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...
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| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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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. |
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irk-123456789-1210862017-06-14T03:05:39Z Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media Ilyin, V. Procaccia, I. Zagorodny, A. 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. На основi немаркiвського узагальнення рiвняння Фокера-Планка запропоновано пiдхiд до об’єднаного опису дифузiйних процесiв, який дозволяє розглядати як балiстичний режим на малих часах, так i аномальну (суб- або супер-) дифузiю на великих часових iнтервалах. Встановлено зв’язок немаркiвських кiнетичних коефiцiєнтiв зi спостережуваними величинами (середiми та середньоквадратичними змiщеннями). Отримано розв’язки, що описують дифузiйнi процеси у фiзичному просторi. Для великих часiв еволюцiї вони узгоджуються з результатами теорiї неперервних в часi випадкових блукань, а на малих часах описують балiстичну динамiку. 2013 Article 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. 1607-324X PACS: 05.40 Fb, 05.40 Jc, 51.10 +y DOI:10.5488/CMP.16.13004 arXiv:1207.6190 http://dspace.nbuv.gov.ua/handle/123456789/121086 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Ilyin, V. Procaccia, I. Zagorodny, A. |
| spellingShingle |
Ilyin, V. Procaccia, I. Zagorodny, A. Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media Condensed Matter Physics |
| author_facet |
Ilyin, V. Procaccia, I. Zagorodny, A. |
| author_sort |
Ilyin, V. |
| title |
Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_short |
Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_full |
Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_fullStr |
Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_full_unstemmed |
Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_sort |
fokker-planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121086 |
| citation_txt |
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. |
| series |
Condensed Matter Physics |
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