The Moment Map: Nonlinear dynamics of density evolution via a few moments

Details The Moment Map: Nonlinear dynamics of density evolution via a few moments The Moment Map: Nonlinear dynamics of density evolution via a few moments

2005-08-23

arxiv.org/abs/cond-mat/0508551v1

Physics

Condensed Matter

Other Condensed Matter

28 pages, 29 figures, submitted to SIADS

Scientific paper

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving distributions, as a means of understanding equations-free multiscale algorithms for these systems. We demonstrate how nonlinearity arises in these maps and how this results in the stabilization of metastable states. Examples are shown for a hierarchy of models, ranging from simple stochastic differential equations to molecular dynamics simulations of a particle in contact with a heat bath.

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