Deterministic and stochastic algorithms for mechanical systems under constraints

We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of a...

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Published inPhilosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 362; no. 1821; pp. 1583 - 1594
Main Authors Ciccotti, Giovanni, Kalibaeva, Galina
Format Journal Article
LanguageEnglish
Published England The Royal Society 15.08.2004
Subjects
Algorithms
Atoms
Conservation laws
Differential equations
Dynamical systems
Equations of motion
Holonomic Constraints
Mathematical expressions
Molecular dynamics
Molecules
Non-Hamiltonian And Brownian Dynamics
Statistical mechanics
Trajectories
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ISSN1364-503X
1471-2962
DOI10.1098/rsta.2004.1400

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Summary:We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations.
Bibliography:istex:4DA13C61B8DFAE899341788B89B4E1F1FAD56DE3
ark:/67375/V84-V5KL08BQ-7
Theme Issue 'Connecting scales: micro, meso and macro processes' compiled by M. Al-Ghoul, J. P. Boon and P. V. Coveney
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ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2004.1400