| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Growth phenomena
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/mmnp/2019033 | |
| Published online | 14 February 2020 | |
On integrability and exact solvability in deterministic and stochastic Laplacian growth
Laboratoire de Physique Mathematique, Centre de recherches mathématiques, Université de Montréal,
P.O. Box 6128,
Centre-ville Station Montréal (Québec)
H3C 3J7, Canada.
* Corresponding author: loutseni@crm.umontreal.ca
Received:
31
January
2019
Accepted:
18
July
2019
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.
Mathematics Subject Classification: 31B20 / 35R35 / 82B24 / 76M40 / 76D27 / 37K10 / 15B52 / 60J67
Key words: Laplacian growth / elliptic growth / integrable and exactly-solvable models / multi-fractal systems
© EDP Sciences, 2020
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