Search results for "Anomalous diffusion"
showing 10 items of 33 documents
Applications and Implications of Fractional Dynamics for Dielectric Relaxation
2012
This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on “Broadband Dielectric Spectroscopy and its Advanced Technological Applications”, held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. …
One-Dimensional Diffusion
2009
Electron dynamical response in InP semiconductors driven by fluctuating electric fields
2015
Abstract The complexity of electron dynamics in low-doped n-type InP crystals operating under fluctuating electric fields is deeply explored and discussed. In this study, we employ a multi-particle Monte Carlo approach to simulate the non-linear transport of electrons inside the semiconductor bulk. All possible scattering events of hot electrons in the medium, the main details of the band structure, as well as the heating effects, are taken into account. The results presented in this study derive from numerical simulations of the electron dynamical response to the application of a sub-Thz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise.…
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.
Acceleration of diffusion in randomly switching potential with supersymmetry
2004
We investigate the overdamped Brownian motion in a supersymmetric periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ from each other by a shift of one-half period. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential. For the sawtooth potential, we obtain the exact expression for the effective diffusion coefficient, which is valid for the arbitrary mean rate of potential switchings and arbitrary intensity of white Gaussian noise. We…
Statics and dynamics of dense polymer systems studied by monte carlo simulation
1995
Monte Carlo simulations of coarse–grained models of macromolecules offer a unique tool to study the interplay between coil conformations, thermodynamic properties, and chain configurational relaxation and diffusion. Two examples are discussed where the chain conformation strongly differs from a gaussian coil: (i) collapsed chains in a bad solvent, where anomalous diffusion occurs in the Rouse limit and the relaxation time increases at least with the third power of chain length. (ii) Expulsion of a chain from a semidilute polymer brush. The initially stretched chain contracts to a gaussian coil and the center of mass moves outward with constant velocity until it reaches the region of the “la…
On fractional diffusion and continuous time random walks
2003
Abstract A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.
Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability
2006
Abstract Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.
Anomalous diffusion and nonlinear relaxation phenomena in stochastic models of interdisciplinary physics
2020
The study of nonlinear dynamical systems in the presence of both Gaussian and non-Gaussian noise sources is the topic of this research work. In particular, after shortly present new theoretical results for statistical characteristics in the framework of Markovian theory, we analyse four different physical systems in the presence of Levy noise source. (a) The residence time problem of a particle subject to a non-Gaussian noise source in arbitrary potential profile was analyzed and the exact analytical results for the statistical characteristics of the residence time for anomalous diffusion in the form of Levy flights in fully unstable potential profile was obtained. Noise enhanced stability …