A universal dimensionality function for the fractal dimensions of Laplacian growth
| Autor: | J. R. Nicolás-Carlock, J. L. Carrillo-Estrada |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0301 basic medicine
Multidisciplinary lcsh:R lcsh:Medicine Function (mathematics) Fractal dimension Article 03 medical and health sciences 030104 developmental biology 0302 clinical medicine Fractal Euclidean geometry lcsh:Q Point (geometry) Statistical physics lcsh:Science Laplace operator Scaling 030217 neurology & neurosurgery Curse of dimensionality Mathematics |
| Zdroj: | Scientific Reports Scientific Reports, Vol 9, Iss 1, Pp 1-11 (2019) |
| ISSN: | 2045-2322 |
| DOI: | 10.1038/s41598-018-38084-3 |
| Popis: | 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 control parameter of the system. Numerical and theoretical approaches are used in order to determine this information-function for both DLA and DBM. In the latter, a connection to the Rényi entropies and generalized dimensions of the cluster is made, showing that DLA could be considered as the point of maximum information-entropy production along the DBM transition. The results are in good agreement with previous theoretical and numerical estimates for two- and three-dimensional DBM, and high-dimensional DLA. Notably, the DBM dimensions conform to a universal description independently of the initial cluster-configuration and the embedding-space. |
| Databáze: | OpenAIRE |
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