The smoothening kinetics of a rough surface due to surface diffusion is studied theoretically. After a long time t , the surface is predicted to be flat on lengthscales smaller than R(t) ∼ t 1/3 . At higher lengthscales the roughness is almost the same as at t = 0. The method is analogous to the Lifshitz-Slyozov theory of nucleation in a supersaturated solution. Our result R ∼ t 1/3 disagrees with existing theories of smoothening.
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Jacques Villain (1986) studied this question.
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