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	DYNAMIC TRANSITIONS AND PATTERN FORMATIONS FOR A CAHN-HILLIARD MODEL WITH LONG-RANGE REPULSIVE INTERACTIONS
	Liu, Honghu ; Sengul, Taylan ; Wang, Shouhong ; Zhang, Pingwen
	2015
关键词	Phase transition pattern formation long-range interaction a Cahn-Hilliard model center manifold reduction hexagonal pattern MICROPHASE SEPARATION DIBLOCK COPOLYMERS SPINODAL DECOMPOSITION
英文摘要	The main objective of this article is to study the order-disorder phase transition and pattern formation for systems with long-range repulsive interactions. The main focus is on a Cahn-Hilliard model with a nonlocal term in the corresponding energy functional, representing certain long-range repulsive interaction. We show that as soon as the trivial steady state loses its linear stability, the system always undergoes a dynamic transition of one of three types - continuous, catastrophic and random - forming different patterns/structures, such as lamellae, hexagonally packed cylinders, rectangles, and spheres. The types of transitions are dictated by a non-dimensional parameter, measuring the interactions between the long-range repulsive term and the quadratic and cubic nonlinearities in the model. In particular, the hexagonal pattern is unique to this long-range interaction, and it is captured by the corresponding two-dimensional reduced equations on the center manifold, which involve (degenerate) quadratic terms and non-degenerate cubic terms. Explicit information on the metastability and basins of attraction of different ordered states, corresponding to different patterns, are derived as well.; Office of Naval Research; National Science Foundation; SCI(E); ARTICLE; hliu@atmos.ucla.edu; taylansengul@gmail.com; showang@indiana.edu; pzhang@pku.edu.cn; 5; 1289-1315; 13
语种	英语
出处	SCI
出版者	COMMUNICATIONS IN MATHEMATICAL SCIENCES
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/423303]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, Honghu,Sengul, Taylan,Wang, Shouhong,et al. DYNAMIC TRANSITIONS AND PATTERN FORMATIONS FOR A CAHN-HILLIARD MODEL WITH LONG-RANGE REPULSIVE INTERACTIONS. 2015-01-01.

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