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SUMMARY:Coarse-graining of collective dynamics models - Pierre Degond (Imp
 erial College London)
DTSTART:20170921T092000Z
DTEND:20170921T100000Z
UID:TALK80081@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we will report on some new individual-based mod
 els of collective dynamics and their coarse-graining into continuum models
 . The applications span from collective cell dynamics (such as social bact
 eria or  sperm) to flocking of birds or fish. Models of social behavior ar
 e best set up at the individual scale where behavioral rules can be easily
  introduced and tested. However\, the complexity of individual-based model
 s increases rapidly with the number of individuals and their calibration o
 r control can hardly be implemented at this level. To overcome this limita
 tion\, one often uses continuum model that describe the system through ave
 rage quantities such as densities or mean orientation. But the downside of
  most models in the literature is that the link between the rules at the i
 ndividual behavior and the coefficients in the macroscopic model are not k
 nown exactly and are at best extrapolated from heuristic consideration. He
 re\, we propose a systematic and mathematical rigorous way to derive conti
 nuum models from collective dynamics models. It relies on the introduction
  of a new concept\, the &lsquo\;generalized collision invariants&rsquo\;\,
  which permit to overcome the lack of physical invariance in most systems 
 undergoing collective dynamics. In this talk\, we will review some recent 
 developments of these concepts and how they can be used to model systems o
 f practical scientific importance.
LOCATION:Seminar Room 1\, Newton Institute
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