Superexponential droplet fractalization as a hierarchical formation of dissipative compactons
- We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal.
Author details: | Sergey Shklyaev, Arthur V. Straube |
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URL: | http://pre.aps.org/ |
DOI: | https://doi.org/10.1103/Physreve.82.020601 |
ISSN: | 1539-3755 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2010 |
Publication year: | 2010 |
Release date: | 2017/03/24 |
Source: | Physical Review E. - ISSN 1539-3755. - 82 (2010), 2, Art. 020601 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |