Search results for "Stochastic process"

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.

Stochastic seismic analysis of structures with nonlinear viscous dampers

2007

Fluid damper devices inserted in buildings or bridges are commonly used as energy sinks for seismic protection. In the response analysis of structures with filled damper devices the main problem exists in the strong nonlinear behavior of such equipment, as a consequence the differential equation of motion remains nonlinear and the response spectrum analysis still cannot be applied. In this note, by using the concept of power spectral density function coherent with the elastic response spectrum and by using the statistical linearization technique, expressions for finding the equivalent linear damping have been found. Comparisons with results obtained by Monte Carlo simulations confirm that f…

Apodization of imaging systems by means of a random spatially nonstationary absorbing screen

1992

The amplitude impulse response (AIR) of coherent imaging systems with random binary apodizers is analyzed. Formulas for the mean value and the variance of the AIR are derived for two statistical one-dimensional models of apodizers: (1) nonuniform low-density shot noise and (2) a nonuniform unipolar synchronous random process. We show that for both models a high signal-to-noise ratio is achieved within the central peak and the low-order sidelobes of the AIR. Apodizers based on the second model permit higher values of the signal-to-noise ratio than those based on the first one.