Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Carlen, E and Carvalho, MC and Degond, P and Wennberg, B},
doi = {6/1783},
journal = {Nonlinearity},
pages = {1783--1803},
title = {A Boltzmann model for rod alignment and schooling fish},
url = {},
volume = {28},
year = {2015}

RIS format (EndNote, RefMan)

AB - We consider a Boltzmann model introduced by Bertin, Droz and Grégoire as a binary interaction model of the Vicsek alignment interaction. This model considers particles lying on the circle. Pairs of particles interact by trying to reach their mid-point (on the circle) up to some noise. We study the equilibria of this Boltzmann model and we rigorously show the existence of a pitchfork bifurcation when a parameter measuring the inverse of the noise intensity crosses a critical threshold. The analysis is carried over rigorously when there are only finitely many non-zero Fourier modes of the noise distribution. In this case, we can show that the critical exponent of the bifurcation is exactly 1/2. In the case of an infinite number of non-zero Fourier modes, a similar behavior can be formally obtained thanks to a method relying on integer partitions first proposed by Ben-Naïm and Krapivsky.
AU - Carlen,E
AU - Carvalho,MC
AU - Degond,P
AU - Wennberg,B
DO - 6/1783
EP - 1803
PY - 2015///
SN - 1361-6544
SP - 1783
TI - A Boltzmann model for rod alignment and schooling fish
T2 - Nonlinearity
UR -
UR -
VL - 28
ER -