In this paper, we give a review of recent results about the homogenization of particle systems with applications to Frenkel-Kontorova models and dislocation dynamics of curves. We underline the main ideas which allow us to extend the nonlinear homogenization methods for viscosity solutions, to the present framework of particles in interactions, or moving fronts in interactions. AMS Classificati...

The effects of mechanical stress during emulsification on the oxidation of methyl linoleate were investigated by four methods (high-pressure homogenization, high-speed stirring, ultrasonic homogenization, and membrane emulsification). The oxidation rates and induction periods were almost constant, regardless of the emulsification method, except for membrane emulsification, by which the inductio...

We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient), we establish a homogenization result and characterize the effective Hamiltonian for arbitrary (possibly degenerate) elliptic diffusion matrices. The result extends p...

We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L ∞ (Ω), Ω ⊂ R d) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most g...

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L ∞ (Ω), Ω ⊂ R d) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most general ...

We consider linear divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L∞(Ω), Ω ⊂ R) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most gener...

The standard collisional model paradigm consists of a system that interacts sequentially with identically prepared ancillas. After infinitely many collisions, and under appropriate conditions, the may converge to same state as This process, known homogenization, is independent ancilla initial state, being property only underlying dynamics. In this paper we extend idea locally identical, but glo...