Research seminars consist of an approximately one-hour long talk, given by team member or a guest, followed by 30 min discussion on the presented topic. They are part of the Research seminar for Differential Equations and Numerical Analysis held at the Faculty of Science, Department of Mathematics.
On Monday, February 9th, 2015, the talk at the Research seminar for Differential Equations and Numerical Analysis was held by Barbara Zwicknagl, Ph.D. (Universität Bonn).
Title: Mathematical analysis of island formation in epitaxially strained crystalline films.
Abstract: I will discuss analytical results on variational models that have been introduced in the physical literature to describe the shapes of epitaxially strained crystalline films deposited on rigid substrates, when there is a mismatch between the lattice parameters of the two crystals. The driving energy functional accounts for the elastic energy stored in the film due to a crystallographic misfit, and the surface energy of the film’s free surface. We discuss existence of optimal film profiles and some geometric properties of minimizers if they exist. The influence of a non-vanishing miscut angle is also considered. This talk is based on joint works with P. Bella and M. Goldman, and with I. Fonseca and A. Pratelli.