Search results
Results From The WOW.Com Content Network
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle.
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. In statistical mechanics applications prior to the introduction of the Metropolis algorithm, the method consisted of generating a large number of random configurations of the system, computing the properties of interest (such as energy or density) for each configuration ...
Markov chain Monte Carlo methods that change dimensionality have long been used in statistical physics applications, where for some problems a distribution that is a grand canonical ensemble is used (e.g., when the number of molecules in a box is variable).
The general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics .
Variants of the Monte Carlo method: Direct simulation Monte Carlo; Quasi-Monte Carlo method; Markov chain Monte Carlo. Metropolis–Hastings algorithm. Multiple-try Metropolis — modification which allows larger step sizes; Wang and Landau algorithm — extension of Metropolis Monte Carlo
In contrast with traditional Monte Carlo and Markov chain Monte Carlo methods these mean-field particle techniques rely on sequential interacting samples. The terminology mean-field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the ...
The Quasi-Monte Carlo method recently became popular in the area of mathematical finance or computational finance. [1] In these areas, high-dimensional numerical integrals, where the integral should be evaluated within a threshold ε, occur frequently. Hence, the Monte Carlo method and the quasi-Monte Carlo method are beneficial in these ...
The direct simulation Monte Carlo algorithm is like molecular dynamics in that the state of the system is given by the positions and velocities of the particles, {,}, for =, …,. Unlike molecular dynamics, each particle in a DSMC simulation represents F N {\displaystyle F_{N}} molecules in the physical system that have roughly the same ...