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SUMMARY:Aggregation-pattern due to repulsive-aggregating interaction poten
 tials - Fellner\, K (Cambridge)
DTSTART:20100910T145000Z
DTEND:20100910T153000Z
UID:TALK26076@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We study non-local evolution equations for a density of indivi
 duals\, which interact through a given symmetric potential. Such models ap
 pear in many applications such as swarming and flocking\, opinion formatio
 n\, inelastic materials\, .... In particular\, we are interested in intera
 ction potentials\, which behave locally repulsive\, but aggregating over l
 arge scales. A particular example for such potentials was recently given i
 n models of the alignment of the directions of filaments in the cytoskelet
 on. \n\nWe present results on the structure and stability of steady states
 . We shall show that stable stationary states of regular interaction poten
 tials generically consist of sums of Dirac masses. However the amount of D
 iracs depends on the interplay between local repulsion and aggregation. In
  particular we shall see that singular repulsive interaction potentials in
 troduce diffusive effects in the sense that stationary state are no longer
  sums of Diracs but continuous densities. This is comparted to effects of 
 added linear diffusion.
LOCATION:Seminar Room 1\, Newton Institute
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