Dynamic effects induced by renormalization in anisotropic pattern forming systems
Dynamic effects induced by renormalization in anisotropic pattern forming systems
Keller, A.; Nicoli, M.; Facsko, S.; Cuerno, R.
The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can lead to unexpected dynamical behavior. As an example we consider the anisotropic Kuramoto-Sivashinsy equation, that is a generic model of anisotropic pattern forming systems and has been derived in different instances of thin film dynamics. A rotation of a ripple pattern by 90◦ occurs in the system evolution when nonlinearities are strongly suppressed along one direction. This effect originates in non-linear parameter renormalization at different rates in the two system dimensions, showing a dynamical interplay between scale invariance and wavelength selection. Potential experimental realizations of this phenomenon are identified.
Keywords: anisotropy; renormalization; Kuramoto-Sivashinsky euqation; pattern formation
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Physical Review E 84(2011), 015202(R)
DOI: 10.1103/PhysRevE.84.015202
Cited 11 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-15615