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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
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 |
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| Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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| 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 |
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