Norris, S.A. and Watson, S.J. (2012) Mean-field theory for coarsening faceted surfaces. Physical Review E, 85(2), 021608. (doi: 10.1103/PhysRevE.85.021608)
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Abstract
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics.
| Item Type: | Articles |
|---|---|
| Additional Information: | 7 pages |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Watson, Dr Stephen |
| Authors: | Norris, S.A., and Watson, S.J. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Physical Review E |
| ISSN: | 1539-3755 |
| Related URLs: |
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