Spontaneous clustering in Markov chains. IV. Clustering in turbulent environments

V. V. Uchaikin ; V. A. Litvinov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Tome 228 (2023), pp. 58-84.

Résumé

In the fourth part of the review, we discuss mathematical models of clustering that describe the behavior of impurity particles (markers, tags, etc.) in a turbulent environment. Along with the classical approach (Smoluchowski, Richardson), we describe statistical models used in computer modeling of processes (the Neyman–Scott and Metropolis models and Markov chains). Some aspects of the processes of local accumulation and gravitational sedimentation of particles in a turbulent environment are discussed. The last section is devoted to the concept of a representative sample, which is important in natural and numerical experiments. The first part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 220. — P. 125–144. The second part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 221. — P. 128–147. The third part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 222. — P. 115–133.

Détail

Mots-clés : turbulence, Markov chain
Keywords: power spectrum, radial function, numerical modeling

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