Synchronous Multi-particle Cellular Automaton Model of Diffusion with Self-annihilation

Kireeva, A. E.; Sabelfeld, Karl K.; Kireev, Sergey

doi:10.1007/978-3-030-25636-4_27

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…Note that along with the MCA with the Boolean alphabet the one with the integer alphabet is also used [7,26]. Such approach allows one to lower the concentration noise [27] when modelling reaction-diffusion systems.…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…Since the diffusion rate of real substances is usually given by their diffusion coefficient, the Formula ( 30) is an important mathematical result for modelling the diffusion using MCA. Theorem 1 gives the probability distribution of a single particle in MCA that is given by the exact solutions to the two-dimensional Markov chain (7), (8), while (30) is of main applied interest, Theorem 1 is a more general fundamental result. It allows us to study specific features of various realizations of MCA discussed in Section 6.…”

Section: Discussionmentioning

confidence: 99%

“…The last one is the object of our study. Exactly this type of the CA attracted our attention since synchronous CA are more advantageous in terms of the computing speed (see, e.g., comparison in [7]). Note that the MCA is representative of partitioning CA.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Kulagin

Шаповалов

2023

Mathematics

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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.

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Section: Discussion Of the Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Kulagin

Шаповалов

2023

Mathematics

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“…In the case of the reduction of iron ores, the solutions of matter and thermal diffusion have been implemented, because the synchronized cellular automata are more suitable in terms of calculating the speed if compared with other computational techniques. [ 10 ] A significant advantage of models built by cellular automata is their modularity, where each module is focused on the solution of specific issues (e.g., diffusion, stirring, swelling of a solid structure) and the capability of the modules to exchange their results. [ 11 ] This makes the computational system simpler than the solution of the overall differential equation‐based models since it decreases the effort of model design and coding.…”

Section: Introductionmentioning

confidence: 99%

A Simplified Approach Based on Cellular Automata for Describing Direct Reduced Iron Production in Different Reducing Conditions

Mapelli,

Dall’Osto,

Mombelli

et al. 2023

steel research int.

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A quick computation approach based on cellular automata is developed and implemented to describe the reduction of iron ore pellets by a mixture of reducing agents featured by different H2/CO ratios. The evolution of oxygen concentration inside the pellet is followed from the beginning to the end of contact between reducing agent and pellet. The variation of thermal state of pellets and gas mixture is computed based on their initial temperature, considering the heat involved and the convective heat exchange between pellet and gas mixture. The use of cellular automata and finite‐difference method to solve the diffusion equation point out the absence of any diffusion coefficient value, allowing to make the model fit the experimental trial, because the problem is that it is not ruled just by diffusion but also by the concentration variation of reducing agent inside the pellet due to porosity increasing during reduction. The updating of the reducing agents concentration implies a sharp decrease of oxygen concentration that the cellular automata model considers. The developed model is able to provide the in‐line control of reduction process and could be used to adjust the chemical concentration and temperature of injected reducing agents.

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Parallel Implementation of Stochastic Simulation Algorithm for Nonlinear Systems of Electron-Hole Transport Equations in a Semiconductor

Sabelfeld

Kireeva

2020

Communications in Computer and Information Science

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Synchronous Multi-particle Cellular Automaton Model of Diffusion with Self-annihilation

Cited by 6 publications

References 16 publications

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain

A Simplified Approach Based on Cellular Automata for Describing Direct Reduced Iron Production in Different Reducing Conditions

Parallel Implementation of Stochastic Simulation Algorithm for Nonlinear Systems of Electron-Hole Transport Equations in a Semiconductor

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