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Daily Overview |
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Pms1: Partial Differential Equations with multiple scales Location: G309 Session Chair: Matthias Röger Session Chair: Ben Schweizer | |
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Stability in Variational Models for Stress Driven Pattern Formation in Crystalline Films without Subgraph Assumption Humboldt-Universität zu Berlin, Germany We investigate variational models for thin crystalline films on a rigid substrate under heteroepitaxial growth. The key feature of these models is a competition between the elastic energy, coming from a lattice mismatch, and the surface energy. Understanding the dependence and stability of energy minimisers on the underlying model parameters is of interest, one particular example being the wetting regime in which a completely flat configuration is favourable. So far these models have mostly been studied under the assumption that the geometry of the film can be described as the subgraph of a function over the substrate. We relax this restriction to allow for a larger class of competitors and are still able to establish concrete parameter thresholds for which the flat configuration is energetically stable. Based on joint work with Barbara Zwicknagl. | |
