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.
Shklyaev
Sergey
S
Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125, USA.
Straube
Arthur V
AV
Pikovsky
Arkady
A