Search results for "Statistical physic"

Evolution of a Quantum System: Lifetime of a Determinant

1976

A measure of the ''dependency'' of a many-particle system is defined and its time dependence is evaluated for systems initially described by a single Slater determinant. An uncertainty product between the energy spread of the initial determinant and the lifetime of a system's independence is established. Numerical estimates of some lifetimes are given. They are not so long as to be reassuring for nuclear time-dependent Hartree--Fock calculations. Each separate case ought to be checked. 1 table.

Non-reversible Monte Carlo simulations of spin models

2011

Abstract Monte Carlo simulations are used to study simple systems where the underlying Markov chain satisfies the necessary condition of global balance but does not obey the more restrictive condition of detailed balance. Here, we show that non-reversible Markov chains can be set up that generate correct stationary distributions, but reduce or eliminate the diffusive motion in phase space typical of the usual Monte Carlo dynamics. Our approach is based on splitting the dynamics into a set of replicas with each replica representing a biased movement in reaction-coordinate space. This introduction of an additional bias in a given replica is compensated for by choosing an appropriate dynamics …

ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields

2016

In the last 20 years, we have witnessed the dramatic development of new data acquisition technologies allowing to collect massive amount of data with relatively low cost. is new feature leads Donoho to define the twenty-first century as the century of data. A major characteristic of this modern data set is that the number of measured variables is larger than the sample size; the word high-dimensional data analysis is referred to the statistical methods developed to make inference with this new kind of data. This chapter is devoted to the study of some of the most recent ℓ1-penalized methods proposed in the literature to make sparse inference in a Gaussian Markov random field (GMRF) defined …

On the adoption of the Monte Carlo method to solve one-dimensional steady state thermal diffusion problems for non-uniform solids

2013

Abstract The present paper is focussed on the investigation of the potential adoption of the Monte Carlo method to solve one-dimensional, steady state, thermal diffusion problems for continuous solids characterised by an isotropic, space-dependent conductivity tensor and subjected to non-uniform heat power deposition. To this purpose the steady state form of Fourier’s heat diffusion equation relevant to a continuous, heterogeneous and isotropic solid, undergoing a space-dependent heat power density has been solved in a closed analytical form for the general case of Cauchy’s boundary conditions. The thermal field obtained has been, then, put in a peculiar functional form, indicating that it …

A local chemical potential approach within the variable charge method formalism

2008

A new and computationally efficient implementation of the variable charge method of Streitz and Mintmire (1994 Phys. Rev. B 50 11996) is presented. In particular a local chemical potential approach that optimizes the charge on only those atoms expected to be ionic is developed. By doing so, the charge fluctuation problem experienced in regions far from any oxygen is solved, leading to a linear minimization problem of the electrostatic energy. In the dilute oxygen limit, such an approach can lead to at least an order of magnitude saving in computation.

Piezoelectric coefficients by molecular dynamics simulations in the constant stress ensemble: A case study of quartz

2006

Piezoelectric (strain) coefficients dij of quartz are calculated in terms of molecular dynamics as a function of pressure and temperature. We review the necessary formulas for the computation of electromechanical materials coefficients obtained at constant stress and temperature, and discuss how to overcome complications of the definition of polarization variations due to fluctuating box geometries. A method is employed suppressing significantly stochastic fluctuations of the estimators for piezoelectric coefficients. A recently suggested force field for the simulation of SiO2 reproduces available experimental data quite accurately. Predictions are made for the pressure dependence of dij of…

Exact solution of ‘‘hot dimer’’ adsorption in one-dimensional lattices

1993

An analytical solution for the kinetics of the ``hot-dimer'' adsorption in a one-dimensional lattice is reported. Hot dimers are molecules that dissociate after deposition, and each of the remaining monomers fly apart up to a maximum distance R from the original adsorption sites. The kinetics of this process is strongly dependent on the flying distance R. We find a particular behavior of the jamming coverage as a function of R. Monte Carlo simulation results are in agreement with such a calculation.

Local Structure of Multiferroic MnWO4 and Mn0.7Co0.3WO4 Revealed by the Evolutionary Algorithm

2015

A novel reverse Monte Carlo/evolutionary algorithm scheme was applied to the analysis of the W L3-edge and Mn(Co) K-edges EXAFS spectra from multiferroic MnWO4 and Mn0.7Co0.3WO4. A 3D structural model, consistent with the experimental data, was obtained, and the influence of composition and temperature on the local structure of tungstates is discussed.

On the estimation of unperturbed dimensions of long-chain molecules in solution

1965

Multiscale modeling of polymers at interfaces

2009

A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this process, degrees of freedom on smaller scales are eliminated to the favor of a model suitable for efficient study of the system behavior on larger length and time scales. We emphasize the need to distinguish between dynamic and static properties regarding the model validation. A model which accurately reproduces static properties may fail completely, when it comes to the dynamic behavior of the system. Furthermore, we comment on the use of Monte Carlo method i…