Multiple scales in phase separating systems with elastic misfit

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It is the aim of this project to study morphological changes in alloys with elastic misfit by developing, analyzing and relating models corresponding to different length scales inherent in this process. It is planed to analyze the relationship of models for these phenomena that are formulated on different length scales. Here, in particular the relation between the elastically modified Cahn-Hilliard model and sharp interface models will be studied. Furthermore, we want to understand the statistical behaviour of the evolution of particles, e.g. growth rates for the average particle size will be studied. Different length scales and elastic interactions are also important in the growth of thin solid films. Issues will be: (in)stability of the film surface, coarsening and numerical simulations. Furthermore, we will consider efficient numerical methods for the macroscopic as well as the mesoscopic model in these phase separation problems with elastic effects. Appropriate time step schemes and adaptive multilevel finite elements in space enable the adequate resolution of Cahn-Hilliard models with moderately many particles. Multipole type methods for the sharp interface model, with build in restrictions on the particle shape and interaction type will be studied for systems with very many particles. Statistical evaluations of growth rates and the structure of the particle environment are indended.