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Publication details

Document type
Journal articles

Document subtype
Full paper

Title
A Boltzmann model for rod alignment and schooling fish

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
Maria C. Carvalho (Author)
Dep. Matemática
CMAFcIO - Centro de Matemática, Aplicações Fundamentais e Investigação Operacional
Pierre Degond (Author)
IMPERIAL COLLEGE LONDON
Bernt Wennberg (Author)
CHALMERS TEKNISKA HOEGSKOLA AB

Scope
International

Refereeing
Yes

Summary
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.

Editor(s)
IOP Publishing Ltd & London Mathematical Society

Date of Publication
2015-05-14

Where published
NONLINEARITY

Publication Identifiers
ISSN - 0951-7715

Volume
28
Number
6

Starting page
1783
Last page
1803

Document Identifiers
URL - http://iopscience.iop.org/article/10.1088/0951-7715/28/6/1783


Export

APA
Eric A. Carlen, Maria C. Carvalho, Pierre Degond, Bernt Wennberg, (2015). A Boltzmann model for rod alignment and schooling fish. NONLINEARITY, 28, 1783-1803. ISSN 0951-7715. eISSN . http://iopscience.iop.org/article/10.1088/0951-7715/28/6/1783

IEEE
Eric A. Carlen, Maria C. Carvalho, Pierre Degond, Bernt Wennberg, "A Boltzmann model for rod alignment and schooling fish" in NONLINEARITY, vol. 28, pp. 1783-1803, 2015.

BIBTEX
@article{22949, author = {Eric A. Carlen and Maria C. Carvalho and Pierre Degond and Bernt Wennberg}, title = {A Boltzmann model for rod alignment and schooling fish}, journal = {NONLINEARITY}, year = 2015, pages = {1783-1803}, volume = 28 }