Search results for "Stochastic Proce"

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…

Drift-controlled anomalous diffusion: a solvable Gaussian model

2000

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution is power-law in time with an exponent controlled by one of model parameters.

Probabilistic description of traffic breakdowns

2001

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, may be, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car …

Accelerated transport and growth with symmetrized dynamics

2013

In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in $1+1$ dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the ``distance of interaction'' denoted by ${\ensuremath{\ell}}_{\mathrm{max}}$. We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening …

The Fokker-Planck Equation

2009

Stochastic Kinetics with Wave Nature

2003

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

A New Non-stationary Channel Model Based on Drifted Brownian Random Paths

2014

This paper utilizes Brownian motion (BM) processes with drift to model mobile radio channels under non-stationary conditions. It is assumed that the mobile station (MS) starts moving in a semi-random way, but subject to follow a given direction. This moving scenario is modelled by a BM process with drift (BMD). The starting point of the movement is a fixed point in the two-dimensional (2D) propagation area, while its destination is a random point along a predetermined drift. To model the propagation area, we propose a non-centred one-ring scattering model in which the local scatterers are uniformly distributed on a ring that is not necessarily centred on the MS. The semi-random movement of …

Reconstruction of time-dependent coefficients: a check of approximation schemes for non-Markovian convolutionless dissipative generators

2010

We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography based approach with a proper data sampling, our proposal allows to relate the time-dependent coefficients governing the dissipative evolution of a quantum system to experimentally accessible quantities. The proposed scheme not only provides a way to retrieve full information about potentially unknown dissipative coefficients but also, most valuably, can be employed as a reliable consistency test for the approximations involved in the theoretical derivation of a given non-Markovian convo…

Temporal evolution of neoclassical tearing modes in the frequently interrupted regime

2010

A phenomenological method for description of temporal evolution of neoclassical tearing modes in the frequently interrupted regime (FIR) is proposed. The method makes it possible to predict the beginning and the end of the FIR regime as well as the frequency of the FIR drops. A few experimental parameters which are used in the model are commonly measured quantities. Several specific ASDEX Upgrade (http://en.wikipedia.org/wiki/ASDEX_Upgrade) FIR discharges with different heating and different FIR behavior are analyzed in detail.