Search results for "Monte Carlo method."
showing 10 items of 1217 documents
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…
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…
Peculiarities of the local structure in new medium- and high-entropy, low-symmetry tungstates
2022
G. Bakradze acknowledges financial support provided by the Latvian Council of Science for project no. 1.1.1.2/VIAA/3/19/444 (agreement no. 1.1.1.2/16/I/001) realized at the Institute of Solid State Physics, University of Latvia. The Institute of Solid State Physics, University of Latvia, as a centre of excellence, has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement no. 739508, project CAMART2.
Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study
1996
In this paper we present a classical Monte Carlo simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles and periodic boundary conditions. We used a recently developed algorithm which apart from standard Metropolis local moves employs also global moves consisting of displacements of the center of mass of the whole chains in all three spatial directions as well as rotations of the chains around an axis parallel to the crystallographic c-direction. Our simulations are performed in the NpT ensemble, at zero pressure, and extend over the whole range of temperatures in which the orthorhombic phase is experime…
Speeding up of microstructure reconstruction: I. Application to labyrinth patterns
2011
Recently, entropic descriptors based the Monte Carlo hybrid reconstruction of the microstructure of a binary/greyscale pattern has been proposed (Piasecki 2011 Proc. R. Soc. A 467 806). We try to speed up this method applied in this instance to the reconstruction of a binary labyrinth target. Instead of a random configuration, we propose to start with a suitable synthetic pattern created by cellular automaton. The occurrence of the characteristic attributes of the target is the key factor for reducing the computational cost that can be measured by the total number of MC steps required. For the same set of basic parameters, we investigated the following simulation scenarios: the biased/rando…
In Situ Study of Zinc Peroxide Decomposition to Zinc Oxide by X‐Ray Absorption Spectroscopy and Reverse Monte Carlo Simulations
2022
The authors wish to thank Dr. R. Kalendarev for the synthesis of ZnO2 sample. A.K. would like to thank the financial support of the ERDF Project No. 1.1.1.1/20/A/060. The experiment at the MAX IV synchrotron was performed within the project 20190823. Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union's Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.