Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
| Autor: | Edoardo Vivo, Rodolfo Cuerno, Matteo Nicoli |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Integrable system
Surface Properties Critical phenomena Gaussian Normal Distribution FOS: Physical sciences Context (language use) Pattern Formation and Solitons (nlin.PS) symbols.namesake Computer Simulation Statistical physics Anisotropy Condensed Matter - Statistical Mechanics Ansatz Physics Condensed Matter - Materials Science Stochastic Processes Models Statistical Statistical Mechanics (cond-mat.stat-mech) Mathematical analysis Materials Science (cond-mat.mtrl-sci) Membranes Artificial Scale invariance Nonlinear Sciences - Pattern Formation and Solitons Energy Transfer symbols Linear equation |
| Zdroj: | Physical Review E. 86 |
| ISSN: | 1550-2376 1539-3755 |
| DOI: | 10.1103/physreve.86.051611 |
| Popis: | Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention, specially 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)], that 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 non-local linear equation that shares the same asymptotic properties. |
| Databáze: | OpenAIRE |
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