Abstract
We study a recently proposed 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)]. A careful numerical analysis shows that the dynamically selected step profile consists of sloped segments, given by an inverse error function and steepening as sqrt[t], which are matched to pieces of a stationary (time-independent) solution describing the maxima and minima. The effect of smoothening by step-edge diffusion is included heuristically, and a one-parameter family of evolution equations is introduced that contains relaxation by step-edge diffusion and by attachment-detachment as special cases. The question of the persistence of an initially imposed meander wavelength is investigated in relation to recent experiments.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.