Editorial for Feature Papers 2021–2022

Odintsov, Sergei D.

doi:10.3390/sym15010032

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…A similar classification problem has been solved for PSS-spaces as well. In [32] PSS-spaces with transitive four-parameter groups of motions are considered; in [33] HPSS-spaces are considered (see also [34]); in [35] PSS-spaces with groups acting on isotropic hypersurfaces of transitivity are considered. PSS-spaces with fourparameter groups of motions are considered in [36], provided that these groups have transitive three-parameter subgroups.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(IX)

Обухов

2023

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Section: Introductionmentioning

confidence: 99%

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(IX)

Обухов

2023

Axioms

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“…The diffusion coefficient is usually invariant when the movements of particles are caused just by random fluctuations rather than by any fields. Nevertheless, the processes with the time-dependent diffusion coefficient are also of interest, e.g., in the ambipolar diffusion phenomena [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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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Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions

Obukhov

2023

Journal of Mathematical Physics

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Metric components of potentials of admissible electromagnetic fields in spaces with simply transitive motion group G4 are found. The components of vector tetrads corresponding to the components of the metric tensors found by Petrov are given. The results obtained complement the coordinate-free classification given in Magazev et al. [Theor. Math. Phys. 156, 1127–1141 (2008)]. Previously, admissible electromagnetic fields were found for the case when three- and four-parameter groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets of potentials for all electromagnetic fields that admit three- and four-parameter groups of motions are known now.

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Editorial for Feature Papers 2021–2022

Abstract: This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...]

Cited by 5 publications

References 11 publications

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(IX)

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(IX)

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

Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions

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