Курс лекций профессора Марка Минеева (Лос-Аламос, США) "Integrable Laplacian Growth (Critical Account)"
Курс лекций по теме:
"Integrable Laplacian Growth (Critical Account)"
1. Introduction:Experimental background in physics, geophysics, and biophysics.
Classical background in the Inverse Potential Problem and the dynamical systems with a "pole decomposition".
2. Pattern selection far from equilibrium:The Saffman-Taylor finger, failed
attempts to include surface tension into the theory. The infinite list of the
conservation laws. Exact singular solutions (which blow up in a finite time).
3. Non-singular exact solutions and the selection without
surface tension: genus zero, genus one, and arbitrary genus (multi-bubble
4. Integrable structure of Laplacian growth: quantum gravity, two-
dimensional Toda hierarchy, and LG in terms of normal random matrices.
Relations to existing integrable systems of the hydrodynamic type.
5. Universal fractal growth of diffusion-limited aggregation. Stochastic
Laplacian growth. Tau-function and the statistical mechanics of unstable
6. If time permits, I'll also deliver a sixth lecture on integrable structure of
other unstable processes, such as a Stokes growth and a