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SUMMARY:Pattern formation of a nonlocal\, anisotropic interaction model - 
 Lisa Maria Kreusser\, University of Cambridge
DTSTART:20170201T160000Z
DTEND:20170201T170000Z
UID:TALK70823@talks.cam.ac.uk
CONTACT:Mo Dick Wong
DESCRIPTION:Motivated by the formation of fingerprint patterns during preg
 nancy we consider a large system of interacting particles. These interacti
 ons among the particles can be described by short-range repulsion forces t
 o prevent collisions as well as long-range attraction forces keeping the p
 articles together\, and lead to an isotropic interaction model. To describ
 e the pattern formation accurately we extend this isotropic model and cons
 ider an underlying tensor field representing the stress. This leads to an 
 additional anisotropy and the resulting class of models captures more comp
 lex\, anisotropic patterns than in the isotropic model. Mathematically\, t
 his class of interacting particle models is given by a large system of non
 linear ordinary differential equations and can be regarded as a generaliza
 tion of the isotropic interaction model. Using mathematical analysis and n
 umerical simulations we analyse this class of models for the first time an
 d adapt it in such a way that fingerprint patterns can be obtained as stat
 ionary solutions. This is joint work with M. Burger\, B. Duering\, P. Mark
 owich and C.-B. Schoenlieb.
LOCATION:MR14\, Centre for Mathematical Sciences
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