Search results for "statistical"

Efficient simulation of the random-cluster model

2013

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present…

Representation of Strongly Stationary Stochastic Processes

1993

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

Role of conditional probability in multiscale stationary markovian processes.

2010

The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range correlated process with an infinite set of time-scales bounded from below, and (ii) a power-law correlated process with an infinite and unbounded set of time-scales. For these processes we investigate the equal position conditional probability P(x,t|x,0) and the mean First Passage Time T(L). The function P(x,t|x,0) can be considered as a proxy of the persistence, i.e. the fact that when a process reaches a position x then it spends some time around that posit…

The Master Equation

2009

Fractional calculus in solid mechanics: local versus non-local approach

2009

Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …

Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…

2016

In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…

Looking More Closely at the Rabinovich-Fabrikant System

2016

Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.

Stochastic linearization critically re-examined

1997

Abstract The stochastic linearization technique, widely used for the analysis of nonlinear dynamic systems subjected to random excitations, is revisited. It is shown that the standard procedure universally adopted for determining the so-called effective stiffness of the equivalent linear system is erroneous in all previous publications. Two error-free stochastic linearization techniques are elucidated, namely those based on (1) the force linearization and (2) energy linearization.

Quantitative View on the Processes Governing the Upscale Error Growth up to the Planetary Scale Using a Stochastic Convection Scheme

2019

Abstract Two diagnostics based on potential vorticity and the envelope of Rossby waves are used to investigate upscale error growth from a dynamical perspective. The diagnostics are applied to several cases of global, real-case ensemble simulations, in which the only difference between the ensemble members lies in the random seed of the stochastic convection scheme. Based on a tendency equation for the enstrophy error, the relative importance of individual processes to enstrophy-error growth near the tropopause is quantified. After the enstrophy error is saturated on the synoptic scale, the envelope diagnostic is used to investigate error growth up to the planetary scale. The diagnostics re…

Convection and thermodiffusion of colloidal gold tracers by laser light scattering

1999

In a dynamic light scattering experiment, we have investigated the time intensity correlation function and the profile of the transmitted laser beam for organic dispersions of light absorbing colloidal particles containing tiny gold clusters. The correlation functions have been found to show a superposition of an exponential decay, corresponding to Brownian motion of the tracers, and well-defined oscillations. These oscillations are caused by convection due to local heating of the sample by the incident laser beam, which has been confirmed independently via measurements of the local temperature within the sample. It will be shown how the particle convection velocity, which is the order of 1…