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Project A10 (New): Population control of multiple walker simulations via a birth/death process Conventional Molecular Dynamics (MD) simulations are generally unable to access the long-timescale phenomena that are common in nature. This timescale problem comes from the fact that a typical free energy landscape consists of many metastable states separated by high free energy barriers. If the barriers are much higher than the thermal energy, the system is kinetically trapped in some metastable state and barrier crossings will be rare events on the time scales that we can simulate. One strategy to alleviate this time scale problem is to employ collective variable (CV) based enhanced sampling methods such as metadynamics. A common way to improve the performance of CV-based methods is to employ multiple walkers that share a bias potential and collaboratively sample the free energy landscape. In this way, one reduces the wall-clock time for convergence and makes better […]

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

Dr. Alf Gerisch Institut für Mathematik Technische Universität Darmstadt Dolivostr. 15 D-64293 Darmstadt Tel: +49 6151 16 70994 Fax: +49 6151 16 2747 Secr: +49 6151 16 4687 Mail: gerisch@mathematik.tu-darmstadt.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

Prof. Dr. Omar Valsson Department of Chemistry University of North Texas 1155 Union Circle #305070 Denton, Texas 76203 Tel: +1 940 369 7593 Mail: omar.valsson@unt.edu 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 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 […]

TRR 146: Multiscale Simulation Methods for Soft Matter Systems Multiscale modeling is a central topic in theoretical condensed matter physics and materials science. One prominent class of materials, whose properties can rarely be understood on one length scale and one time scale alone, is soft matter. The properties of soft materials are determined by an intricate interplay of energy and entropy, and minute changes of molecular interactions may lead to massive changes of the system’s macroscopic properties. In our collaborative research center (CRC TRR 146), we plan to tackle some of the most pressing problems in multiscale modeling in a joint effort of physicists, chemists, applied mathematicians, and computer scientists. The TRR 146 receives funding from the german science foundation (DFG) since October 2014. We address three major challenges: (A) Dynamics In the past, multiscale coarse-graining approaches have to a large extent focused on static equilibrium properties. However, a thorough […]