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 with the two-stage scenario underlying the anomalous diffusion mechanism, in which trapping events are superimposed on the Langevin dynamics. We develop an efficient computer algorithm for visualization of fractional Klein-Kramers dynamics and present some simulation results based on Monte Carlo techniques.
Magdziarz
Marcin
M
Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland. marcin.magdziarz@pwr.wroc.pl
Weron
Aleksander
A