Exact steady states to a nonlinear surface growth model

• Published in: The European physical journal. B, Condensed matter physics Vol. 83; no. 1; pp. 29 - 37
• Main Authors: Guedda, M., Benlahsen, M., Misbah, C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.09.2011; EDP Sciences; Springer
• Subjects: Complex Systems; Condensed Matter Physics; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Solid surfaces and solid-solid interfaces; Surface structure and topography; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Local Slope; Step Edge; Stationary Solution; Steady State Solution; Nonlinear Evolution Equation; Singularity; Vicinal surface; Numerical solution; Roughness; Crowth model; Instability; Diffusion; Non linear effect; Surface structure
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2011-20403-8

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80 , 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.