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.

Simulation and Monte Carlo Methods

Abstract: Simulation involves using a model to produce results. The growing power of computers and the evolving simulation methodology have led to the recognition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Many applications of simulation are based on purely deterministic models. If the model contains a stochastic element, we have stochastic simulation, which will be the issue in this article. Stochastic simulation is often called Monte Carlo sampling, especially in engineering and physics literature.

Applications of quantum Monte Carlo methods in condensed systems

Abstract: The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

Hamiltonian Monte Carlo for Hierarchical Models

Abstract: Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly limit the efficiency of most common methods of in- ference. In this paper we explore the use of Hamiltonian Monte Carlo for hierarchical models and demonstrate how the algorithm can overcome those pathologies in practical applications.

Generalised Gibbs sampler and multigrid Monte Carlo for Bayesian computation

Abstract: SUMMARY Although Monte Carlo methods have frequently been applied with success, indiscriminate use of Markov chain Monte Carlo leads to unsatisfactory performances in numerous applications. We present a generalised version of the Gibbs sampler that is based on conditional moves along the traces of groups of transformations in the sample space. We explore its connection with the multigrid Monte Carlo method and its use in designing more efficient samplers. The generalised Gibbs sampler provides a framework encompassing a class of recently proposed tricks such as parameter expansion and reparameterisation. To illustrate, we apply this new method to Bayesian inference problems for nonlinear state-space models, ordinal data and stochastic differential equations with discrete observations.

Matrix inversion by a Monte Carlo method

Abstract: The following unusual method of inverting a class of matrices was devised by J. von Neumann and S. M. Ulam. Since it appears not to be in print, an exposition may be of interest to readers of MTAC. The method is remarkable in that it can be used to invert a class of re-th order matrices (see final paragraph) with only re2 arithmetic operations in addition to the scanning and discriminating required to play the solitaire game. The method therefore appears best suited to a human computer with a table of random digits and no calculating machine. Moreover, the method lends itself fairly well to obtaining a single element of the inverse matrix without determining the rest of the matrix. The term \"Monte Carlo\" refers to mathematical sampling procedures used to approximate a theoretical distribution [see MTAC, v. 3, p. 546]. Let B be a matrix of order re whose inverse is desired, and let A = I — B, where / is the unit matrix. For any matrix M, let \\T(M) denote the r-th proper value of M, and let M,-,denote the element of M in the i-th row and j-th column. The present method presupposes that