Applied Math And Analysis Seminar
Monday, January 16, 2012, 4:30pm, 119 Physics
Amic Frouvelle (University of Crete, Greece)
Macroscopic limits of a system of self-propelled particles with phase transition
Abstract:- The Vicsek model, describing alignment and self-organisation in large
systems of self-propelled particles, such as fish schools or flocks of
birds, has attracted a lot of attention with respect to its simplicity and
its ability to reproduce complex phenomena. We consider here a
time-continuous version of this model, in the spirit of the one proposed by
P. Degond and S. Motsch, but where the rate of alignment is proportional to
the mean speed of the neighboring particles. In the hydrodynamic limit, this
model undergoes a phase transition phenomenon between a disordered and an
ordered phase, when the local density crosses a threshold value. We present
the two different macroscopic limits we can obtain under and over this
threshold, namely a nonlinear diffusion equation for the density, and a
first-order non-conservative hydrodynamic system of evolution equations for
the local density and orientation. (joint work with Pierre Degond and Jian-Guo Liu). [video]
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