On a Generalization of One-Dimensional Kinetics
One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/11/1264 |
| _version_ | 1797531873791967232 |
|---|---|
| author | Vladimir V. Uchaikin Renat T. Sibatov Dmitry N. Bezbatko |
| author_facet | Vladimir V. Uchaikin Renat T. Sibatov Dmitry N. Bezbatko |
| author_sort | Vladimir V. Uchaikin |
| collection | DOAJ |
| description | One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided. |
| first_indexed | 2024-03-10T10:50:00Z |
| format | Article |
| id | doaj.art-a94c863e559843b19b6383f470d48649 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:50:00Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a94c863e559843b19b6383f470d486492023-11-21T22:17:58ZengMDPI AGMathematics2227-73902021-05-01911126410.3390/math9111264On a Generalization of One-Dimensional KineticsVladimir V. Uchaikin0Renat T. Sibatov1Dmitry N. Bezbatko2Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432017, RussiaMoscow Institute of Physics and Technology, Moscow 141701, RussiaDepartment of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432017, RussiaOne-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.https://www.mdpi.com/2227-7390/9/11/1264random walktelegraph equationfractional material derivativeMonte Carlo simulation |
| spellingShingle | Vladimir V. Uchaikin Renat T. Sibatov Dmitry N. Bezbatko On a Generalization of One-Dimensional Kinetics Mathematics random walk telegraph equation fractional material derivative Monte Carlo simulation |
| title | On a Generalization of One-Dimensional Kinetics |
| title_full | On a Generalization of One-Dimensional Kinetics |
| title_fullStr | On a Generalization of One-Dimensional Kinetics |
| title_full_unstemmed | On a Generalization of One-Dimensional Kinetics |
| title_short | On a Generalization of One-Dimensional Kinetics |
| title_sort | on a generalization of one dimensional kinetics |
| topic | random walk telegraph equation fractional material derivative Monte Carlo simulation |
| url | https://www.mdpi.com/2227-7390/9/11/1264 |
| work_keys_str_mv | AT vladimirvuchaikin onageneralizationofonedimensionalkinetics AT renattsibatov onageneralizationofonedimensionalkinetics AT dmitrynbezbatko onageneralizationofonedimensionalkinetics |