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| 001 | 669384 | ||
| 005 | 20231030042220.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\40624 | ||
| 035 | _aRU\TPU\network\40458 | ||
| 090 | _a669384 | ||
| 100 | _a20230427a2023 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 135 | _adrgn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aAnalytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain _fA. E. Kulagin, A. V. Shapovalov |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 320 | _a[References: 32 tit.] | ||
| 330 | _aThe 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 | _tMathematics | ||
| 463 |
_tVol. 11, iss. 3 _v[584, 18 p.] _d2023 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _atwo-dimensional Markov chain | |
| 610 | 1 | _acellular automata | |
| 610 | 1 | _aMargolus neighbourhood | |
| 610 | 1 | _adiffusion | |
| 610 | 1 | _aprobability distribution | |
| 700 | 1 |
_aKulagin _bA. E. _cmathematician _claboratory assistant of Tomsk Polytechnic University _f1992- _gAnton Evgenievich _2stltpush _3(RuTPU)RU\TPU\pers\35727 |
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| 701 | 1 |
_aShapovalov _bA. V. _gAleksandr Vasiljevich |
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| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет _bИнженерная школа неразрушающего контроля и безопасности _bОтделение электронной инженерии _h7977 _2stltpush _3(RuTPU)RU\TPU\col\23507 |
| 801 | 2 |
_aRU _b63413507 _c20230427 _gRCR |
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| 856 | 4 | _uhttps://doi.org/10.3390/math11030584 | |
| 942 | _cCF | ||