Scaling behavior of the time-fractional equations for molecular-beam epitaxy growth: scaling analysis versus numerical stimulations
Department of Physics, China University of Mining and Technology, Xuzhou, 221116, P.R. China
Revised: 29 June 2009
Published online: 18 August 2009
The scaling behavior of the time-fractional molecular-beam epitaxy (TFMBE) equations in 1+1 dimensions is investigated by numerical simulations and scaling analysis, respectively. The growth equations studied include the time-fractional linear molecular-beam epitaxy (TFLMBE) and the time-fractional Lai-Das Sarma-Villain (TFLDV). Growth exponents are obtained using the two methods. The analytical results are consistent with the corresponding numerical solutions based on Caputo-type fractional derivative.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 45.10.Hj – Perturbation and fractional calculus methods / 68.35.Fx – Diffusion; interface formation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009