Existence of pearled patterns in the planar functionalized Cahn–Hilliard equation
Existence of pearled patterns in the planar functionalized Cahn–Hilliard equation
复制标题
平面函数化 Cahn-Hilliard 方程中珍珠图案的存在
DOI：
10.1016/j.jde.2015.04.022
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发表时间：
2014
影响因子：
2.4
通讯作者：
Qi
中科院分区：
文献类型：
--
作者：
K. Promislow;Qi
功能化 Cahn-Hilliard (FCH) 方程支持平面和圆形双层界面作为平衡，这可能会因珠光分岔而失去稳定性：双层厚度的周期性、高频、面内调制。在二维空间维度中，我们采用空间动力学和中心流形约简将 FCH 方程简化为 8 阶 ODE 系统。范式分析和不动点定理论证表明，简化系统承认简并的 1:1 共振范式，由此我们推断珠光分岔的开始与珠光平衡的双参数族的创建相一致，该族在面内方向上呈周期性，在横向上呈指数局域化。
The functionalized Cahn–Hilliard (FCH) equation supports planar and circular bilayer interfaces as equilibria which may lose their stability through the pearling bifurcation: a periodic, high-frequency, in-plane modulation of the bilayer thickness. In two spatial dimensions we employ spatial dynamics and a center manifold reduction to reduce the FCH equation to an 8th order ODE system. A normal form analysis and a fixed-point-theorem argument show that the reduced system admits a degenerate 1:1 resonant normal form, from which we deduce that the onset of the pearling bifurcation coincides with the creation of a two-parameter family of pearled equilibria which are periodic in the in-plane direction and exponentially localized in the transverse direction.
DOI：
10.1103/physreve.79.031926
发表时间：
2009-03
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
Lowengrub JS;Rätz A;Voigt A
通讯作者：
Voigt A