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2017 – Publications

Prof. Dr. Thorsten Raasch Institut für Mathematik Universität Mainz Staudingerweg 9 D-55128 Mainz Tel: +49 6131 3920172 Fax: +49 6131 3923331 Mail: raasch@uni-mainz.de Further information

Prof. Dr. Yongqi Wang Department of Mechanical Engineering Technische Universität Darmstadt Otto-Berndt-Str. 2 D-64287 Darmstadt Tel: +49 6151 1626202 Fax: +49 6151 1626203 Mail: wang@fdy.tu-darmstadt.de Further information

Prof. Dr. Markus Bachmayr Institut für Mathematik Universität Mainz Staudingerweg 9 D-55128 Mainz Tel: +49 6131 3920172 Fax: +49 6131 3923331 Secr: +49 6131 3922270 Mail: bachmayr@uni-mainz.de Further information

Prof. Dr. Herbert Egger Department of Mathematics Technische Universität Darmstadt Dolivostraße 15 D-64293 Darmstadt Tel: +49 6151 16-23170 Mail: egger@mathematik.tu-darmstadt.de Further information

Project C7: Dense active suspensions in the chaotic regime Active matter has become a quickly evolving field spanning from biology and physics to chemistry and engineering. Its defining property is the directed motion—translational, rotational, or both—of its constituents. This directed motion requires the steady input of free energy. Freed from the constraints of thermal equilibrium, active matter exhibits a wide range of novel phenomena; on the level of its single constituents up to emergent many-body collective and dynamic behavior. Extensively studied have been the aggregation of active particles into clusters, swarms, and other highly collective and dynamics states; but also spontaneous flow states where sufficiently high activity triggers the transition from a quiescent to a flowing fluid. At high densities, chaotic behavior has been reported in suspensions of bacteria and in numerical simulations. The aim of this project is to develop a comprehensive multiscale framework that bridges the properties of […]

Project C8: Numerical approximation of high-dimensional Fokker-Planck equations Stochastic processes driven by Brownian motion, which play a fundamental role in soft matter physics, can also be described by associated deterministic Fokker-Planck equations for probability distributions, where the dimensionality of the space on which this equation is posed increases linearly with respect to the number of particles. The aim of this project is to develop numerical solution methods for such high-dimensional problems that allow for the efficient extraction of quantities of interest, which typically take the form of certain integrals with respect to the computed distributions. In the high-dimensional case, beyond the basic numerical feasibility, a central issue is to ensure the accuracy of the computed solutions by suitable a posteriori error control. The initial focus of the project, which started during the second funding period, was on the development of numerical methods. On the one hand, we considered adaptive low-rank […]

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