Scaling of the Euler characteristic, surface area, and curvatures in the phase separating or ordering systems

  • Fiałkowski M
  • Aksimentiev A
  • Hołyst R
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We present robust scaling laws for the Euler characteristic and curvatures applicable to any symmetric system undergoing phase separating or ordering kinetics. We apply it to the phase ordering in a system of the nonconserved scalar order parameter and find three scaling regimes. The appearance of the preferred nonzero curvature of an interface separating $\ifmmode\pm\else\textpm\fi{}$ domains marks the crossover to the late stage regime characterized by the Lifshitz-Cahn-Allen scaling.

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