Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems (Communications in Computational Physics, 2018)
In this article, we discuss the stability of soft quasicrystalline phases in acoupled-mode Swift-Hohenberg model for three-component systems, where the characteristiclength scales are governed by the positive-definite gradient terms. Classictwo-mode approximation method and direct numerical minimization are applied tothe model. In the latter approach, we apply the projection method to deal with the potentiallyquasiperiodic ground states. A variable cell method of optimizing the shapeand size of higher-dimensional periodic cell is developed to minimize the free energywith respect to the order parameters. Based on the developed numerical methods,we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverseperiodic phases and complex modulated phases. Furthermore, phase diagrams areobtained in various phase spaces by comparing the free energies of different candidatestructures. It does show not only the important roles of system parameters, but alsothe effect of optimizing computational domain. In particular, the optimization of computationalcell allows us to capture the ground states and phase behavior with higherfidelity. We also make some discussions on our results and show the potential of applyingour numerical methods to a larger class of mean-field free energy functionals.