R. Thouy et al., FRAGMENTATION OF 2-DIMENSIONAL MASS FRACTALS BY SURFACE-DIFFUSION SINTERING, Physical review. B, Condensed matter, 56(9), 1997, pp. 5321-5327
The sintering process by surface diffusion of computer-generated two-d
imensional mass-fractal aggregates with tunable fractal dimension D is
numerically studied. The evolution of the contour is obtained by disc
retizing and numerically solving the relevant partial differential equ
ation, taking care of possible fragmentation and/or coalescence events
. It is shown that, when the cluster is sufficiently large, it splits
into several pieces during the sintering process which all evolve towa
rds circular shapes as time goes on. The final number of pieces is rou
ghly proportional to the surface area of the initial cluster but the p
recise way it decreases when the fractal dimension increases turns out
to be nontrivial. These general trends are explained using rough theo
retical arguments.