A quasicrystallic domain wall in nonlinear dissipative patterns

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 eightfold QP pattern can be created as a broad transient layer between two domains filled by square cells (SC) oriented under an angle of 45 degrees relative to each other. A simplest particular type of 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 similar to 1. Similarly, a broad stripe of a twelvefold QP pattern can be generated as a transient region between two domains of hexagonal cells oriented at an angle of 30 degrees.