Communications in Mathematical Sciences

Volume 8 (2010)

Number 2

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part II

Application of the stochastic mode-reduction strategy and a priori prediction of symmetry breaking in stochastic systems with underlying symmetry

Pages: 393 – 408

DOI: http://dx.doi.org/10.4310/CMS.2010.v8.n2.a6

Authors

N. Barlas

I. Timofeyev

Abstract

We consider application of the stochastic mode-reduction strategy to a particular class of coupled models where a part of self-interactions of the slow variables is given by a rotationally invariant gradient system. The stochastic mode-reduction strategy is utilized to derive stochastic reduced models which yield a simple description of the phenomena resulting from breaking the original rotational symmetry. It is demonstrated that the direction of the symmetry breaking can be predicted a priori without any knowledge of the statistical behavior of the fast modes.

Keywords

Stochastic modeling; mode reduction; symmetry breaking

2010 Mathematics Subject Classification

60H10, 60H35, 65C30

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