Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles
Nicolas Forcadel, Cyril Imbert, Régis Monneau · Transactions of the American Mathematical Society · 2012
We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including a damping term and an acceleration term) where the force is created by the interactions with other particles and with a periodic potential. The presence of a damping term allows the system to be monotone. Our study takes into account the fact that the particles can be different. After a proper hyperbolic rescaling, we show that solutions of these systems of ODEs converge to solutions of some macroscopic homogenized Hamilton-Jacobi equations.