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A Baker Function for Laplacian Growth and Phase Transitions

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CATW01 - The complex analysis toolbox: new techniques and perspectives

Laplacian growth describes the evolution of an incompressible fluid droplet with zero surface tension in 2D, as fluid is pumped through a well into the droplet. A major obstacle in the theory of Laplacian growth is the formation of finite-time singularities (cusps) that form on the boundary of the fluid droplet. Although some work has been done with regards to continuation of the solution past this critical point, most results are phenomenological in nature, and a general theory is yet to be developed. Due to Laplacian growth's realization as a dispersionless limit of the 2D Toda Hierarchy, we investigate certain scaling limits of this hierarchy's Baker function. We pose the question, “what can the Baker function tell us about phase transitions in the droplet?”, for particular classes of initial domains.

This talk is part of the Isaac Newton Institute Seminar Series series.

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