平面函数化Cahn-Hilliard方程中的波动双层界面
Undulated Bilayer Interfaces in the Planar Functionalized Cahn-Hilliard Equation
摘要：
用二嵌段共聚物熔体的实验显示出源自缺陷如三重连接和端盖\cite{batesjain_2004}的波状双层。起伏双层的特征在于双层宽度的振荡扰动，其在比双层宽度长的空间长度尺度上衰减。我们模仿缺陷内的功能化的Cahn-Hillard自由能通过引入空间局部化的不均匀性在其参数。对于长度参数$\varepsilon\ll1$，我们表明，这会导致起伏的双层解决方案，其宽度扰动衰减的$O\!\left(\varepsilon^{-1/2}\right)$内的长度尺度是长的相比，$O(1)$规模的双层宽度的特征。
英文摘要：
Experiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, \cite{batesjain_2004}. Undulated bilayers are characterized by oscillatory perturbations of the bilayer width, which decay on a spatial length scale that is long compared to the bilayer width. We mimic defects within the functionalized Cahn-Hillard free energy by introducing spatially localized inhomogeneities within its parameters. For length parameter $\varepsilon\ll1$, we show that this induces undulated bilayer solutions whose width perturbations decay on an $O\!\left(\varepsilon^{-1/2}\right)$ inner length scale that is long in comparison to the $O(1)$ scale that characterizes the bilayer width.
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