Search results for "stochastic process"

Probabilistic description of traffic flow

2005

Abstract A stochastic description of traffic flow, called probabilistic traffic flow theory, is developed. The general master equation is applied to relatively simple models to describe the formation and dissolution of traffic congestions. Our approach is mainly based on spatially homogeneous systems like periodically closed circular rings without on- and off-ramps. We consider a stochastic one-step process of growth or shrinkage of a car cluster (jam). As generalization we discuss the coexistence of several car clusters of different sizes. The basic problem is to find a physically motivated ansatz for the transition rates of the attachment and detachment of individual cars to a car cluster…

Stochastic Analysis of a Nonlocal Fractional Viscoelastic Bar Forced by Gaussian White Noise

2017

Recently, a displacement-based nonlocal bar model has been developed. The model is based on the assumption that nonlocal forces can be modeled as viscoelastic (VE) long-range interactions mutually exerted by nonadjacent bar segments due to their relative motion; the classical local stress resultants are also present in the model. A finite element (FE) formulation with closed-form expressions of the elastic and viscoelastic matrices has also been obtained. Specifically, Caputo's fractional derivative has been used in order to model viscoelastic long-range interaction. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non…

Determination of the stochastic evolution equation from noisy experimental data

2003

We have determined the coefficients of the Kardar-Parisi-Zhang equation as functions of coarse graining, which best describe the time evolution and spatial behavior observed for slow-combustion fronts in sheets of paper and magnetic flux fronts in a thin-film high-Tc superconductor. Reconstruction of the relevant equation of motion and its coefficients was mainly based on the inverse method proposed by Lam and Sander [Phys. Rev. Lett. 71, 561 (1993)]. The coefficient of the nonlinear term was also determined from the local slope-dependence of the front velocity.

Many-Particle Systems

2009

Size effect in phase transition kinetics

1988

The growth of a spontaneous lattice average magnetization in a magnetic system which is suddenly brought below the transition temperature is a stochastic process in which the very small fluctuations of the initial magnetization are amplified to a macroscopic size. The initial magnetization fluctuates in time around the zero average value because of the finite size of the system. As a consequence of the fluctuation-amplification phenomenon the nonlinear relaxation of the finite system is qualitatively different from that of the infinite one. The present paper studies this feature of phase-transition kinetics in the framework of a very simple model: the dynamical generalization of the spheric…

Noise-Induced Phase Transitions

2009

Killing (absorption) versus survival in random motion

2017

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (L\'{e}vy-stable cases are briefly mentioned) model-independent features are established, of the dynamical law that underlies the short time behavior of these random paths, whose overall life-time is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-…

STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS

2011

Random mass distribution in one-dimensional (1D) elastic solids in the presence of long-range interactions is studied in this paper. Besides the local Cauchy contact forces among adjacent elements, long-range forces depending on the product of interacting masses, as well as on their relative displacements, are considered. In this context, the random fluctuations of the mass distribution involve a stochastic model of the nonlocal interactions, and the random displacement field of the body is provided as the solution of a stochastic integro-differential equation. The presence of the random field of mass distribution is reflected in the random kernel of the solving integro-differential equatio…

Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes

2001

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The result…

Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator

2021

Abstract In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard s…