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A hyperbolic flow by mean curvature equation, R #v", for the evolution of interfaces is studied. Here v, and R are the normal velocity, curvature and normal acceleration of the interface. A crystalline algorithm is developed for the motion of closed convex polygonal curves; such curves may exhibit damped oscillations and their shape appears to rotate during… (More)

We present a phenomenological theory for phase transition dynamics with memory which yields a hyperbolic generalization of the classical phase field model when the relaxation kernels are assumed to be exponential. Thereafter, we focus on the implications of our theory in the hyper-bolic case, and we derive asymptotically an equation of motion in two… (More)

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