Self-similarity in Laplacian Growth

Details Self-similarity in Laplacian Growth Self-similarity in Laplacian Growth

2006-06-27

arxiv.org/abs/nlin/0606068v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 9 figures

Scientific paper

10.1016/j.physd.2007.04.012

We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the integral equation for the conformal map. It is shown that solutions to the integral equation obey also a second order differential equation which is the one dimensional Schroedinger equation with the sinh inverse square potential. The solutions, which are expressed through the Gauss hypergeometric function, characterize the geometry of self-similar patterns in a wedge. We also find the potential for the Coulomb gas representation of the self-similar Laplacian growth in a wedge and calculate the corresponding free energy.

Affiliated with

Also associated with

No associations

Rating

Self-similarity in Laplacian Growth does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Self-similarity in Laplacian Growth, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Self-similarity in Laplacian Growth will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-535539