Growth rate of crystal surfaces with several dislocation centers
  We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method for spirals by the authors (Journal of Scientific Computing 62, 831-874, 2015). We carefully compare our simulation results on the growth rates with predictions in a classical paper by Burton et al. (Philos Trans R Soc Lond Ser A Math Phys Sci 243,299-358, 1951). Then, we propose improved estimates on the growth rate with several different configurations, which are in agreement with our numerical simulations. The influence of distribution of screw dislocations in a group on a line to the growth rate, and the growth rate by a group including different rotational orientations of spirals are also studied in this paper. 
Takeshi Ohtsuka, Yen-Hsi Richard Tsai, and Yoshikazu Giga
cond-mat.mtrl-sci math-ph math.MP math.NA