Integrability-preserving regularizations of Laplacian Growth

Razvan Teodorescu¹

¹ 4202 E. Fowler Ave., CMC342, Tampa, FL 33620, USA.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 9.

Résumé

The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.

Détail

DOI : 10.1051/mmnp/2019032

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