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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - Jul 5 2006|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics