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The moment map : nonlinear dynamics of density evolution via a few moments

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Barkley, Dwight, Kevrekidis, I. G. and Stuart, A. M. (2006) The moment map : nonlinear dynamics of density evolution via a few moments. SIAM Journal on Applied Dynamical Systems, Volume 5 (Number 3). pp. 403-434. doi:10.1137/050638667

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Official URL: http://dx.doi.org/10.1137/050638667

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Abstract

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We de. ne and study moment maps, maps on spaces of low-order moments of evolving distributions, as a means of understanding equation-free multiscale algorithms for these systems. The moment map itself is deterministic and attempts to capture the implied probability distribution of the dynamics. By choosing situations where the low-dimensional dynamics can be understood a priori, we evaluate the moment map. Despite requiring the evolution of an ensemble to de. ne the map, this can be an efficient numerical tool, as the map opens up the possibility of bifurcation analyses and other high level tasks being performed on the system. 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: SIAM Journal on Applied Dynamical Systems
Publisher: Society for Industrial and Applied Mathematics
ISSN: 1536-0040
Official Date: 2006
Dates:
DateEvent
2006Published
Volume: Volume 5
Number: Number 3
Number of Pages: 32
Page Range: pp. 403-434
DOI: 10.1137/050638667
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

Data sourced from Thomson Reuters' Web of Knowledge

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