Microscopic vs. macroscopic transport behavior on a conveyor belt

The group’s research activities concentrate on current topics in applied mathematics, with particular emphasis on differential equations and their numerical implementation. We provide expertise in modeling techniques and development of new methodologies for solving dynamic processes and resulting optimization problems.

The research group is currently engaged in the following application areas:

  • manufacturing systems,
  • traffic flow, pedestrian and evacuation dynamics,
  • complex systems (power grids, systems biology, water networks).

Our vision is to unravel the uniform principles that govern the dynamic behavior of different applications and to provide evolved mathematical methods for simulation and optimization purposes. We have extensive experiences with the development of solution algorithms as well as the evaluation on realistic data sets. Our expertise is mainly related to

Mathematical modeling of economic or physical phenomena

  • Flows on networks, e.g. traffic flow on highways, interlinked production systems, transmission lines, water networks
  • Hierarchy of models ranging from microscopic considerations (systems of ordinary differential equations) to macroscopic models (partial differential equations), e.g. pedestrian movement, material flow

Numerical methods for differential equations

  • Development of numerical schemes and analysis of the derived algorithms, e.g. uncertainty quantification
  • Theoretical framework for hyperbolic balance laws, e.g. coupled systems, wave-front tracking

Solution algorithms for optimization problems

  • Control problems governed by differential equations, e.g. optimality conditions, adjoint calculus, feedback stabilization
  • Nonlinear and mixed integer linear programming, e.g. tailored Branch-and-Bound schemes