Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain
| Parent link: | Mathematics Vol. 11, iss. 3.— 2023.— [584, 18 p.] |
|---|---|
| Autor principal: | |
| Autor corporatiu: | |
| Altres autors: | |
| Sumari: | Title screen The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated with the direction of the movement, we reduce the problem under consideration to the study of a two-dimensional Markov chain. The master equation for the probability distribution is derived and solved exactly using the probability-generating function method. The probability distribution is expressed analytically in terms of Jacobi polynomials. The moments of the obtained solution allowed us to derive the exact analytical formula for the parametric dependence of the diffusion coefficient in the two-dimensional cellular automaton with the Margolus neighbourhood. Our analytic results agree with earlier empirical results of other authors and refine them. The results are of interest for the modelling two-dimensional diffusion using cellular automata especially for the multicomponent problem. |
| Idioma: | anglès |
| Publicat: |
2023
|
| Matèries: | |
| Accés en línia: | http://earchive.tpu.ru/handle/11683/132654 https://doi.org/10.3390/math11030584 |
| Format: | Electrònic Capítol de llibre |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=669384 |
MARC
| LEADER | 00000naa0a2200000 4500 | ||
|---|---|---|---|
| 001 | 669384 | ||
| 005 | 20251006141526.0 | ||
| 035 | |a (RuTPU)RU\TPU\network\40624 | ||
| 035 | |a RU\TPU\network\40458 | ||
| 090 | |a 669384 | ||
| 100 | |a 20230427d2023 k||y0rusy50 ba | ||
| 101 | 0 | |a eng | |
| 102 | |a CH | ||
| 135 | |a drgn ---uucaa | ||
| 181 | 0 | |a i | |
| 182 | 0 | |a b | |
| 200 | 1 | |a Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain |f A. E. Kulagin, A. V. Shapovalov | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 32 tit.] | ||
| 330 | |a The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated with the direction of the movement, we reduce the problem under consideration to the study of a two-dimensional Markov chain. The master equation for the probability distribution is derived and solved exactly using the probability-generating function method. The probability distribution is expressed analytically in terms of Jacobi polynomials. The moments of the obtained solution allowed us to derive the exact analytical formula for the parametric dependence of the diffusion coefficient in the two-dimensional cellular automaton with the Margolus neighbourhood. Our analytic results agree with earlier empirical results of other authors and refine them. The results are of interest for the modelling two-dimensional diffusion using cellular automata especially for the multicomponent problem. | ||
| 461 | |t Mathematics | ||
| 463 | |t Vol. 11, iss. 3 |v [584, 18 p.] |d 2023 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a two-dimensional Markov chain | |
| 610 | 1 | |a cellular automata | |
| 610 | 1 | |a Margolus neighbourhood | |
| 610 | 1 | |a diffusion | |
| 610 | 1 | |a probability distribution | |
| 700 | 1 | |a Kulagin |b A. E. |c mathematician |c Associate Professor of Tomsk Polytechnic University, Candidate of Physical and Mathematical Sciences |f 1992- |g Anton Evgenievich |3 (RuTPU)RU\TPU\pers\35727 |9 18885 | |
| 701 | 1 | |a Shapovalov |b A. V. |g Aleksandr Vasiljevich | |
| 712 | 0 | 2 | |a Национальный исследовательский Томский политехнический университет |b Инженерная школа неразрушающего контроля и безопасности |b Отделение электронной инженерии |3 (RuTPU)RU\TPU\col\23507 |
| 801 | 0 | |a RU |b 63413507 |c 20230427 |g RCR | |
| 856 | 4 | |u http://earchive.tpu.ru/handle/11683/132654 |z http://earchive.tpu.ru/handle/11683/132654 | |
| 856 | 4 | |u https://doi.org/10.3390/math11030584 | |
| 942 | |c CF | ||