Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamics
Condensed Matter
2009-10-22 v2 Pattern Formation and Solitons
patt-sol
Abstract
It is shown that the dynamics of the growth of a two dimensional surface in a Laplacian field can be mapped onto Hamiltonian dynamics. The mapping is carried out in two stages: first the surface is conformally mapped onto the unit circle, generating a set of singularities. Then the dynamics of these singularities are transformed to Hamiltonian action-angle variables. An explicit condition is given for the existence of the transformation. This formalism is illustrated by solving explicitly for a particular case where the result is a separable and integrable Hamiltonian.
Keywords
Cite
@article{arxiv.cond-mat/9401068,
title = {Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamics},
author = {Raphael Blumenfeld},
journal= {arXiv preprint arXiv:cond-mat/9401068},
year = {2009}
}
Comments
11 pages, tex, 1 postscript figure not included (available upon request), (This version less than 80 characters per line)