منابع مشابه
Numerical approach to the fractional Klein-Kramers equation.
Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees wit...
متن کاملKramers-like escape driven by fractional Gaussian noise.
We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the Hurst exponent H and the particle diffusivity D. We observe different behavior for the subdiffusive...
متن کاملUnified Fractional Kinetic Equation and a Fractional Diffusion Equation
Abstract. In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t),...
متن کاملSemiclassical Analysis for the Kramers–Fokker–Planck Equation
In certain applications one is interested in the long-time behavior of systems described by a linear partial differential equation. For example, in kinetic equations one studies the decay to equilibrium of various linear and nonlinear systems. For the Kramers–Fokker–Planck equation, which will be studied here, exponential decay was shown in Talay (1999) and an explicit rate was given in Hérau a...
متن کاملNonlinear Kramers equation associated with nonextensive statistical mechanics.
Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics. Since no general analytical time-dependent solutions are found for such a nonlinear Kramers equation, an ansatz is considered and the corresponding asymptotic behavior is studied a...
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ژورنال
عنوان ژورنال: The Journal of Physical Chemistry B
سال: 2000
ISSN: 1520-6106,1520-5207
DOI: 10.1021/jp993491m