Search results for "Statistical physics"
showing 10 items of 1402 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.
Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation
2013
From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attracto…
Modelling of non-stationary mobile radio channels using two-dimensional brownian motion processes
2013
The interdisciplinary idea of this paper is to employ a two-dimensional (2D) Brownian motion (BM) process to model non-stationary mobile fading channels. It is assumed that the mobile station (MS) starts moving from a fixed point along a random path in the 2D plane. We model such a moving scenario by a 2D BM process, in which the variance of the process determines the deviation of the MS from its starting point. The propagation area is modelled by a non-centred one-ring scattering model, where the local scatterers are uniformly distributed on a ring centred not necessarily on the MS. The random movement of the MS in the proposed scattering model results in local angles-of-arrival (AOAs) and…
The Ground State Electronic Energy of Benzene.
2020
We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$\zeta$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square devia…
On the correction of conserved variables for numerical RMHD with staggered constrained transport
2015
Despite the success of the combination of conservative schemes and staggered constrained transport algorithms in the last fifteen years, the accurate description of highly magnetized, relativistic flows with strong shocks represents still a challenge in numerical RMHD. The present paper focusses in the accuracy and robustness of several correction algorithms for the conserved variables, which has become a crucial ingredient in the numerical simulation of problems where the magnetic pressure dominates over the thermal pressure by more than two orders of magnitude. Two versions of non-relativistic and fully relativistic corrections have been tested and compared using a magnetized cylindrical …
Enhanced structural correlations accelerate diffusion in charge-stabilized colloidal suspensions
1999
Theoretical calculations for colloidal charge-stabilized and hard sphere suspensions show that hydrodynamic interactions yield a qualitatively different particle concentration dependence of the short-time self-diffusion coefficient. The effect, however, is numerically small and hardly accessible by conventional light scattering experiments. Applying multiple-scattering decorrelation equipment and a careful data analysis we show that the theoretical prediction for charged particles is in agreement with our experimental results from aqueous polystyrene latex suspensions.
Statistical Reconstruction of Microstructures Using Entropic Descriptors
2018
We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called entropic descriptors (EDs). For a binary pattern, they quantify spatial inhomogeneity or statistical complexity at discrete length-scales. The EDs extract dissimilar structural information to that given by two-point correlation functions (CFs). Within the SA, we use an appropriate cost function consisting of EDs or comprised of EDs and CFs. It was found that the stochastic reconstruction is computationally efficient when we begin with a preliminary synthetic…
Multiscale modelling of structure formation of C$_{60}$ on insulating CaF$_2$ substrates
2021
Morphologies of adsorbed molecular films are of interest in a wide range of applications. To study the epitaxial growth of these systems in computer simulations requires access to long time and length scales, and one typically resorts to kinetic Monte Carlo (KMC) simulations. However, KMC simulations require as input transition rates and their dependence on external parameters (such as temperature). Experimental data allow only limited and indirect access to these rates, and models are often oversimplified. Here, we follow a bottom-up approach and aim at systematically constructing all relevant rates for an example system that has shown interesting properties in experiments, buckminsterfull…
Percolation on correlated random networks
2011
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in o…
Quantum mechanics-classical molecular dynamics approach to EXAFS
2009
Recently developed approach to the simulation of configuration-averaged EXAFS spectra using the combination of quantum mechanics and classical Molecular Dynamics (MD) methods is presented on the example of the Ti K-edge in SrTiO3 at T = 300 K. The method allows one to significantly reduce the number of fitting parameters required in the EXAFS signal calculation and to account entirely for disorder contributions. We show also that the sensitivity of configuration-averaged EXAFS spectra to the force field model employed in the MD simulations allows one to use them as additional information for the force field parameters fitting.