Homogenization of some particle systems with two-body interactions and of the dislocation dynamics

@inproceedings{Forcadel2008HomogenizationOS,
  title={Homogenization of some particle systems with two-body interactions and of the dislocation dynamics},
  author={N. Forcadel and C. Imbert and R{\'e}gis Monneau},
  year={2008}
}
This paper is concerned with the homogenization of some particle systems with two-body interactions in dimension one and of dislocation dynamics in higher dimensions. The dynamics of our particle systems are described by some ODEs. We prove that the rescaled ``cumulative distribution function'' of the particles converges towards the solution of a Hamilton-Jacobi equation. In the case when the interactions between particles have a slow decay at infinity as $1/x$, we show that this Hamilton… CONTINUE READING

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