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Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

Javier Muñoz-García, Rodolfo Cuerno, and Mario Castro
Phys. Rev. E 74, 050103(R) – Published 30 November 2006

Abstract

A local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.

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  • Received 30 May 2006

DOI:https://doi.org/10.1103/PhysRevE.74.050103

©2006 American Physical Society

Authors & Affiliations

Javier Muñoz-García1, Rodolfo Cuerno1, and Mario Castro2

  • 1Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Spain
  • 2GISC and Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, E-28015 Madrid, Spain

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Issue

Vol. 74, Iss. 5 — November 2006

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