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Dynamic Monte Carlo method
About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.
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TL;DR: In this article, the Monte Carlo method is extended to evaluate the integrals of complex-valued functions, i.e. the Feynman path integrals representing the time-dependent Green function of the one-dimensional non-stationary Schrodinger equation.
149 citations
01 Jan 1962
TL;DR: Three workable sequential processes, derived from a non-sequential method of J. von Neumann and S. Ulam for solving systems of linear algebraic equations, are described and analysed in detail.
Abstract: This paper defines the concept of sequential Monte Carlo and outlines the principal modes of approach which may be expected to yield useful sequential processes. Three workable sequential processes, derived from a non-sequential method of J. von Neumann and S. M. Ulam for solving systems of linear algebraic equations, are described and analysed in detail.
149 citations
TL;DR: Finite size corrections are proposed, which allow us to estimate approximately the free energy of the solid phase in the thermodynamic limit from the known value of the freeEnergy of theSolid phase with N molecules.
Abstract: In this paper a new method to evaluate the free energy of solids is proposed. The method can be regarded as a variant of the method proposed by Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. The main equations of the method can be derived in a simple way. The method can be easily implemented within a Monte Carlo program. We have applied the method to determine the free energy of hard spheres in the solid phase for several system sizes. The obtained free energies agree within the numerical uncertainty with those obtained by Polson et al. [J. Chem. Phys. 112, 5339 (2000)]. The fluid-solid equilibria has been determined for several system sizes and compared to the values published previously by Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] using the phase switch methodology. It is shown that both the free energies and the coexistence pressures present a strong size dependence and that the results obtained from free energy calculations agree with those obtained using the phase switch method, which constitutes a cross-check of both methodologies. From the results of this work we estimate the coexistence pressure of the fluid-solid transition of hard spheres in the thermodynamic limit to be p*=11.54(4), which is slightly lower than the classical value of Hoover and Ree (p*=11.70) [J. Chem. Phys. 49, 3609 (1968)]. Taking into account the strong size dependence of the free energy of the solid phase, we propose to introduce finite size corrections, which allow us to estimate approximately the free energy of the solid phase in the thermodynamic limit from the known value of the free energy of the solid phase with N molecules. We have also determined the free energy of a Lennard-Jones solid by using both the methodology of this work and the finite size correction. It is shown how a relatively good estimate of the free energy of the system in the thermodynamic limit is obtained even from the free energy of a relatively small system.
149 citations
TL;DR: The authors compare the results using nonmetric analysis, full factorial designs, and rank data with quicker and less expensive methods of metric analysis, orthogonal arrays and stimulus ratings to indicate that metric analysis using ratings data and orthogonic arrays is very robust.
Abstract: In many industrial applications of conjoint analysis the use of nonmetric algorithms to analyze respondent ranks of products described by more than eight or 10 attributes is time consuming and very...
148 citations
TL;DR: A simulation procedure for estimating the distribution functions of the time to complete stochastic networks, called conditional Monte Carlo, is shown to be substantially more efficient than traditional simulation methods.
Abstract: This paper is concerned with a simulation procedure for estimating the distribution functions of the time to complete stochastic networks. The procedure, called conditional Monte Carlo, is shown to be substantially more efficient (in terms of the computational effort required) than traditional simulation methods. The efficacy of conditional Monte Carlo and its use in conjunction with other Monte Carlo methods is illustrated for the Wheatstone bridge network. The applicability of the procedure to larger networks, as well as other stochastic systems, is discussed, and a general method is given for its implementation.
148 citations