WIAS Research Highlights

Research results are highlighted that have been achieved with the goal of formulating of a general mathematical structure that supports the mathematical modeling and analysis of processes with bulk-interface coupling in a variational framework

The microscope, from its invention in the seventeenth century to modern transmission electron microscopy (TEM), has revolutionized the fields of science and technology. We explore the structure and composition of materials such as semiconductor quantum dots and discover how mathematical theory plays a critical role in solving the reconstruction problem and automated processing of TEM images.

Thinking of everyday biochemical processes, chemical reaction systems are intrinsically of multi-scale nature, which involves many challenging difficulties. We show, how, in a thermodynamical consistent way, the complexity can be reduced by deriving effective gradient systems. This reduction procedure uncovers previously unknown physical structures, and hence, provide theoretical insights in chemical reaction systems.

The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. It allows to estimate the integration error when approximating spherical integrals. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates. We provide a fully explicit, easy to implement formula for the spherical cap discrepancy.

Perovskite solar cells outperform classical silicon solar cells, presenting an efficient green energy solution. Unfortunately, they degrade too fast. So how can we further improve efficiency while preventing degradation? We answer such a question in four stages: modeling, discretization, analysis, and simulation.

The explosion of interconnected devices requires radical advancements in the design of communication networks including for example peer-to-peer data transmission. Probabilistic methods can help to analyze the potential benefits but also challenges of such systems.

Quasi-variational inequalities (QVIs) are powerful mathematical objects that can be used to describe real-world phenomena as varied as thermoforming, or fluid flow in the heart. The inherently complex structure of QVIs makes their analysis a delicate matter. The control of QVIs is also important from the point of view of theoretical understanding as well as for applications.