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CATEGORIES:Applied and Computational Analysis
SUMMARY:Nonlinear Waves in Granular Crystals: Modeling\, A
nalysis\, Computations and Experiments - Panayotis
Kevrekidis
DTSTART;TZID=Europe/London:20200312T150000
DTEND;TZID=Europe/London:20200312T160000
UID:TALK134638AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/134638
DESCRIPTION:In this talk\, we will provide an overview of resu
lts in the setting of granular crystals\, consisti
ng of beads interacting through Hertzian contacts.
In 1d we show that there exist three prototypical
types of coherent nonlinear waveforms: shock wave
s\, traveling solitary waves and discrete breather
s. The latter are time-periodic\, spatially locali
zed structures. For each one\, we will analyze the
existence theory\, presenting connections to prot
otypical models of nonlinear wave theory\, such as
the Burgers equation\, the Korteweg-de Vries equa
tion and the nonlinear Schrodinger (NLS) equation\
, respectively. We will also explore the stability
of such structures\, presenting some explicit sta
bility criteria analogous to the Vakhitov-Kolokolo
v criterion in the NLS model. Finally\, for each o
ne of these structures\, we will complement the ma
thematical theory and numerical computations with
state-of-the-art experiments\, allowing their quan
titative identification and visualization. Finally
\, time permitting\, ongoing extensions of these t
hemes will be briefly touched upon\, most notably
in higher dimensions\, in heterogeneous or disorde
red chains and in the presence of damping and driv
ing\; associated open questions will also be outli
ned.
LOCATION:MR 14
CONTACT:Edriss S. Titi
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