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Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

Published online by Cambridge University Press:  16 March 2016

Kai Jiang ,
Jiajun Tong  and
Pingwen Zhang
Kai Jiang
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, P.R. China
Jiajun Tong
Affiliation:
School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China
Pingwen Zhang*
Affiliation:
LMAM, CAPT and School of Mathematical Sciences, Peking University, Beijing, 100871P.R. China
*
*Corresponding author. Email addresses:kaijiang@xtu.edu.cn (K. Jiang), jiajun.tong@nyu.edu (J. Tong), pzhang@pku.edu.cn (P. Zhang)
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Abstract

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.

Keywords

Quasicrystalscoupled-mode Swift-Hohenberg modelvariable cell methodprojection methodphase diagram
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 559 - 581
Copyright
Copyright © Global-Science Press 2016 

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