Topic
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: A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided in this article, where the theoretical basis of the method is derived and then a numerical algorithm is formulated.
Abstract: A self‐contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2 ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.
112 citations
TL;DR: A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions to compute ground- and excited- state energies of bosonic van der Waals clusters of up to seven particles.
Abstract: A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions. The method is applied in a correlation function Monte Carlo calculation to compute ground- and excited-state energies of bosonic van der Waals clusters of up to seven particles. The calculations are performed using trial wave functions with general three-body correlations.
112 citations
TL;DR: In this article, the posterior probability density is used to estimate the probability of the existence of interesting Earth structures, such as discontinuities and flow patterns, in the model space.
Abstract: The general inverse problem is characterized by at least one of the following two complications: (1) data can only be computed from the model by means of a numerical algorithm, and (2) the a priori model constraints can only be expressed via numerical algorithms. For linear problems and the so-called `weakly nonlinear problems', which can be locally approximated by a linear problem, analytical methods can provide estimates of the best fitting model and measures of resolution (nonuniqueness and uncertainty of solutions). This is, however, not possible for general problems. The only way to proceed is to use sampling methods that collect information on the posterior probability density in the model space. One such method is the inverse Monte Carlo strategy for resolution analysis suggested by Mosegaard and Tarantola. This method allows sampling of the posterior probability density even in cases where prior information is only available as an algorithm that samples the prior probability density. Once a collection of models sampled according to the posterior is available, it is possible to estimate, not only posterior model parameter covariances, but also resolution measures that are more useful in many applications. For example, posterior probabilities of the existence of interesting Earth structures like discontinuities and flow patterns can be estimated. These extended possibilities for resolution analysis may also provide new insight into problems that are usually treated by means of analytical methods.
112 citations
TL;DR: In this article, a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods was proposed for neutrino transport calculations in core-collapse supernovae.
Abstract: Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.
112 citations
TL;DR: In this article, the mean square end-to-end distance and radius of gyration are found to vary exponentially with chain length, and the results are similar to those obtained in Monte Carlo and self-avoiding walk studies.
Abstract: Molecular dynamics simulation techniques have been used to study the equilibrium configurational properties of freely moving polymer chains constructed from linked elastic spheres. The mean square end-to-end distance and radius of gyration are found to vary exponentially with chain length, and the results are similar to those obtained in Monte Carlo and self-avoiding walk studies. It is suggested that molecular dynamics is capable of yielding results of the same quality as Monte Carlo, while avoiding the inherent sampling problems.
112 citations