Superexponential droplet fractalization as a hierarchical formation of dissipative compactons

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.

arXiv comment4 pages, 5 figures, submitted

References in corpus (1)

• Long-Wavelength Instability in Surface-Tension-Driven Benard Convection

Cited by in corpus (2)

• Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
• Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows