title: 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-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.
authors.affiliation: Department of Chemical Engineering, California Institute of Technology, Pasadena, 91125, USA.
authors.forename: Sergey
authors.initials: S
authors.lastname: Shklyaev
authors.forename: Arthur V
authors.initials: AV
authors.lastname: Straube
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky