Search results for "Monte Carlo method"

A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements

2014

In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wi…

Monte Carlo test of the self-consistent field theory of a polymer brush

1992

Medium-range interactions and crossover to classical critical behavior

1996

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be …

Critical phenomena without “hyper scaling”: How is the finite-size scaling analysis of Monte Carlo data affected?

2010

Abstract The finite size scaling analysis of Monte Carlo data is discussed for two models for which hyperscaling is violated: (i) the random field Ising model (using a model for a colloid-polymer mixture in a random matrix as a representative) (ii) The Ising bi-pyramid in computing surface fields.

Path-integral Monte Carlo study of crystalline Lennard-Jones systems.

1995

The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…

Cluster Expansions and Variational Monte Carlo in Medium Light Nuclei

1993

The B1 Brink-Boeker effective interaction is used to compute variational upper bounds for the ground state energy of nuclei from 16 O up to 40 Ca. The calculations are carried out by means of the Variational Monte Carlo method and with a multiplicative cluster expansion up to fourth order.

Path integral Monte Carlo study of the internal quantum state dynamics of a generic model fluid

1996

We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.

Molecular-Level Characterization of Heterogeneous Catalytic Systems by Algorithmic Time Dependent Monte Carlo

2009

Monte Carlo algorithms and codes, used to study heterogeneous catalytic systems in the frame of the computational section of the NANOCAT project, are presented along with some exemplifying applications and results. In particular, time dependent Monte Carlo methods supported by high level quantum chemical information employed in the field of heterogeneous catalysis are focused. Technical details of the present algorithmic Monte Carlo development as well as possible evolution aimed at a deeper interrelationship of quantum and stochastic methods are discussed, pointing to two different aspects: the thermal-effect involvement and the three-dimensional catalytic matrix simulation. As topical app…

Sequential Monte Carlo Methods in Random Intercept Models for Longitudinal Data

2017

Longitudinal modelling is common in the field of Biostatistical research. In some studies, it becomes mandatory to update posterior distributions based on new data in order to perform inferential process on-line. In such situations, the use of posterior distribution as the prior distribution in the new application of the Bayes’ theorem is sensible. However, the analytic form of the posterior distribution is not always available and we only have an approximated sample of it, thus making the process “not-so-easy”. Equivalent inferences could be obtained through a Bayesian inferential process based on the set that integrates the old and new data. Nevertheless, this is not always a real alterna…

Coarse-graining dipolar interactions in simple fluids and polymer solutions: Monte Carlo studies of the phase behavior

2009

In this paper we investigate the phase diagram of pure dipolar substances and their mixtures with short alkanes, using grand canonical Monte Carlo simulations of simplified coarse-grained models. Recently, an efficient coarse-grained model for simple quadrupolar molecules, based on a Lennard-Jones (LJ) interaction plus a spherically averaged quadrupolar potential, has been shown to be successful in predicting single-component and mixture phase diagrams. Motivated by these results, we investigate the phase diagrams of simple dipolar molecules (and their mixtures with alkanes) using a spherically averaged potential. First, we test the model on pure components. A generalized (state-dependent) …