Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
复制标题
周期性相分离：周期性 Cahn-Hilliard 和等周问题
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Sternberg
中科院分区：
文献类型：
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作者：
Rustum Choksi;P. Sternberg
我们考虑了与相分离现象有关的两个著名的变分问题：等周问题和Cahn-Hilliard能量的最小化。这两个问题通过一个经典的收敛结果联系在一起，我们研究了这两个问题在周期环境下的全局和局部极小点的行为。更准确地说，我们研究了定义在平面2-或3-环面上的竞争者的这些变分问题。我们将这两个问题视为周期性相分离的原型。我们完整地分析了二维周期等周问题的稳定临界点，并得到了二维和三维周期Cahn-Hilliard问题的稳定解。我们还讨论了关于三维三周期常平均曲率曲面和Cahn-Hilliard环境中可能的对应曲面的一些有趣的公开问题。
We consider two well known variational problems associated with the phenomenon of phase separation: the isoperimetric problem and minimization of the Cahn‐Hilliard energy. The two problems are related through a classical result in -convergence and we explore the behavior of global and local minimizers for these problems in the periodic setting. More precisely, we investigate these variational problems for competitors defined on the flat 2- or 3-torus. We view these two problems as prototypes for periodic phase separation. We give a complete analysis of stable critical points of the 2-d periodic isoperimetric problem and also obtain stable solutions to the 2-d and 3-d periodic Cahn‐Hilliard problem. We also discuss some intriguing open questions regarding triply periodic constant mean curvature surfaces in 3-d and possible counterparts in the Cahn‐Hilliard setting.