Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation

Watson, S.J. and Norris, S.A. (2006) Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation. Physical Review Letters, 96(17), p. 176103. (doi: 10.1103/PhysRevLett.96.176103)

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Abstract

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 predict the scaling law LM∼t1/3, for the growth in time t of a characteristic morphological length scale LM. A novel computational geometry tool which directly simulates a million-facet piecewise-affine dynamic surface is also introduced. Our computed data are consistent with the dynamic scaling hypothesis, and we report a variety of associated morphometric scaling functions.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Watson, Dr Stephen
Authors: Watson, S.J., and Norris, S.A.
Subjects:Q Science > QC Physics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Physical Review Letters
Journal Abbr.:Phys. Rev. Lett.
Publisher:American Physical Society
ISSN:0031-9007
ISSN (Online):1079-7114
Published Online:04 May 2006

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