Superexponential droplet fractalization as a hierarchical formation of dissipative compactons.
Superexponential droplet fractalization as a hierarchical formation of dissipative compactons.
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超指数液滴分形作为耗散压密子的分层形成。
DOI：
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发表时间：
2010
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通讯作者：
A. Pikovsky
中科院分区：
文献类型：
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作者：
S. Shklyaev;A. V. Straube;A. Pikovsky
本文在强非线性一维Cahn-Hilliard方程的框架下研究了衬底上薄膜的动力学行为。这种演变导致分形化成越来越小的尺度。我们证明了出现的等级结构中的一个原始元素是一个耗散子。直接模拟和自相似解的分析都表明，分形子出现在超指数递减的尺度上，这意味着分形维数的消失。
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.