Dynamics in classical mean-field models for Ostwald ripening

Ostwald Ripening, a fundamental process in the aging of materials,   denotes the last stage in a phase transition in binary mixtures. Particles of a new phase interact to reduce their total surface energy. As a result larger particles grow at the expense of smaller one, which results in a coarsening of the microstructure. An important feature of this process is its statistical self-similarity, which means that   the patterns at different times look identical after rescaled by one typical length scale.

In the nowadays classical theory by Lifshitz-Slyozov and Wagner ("LSW") this process is described by a nonlocal evolution equation for the   particle size distribution. For this model universal self-similar large-time behavior is predicted. However, a mathematically rigorous analysis reveals that in strong contrast to these  predictions the large time dynamics are not universal but depend sensitively on the initial data. We will give an overview of the results on the long-time dynamics of the LSW model and will also discuss possible mechanisms which could provide a regularization of the model which overcomes the above described weak selection problem.

Barbara Niethammer

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