Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles

Nicolas Forcadel; Cyril Imbert; Régis Monneau

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arXiv · 0906.1722

Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles

Nicolas Forcadel·Cyril Imbert·Régis Monneau

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Abstract

We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the interactions with the 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 the solutions to this system of ODEs converge to the solution of a macroscopic homogenized Hamilton-Jacobi equation.

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Nicolas Forcadel, Cyril Imbert, Régis Monneau. 2011-06-07. Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles. https://arxiv.org/abs/0906.1722

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