Nonuniversality in Low-Volume-Fraction Ostwald Ripening |
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Authors: | Sergio Conti Andreas Hönig Barbara Niethammer Felix Otto |
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Institution: | 1. Fachbereich Mathematik, Universit?t Duisburg-Essen, Lotharstr. 65, 47057, Duisburg, Germany 2. CAESAR Institute, Ludwig-Erhard-Allee 22, 53175, Bonn, Germany 3. Institut für Mathematik, Humboldt Universit?t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany 4. Institut für Angewandte Mathematik, Universit?t Bonn, Wegelerstrasse 6, 53115, Bonn, Germany
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Abstract: | We study Ostwald ripening in the regime of small volume fraction and consider spatially periodic systems whose size is smaller than the screening length. Within the snapshot perspective we obtain an explicit characterization of the leading-order deviation to the classical mean-field theory by Lifshitz, Slyozov and Wagner (LSW). Using this representation, we show that the corrections are not universal, in the sense that the mean value has a strong dependence on geometry, and arbitrarily large fluctuations can happen with finite probability.
AMS Subject classification: 35B27, 74N20, 82C26. |
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Keywords: | Ostwald ripening monopole approximation |
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