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SUMMARY:Nonlinear Waves in Granular Crystals: Modeling\, Analysis\, Comput
 ations and Experiments - Panayotis Kevrekidis
DTSTART:20200312T150000Z
DTEND:20200312T160000Z
UID:TALK134638@talks.cam.ac.uk
CONTACT:Edriss S. Titi
DESCRIPTION:In this talk\, we will provide an overview of results in the s
 etting of granular crystals\, consisting of beads interacting through Hert
 zian contacts. In 1d we show that there exist three prototypical types of 
 coherent nonlinear waveforms: shock waves\, traveling solitary waves and d
 iscrete breathers. The latter are time-periodic\, spatially localized stru
 ctures. For each one\, we will analyze the existence theory\, presenting c
 onnections to prototypical models of nonlinear wave theory\, such as the B
 urgers equation\, the Korteweg-de Vries equation and the nonlinear Schrodi
 nger (NLS) equation\, respectively. We will also explore the stability of 
 such structures\, presenting some explicit stability criteria analogous to
  the Vakhitov-Kolokolov criterion in the NLS model. Finally\, for each one
  of these structures\, we will complement the mathematical theory and nume
 rical computations with state-of-the-art experiments\, allowing their quan
 titative identification and visualization. Finally\, time permitting\, ong
 oing extensions of these themes will be briefly touched upon\, most notabl
 y in higher dimensions\, in heterogeneous or disordered chains and in the 
 presence of damping and driving\; associated open questions will also be o
 utlined.
LOCATION:MR 14
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