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SUMMARY:Collective motion &amp\; Hydrodynamic limit for an active matter m
 odel - Clement Erignoux\, Ecole Polytechnique
DTSTART:20160525T150000Z
DTEND:20160525T160000Z
UID:TALK66172@talks.cam.ac.uk
CONTACT:Josephine Evans
DESCRIPTION:Collective dynamics can be observed among many animal species\
 , and have given rise in the last decades to an active and interdisciplina
 ry field of study. Such behaviours are usually modelled by active matter\,
  in which each individual is self-driven and tends to align its velocity w
 ith that of its neighbours.\nIn a classical model introduced by Vicsek & a
 l.\, as well as in numerous related active matter models\, a phase transit
 ion between chaotic behaviour at high temperature and global order at low 
 temperature can be observed. Even though ample evidence of these phase tra
 nsitions has been obtained for collective dynamics\, from a mathematical s
 tandpoint\, such active systems are not fully understood yet. Some progres
 s has been achieved in the recent years under an assumption of mean-field 
 interactions\, however to this day\, few mathematical results have been ob
 tained for models involving purely local interactions.\nI will describe a 
 lattice active particle system interacting locally to align\ntheir velocit
 ies\, and give some elements on how to derive the hydrodynamic limit for s
 uch an out-of equilibrium system.
LOCATION:MR14\, Centre for Mathematical Sciences
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