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CATEGORIES:DAMTP BioLunch
SUMMARY:The Subtle Road to Equilibrium in the FPUT Model -
David K. Campbell (Boston University)
DTSTART;TZID=Europe/London:20190523T130000
DTEND;TZID=Europe/London:20190523T140000
UID:TALK125395AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125395
DESCRIPTION:The interpretation and consequences of the celebra
ted Fermi\, Pasta\, Ulam\, Tsingou (FPUT) numerica
l experiment have challenged scientists for more t
han six decades. \nThe history of how the original
FPUT discovery led to the theory of “solitons\,”
was key in the understanding of Hamiltonian chaos\
, and led to the birth of “nonlinear science” is w
ell documented\, but there are many fascinating de
tails which are only now being explored and unders
tood. In this presentation\, I will discuss two re
cently studied examples: namely\, the details of t
he existence and breakdown of recurrences and supe
r-recurrences in both the alpha- and beta- version
s of the FPUT system\, and the remarkable intermit
tent dynamics\, involving long-time\, large deviat
ions\, that occur once the systems has nominally r
eached equilibrium. \n\nIn the first study [1]\, w
e find higher-order recurrences (HoR)s—which amou
nt to “super-super-recurrences” in both the alpha
and beta models. The periods of these HoR scale n
on-trivially with energy due to apparent singulari
ties caused by nonlinear resonances\, which differ
in the two models. Further\, the mechanisms by wh
ich the HoR breakdown differ strikingly in the two
models. \n\nIn the second study [2]\, we find th
at the dynamics at equilibrium is characterized by
a power-law distribution of excursion times far o
ff equilibrium\, with diverging variance. Long exc
ursions arise from sticky dynamics close to locali
zed excitations in normal mode space (q-breathers)
. Measuring the exponent allows to predict the tra
nsition into nonergodic dynamics. \n\n*Work in col
laboration with Carlo Danielli\, Sergej Flach\, an
d Salvatore Pace.\n\n[1] Salvatore D. Pace and Da
vid K. Campbell\, “Behavior and Breakdown of Highe
r-Order-Fermi- \n Pasta-Ulam-Tsignou Recurrences
\,” arXiv:181100663 (Chaos\, to appear)\n\n[2] C.
Danieli\, D. K. Campbell\, and S. Flach\, “Interm
ittent many-body dynamics at equilibrium\,”\n Ph
ys. Rev. E 95 060202(R) (2017).\n
LOCATION:MR14\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:Anne Herrmann
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