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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, a generalization of Wertheim's theory of associated fluids to multicomponent liquid mixtures is presented, for a model binary fluid mixture with site-site coulombic interactions.
Abstract: We present the generalization of Wertheim's theory of associated fluids to multicomponent liquid mixtures. For a model binary fluid mixture with site-site coulombic interactions, the theory yields results in excellent agreement with Monte Carlo simulations. The simulations also provide pair distribution functions.
84 citations
TL;DR: In this paper, a new class of Monte Carlo moves based on nonequilibrium dynamics is introduced, where candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution.
Abstract: Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Here, we introduce a new class of moves based on nonequilibrium dynamics: Candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution. The acceptance rule is similar to the Metropolis acceptance probability, but related to the nonequilibrium work rather than the instantaneous energy difference. Our method is applicable to sampling from both a single thermodynamic state or a mixture of thermodynamic states, and allows both coordinates and thermodynamic parameters to be driven in nonequilibrium proposals. Whereas generating finite-time switching trajectories incurs an additional cost, driving some degrees of freedom while allowing others to evolve naturally can lead to large enhancements in acceptance probabilities, greatly reducing structural correlation times. Using nonequilibrium driven processes vastly expands the repertoire of useful Monte Carlo proposals in simulations of dense solvated systems.
84 citations
TL;DR: In this article, transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation, such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium.
Abstract: Transition probabilities governing the interaction of energy packets and matter are derived that allow Monte Carlo NLTE transfer codes to be constructed without simplifying the treatment of line formation. These probabilities are such that the Monte Carlo calculation asymptotically recovers the local emissivity of a gas in statistical equilibrium. Numerical experiments with one-point statistical equilibrium problems for Fe II and Hydrogen confirm this asymptotic behaviour. In addition, the resulting Monte Carlo emissivities are shown to be far less sensitive to errors in the populations of the emitting levels than are the values obtained with the basic emissivity formula.
83 citations
TL;DR: In this article, a computational algorithm for random complete packing by discs is proposed and Monte Carlo simulations using this algorithm give the value 0.5473 for random packing density of discs.
Abstract: A computational algorithm for random complete packing by discs is proposed. Monte Carlo simulations using this algorithm give the value 0.5473 for random packing density of discs. It greatly improves the Solomon's result, 04756.
83 citations
TL;DR: In this paper, the convergence of the Monte Carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi-random, and the results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard Monte Carlo simulations for certain low-dimensional problems.
Abstract: The convergence of the Monte Carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi-random. In this paper the convergence of Monte Carlo particle simulation is studied when these quasi-random sequences are used. For the one-dimensional heat equation discretized in both space and time, convergence is proved for a quasi-random simulation using reordering of the particles according to their position. Experimental results are presented for the spatially continuous heat equation in one and two dimensions. The results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard Monte Carlo simulations for certain low-dimensional problems.
83 citations