Please use this identifier to cite or link to this item: https://doi.org/10.1016/S0167-2789(02)00737-6
Title: Geometry and boundary control of pattern formation and competition
Authors: Guan, S. 
Lai, C.-H. 
Wei, G.W. 
Keywords: Cahn-Hilliard equation
Circular domain
Controlling pattern formation
Fourier-Bessel analysis
Issue Date: 15-Feb-2003
Source: Guan, S., Lai, C.-H., Wei, G.W. (2003-02-15). Geometry and boundary control of pattern formation and competition. Physica D: Nonlinear Phenomena 176 (1-2) : 19-43. ScholarBank@NUS Repository. https://doi.org/10.1016/S0167-2789(02)00737-6
Abstract: This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn-Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed to provide high-precision numerical solutions. By extensive numerical experiments, a set of cellular ordered state patterns are generated. Theoretical analysis is carried out by using the Fourier-Bessel series. Modal decomposition shows that the pattern morphology of an ordered state pattern is dominated by a principal Fourier-Bessel mode, which has the largest Fourier-Bessel decomposition amplitude. Interesting modal competition is also observed. It is found that the formation and competition of cellular patterns are effectively controlled by the confined geometry and boundary condition. © 2002 Elsevier Science B.V. All rights reserved.
Source Title: Physica D: Nonlinear Phenomena
URI: http://scholarbank.nus.edu.sg/handle/10635/96724
ISSN: 01672789
DOI: 10.1016/S0167-2789(02)00737-6
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