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8 papers · 2 filters
Effective dynamics using conditional expectations
Frederic Legoll, Tony Lelievre
The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variab…
Homogenization of dislocation dynamics
A. El Hajj, H. Ibrahim, R. Monneau
In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study t…
Dislocation dynamics: from microscopic models to macroscopic crystal plasticity
A. El Hajj, H. Ibrahim, R. Monneau
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model,…
On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations
H. Ibrahim, R. Monneau
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions…
On a parabolic logarithmic Sobolev inequality
H. Ibrahim, R. Monneau
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) $BMO…
Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system
H. Ibrahim, M. Jazar, R. Monneau
We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the sol…