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Abstract: We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral droplet. We also...
Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential
Laplacian Growth Elliptic Growth Singularities Schwarz Potential
2010/12/13
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or \Hele-Shaw\) problem in the plane.
We investigate a version of the Laplacian growth problem with zero surface tension in the half plane and find families of self-similar exact solutions.
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc....