Motion of spirals by crystalline curvature
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...