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arXiv · 1001.4996

Superexponential droplet fractalization as a hierarchical formation of dissipative compactons

Sergey Shklyaev·Arthur V. Straube·Arkady Pikovsky
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Abstract

We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hillard 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, what means vanishing dimension of the fractal.

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Sergey Shklyaev, Arthur V. Straube, Arkady Pikovsky. 2010-01-27. Superexponential droplet fractalization as a hierarchical formation of dissipative compactons. https://doi.org/10.1103/physreve.82.020601

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