Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces.

نویسندگان

  • B I Henry
  • T A M Langlands
  • P Straka
چکیده

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

متن کامل

Fractional Fokker-Planck equation with tempered α-stable waiting times: langevin picture and computer simulation.

In this paper we introduce a Langevin-type model of subdiffusion with tempered α-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales. We derive general properties of tempered anomalous diffusion from the theory of tempered α-stable proce...

متن کامل

Use and abuse of a fractional Fokker-Planck dynamics for time-dependent driving.

We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an ad hoc manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force fields. ...

متن کامل

Modeling of subdiffusion in space-time-dependent force fields beyond the fractional Fokker-Planck equation.

In this paper we attack the challenging problem of modeling subdiffusion with an arbitrary space-time-dependent driving. Our method is based on a combination of the Langevin-type dynamics with subordination techniques. For the case of a purely time-dependent force, we recover the death of linear response and field-induced dispersion -- two significant physical properties well-known from the stu...

متن کامل

A pr 2 01 0 Fractional Fokker - Planck Equations for Subdiffusion with Space - and - Time - Dependent

Over the past few decades there has been an enormous growth in the numbers of papers devoted to experimental and theoretical aspects of anomalous diffusion [1, 2]. The landmark review by Metzler and Klafter in 2000 [1] has been particularly influential, promoting the description of anomalous diffusion within the framework of continuous time random walks (CTRWs) and fractional calculus. There ar...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Physical review letters

دوره 105 17  شماره 

صفحات  -

تاریخ انتشار 2010