Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-03-12
Phys. Rev. E 84, 015202(R) (2011); Phys. Rev. E 85, 029905(E) (2012)
Physics
Condensed Matter
Statistical Mechanics
5 pages, 3 figures; supplemental material available at journal web page and/or on request
Scientific paper
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-Sivashinsky 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 $90^{\circ}$ 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.
Cuerno Rodolfo
Facsko Stefan
Keller Adrian
Nicoli Matteo
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