Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Blanchet, A and Degond, PAA},
doi = {10.1007/s10955-016-1471-6},
journal = {Journal of Statistical Physics},
pages = {41--60},
title = {Topological interactions in a Boltzmann-type framework},
url = {},
volume = {163},
year = {2016}

RIS format (EndNote, RefMan)

AB - We consider a finite number of particles characterised by their positionsand velocities. At random times a randomly chosen particle, the follower,adopts the velocity of another particle, the leader. The follower choosesits leader according to the proximity rank of the latter with respect to theformer. We study the limit of a system size going to infinity and, under theassumption of propagation of chaos, show that the limit equation is akinto the Boltzmann equation. However, it exhibits a spatial non-localityinstead of the classical non-locality in velocity space. This result relies onthe approximation properties of Bernstein polynomials. We illustrate thedynamics with numerical simulations.
AU - Blanchet,A
AU - Degond,PAA
DO - 10.1007/s10955-016-1471-6
EP - 60
PY - 2016///
SN - 1572-9613
SP - 41
TI - Topological interactions in a Boltzmann-type framework
T2 - Journal of Statistical Physics
UR -
UR -
VL - 163
ER -