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Research Group

Pattern Formation, Energy Landscapes and Scaling Laws

Welcome to the website of our research group at the Max-Planck-Institute for Mathematics in the Sciences. On the following pages, we give an overview over our work of the past years, as well as a glance at the ongoing research.

Our goal

Experiments and, nowadays, numerical simulation are a main tool for gaining insight into nature. However, these approaches share two main disadvantages: On the one hand, there are certain phenomena that are difficult to access via experiments or numerical simulation, for example problems involving several length scales that greatly differ in their order of magnitude. On the other hand, even in the case where a problem can be treated experimentally or numerically,  there might still be a lack of understanding - one searches not only for a description, but also for a satisfactory explanation of the mechanisms behind an observation.

This is the point at which a more theoretical analysis comes into play: There are many mathematical models in physics where the interplay of only a very small number of basic effects is believed to create a wealth of phenomena, including ones that are experimentally and numerically largely inaccessible due to their multi-scale nature. But with the help of mathematical analysis, one can often rigorously derive predictions that explain the real-world observations by relating them to the few basic effects that are the foundation of the model - thereby seconding (or disproving) its validity.

The focus of our research group is the analysis of (typically continuum) models that mostly come from materials science and fluid mechanics. We seek to understand specific phenomena, like the formation of certain patterns or the emergence of certain scaling laws, some of which are presented below. Our technical expertise is in the calculus of variations and in partial differential equations. Moreover, we use numerical simulation for quantitative comparison of our analysis to experiments. In recent years, probabilistic elements of the models and techniques play an increasing role in our group.

Our ambition is to give more insight on physically relevant phenomena while at the same time innovating mathematics.

Research Topics

Group Members

Group Publications

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