Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks
Using the continuous-time random walk theory we investigate the phenomenon of anomalous superslow diffusion for which the variance of the particle position increases slowly than any positive power of time. This type of diffusion emerges in the case when the probability densities of the waiting times...
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| Format: | Article |
| Language: | English |
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Sumy State University
2016-03-01
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| Series: | Журнал нано- та електронної фізики |
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| Online Access: | http://jnep.sumdu.edu.ua/download/numbers/2016/1/articles/jnep_2016_V8_01044.pdf |
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| _version_ | 1850236961806090240 |
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| author | Yu.S. Bystrik |
| author_facet | Yu.S. Bystrik |
| author_sort | Yu.S. Bystrik |
| collection | DOAJ |
| description | Using the continuous-time random walk theory we investigate the phenomenon of anomalous superslow diffusion for which the variance of the particle position increases slowly than any positive power of time. This type of diffusion emerges in the case when the probability densities of the waiting times between the successive jumps characterized by the superheavy tails with infinite moments of any fractional order. We propose a numerical method to study the behavior of the diffusion laws and show that our numerical results are in very good agreement with the theoretical predictions. |
| format | Article |
| id | doaj-art-2d78dc91a9b64db9a5e3a090bb7b9e6b |
| institution | OA Journals |
| issn | 2077-6772 |
| language | English |
| publishDate | 2016-03-01 |
| publisher | Sumy State University |
| record_format | Article |
| series | Журнал нано- та електронної фізики |
| spelling | doaj-art-2d78dc91a9b64db9a5e3a090bb7b9e6b2025-08-20T02:01:51ZengSumy State UniversityЖурнал нано- та електронної фізики2077-67722016-03-018101044-101044-5Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random WalksYu.S. Bystrik0Sumy State University, 2, Rimsky Korsakov St., 40007 Sumy, UkraineUsing the continuous-time random walk theory we investigate the phenomenon of anomalous superslow diffusion for which the variance of the particle position increases slowly than any positive power of time. This type of diffusion emerges in the case when the probability densities of the waiting times between the successive jumps characterized by the superheavy tails with infinite moments of any fractional order. We propose a numerical method to study the behavior of the diffusion laws and show that our numerical results are in very good agreement with the theoretical predictions.http://jnep.sumdu.edu.ua/download/numbers/2016/1/articles/jnep_2016_V8_01044.pdfAnomalous diffusionContinuous-time random walksSuperheavy-tailed probability densitie |
| spellingShingle | Yu.S. Bystrik Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks Журнал нано- та електронної фізики Anomalous diffusion Continuous-time random walks Superheavy-tailed probability densitie |
| title | Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks |
| title_full | Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks |
| title_fullStr | Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks |
| title_full_unstemmed | Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks |
| title_short | Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks |
| title_sort | numerical investigation of superslow diffusion laws for a certain class of continuous time random walks |
| topic | Anomalous diffusion Continuous-time random walks Superheavy-tailed probability densitie |
| url | http://jnep.sumdu.edu.ua/download/numbers/2016/1/articles/jnep_2016_V8_01044.pdf |
| work_keys_str_mv | AT yusbystrik numericalinvestigationofsuperslowdiffusionlawsforacertainclassofcontinuoustimerandomwalks |