Analytical nodal methods for diffusion equations.
Analyticité des solutions des équations de Vlassov-Poisson
Anisotropic functions : a genericity result with crystallographic implications
In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
Anisotropic functions: a genericity result with crystallographic implications
In the 1950's and 1960's surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
Anomalous resistance of the fractal current-carrying corona of Z-pinch.
Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas
A computer aided method using symbolic computations that enables the calculation of the source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely powerful, easy to program and allows the derivation of balance equations to very high moments (limited only by computer resources). For sake of demonstration the method is applied to a simple case: the one-dimensional stationary granular gas under gravity. The method should...
Applications of symmetry methods to the theory of plasma physics.
Approximation of crystalline dendrite growth in two space dimensions.
Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...
Asymptotic behavior of the magnetization for the perceptron model
Asymptotic behavior of thin ferroelectric materials.
Asymptotic stability of an equilibrium for the gas dynamics model of charge transport in semiconductors.
Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space
We study the initial value problem for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We show that the corresponding stationary problem in the whole space ℝn admits a unique stationary solution in a general situation. Moreover, it is proved that when n ≥ 3, a unique solution to the initial value problem exists globally in time and converges to the corresponding stationary solution as time tends to infinity, provided that the amplitude of the stationary solution...
Asymptotics of time harmonic solutions to a thin ferroelectric model.
Bouteilles magnétiques et supraconductivité
Brownian motion and random obstacles.
Brownian motion in a Poisson obstacle field
Bulk superconductivity in Type II superconductors near the second critical field
We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].
Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment
We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. [18], [7]. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.
Chains, Flowers, Rings and Peanuts: Graphical Geodesic Lines and Their Application to Penrose Tiling