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CATEGORIES:SIAM-IMA Cambridge Student Chapter
SUMMARY:Perturbation\, Noise\, and Averaged Dynamics - Xue
-Mei Li (Imperial College London)
DTSTART;TZID=Europe/London:20190502T112500
DTEND;TZID=Europe/London:20190502T121000
UID:TALK123895AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123895
DESCRIPTION:Perturbation and approximation underly almost all
applications of physical mathematical models. The
averaging method\, first introduced for approximat
e periodic motions\, is now widely used for a larg
e class of problems in both pure and applied mathe
matics.\nThe purpose of averaging is easy to descr
ibe. Suppose that we have a system of variables in
teracting with each other and moving at different
scales of speed (of order 1 and of order 1/epsilon
) with the fast variables `fast oscillatoryâ€™. Both
slow and fast variables evolve in time according
to some rules\, for example solving a family of di
fferential or stochastic differential equations. T
he aim is to determine whether the slow variables
can be approximated by an autonomous systems of eq
uations\, called the effective dynamic\, as epsilo
n is taken to 0 and the speed of the fast variable
s tends to infinity. Slow/fast systems arise from
perturbations of conservation laws and breaking of
symmetries.\nWe will discuss the latest developme
nts in averaged dynamics\, touching on recent work
with M. Hairer on averaged dynamics with fraction
al noise (this leads to very different behaviour f
rom the white noise case and requires new techniqu
es).
LOCATION:Centre for Mathematical Sciences\, MR2
CONTACT:Ferdia Sherry
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