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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Some Vignettes of Nonlinear Waves in Granular Crys
tals: From Modeling and Analysis to Computations a
nd Experiments - Panayotis Kevrekidis (University
of Massachusetts)
DTSTART;TZID=Europe/London:20221207T103000
DTEND;TZID=Europe/London:20221207T110000
UID:TALK183785AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/183785
DESCRIPTION:In this talk\, we will provide an overview of some
results in the setting of granular crystals\, con
sisting of beads interacting through Hertzian cont
acts. In 1d we show that there exist three prototy
pical types of coherent nonlinear waveforms: shock
waves\, traveling solitary waves and discrete bre
athers. The latter are time-periodic\, spatially l
ocalized structures. For each one\, we will discus
s the existence theory\, presenting connections to
prototypical models of nonlinear wave theory\, su
ch as the Burgers equation\, the Korteweg-de Vries
equation and the nonlinear Schrodinger (NLS) equa
tion\, respectively. We will also explore the stab
ility of such structures\, presenting some explici
t stability criteria analogous to the famous Vakhi
tov-Kolokolov criterion in the NLS model. Finally\
, for each one of these structures\, we will compl
ement the mathematical theory and numerical comput
ations with recent experiments\, allowing their qu
antitative identification and visualization. Final
ly\, time permitting\, ongoing extensions of these
themes will be briefly touched upon\, most notabl
y towards the study of dispersive shock waves in d
iscrete systems\, in higher dimensions\, in hetero
geneous or disordered chains and in the presence o
f damping and driving\; associated open questions
will also be outlined. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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