Diffusion equations for a Markovian jumping process

Details Diffusion equations for a Markovian jumping process Diffusion equations for a Markovian jumping process

2006-04-28

arxiv.org/abs/cond-mat/0604660v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 3 figures

Scientific paper

10.1103/PhysRevE.74.021103

We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency. For small steps, we derive the Fokker-Planck equation and show the presence of the normal diffusion, subdiffusion and superdiffusion. For the L\'evy distribution of the step-size, we construct a fractional equation, which possesses a variable coefficient, and solve it in the diffusion limit. Then we calculate fractional moments and define fractional diffusion coefficient as a natural extension to the cases with the divergent variance. We also solve the master equation numerically and demonstrate that there are deviations from the L\'evy stable distribution for large wave numbers.

Affiliated with

Also associated with

No associations

Rating

Diffusion equations for a Markovian jumping process does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Diffusion equations for a Markovian jumping process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusion equations for a Markovian jumping process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-327498