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
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ISSN1364-503X
1471-2962
DOI10.1098/rsta.2004.1400

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Abstract 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.
AbstractList 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.
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.
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.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.
Author Giovanni Ciccotti
Galina Kalibaeva
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10.1007/978-3-540-39895-0_5
10.1090/S0002-9939-1959-0108732-6
10.1063/1.463137
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10.1063/1.434317
10.1063/1.444728
10.1063/1.1378321
10.2183/pjab.69.161
10.1103/PhysRevE.61.6165
10.1080/0026897031000108113
10.1016/0167-7977(86)90022-5
10.1103/PhysRevB.17.1302
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Snippet We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems...
We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems...
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SubjectTerms 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
Title Deterministic and stochastic algorithms for mechanical systems under constraints
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