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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Phase transitions and solitons in self-propelled p
articles: kinetic theory and diagrammatic approach
- Ihle\, T (North Dakota State University)
DTSTART;TZID=Europe/London:20130627T171500
DTEND;TZID=Europe/London:20130627T174500
UID:TALK45939AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45939
DESCRIPTION:In this talk\, I will summarize our recent progres
s on the kinetic theory of collective motion. The
theory starts with an exact Markov chain for the V
icsek model in phase space and is made tractable b
y the mean-field-like Molecular Chaos approximatio
n. This leads to an Enskog-like equation which we
solve numerically as well as analytically in certa
in limits. The kinetic equation was also used to r
igorously derive the hydrodynamic equations from t
he microscopic collision rules. We show that our r
esults on the phase diagram and the formation of s
oliton-like waves agree quantitatively with direct
simulations for large particle velocities. We fin
d that the solitons modify the character of the fl
ocking transition from continuous to discontinuous
. To understand the behavior in the small velocity
limit where mean-field theory is invalid\, we dev
eloped a diagrammatic approach to systematically i
nclude particle correlations and show how they shi
ft the flocking transition.\n
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
CONTACT:Mustapha Amrani
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