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Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models

Edoardo Vivo1, Matteo Nicoli2, and Rodolfo Cuerno1

  • 1Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Spain
  • 2Physique de la Matière Condensée, École Polytechnique-CNRS, 91128 Palaiseau, France

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Phys. Rev. E 86, 051611 – Published 29 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.051611

Abstract

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received relatively less attention, especially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g., in the context of thin-film production by diverse techniques. Based on exact results for integrable (linear) cases, here we formulate a SA ansatz that, albeit equivalent to existing ones borrowed from equilibrium critical phenomena, is more naturally adapted to the type of observables that are measured in experiments on the dynamics of thin films, such as one- and two-dimensional height structure factors. We test our ansatz on a paradigmatic nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar equation [Phys. Rev. Lett. 62, 1813 (1989)], which was initially proposed to describe the interface dynamics of running sand piles. A very important role to elucidate its SA properties is played by an accurate (Gaussian) approximation through a nonlocal linear equation that shares the same asymptotic properties.

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Phys. Rev. E 86, 051611– Published 29 November, 2012
  • Received 7 August 2012

©2012 American Physical Society

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