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Anisotropic functions : a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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

Victor J. Mizel, Alexander J. Zaslavski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Annealed upper tails for the energy of a charged polymer

Amine Asselah (2011)

Annales de l'I.H.P. Probabilités et statistiques

We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider annealed estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.

Annealed vs quenched critical points for a random walk pinning model

Matthias Birkner, Rongfeng Sun (2010)

Annales de l'I.H.P. Probabilités et statistiques

We study a random walk pinning model, where conditioned on a simple random walk Y on ℤd acting as a random medium, the path measure of a second independent simple random walk X up to time t is Gibbs transformed with hamiltonian −Lt(X, Y), where Lt(X, Y) is the collision local time between X and Y up to time t. This model arises naturally in various contexts, including the study of the parabolic Anderson model with moving catalysts, the parabolic Anderson model with brownian noise, and the directed...

Anomalous heat-kernel decay for random walk among bounded random conductances

N. Berger, M. Biskup, C. E. Hoffman, G. Kozma (2008)

Annales de l'I.H.P. Probabilités et statistiques

We consider the nearest-neighbor simple random walk on ℤd, d≥2, driven by a field of bounded random conductances ωxy∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of ωxy>0 exceeds the threshold for bond percolation on ℤd. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2n-step return probability 𝖯 ω 2 n ( 0 , 0 ) . We prove that 𝖯 ω 2 n ( 0 , 0 ) is bounded by a random constant timesn−d/2 in d=2, 3, while it...

Application of accretive operators theory to evolutive combined conduction, convection and radiation.

María Michaela Porzio, Oscar López-Pouso (2004)

Revista Matemática Iberoamericana

The accretive operators theory is employed for proving an existence theorem for the evolutive energy equations involving simultaneously conduction, stationary convection (in the sense that the velocity field is assumed to be time independent), and radiation. In doing that we need to use new existence results for elliptic linear problems with mixed boundary conditions and irregular data.

Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas

S. H. Noskowicz, D. Serero (2011)

Mathematical Modelling of Natural Phenomena

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...

Approximation of Parabolic Equations Using the Wasserstein Metric

David Kinderlehrer, Noel J. Walkington (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the variational...

Around 3D Boltzmann non linear operator without angular cutoff, a new formulation

Radjesvarane Alexandre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.

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