Tel Aviv University, Applied Mathematics Seminar
 
Date:       Tuesday April 30, 2013 at 15:10
 
Place:      Schreiber Bldg, Room 309
 
Speaker: Edriss Titi, Weizmann institute
 
Title: A Numerical Algorithm for Advancing Slow Features in Fast-Slow
Systems without Scale Separation - A Young Measure Approach
 
Abstract:
 
In the first part of the talk, and in order to set the stage, we will
offer a multi-scale and averaging strategy to compute the solution of
a singularly perturbed system when the fast dynamics oscillates
rapidly; namely, the fast dynamics forms cycle-like limits which
advance along with the slow dynamics. We describe the limit as a
Young measure with values being supported on the limit cycles,
averaging with respect to which induces the equation for the slow
dynamics. In particular, computing the tube of the limit cycles
establishes a good approximation for arbitrarily small singular
parameters. We will demonstrate this by exhibiting concrete numerical
examples.
 
In the second part of the talk we will examine singularly perturbed
systems which may not possess a natural split into fast and slow
state variables. Once again, our approach depicts the limit behavior
as a Young measure with values being invariant measure of the fast
contribution to the flow. These invariant measures are drifted by the
slow contribution to the value. We keep track of this drift via
slowly evolving observables. Averaging equations for the latter lead
to computation of characteristic features of the motion and the
location the invariant measures. To demonstrate our ideas
computationally, we will present some numerical experiments involving
a system derived from a spatial discretization of a Korteweg-de
Vries-Burgers type equation, with fast dispersion and slow diffusion.
 
This is a joint work with Z. Artstein, W. Gear, I. Kevrekidis, J.
Linshiz and M. Slemrod.
 
Webpage of the applied mathematics seminar:
 <https://sites.google.com/site/tauamathseminar/>
 
______________________________________________________________________
 
Dr. Yoel Shkolnisky
Department of Applied Mathematics
School of Mathematical Sciences        phone:  972-3-640-8705
Tel Aviv University,                   fax  :  972-3-640-9357
Tel Aviv, 69978 Israel                 email:   <yoelsh@post.tau.ac.il>
______________________________________________________________________
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yoel Shkolnisky   <yoelsh@post.tau.ac.il>