Superexponential droplet fractalization as a hierarchical formation of dissipative compactons

Details Superexponential droplet fractalization as a hierarchical formation of dissipative compactons Superexponential droplet fractalization as a hierarchical formation of dissipative compactons

2010-01-27

arxiv.org/abs/1001.4996v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 5 figures, submitted

Scientific paper

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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