Integrability-preserving regularizations of Laplacian Growth
arXiv:2405.06167 · doi:10.1051/mmnp/2019032
Abstract
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.
References in corpus (7)
- 2D growth processes: SLE and Loewner chains
- Normal random matrix ensemble as a growth problem
- Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy
- Planar elliptic growth
- Random Matrices in 2D, Laplacian Growth and Operator Theory
- Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent
- Shocks and finite-time singularities in Hele-Shaw flow