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- W1669403692 abstract "We consider a Boltzmann model introduced by Bertin, Droz and Greegoire 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-Naim and Krapivsky." @default.
- W1669403692 created "2016-06-24" @default.
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- W1669403692 date "2015-05-14" @default.
- W1669403692 modified "2023-09-25" @default.
- W1669403692 title "A Boltzmann model for rod alignment and schooling fish" @default.
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- W1669403692 doi "https://doi.org/10.1088/0951-7715/28/6/1783" @default.
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