论文标题
在具有非不同耦合的Cahn-Hilliard模型中抑制振荡和出现振荡行为
Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
论文作者
论文摘要
我们研究了具有变异和非不同耦合的通用两场Cahn-Hilliard模型。它分别描述了被动和主动三元混合物。已经对均质混合状态进行了线性稳定性分析表明，活动不仅允许众所周知的被动案例的通常大规模固定（Cahn-Hilliard）不稳定性，而且还允许小型固定（Turing）和大型振动性（Hopf）不稳定性。由于图灵的不稳定性，活动可能会完全抑制通常的粗糙动力学。在完全非线性分析中，我们首先在关注活性情况之前先简要讨论被动案例。提出了分叉图和选定的直接时间模拟，使我们能够确定非不同的耦合（i）可以部分或完全抑制粗糙的凝结，并且（ii）可能导致出现漂移和振荡状态。在整个过程中，我们强调了遇到复杂的分叉行为的保护定律和相关对称性的相关性。
We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.
