https://doi.org/10.1140/epjb/e2009-00289-9
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
Corresponding authors: a xiahui_cumt@163.com - b gangtang@cumt.edu.cn
Received:
10
March
2009
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
