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

Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles,Nicolas Forcadel,Cyril Imbert,Régis Monneau

Homogenization of accelerated Frenkel-Kontorova models with $n$ types of particles  
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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.
Published in 2009.
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