Localized states in passive and active phase-field-crystal models
Localized states in passive and active phase-field-crystal models
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DOI：
10.1093/imamat/hxab025
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发表时间：
2020-10
影响因子：
1.2
通讯作者：
Max Philipp Holl;A. Archer;S. Gurevich;E. Knobloch;Lukas Ophaus;U. Thiele
中科院分区：
文献类型：
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作者：
Max Philipp Holl;A. Archer;S. Gurevich;E. Knobloch;Lukas Ophaus;U. Thiele
被动守恒的Swift-Hohenberg方程(或称相场-晶体[PFC]模型)描述了与密度有关的一阶参数场的梯度动力学。它对液态和晶态之间的热力学转变提供了一个简单的微观描述。除了空间扩展的周期结构外，该模型还描述了大量稳定的空间局域结构。在适当的分岔图中，相应的解分支表现出典型的倾斜同宿蛇形。在主动PFC模型中，例如编码自推进胶体粒子的主动运动，密度和附加极化场之间的耦合打破了梯度动力学结构。然后，发现了具有宇称破缺漂移分叉特征的跃迁的静止态和行进局域态。本文首先简要回顾了无源和有源PFC模型中局域态的蛇行行为，然后讨论了(I)两个耦合的具有共同梯度动力学的无源PFC模型，(Ii)两个耦合的无源PFC模型，其中耦合打破了梯度动力学结构，以及(Iii)一个无源PFC模型与一个有源PFC模型耦合的系统的局域态的分叉行为。
The passive conserved Swift–Hohenberg equation (or phase-field-crystal [PFC] model) describes gradient dynamics of a single-order parameter field related to density. It provides a simple microscopic description of the thermodynamic transition between liquid and crystalline states. In addition to spatially extended periodic structures, the model describes a large variety of steady spatially localized structures. In appropriate bifurcation diagrams the corresponding solution branches exhibit characteristic slanted homoclinic snaking. In an active PFC model, encoding for instance the active motion of self-propelled colloidal particles, the gradient dynamics structure is broken by a coupling between density and an additional polarization field. Then, resting and traveling localized states are found with transitions characterized by parity-breaking drift bifurcations. Here, we briefly review the snaking behavior of localized states in passive and active PFC models before discussing the bifurcation behavior of localized states in systems of (i) two coupled passive PFC models with common gradient dynamics, (ii) two coupled passive PFC models where the coupling breaks the gradient dynamics structure and (iii) a passive PFC model coupled to an active PFC model.