Head:
Alexander Mielke

Coworkers:
Pierre-Étienne Druet, Thomas Eiter, Annegret Glitzky, Martin Heida, Katharina Hopf, Thomas Koprucki, Matthias Liero, Anieza Maltsi, Oliver Marquardt, Arbi Moses Badlyan, Grigor Nika, Petr Pelech, Joachim Rehberg, Stefanie Schindler, Artur Stephan, Willem van Oosterhout

Secretary:
Andrea Eismann

Honorary Members:
Jürgen Sprekels


Former Honorary Members:
Herbert Gajewski
Konrad Gröger

 

Overview

Many fundamental processes in nature and technology can be described by partial differential equations. The research group is working on the analytical theory of such equations (existence, uniqueness, qualitative behaviour) and on the development and implementation of algorithms for their numerical solution. The algorithms are used for the numerical simulation in industrial applications. The functionality of modern materials, for instance, relies on the complex interplay of effects on several length and time scales as well as on different physical effects, such as mechanics, thermodynamics, optics, and electromagnetism. The main topics of research are mathematical models of carrier transport in semiconductors and optoelectronic devices and reaction-diffusion equations for the transport of dopants in solids. Furthermore, nonlinear material models for linearized and nonlinear elasticity and plasticity as well as for systems with internal variables are under study. In this context, we develop in particular methods for abstract evolutionary equations, e.g. gradient systems, and for multiscale problems.

Highlights

The interdisciplinary workshop ”Applied Mathematics and Simulation for Semiconductors and Electrochemical Systems (AMaSiS 2021)” took place from 6th -- 9th September, 2021, and attracted more than 100 participants from 17 countries (Germany, France, USA, China, Italy, UK, Austria, ...). This online-workshop was dedicated to the mathematical modeling of semiconductors and electrochemical systems. Due to inherent similarities between both disciplines, AMaSiS 2021 explored synergies in mathematical modeling, analysis, numerics, and simulation techniques. The conference brought together experts from applied mathematics, physics, engineering, chemistry, and material science. AMaSiS 2021 covered the topics electronic structure theory, non-equilibrium thermodynamics and transport theories, mathematical upscaling from quantum mechanics and particle systems to continuum scale, numerical methods, as well as special semiconductor devices, and electrochemical systems.

Artur Stephan successfully defended his PhD thesis entitled ”Coarse-graining for gradient systems and Markov processes” on 11th May, 2021. Congratulations!

Closing conference "Structures in Evolution: Theory and Applications" (23rd -- 25th February 2021) online within the Thematic Einstein Semester, winter term 2020/21: A programme that included renowned speakers such as Pamela Cook (U Delaware), Günther Grün (U Erlangen-Nürnberg), Paul Kotyczka (TU München), Josef Málek (Charles University Prague), Marcel Oliver (U Bremen), Jacquelien Scherpen (U Groningen), Guido Schneider (U Stuttgart), and Ulisse Stefanelli (U Wien) was offered. The full thematic range of application, scale transitions, numerical methods, and mathematical analysis was covered by the talks, which were complemented by discussions in breakout rooms. The conference had 79 registered participants from 10 countries.

 
"MA4M: Mathematical Analysis for Mechanics" (23rd -- 25th November 2020) online within the Thematic Einstein Semester, winter term 2020/21: This workshop was organised by Matthias Liero, Alexander Mielke, and Marita Thomas and realised in close cooperation with the DFG Priority Programme SPP 2256 “Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials”. The focus was on the derivation of effective models in continuum mechanics for problems with different scales, on mechanical modelling and mathematical analysis for complex materials, and on variational formulations and relaxation methods. Despite the limitations of the online format, the opportunity to discuss and to compare methods and approaches in the above-mentioned fields was given by virtual discussion boards and extensive breaks between talks. Thereby, exchange between junior and senior scientists was ensured. There were about 120 participants and 19 invited talks, eight of which were given by junior researchers.

 
"Student Compact Course on Variational Methods and Fluids" online (12th -- 23rd October 2020) and "Kick-off Conference" online (26th -- 30th October 2020) within the Thematic Einstein Semester, winter term 2020/21: A broad programme of online lectures on gradient structures, Hamiltonian systems, GENERIC and port-Hamiltonian structures, evolutionary Gamma-convergence, large deviations theory, structure-preserving numerical methods, and much more was offered to about 100 participants of the ”Student Compact Course”. Interested PhD-students had the opportunity to give short presentations of their work and to further explore the TES topics. Subsequently, a ”Kick-off Conference” with 25 invited talks and about 150 participants took place.