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SUMMARY:Phase transitions and solitons in self-propelled particles: kineti
 c theory and diagrammatic approach - Ihle\, T (North Dakota State Universi
 ty)
DTSTART:20130627T161500Z
DTEND:20130627T164500Z
UID:TALK45939@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this talk\, I will summarize our recent progress on the kin
 etic theory of collective motion. The theory starts with an exact Markov c
 hain for the Vicsek model in phase space and is made tractable by the mean
 -field-like Molecular Chaos approximation. This leads to an Enskog-like eq
 uation which we solve numerically as well as analytically in certain limit
 s. The kinetic equation was also used to rigorously derive the hydrodynami
 c equations from the microscopic collision rules. We show that our results
  on the phase diagram and the formation of soliton-like waves agree quanti
 tatively with direct simulations for large particle velocities. We find th
 at the solitons modify the character of the flocking transition from conti
 nuous to discontinuous. To understand the behavior in the small velocity l
 imit where mean-field theory is invalid\, we developed a diagrammatic appr
 oach to systematically include particle correlations and show how they shi
 ft the flocking transition.\n
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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