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math.PR2022★ 3 cited
Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain
Anton Kulagin, Alexander Shapovalov
The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single par…
math-ph2022★ 6 cited
Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity
Alexander V. Shapovalov, Anton E. Kulagin, Sergei A. Siniukov
We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. T…