A universal dimensionality function for the fractal dimensions of Laplacian growth.

ABSTRACT: Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic fractal/non-fractal morphologies. However, despite diverse numerical and theoretical attempts, a data-consistent description of the fractal dimensions of the mass-distributions of these structures has been missing. Here, an analytical model of the fractal dimensions of the DBM and DLA is provided by means of a recently introduced dimensionality equation for the scaling of clusters undergoing a continuous morphological transition. Particularly, this equation relies on an effective information-function dependent on the Euclidean dimension of the embedding-space and the cont

SUBMITTER: Nicolas-Carlock JR 

PROVIDER: S-EPMC6362037 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature