Non-Laplacian growth, algebraic domains and finite reflection groups
Mathematical Physics
2009-11-11 v3 High Energy Physics - Theory
Complex Variables
math.MP
Fluid Dynamics
Abstract
Dynamics of planar domains with moving boundaries driven by the gradient of a scalar field that satisfies an elliptic PDE is studied. We consider the question: For which kind of PDEs the domains are algebraic, provided the field has singularities at a fixed point inside the domain? The construction reveals a direct connection with the theory of the Calogero-Moser systems related to finite reflection groups and their integrable deformations.
Keywords
Cite
@article{arxiv.math-ph/0601066,
title = {Non-Laplacian growth, algebraic domains and finite reflection groups},
author = {Igor Loutsenko and Oksana Yermolayeva},
journal= {arXiv preprint arXiv:math-ph/0601066},
year = {2009}
}