Format

Send to:

Choose Destination
See comment in PubMed Commons below
Proc Natl Acad Sci U S A. 2009 Jul 7;106(27):10884-9. doi: 10.1073/pnas.0902633106. Epub 2009 Jun 19.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Author information

  • 1Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA. darve@stanford.edu

Abstract

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

PMID:
19549838
[PubMed]
PMCID:
PMC2708778
Free PMC Article
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for HighWire Icon for PubMed Central
    Loading ...
    Write to the Help Desk