Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media
The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non- Markovian...
Збережено в:
| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121086 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media / V. Ilyin, I. Procaccia, A. Zagorodny // Condensed Matter Physics. — 2013. — Т. 16, № 1. — С. 13004:1–18. — Бібліогр.: 36 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non- Markovian kinetic coefficients are determined by the observable quantities (mean- and mean square displacements). Solutions of the non-Markovian equation describing diffusive processes in the physical space are obtained. For long times these solutions agree with the predictions of continuous random walk theory; they are however much superior at shorter times when the effect of the ballistic behavior is crucial. |
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