WWU Dissertation Prize for Dr. Annika Bach

Last week, the WWU University Management honoured the best doctors of the year 2019. The mathematician Annika Bach not only received the title "summa-cum-laude", but also a thesis prize which is endowed with 3,500 euros.

Within the field of the Calculus of Variations, this thesis (supervisor: Prof. Dr. Caterina Zeppieri) deals with the elliptic approximation of the so-called free-discontinuity functionals. The latter are variational integrals which consist of the sum of a volume term and a surface term. The minimization of free-discontinuity functionals plays a pivotal role in a variety of applied fields, such as Materials Science, Mathematical Physics, and Computer Vision. The approximations considered in this thesis are based on the so-called phase field models, with a special emphasis on the discretization of such models, which is of central importance, for instance, in numerical simulations. The discretization process introduces in the problem different approximation parameters, the interaction of which determines the limit behavior of the resulting discrete phase-filed model. Using the tool of Gamma-convergence, this work provides a quantitative description of the limit functional. In fact, it is shown that the surface term in the limit functional is highly sensitive to the interaction between the different parameters and that in some regime the discretization gives rise to a limit model where the orientation of the discontinuity surface has certain favoured directions.

In the meantime, Annika Bach has moved from Münster to Southern Germany: She is now doing postdoctoral research at the Technical University of Munich in the project "Curvature Effects in Molecular and Spin Systems" of the SFB Transregio "Discretization in Geometry and Dynamics".

More information about the Dissertation Prize: press release [de] of the University of Münster