Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamics

Details Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamics Two-dimensional Laplacian growth can be mapped onto Hamiltonian dynamics

1994-01-28

arxiv.org/abs/cond-mat/9401068v2

Physics

Condensed Matter

11 pages, tex, 1 postscript figure not included (available upon request), (This version less than 80 characters per line)

Scientific paper

10.1016/0375-9601(94)91177-0

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.

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