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A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns

Boris A. Malomed·Horacio G. Rotstein
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Abstract

We propose an indirect approach to the generation of a two-dimensional quasiperiodic (QP) pattern in convection and similar nonlinear dissipative systems where a direct generation of stable uniform QP planforms is not possible. An {\it eightfold} QP pattern can be created as a broad transient layer between two domains filled by square cells (SC) oriented under the angle of 45 degrees relative to each other. A simplest particular type of the transient layer is considered in detail. The structure of the pattern is described in terms of a system of coupled real Ginzburg-Landau (GL) equations, which are solved by means of combined numerical and analytical methods. It is found that the transient ``quasicrystallic'' pattern exists exactly in a parametric region in which the uniform SC pattern is stable. In fact, the transient layer consists of two different sublayers, with a narrow additional one between them. The width of one sublayer (which locally looks like the eightfold QP pattern) is large, while the other sublayer (that seems like a pattern having a quasiperiodicity only in one spatial direction) has a width $\sim 1$. Similarly, a broad stripe of a {\it % twelvefold} QP pattern can be generated as a transient region between two domains of hexagonal cells oriented at the angle of 30 degrees.

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Boris A. Malomed, Horacio G. Rotstein. 2000-03-09. A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns. https://doi.org/10.1238/physica.regular.062a00164

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