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 (33)
- Integrable Hierarchies and Dispersionless Limit
- Integrable Structure of Interface Dynamics
- 2D growth processes: SLE and Loewner chains
- Conformal maps and dispersionless integrable hierarchies
- Laplacian growth as one-dimensional turbulence
- Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions
- Large n limit of Gaussian random matrices with external source, part I
- Normal random matrix ensemble as a growth problem
- Asymptotics of the instantons of Painleve I
- Laplacian Growth and Whitham Equations of Soliton Theory
- A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation
- Density of eigenvalues of random normal matrices
- Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains
- Selection of the Saffman-Taylor Finger Width in the Absence of Surface Tension: an Exact Result
- Topology of quadrature domains
- Large scale correlations in normal and general non-Hermitian matrix ensembles
- Painleve I asymptotics for orthogonal polynomials with respect to a varying quartic weight
- Hastings-Levitov aggregation in the small-particle limit
- Scaling limits of anisotropic Hastings-Levitov clusters
- Laplacian growth with separately controlled noise and anisotropy
- 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
- Small particle limits in a regularized Laplacian random growth model
- Theory of stochastic Laplacian growth
- Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
- Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion
- Stochastic Laplacian growth
- Generic critical points of normal matrix ensembles
- Statistical mechanics of stochastic growth phenomena
- Weak solution of the Hele-Shaw problem: shocks and viscous fingering