Boundary dynamics of the sweeping interface.
A boundary dynamics of sweeping interface is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is formulated as the small diffusion limit of the Mullins-Sekerka problem of crystal growth. It is demonstrated that a steadily extending finger solution exists for a finite range of propagation speed, but numerical simulations suggest they are unstable and the interface shows a complex time development.
Nakanishi
Hiizu
H
Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan.