Frohoff-Hülsmann Tobias, Wrembel Jana, Thiele Uwe
Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.
Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany.
Phys Rev E. 2021 Apr;103(4-1):042602. doi: 10.1103/PhysRevE.103.042602.
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.
我们研究了一个具有变分和非变分耦合的通用双场Cahn-Hilliard模型。例如，它分别描述了被动和主动三元混合物。对均匀混合态的线性稳定性分析表明，活性不仅允许著名的被动情况下常见的大规模稳态（Cahn-Hilliard）不稳定性，还允许小规模稳态（图灵）和大规模振荡（霍普夫）不稳定性。由于图灵不稳定性，活性可能会完全抑制通常的粗化动力学。在全非线性分析中，我们首先简要讨论被动情况，然后重点关注主动情况。给出了分岔图和选定的直接时间模拟，这使我们能够确定非变分耦合（i）可以部分或完全抑制粗化，（ii）可能导致漂移和振荡状态的出现。在整个过程中，我们强调守恒定律和相关对称性对于所遇到的复杂分岔行为的相关性。
