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SUMMARY:Some Vignettes of Nonlinear Waves in Granular Crystals: From Model
 ing and Analysis to Computations and Experiments - Panayotis Kevrekidis (U
 niversity of Massachusetts)
DTSTART:20221207T103000Z
DTEND:20221207T110000Z
UID:TALK183785@talks.cam.ac.uk
DESCRIPTION:In this talk\, we will provide an overview of some results in 
 the setting of granular crystals\, consisting of beads interacting through
  Hertzian contacts. In 1d we show that there exist three prototypical type
 s of coherent nonlinear waveforms: shock waves\, traveling solitary waves 
 and discrete breathers. The latter are time-periodic\, spatially localized
  structures. For each one\, we will discuss the existence theory\, present
 ing connections to prototypical models of nonlinear wave theory\, such as 
 the Burgers equation\, the Korteweg-de Vries equation and the nonlinear Sc
 hrodinger (NLS) equation\, respectively. We will also explore the stabilit
 y of such structures\, presenting some explicit stability criteria analogo
 us to the famous Vakhitov-Kolokolov criterion in the NLS model. Finally\, 
 for each one of these structures\, we will complement the mathematical the
 ory and numerical computations with recent experiments\, allowing their qu
 antitative identification and visualization. Finally\, time permitting\, o
 ngoing extensions of these themes will be briefly touched upon\, most nota
 bly towards the study of dispersive shock waves in discrete systems\, in h
 igher dimensions\, in heterogeneous or disordered chains and in the presen
 ce of damping and driving\; associated open questions will also be outline
 d.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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