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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Effective Theories for Ostwald Ripening

Effective Theories for Ostwald Ripening

(p.223) 10 Effective Theories for Ostwald Ripening
Analysis and Stochastics of Growth Processes and Interface Models

Barbara Niethammer

Oxford University Press

This chapter discusses the derivation and analysis of reduced models for a coarsening process known as Ostwald ripening, which is a paradigm for statistical self-similarity in coarsening systems. The underlying physical phenomenon appears in the late stage of phase transitions, when—due to a change in temperature or pressure for example — the energy of the underlying system becomes nonconvex and prefers two different phases of the material. Consequently a homogeneous mixture is unstable and, in order to minimze the energy, it separates into the two stable phases. Typical examples are the condensation of liquid droplets in a supersaturated vapur and phase separation in binary alloys after rapid cooling.

Keywords:   Mullins-Sekerka evolution, coarsening, Ostwald ripening, self-similarity, nonconvex energy, phase separation

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