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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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Journal ArticleDOI
15 Jan 1996
TL;DR: In this paper, the site-site pair correlation functions for a fluid of molecules can be used to derive a set of empirical site site potential energy functions, which reproduce the fluid structure accurately but at the present time do not reproduce thermodynamic information on the fluid, such as the internal energy or pressure.
Abstract: It is shown that data on the site-site pair correlation functions for a fluid of molecules can be used to derive a set of empirical site-site potential energy functions. These potential functions reproduce the fluid structure accurately but at the present time do not reproduce thermodynamic information on the fluid, such as the internal energy or pressure. The method works in an iterative manner, starting from a reference fluid in which only Lennard-Jones interactions are included, and generates, by Monte Carlo simulation, successive corrections to those potentials which eventually lead to the correct site-site pair correlation functions. Using the approach the structure of water as determined from neuron scattering experiments is compared to the structure of water obtained from the simple point charge extended (SPCE) model of water interactions. The empirical potentials derived from both experiment and SPCE water show qualitative similarities with the true SPCE potential, although there are quantitative differences. The simulation is driven by a set of potential energy functions, with equilibration of the energy of the distribution, and not, as in the reverse Monte Carlo method, by equilibrating the value of χ2, which measures how closely the simulated site-site pair correlation functions fit a set of diffraction data. As a result the simulation proceeds on a true random walk and samples a wide range of possible molecular configurations.

672 citations

Book ChapterDOI
06 Jun 2001
TL;DR: Applications to stochastic solution of integral equations are given for the case where an approximation of the full solution function or a family of functionals of the solution depending on a parameter of a certain dimension is sought.
Abstract: We study Monte Carlo approximations to high dimensional parameter dependent integrals. We survey the multilevel variance reduction technique introduced by the author in [4] and present extensions and new developments of it. The tools needed for the convergence analysis of vector-valued Monte Carlo methods are discussed, as well. Applications to stochastic solution of integral equations are given for the case where an approximation of the full solution function or a family of functionals of the solution depending on a parameter of a certain dimension is sought.

665 citations

Journal ArticleDOI
TL;DR: In this article, Monte Carlo studies of the dielectric properties of water-like models were performed in order to understand the properties of the water-based models in terms of their dielectrics.
Abstract: (1973). Monte Carlo studies of the dielectric properties of water-like models. Molecular Physics: Vol. 26, No. 3, pp. 789-792.

665 citations

Proceedings ArticleDOI
15 Sep 1995
TL;DR: This work presents a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good, and can reduce variance significantly at little additional cost.
Abstract: Monte Carlo integration is a powerful technique for the evaluation of difficult integrals. Applications in rendering include distribution ray tracing, Monte Carlo path tracing, and form-factor computation for radiosity methods. In these cases variance can often be significantly reduced by drawing samples from several distributions, each designed to sample well some difficult aspect of the integrand. Normally this is done by explicitly partitioning the integration domain into regions that are sampled differently. We present a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good. These estimators are unbiased, and can reduce variance significantly at little additional cost. We present experiments and measurements from several areas in rendering: calculation of glossy highlights from area light sources, the “final gather” pass of some radiosity algorithms, and direct solution of the rendering equation using bidirectional path tracing. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation; G.1.9 [Numerical Analysis]: Integral Equations— Fredholm equations. Additional

633 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202311
202233
20201
20198
201852
2017306