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- ItemAnisotropy in wavelet based phase field models(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Korzec, Maciek; Münch, Andreas; Süli, Endre; Wagner, BarbaraAnisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature
- ItemA phase-field model for solid-state dewetting and its sharp-interface limit(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Dziwnik, Marion; Münch, Andreas; Wagner, BarbaraWe propose a phase field model for solid state dewetting in form of a Cahn-Hilliard equation with weakly anisotropic surface energy and a degenerate mobility together with a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. The resulting sharp interface model is consistent with the pure surface diffusion model. In addition, we show that the natural boundary conditions, as indicated from the first variation of the total free energy, imply a contact angle condition for the dewetting front, which, in the isotropic case, is consistent with the well-known Young's equation