Boundary Dynamics of Sweeping Interface
Hiizu Nakanishi
Abstract
A new type of boundary dynamics 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 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.
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