论文标题
被动和主动相位晶体模型中的局部状态
Localized states in passive and active phase-field-crystal models
论文作者
论文摘要
被动保守的Swift-Hohenberg方程(或相位场晶体[PFC]模型)对应于与密度相关的单个阶参数字段的梯度动力学。它提供了简单的微观描述,描述了液体和结晶状态之间的热力学跃迁。除空间扩展的周期结构外,该模型还描述了各种稳定的空间局部结构。在适当的分叉图中,相应的溶液分支表现出特征性的倾斜同骨蛇。在活跃的PFC模型中,编码例如自propelled胶体颗粒的主动运动,梯度动力学结构通过密度和附加极化场之间的耦合而破坏。然后,发现休息和行进的局部状态,其过渡以破裂的漂移分叉为特征。 Here, we first 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 equations described by common gradient dynamics, (ii) two coupled passive PFC where the coupling breaks the gradient dynamics structure, and (iii) a passive PFC coupled to an active PFC.
The passive conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) corresponds to a gradient dynamics for 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 first 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 equations described by common gradient dynamics, (ii) two coupled passive PFC where the coupling breaks the gradient dynamics structure, and (iii) a passive PFC coupled to an active PFC.