Search results for "Monte Carlo."
showing 10 items of 1571 documents
Investigation of Finite-Size Effects in the Determination of Interfacial Tensions
2014
The interfacial tension between coexisting phases of a material is an important parameter in the description of many phenomena such as crystallization, and even today its accurate measurement remains difficult. We have studied logarithmic finite-size corrections in the determination of the interfacial tension with large scale Monte Carlo simulations, and have identified several novel contributions which not only depend on the ensemble, but also on the type of the applied boundary conditions. We present results for the Lennard-Jones system and the Ising model, as well as for hard spheres, which are particularly challenging. In the future, these findings will contribute to the understanding a…
Recycling Gibbs sampling
2017
Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning and statistics. The key point for the successful application of the Gibbs sampler is the ability to draw samples from the full-conditional probability density functions efficiently. In the general case this is not possible, so in order to speed up the convergence of the chain, it is required to generate auxiliary samples. However, such intermediate information is finally disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. Theoretical and exhaustive numerical co…
Rejection-Free Monte Carlo
2019
So far, we have been using the rejection Monte Carlo algorithms. To remind us, the algorithms proceed from state x to possible state \(x'\) as outlined in Algorithm 1.
Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics
2002
In this chapter we first introduce the basic concepts of Monte Carlo sampling, give some details on how Monte Carlo programs need to be organized, and then proceed to the interpretation and analysis of Monte Carlo results.
Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems
2019
In this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of …
Modeling Snow Dynamics Using a Bayesian Network
2015
In this paper we propose a novel snow accumulation and melt model, formulated as a Dynamic Bayesian Network DBN. We encode uncertainty explicitly and train the DBN using Monte Carlo analysis, carried out with a deterministic hydrology model under a wide range of plausible parameter configurations. The trained DBN was tested against field observations of snow water equivalents SWE. The results indicate that our DBN can be used to reason about uncertainty, without doing resampling from the deterministic model. In all brevity, the DBN's ability to reproduce the mean of the observations was similar to what could be obtained with the deterministic hydrology model, but with a more realistic repre…
Testing for goodness rather than lack of fit of continuous probability distributions.
2021
The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in sta…
Quantum Monte Carlo study of high pressure solid molecular hydrogen
2013
We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating…
Fluctuating Interfaces in Liquid Crystals
2008
We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at l…
Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands
2015
We report a fast, efficient and credible statistical reconstruction of any two-phase patterns of islands of miscellaneous shapes and poly-dispersed in sizes. In the proposed multi-scale approach called a weighted doubly-hybrid, two different pairs of hybrid descriptors are used. As the first pair, we employ entropic quantifiers, while correlation functions are the second pair. Their competition allows considering a wider spectrum of morphological features. Instead of a standard random initial configuration, a synthetic one with the same number of islands as that of the target is created by a cellular automaton. This is the key point for speeding-up of microstructure reconstruction, making u…