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Decay of covariances, uniqueness of ergodic component and scaling limit for a class of φ systems with non-convex potential

Codina Cotar, Jean-Dominique Deuschel (2012)

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

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for φ -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.

Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

Christian Heinemann, Christiane Kraus (2014)

Mathematica Bohemica

This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...

Derivation of Langevin dynamics in a nonzero background flow field

Matthew Dobson, Frédéric Legoll, Tony Lelièvre, Gabriel Stoltz (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed consistently with the background flow field and that interact with the large particle through elastic collisions. In the limit of small bath atom mass, the large particle dynamics converges in law to a stochastic dynamics. This derivation follows the ideas of [P. Calderoni,...

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