Research


(Version October 2021) I can consider myself lucky to have with Marie-Therese (Wolfram) and Christian (Schmeiser) two great supervisors for my PhD. I am interested in a change of scale from a microscopic level to a kinetic or macroscopic level. There you have e.g. analysis (of long-time behaviour), fast numerical solvers (for callibration and machine learning).
In my first paper, our goal was to investigate sociological phenomena in pedestrian dynamics. On a microscopic level we worked with a cellular automaton and derived a non-linear Fokker-Planck equation on a macroscopic level, which we analysed using an entropy-method. We calibrated the model with data from pedestrian experiments from the Jülich Research Centre. I submitted my first paper about pedestrian dynamics with Marie (and Gaspard) in November 2019 [1], you can also find it on arxiv.org.

After that I worked on Elorating systems [2], size-exclusion in microscopic models for bacteria, refinements of our pedestrian model and propably with the Max-Perutz-Labs (Biology) in Vienna. Furthermore, I am brooding with friends about models for gentrification. In my second publication, our focus was on the generalization of previous kinetic works on the ELO rating. Our main contribution was the derivation of a kinetic including a factor for performance fluctuation. Based on numerical simulations, we were able to prove analytically, using energy-methods, that a right choice of parameters leads to a dampening of the fluctuations. Thus the desired long-term behaviour of the rating-system could be regained.  

In the last project for my thesis, our goal is studying repulsion effects with a finite radius on a microscopic and macroscopic level. This effect does not only occur in bacteria during cell division, it could for example replace the trade-off between cohesive and repulsive effects in self-organised systems. A further high relevant use is to modelsocial distancing in pedestrians dynamics. We proved the rigorous limit from the microscopic to the macroscopic level for this non-differentiable cut-off potential.


Find more in my CV or ask me about my current list of projects





Published

Submitted
[2] https://arxiv.org/abs/2109.15046