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SUMMARY:Transition fronts and their universality classes - Anna Vainchtein
  (University of Pittsburgh)
DTSTART:20220713T093000Z
DTEND:20220713T100000Z
UID:TALK175862@talks.cam.ac.uk
DESCRIPTION:Steadily moving transition fronts\, bringing local transformat
 ion\, symmetry breaking or collapse\, are among the most important dynamic
  coherent structures. Nonlinear waves of this type play a major role in ma
 ny modern applications involving the transmission of mechanical informatio
 n in systems ranging from crystal lattices and metamaterials to civil engi
 neering structures. While many different classes of such dynamic fronts ar
 e known\, the relation between them remains obscure.\nIn this talk I will 
 consider a prototypical mechanical system\, the FPU chain with piecewise l
 inear nonlinearity\, and show that there are exactly three distinct classe
 s of transition fronts\, which differ fundamentally in how (and whether) t
 hey produce and transport oscillations. The availability of all three type
 s of fronts as explicit solutions of the discrete problem enables identifi
 cation of the exact mathematical origin of the particular features of each
  class. I will also discuss a quasicontinuum approximation of the FPU mode
 l that captures all three classes of the fronts and the relation between t
 hem. The talk is based on recent joint work with N. Gorbushin and L. Trusk
 inovsky (ESPCI).&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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