the equilibrium temperature is raised (as is consistent with the statistical...
About a Variant of the Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation"
This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.
Abstracts of theses in mathematics
Žemlička, Jan: Structure of steady rings. Zemek, Martin: On some aspects of subdifferentiality of functions on Banach spaces. Hlubinka, Daniel: Construction of Markov kernels with application for moment problem solution. Somberg, Petr: Properties of the BGG resolution on the spheres. Krump, Lukáš: Construction of Bernstein-Gelfand-Gelfand for almost hermitian symmetric structures. Kolář, Jan: Simultaneous extension operators. Porosity.
Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height . In the quenched setting, we also sharply estimate the distribution of the walk at time .
Almost sure functional central limit theorem for ballistic random walk in random environment
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Ammann Bars and Quasicrystals.
An analytic solution of the non-linear equation and its application to the ion-atmosphere theory of strong electrolytes.
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material
An approach through orthogonal projections to the study of inhomogeneous or random media with linear response
An asymptotic result for brownian polymers
We consider a model of the shape of a growing polymer introduced by Durrett and Rogers (Probab. Theory Related Fields92 (1992) 337–349). We prove their conjecture about the asymptotic behavior of the underlying continuous process Xt (corresponding to the location of the end of the polymer at time t) for a particular type of repelling interaction function without compact support.
An axisymmetric PIC code based on isogeometric analysis⋆
Isogeometric analysis has been developed recently to use basis functions resulting from the CAO description of the computational domain for the finite element spaces. The goal of this study is to develop an axisymmetric Finite Element PIC code in which specific spline Finite Elements are used to solve the Maxwell equations and the same spline functions serve as shape function for the particles. The computational domain itself is defined using splines...
An equation for the limit state of a superconductor with pinning sites.
An Operational Calculus for the Euclidean Motion Group with Applications in Robotics and Polymer Science.
An upwinding mixed finite element method for a mean field model of superconducting vortices
An upwinding mixed finite element method for a mean field model of superconducting vortices
In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.
Analytical nodal methods for diffusion equations.
Analyticité des solutions des équations de Vlassov-Poisson