Prof. Dr. Barbara Niethammer

• Homogenization of many-particle systems

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  In this project we study the dynamics of a large number of (generalized) particles which interact in order to reduce the surface energy attached to the boundaries of the particles. We consider two model examples. The first is Ostwald Ripening, a fundamental process in the aging of materials, where particles interact through weak long range diffusional interactions. Second, we consider grain growth, where cellular structures in a plycrystalline material coarsen under capillary effects. here the interactions between grains are not weak, but localized. The general aim in this project is to understand the collective behaviour of a large number of particles; of particular interest is whether universal statistical self-similarity arises, whether correlations are built up during the evolution and how they influence the macroscopic picture.

• Mercator Gastprofessur Prof. Pego

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  Our proposed work will cover two related topics. The first is an analysis of self-similar solutions and their domain of attraction for Smoluchowski's coagulation equations with non-solvable kernels. The second project aims at a mathematical theory for Smoluchowski rate equations in epitaxial growth, more precisely a rigorous derivation of scaling limits in the regime of small Peclet number and a corresponding analysis of the long-time behaviour of solutions for general data.

• Multiple scales in phase separating systems with elastic misfit

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