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 |
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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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