2015/10–present: On leave, fighting a losing battle against cancer.
2015: Postdoc, FU Berlin, Germany
2011–2014: Dr. rer. nat. in mathematics, FU Berlin, Germany1,2
2006–2010: Diploma in mathematics, FU Berlin, Germany
2006: University-entrance diploma, Herder-Gymnasium Berlin, Germany
Member of the Berlin Mathematical School.
1
Supported through a 1-year scholarship by the (FU Berlin) Center for Scientific Simulation (2011).
2
Supported through a 3-year scholarship by the Helmholtz graduate research school
GeoSim (2012–2014).
A framework for rate-and-state friction is proposed in which existence and uniqueness of a solution is shown. These results, for a setting where no discretisation has been carried out, parallel results from my dissertation, which were obtained in a semi-discrete setting using similar methods.
An excerpt from my dissertation, focussed on applications: A mathematical problem is presented but not derived and not analysed. The algorithm is only hinted at, not presented in detail. Instead, an emphasis is put on performance and stability of the numerical solver. Results presented here constitute an improvement over those from my dissertation in that: (1) they also cover a 3D setting and (2) they were obtained after a bug was fixed (see below).
The 2D simulation results have led to the video A:NumEQ.mp4 (linked here is a more recent version) contained in the data publication Supplement to "Analogue earthquakes and seismic cycles: Experimental modelling across timescales". The video shows the velocity field in the upper plate across multiple seismic cycles. The distribution of the arrows representing the vector field is optimized for visual clarity (in particular, it is uniform) and different from the (non-uniform) spatial resolution of the numerical simulation.
An effort has been made to ensure the exact reproducibility of the simulation results and the plots that are generated from them. In particular, any form of source code created or relied upon as a part of this work is available as free software. A detailed guide to reproducing the figures contained in this work can be found here.
Derives a mathematical problem from the geophysical setting of a viscoelastic body undergoing infinitesimal strain while sliding on top of a rigid foundation, subject to rate-and-state friction. The problem is analysed, an algorithm is presented and convergence is proved in a semi-discrete setting. 2D simulation results are obtained, interpreted, and compared to laboratory measurements.
A small bug in the numerical code has been discovered since the publication; it caused the prescribed normal stress to be exaggerated by a factor of two, so that it equalled twice the lithospheric normal stress. This needs to be taken into account when interpreting the simulation results. The 2016 publication contains results where this bug has been fixed. Additional errata: p5, p6
An early attempt to analyse and solve the mathematical problems arising from an elastic body undergoing infinitesimal strain while sliding on top of a rigid foundation, subject to rate-and-state friction. The approach and results are suboptimal, the presentation is difficult to follow. The reader is, therefore, referred to one of the later publications on the subject, since they supersede this work in every way.
The lushness property of a Banach space is shown to be inherited by certain subspaces, namely L-summands and M-ideals. Lush spaces thus behave the same way as almost-CL spaces and spaces of numerical index one in this respect.
