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Article Dans Une Revue Journal of Statistical Physics Année : 2016

Topological interactions in a Boltzmann-type framework

Résumé

We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader according to the proximity rank of the latter with respect to the former. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit equation is akin to the Boltzmann equation. However , it exhibits a spatial non-locality instead of the classical non-locality in velocity space. This result relies on the approximation properties of Bernstein polynomials.
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Dates et versions

hal-01171416 , version 1 (04-07-2015)

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Adrien Blanchet, Pierre Degond. Topological interactions in a Boltzmann-type framework. Journal of Statistical Physics, 2016, 163, pp.41-60. ⟨hal-01171416⟩
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