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Monte Carlo molecular modeling
About: Monte Carlo molecular modeling is a research topic. Over the lifetime, 11307 publications have been published within this topic receiving 409122 citations.
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TL;DR: It is shown that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the anterior distribution is small.
Abstract: We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by “splitting” the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is possible is when the log density of the distribution of interest (the potential energy function) can be written as the log of a Gaussian density, which is a quadratic function, plus a slowly-varying function. Hamiltonian dynamics for quadratic energy functions can be analytically solved. With the splitting technique, only the slowly-varying part of the energy needs to be handled numerically, and this can be done with a larger stepsize (and hence fewer steps) than would be necessary with a direct simulation of the dynamics. Another context where splitting helps is when the most important terms of the potential energy function and its gradient can be evaluated quickly, with only a slowly-varying part requiring costly computations. With splitting, the quick portion can be handled with a small stepsize, while the costly portion uses a larger stepsize. We show that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the posterior distribution is small.
74 citations
TL;DR: In this paper, Monte Carlo simulations of the critical region of the restricted primitive model were performed and it was shown that the critical behavior is compatible with Ising like behavior, although due to statistical error on the simulation data and large correction-to-scaling contributions mean field behavior cannot be totally excluded.
Abstract: Monte Carlo simulations of the critical region of the restricted primitive model are reported. Using mixed-field finite size scaling analysis we show that the critical behavior is compatible with Ising like behavior although due to statistical error on the simulation data and large correction-to-scaling contributions mean-field behavior cannot be totally excluded. With the assumption of Ising criticality the critical temperature is estimated to be 0.0488±0.0002 and the critical density 0.080±0.005.
74 citations
TL;DR: In this paper, a Monte Carlo simulation of the Lennard−Jones liquid−vapor free surface at 84°K was performed and it was shown that there exists no layer structure in the liquid region neighboring the free surface.
Abstract: We report a Monte Carlo simulation of the Lennard−Jones liquid−vapor free surface at 84°K and conclude that, contrary to other recent numerical experiments, there exists no layer structure in the liquid region neighboring the free surface.
74 citations
TL;DR: In this paper, a detailed comparison of the theoretical results for aluminum and polymethylmethacrylate (PMMA) with experimental results show that this approach describes the energy distribution of transmitted electrons through thin films of aluminum and PMMA more realistically than the Monte Carlo approaches utilizing Bethe's stopping power equation.
Abstract: Fundamental characteristics of electron penetration in solids, such as energy and angular distributions of transmitted electrons, have been theoretically calculated using a Monte Carlo approach. The essential features of the Monte Carlo approach are the inclusion of the random nature of inelastic scattering events, and also the extension of Gryzinski’s semiempirical expression for core electron excitation to valence electron excitation through the use of an appropriate mean binding energy. A detailed comparison of the theoretical results for aluminum and polymethylmethacrylate (PMMA) with experimental results show that the direct Monte Carlo approach describes electron scattering events in solids very well. It is also shown that this approach describes the energy distribution of transmitted electrons through thin films of aluminum and PMMA more realistically than the Monte Carlo approaches utilizing Bethe’s stopping power equation.
74 citations