论文标题
耦合的cahn-hilliard方程中的局部状态
Localized states in coupled Cahn-Hilliard equations
论文作者
论文摘要
经典的Cahn-Hilliard（CH）方程对应于描述二元混合物中相位分解的梯度动力学模型。在Spinodal区域中，最初的均匀状态通过大规模的不稳定性自发分解为典型结构长度的滴，孔或迷宫浓度模式，然后是连续持续的粗化过程。在这里，我们考虑了两个浓度场的耦合CH动力学，并表明非偏置（或活性或非不同）耦合可能会引起小规模（图灵）的不稳定性。在相应的主要分叉处，出现了定期模式的稳态分支。此外，存在局部状态，这些状态包括与均匀背景共存的图案化贴片。稳定的平等对称和平价 - 对称局部状态的分支形成了具有保护定律的系统典型的倾斜的同型蛇形结构。与具有梯度动力学的系统中的缝制结构相反，在这里，HOPF不稳定性发生在足够大的活动中，从而导致振荡和行进的局部模式。
The classical Cahn-Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale instability into drop, hole or labyrinthine concentration patterns of a typical structure length followed by a continuously ongoing coarsening process. Here we consider the coupled CH dynamics of two concentration fields and show that nonreciprocal (or active, or nonvariational) coupling may induce a small-scale (Turing) instability. At the corresponding primary bifurcation a branch of periodically patterned steady states emerges. Furthermore, there exist localized states that consist of patterned patches coexisting with a homogeneous background. The branches of steady parity-symmetric and parity-asymmetric localized states form a slanted homoclinic snaking structure typical for systems with a conservation law. In contrast to snaking structures in systems with gradient dynamics, here, Hopf instabilities occur at sufficiently large activity which result in oscillating and traveling localized patterns.
