title: Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models.
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.
authors.affiliation: Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Spain.
authors.forename: Edoardo
authors.initials: E
authors.lastname: Vivo
authors.forename: Matteo
authors.initials: M
authors.lastname: Nicoli
authors.forename: Rodolfo
authors.initials: R
authors.lastname: Cuerno
mesh_terms: D016880:Anisotropy; D003198:Computer Simulation; D004735:Energy Transfer; D008567:Membranes, Artificial; D015233:Models, Statistical; D016011:Normal Distribution; D013269:Stochastic Processes; D013499:Surface Properties
chemical_list: D008567:Membranes, Artificial