Fu-Yao Ren et al 2003 J. Phys. A: Math. Gen. 36 7533 doi:10.1088/0305-4470/36/27/306
Fu-Yao Ren1, Jin-Rong Liang2, Wei-Yuan Qiu1 and Yun Xu1
Show affiliationsWe introduce a heterogeneous fractional Fokker–Planck equation (HFFPE) on heterogeneous fractal structure media describing systems involving external force fields. The HFFPE is shown to obey the generalized Einstein relation, and its stationary solution is the Boltzmann distribution. It is proven that the asymptotic shape of its solution is a stretched Gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for constant and generic potentials with polar singularity at origin.
61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates)
05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
60G07 General theory of processes
60J60 Diffusion processes (See also 58J65)
Issue 27 (11 July 2003)
Received 28 January 2003, in final form 28 April 2003
Published 25 June 2003
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Jason X. Prochaska et al. 2004 ApJ 617 718
P H Gaskell 1979 J. Phys. C: Solid State Phys. 12 4337
Andreas Ringwald 2006 J. Phys.: Conf. Ser. 39 197
F Acernese et al 2007 Class. Quantum Grav. 24 S381
Ning Wu et al 2009 J. Phys.: Condens. Matter 21 474222
Kazushi Sakamoto et al 2004 ApJ 616 L59
Olivier Raccurt et al 2007 J. Micromech. Microeng. 17 2217
Michael J Kearney 2003 J. Phys. A: Math. Gen. 36 2663