Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exa...
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| Veröffentlicht in: | Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2010-03, Vol.81 (3 Pt 1), p.030105-030105, Article 030105 |
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| container_issue | 3 Pt 1 |
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| container_title | Physical review. E, Statistical, nonlinear, and soft matter physics |
| container_volume | 81 |
| creator | Ilyin, Valery Procaccia, Itamar Zagorodny, Anatoly |
| description | We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random-walk approach, but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial. |
| doi_str_mv | 10.1103/PhysRevE.81.030105 |
| format | Article |
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| ispartof | Physical review. E, Statistical, nonlinear, and soft matter physics, 2010-03, Vol.81 (3 Pt 1), p.030105-030105, Article 030105 |
| issn | 1539-3755 1550-2376 |
| language | eng |
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| source | MEDLINE; American Physical Society Journals |
| subjects | Computer Simulation Diffusion Models, Chemical Models, Statistical Stochastic Processes |
| title | Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results |
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