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SUMMARY:Continuum models of kinetic many-particle systems with short-range
  interactions and clustering - Calum Braham (University of Oxford)
DTSTART:20220322T145000Z
DTEND:20220322T153500Z
UID:TALK171548@talks.cam.ac.uk
DESCRIPTION:Models of physical systems as sets of particles interacting th
 rough generalised `forces' are common to a wide variety of sciences. While
  individual-based (microscopic) models of such systems are generally conce
 ptually simple\, they are often intractable analytically and computational
 ly as most systems to be modelled contain an infeasibly large number of pa
 rticles. It is common in such circumstances to derive a macroscopic contin
 uum model\, which tracks the evolution of population-averaged probability 
 densities over an individual particle's phase space. In this talk we will 
 develop a general method for deriving continuum models of second-order (ki
 netic) systems with short-ranged interaction forces using matched asymptot
 ic expansion in the small interaction-length parameter. As an archetypical
  example\, we first show that this approach allows us to derive the Boltzm
 ann equation as a continuum description of a low-density potential-force s
 ystem. We then extend our method to apply to `clustering' systems\, where 
 particles' positions and velocities may be highly correlated post-interact
 ion\, a behaviour that would invalidate many of the typical assumptions ma
 de when deriving such continuum models. We use the Cucker-Smale individual
 -based model of collective behaviour as a test case to evaluate our matche
 d asymptotic method against particle simulations and compare the accuracy 
 to a standard mean-field approach.\n&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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