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Volume 95, Issue 2
15 July 1991
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Research Article| July 15 1991
Kristen A. Fichthorn;
Kristen A. Fichthorn
Department of Chemical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802
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W. H. Weinberg
W. H. Weinberg
Department of Chemical Engineering, University of California, Santa Barbara, California 93106
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J. Chem. Phys. 95, 1090–1096 (1991)
Article history
Received:
December 12 1990
Accepted:
April 10 1991
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Citation
Kristen A. Fichthorn, W. H. Weinberg; Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys. 15 July 1991; 95 (2): 1090–1096. https://doi.org/10.1063/1.461138
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Monte Carlo methods are utilized as computational tools in many areas of chemical physics. In this paper, we present the theoretical basis for a dynamical Monte Carlo method in terms of the theory of Poisson processes. We show that if: (1) a ‘‘dynamical hierarchy’’ of transition probabilities is created which also satisfy the detailed‐balance criterion; (2) time increments upon successful events are calculated appropriately; and (3) the effective independence of various events comprising the system can be achieved, then Monte Carlo methods may be utilized to simulate the Poisson process and both static and dynamic properties of model Hamiltonian systems may be obtained and interpreted consistently.
Topics
Hamiltonian mechanics, Chemical physics, Markov processes, Monte Carlo methods
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