Dynamic effects induced by renormalization in anisotropic pattern forming systems
Abstract
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 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
Cite
@article{arxiv.1203.2536,
title = {Dynamic effects induced by renormalization in anisotropic pattern forming systems},
author = {Adrian Keller and Matteo Nicoli and Stefan Facsko and Rodolfo Cuerno},
journal= {arXiv preprint arXiv:1203.2536},
year = {2015}
}
Comments
5 pages, 3 figures; supplemental material available at journal web page and/or on request