S. J. Watson & S. A. Norris, "Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation", Physical Review Letters vol. 96 (17), Art. No. 176103 (2006). We consider the coarsening dynamics of multiscale solutions to a dissipative singularly perturbed partial differential equation which models the evolution of a thermodynamically unstable crystalline surface. The late-time leading-order behavior of solutions is identified, through the asymptotic expansion of a maximal dissipation principle, with a completely faceted surface governed by an intrinsic dynamical system. The properties of the resulting Piecewise-Affine Dynamic Surface (PADS) predict the power-law scaling law L ~ t^{1/3}, for the growth in time t of a characteristic morphological length scale L. We also introduce a novel computational geometry tool which directly simulates a million-facet (PADS) by explicitly treating all the associated topological and critical events that arise as the surface coarsens. Our computed data is consistent with the dynamic scaling hypothesis and we report a variety of associated morphometric scaling-functions.

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