Published August 12, 2010
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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.
Additional Information
© 2010 The American Physical Society. Received 27 January 2010; published 12 August 2010. We are grateful to A. Nepomnyashchy, A. Oron, M. Zaks, Ph. Rosenau, D. Lyubimov, and D. Goldobin for stimulating discussions. The research was supported by German Science Foundation DFG Projects No. 436 RUS113/977/0-1 and No. STR 1021/1-2 and Russian Foundation for Basic Research Project No. 08-01-91959.Attached Files
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Additional details
- Eprint ID
- 19728
- Resolver ID
- CaltechAUTHORS:20100831-084042191
- 436 RUS113/977/0-1
- German Science Foundation (DFG)
- STR 1021/1-2
- German Science Foundation (DFG)
- 08-01-91959
- Russian Foundation for Basic Research
- Created
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2010-09-01Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field