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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| Published in: | Condensed Matter Physics |
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| Date: | 2013 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут фізики конденсованих систем НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/121086 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862629744520986624 |
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| author | Ilyin, V. Procaccia, I. Zagorodny, A. |
| author_facet | Ilyin, V. Procaccia, I. Zagorodny, A. |
| 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. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| 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.
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.
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| first_indexed | 2025-11-30T10:07:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-121086 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-11-30T10:07:49Z |
| publishDate | 2013 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Ilyin, V. Procaccia, I. Zagorodny, A. 2017-06-13T14:30:32Z 2017-06-13T14:30:32Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/121086 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. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media Рiвняння Фокера-Планка з пам’яттю: кросовер вiд балiстичного до дифузiйного процесу в багаточастинкових системах i нестисних середовищах Article published earlier |
| spellingShingle | 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. |
| title | Fokker-Planck equation with memory: the cross over from ballistic to diffusive processes in many particle systems and incompressible media |
| title_alt | Рiвняння Фокера-Планка з пам’яттю: кросовер вiд балiстичного до дифузiйного процесу в багаточастинкових системах i нестисних середовищах |
| 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/121086 |
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