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Topological Interactions in a Boltzmann-Type Framework

Blanchet, Adrien and Degond, Pierre (2016) Topological Interactions in a Boltzmann-Type Framework. Journal of Statistical Physics, vol. 163 (n° 1). pp. 41-60.

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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. We illustrate the dynamics with numerical simulations.

Item Type: Article
Language: English
Date: April 2016
Refereed: Yes
Uncontrolled Keywords: Rank, Topological interaction, Boltzmann equation
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 17 Mar 2016 08:52
Last Modified: 08 Oct 2019 23:01
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