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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