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On First-order Corrections to the LSW Theory II: Finite Systems

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Abstract

We consider first–order corrections to the classical theory by Lifshitz, Slyozov and Wagner (LSW) for systems with a finite number of particles. Numerical simulations in V. E Fradkov etal. [Phys. Rev. E 53:3925–3932 (1996)] show a cross–over in the scaling of the correction term from φ1/3 to φ1/2 (φ is the volume fraction of particles), when the system size becomes larger than the screening length. We rigorously derive this cross–over for the rate of change of the energy, starting from the monopole approximation. The proof exploits the fact that the rate of change of energy has a variational characterization.

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Authors and Affiliations

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

    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

    Felix Otto

Authors
  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 II: Finite Systems. J Stat Phys 119, 123–164 (2005). https://doi.org/10.1007/s10955-004-2058-1

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  • DOI: https://doi.org/10.1007/s10955-004-2058-1

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