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Prof. Dr. Michael Vogel Institut für Festkörperphysik Technische Universität Darmstadt Hochschulstr. 6 D-64289 Darmstadt Tel: +49 6151 162933 Mail: michael.vogel@physik.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. Maria Lukáčová Institut für Mathematik Universität Mainz Staudingerweg 9 D-55128 Mainz Tel: +49 6131 39 22831 Fax: +49 6131 39 23331 Secr: +49 6131 39 22270 Mail: lukacova@mathematik.uni-mainz.de Further information

Project C3: Spinodal decomposition of polymer-solvent systems We consider the phase separation of dynamically asymmetric mixtures, in particular polymer solutions, after a sudden quench. Crucial aspects are (i) hydrodynamic momentum transport and (ii) the lack of time-scale separation between molecular relaxation and coarsening. This gives rise to complex dynamical processes such as the transient formation of network-like structures of the slow-component-rich phase, its volume shrinking, and lack of dynamic self-similarity, which are frequently summarized under the term viscoelastic phase separation. The relevant length and time scales of the physical phenomena are too large for microscopic (all atom) simulations. Alternative mesoscopic models based on a bead-spring description of polymer chains coupled to a hydrodynamic background, i.e., the Navier-Stokes equations for the solvent, allow to capture the basic physical principles but they are still computationally demanding. Therefore, macroscopic (two-fluid) models have been proposed in the literature which involve only averaged field quantities […]

Project C4 (Completed): Coarse-graining frequency-dependent phenomena and memory in colloidal systems Electrostatic interactions can strongly influence the behavior of macromolecular systems. A particular challenge for their prediction is the accurate, albeit computationally tractable, handling of the influence of water dipoles on the potentials. To address this challenge, we develop an efficient and accurate numerical framework for nonlocal electrostatics of large molecular systems. An improved understanding of the influence of water structure on electrostatics has far-reaching applications: the results of the project can, in principle, be used wherever implicit water models are desired, but where a simple structureless continuum is insufficiently accurate. This project has ended in June 2018.

Project C5: Adaptive hybrid multiscale simulations of soft matter fluids We develop and analyse efficient, hybrid multiscale methods that bridge the continuum-particle gap by combining a discontinuous Galerkin method for the macroscopic model with molecular dynamics. In the second funding period we have focused on the description of non-Newtonian fluids, particularly polymer melts, in sim- ple and complex geometries as well as on theoretical convergence analysis of numerical schemes taking multiscale effects into account. Building on these results we will study the flow behaviour of polymer mixtures and develop methods to separate polymers with similar molecular masses based on differences in rheological properties (WP1). Applying a probabilistic concept of solutions, we will extend our convergence analysis to these non-Newtonian systems (WP3) and investigate effects of uncertainty with machine learning techniques (WP4). In the final funding period, we would also like to expand the scope of our project to a novel, […]

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 […]