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On First-order Corrections to the LSW Theory I: Infinite Systems

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Abstract

We present a new method to efficiently identify the first-order correction to the classical model by Lifshitz, Slyozov and Wagner (LSW). The latter describes the evolution of second phase particles embedded in a matrix during the last stage of a phase transformation and is valid in the regime of vanishing volume fraction φ of particles. We consider a statistically homogeneous (and thus infinite) system, where the first-order correction is of order φ1/2. The key idea is to relate the full system of particles to systems where a finite number of particles has been removed. This method decouples screening and correlation effects and allows to efficiently evaluate conditional expected values of the particle growth rates.

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Authors and Affiliations

  1. Research center caesar, Ludwig-Erhard-Allee 22, 53175, Bonn, Germany

    Andreas Hönig

  2. Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099, Berlin

    Barbara Niethammer

  3. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 10, 53115, Bonn, Germany

    Felix Otto

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  1. Andreas Hönig
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  2. Barbara Niethammer
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  3. Felix Otto
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Correspondence to Barbara Niethammer.

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Hönig, A., Niethammer, B. & Otto, F. On First-order Corrections to the LSW Theory I: Infinite Systems. J Stat Phys 119, 61–122 (2005). https://doi.org/10.1007/s10955-004-2057-2

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