On integrability and exact solvability in deterministic and stochastic Laplacian growth

Igor Loutsenko¹ ; Oksana Yermolayeva¹

¹ Laboratoire de Physique Mathematique, Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station Montréal (Québec) H3C 3J7, Canada.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 3.

Résumé

We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions.

Détail

DOI : 10.1051/mmnp/2019033

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