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Project C1: Using molecular fields to bridge between particle and continuum representations of macromolecular systems In this project, we explore the potential of so-called “molecular field” theories to bridge between particle-based and continuum representations of macromolecular materials. Regarding static equilibrium properties, they canbe linked to particle models via the well-established self-consistent field theory, a sophisticated density functional theory for polymers, and extensions thereof. Our goal is to design systematic mapping procedures for dynamic properties, i.e., devising dynamic density functionals (DDFs) of comparable quality. The work in the second funding period was motivated by a finding at the end of the first funding period, where we had identified severe shortcomings of the previously available DDF models. The central quantities in these DDF models are nonlocal mobility functions describing the response of the monomer current to a spatially varying field. We have devised a bottom-up method to construct these mobility functions from […]

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 C6 (Completed): Linking hydrodynamics and microscopic models of wet active matter with anisotropic particles The goal of this project is to develop a systematic, quantitative coarse-graining approach for a class of inherently non-equilibrium systems, namely suspensions of self-propelled particles. We link particle based models with effective hydrodynamic models within a multiscale framework based on sequential coupling and parameter passing. To this end, we combine microscopic Stokesian dynamics simulations with a mesoscopic kinetic model coupled to the macroscopic Stokes equation, and, in a second step, derive an effective hydrodynamic description in terms of particle density, polarization and nematic order parameter profiles. The multiscale scheme is applied to systems of self-propelled rod-like magnetic colloids suspended in a fluid. This is motivated by recent experiments on magnetotactic bacteria, which have shown that the interplay of internal drive (self-propulsion, mutual interactions) and external drive (magnetic field, oxygen gradient) in these systems leads to […]

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 […]

Project G: Central soft matter simulation platform The goals of project G in the second funding phase of the TRR 146 have been the implementation of new methods of general interest into the molecular dynamics simulation environment ESPResSo++ Guzman et al. (2019), which can be used as foundation for research projects inside the TRR 146, and the optimization of ESPResSo++ to efficiently use modern HPC resources and therefore to become performance competitive with state-of-the-art MD environments like LAMMPS. Project G has been successful integrating new simulation methods by coupling ESPResSo++ with the ScaFaCos library Hofmann et al. (2018), Arnold et al. (2013) to provide fast parallelized long-range interaction algorithm (e.g. P3M / multipolar P3M), developing and implementing a new approach for Lees-Edwards boundary conditions to provide a fast parallel implementation of shear boundary conditions. The performance optimization of the ESPResSo++ environment included to change the memory layout to benefit from […]

MGK: Integrated Research Training Group The integrated research training group (IRTG) of the TRR 146 provides a joint structured graduate education in the area of Computational Materials Science for the graduate students and young postdocs in the TRR 146 as well as other interested candidates working in related areas. The goals of the IRTG are threefold: 1) to provide students with the interdisciplinary background required for the research activities in the TRR 146, and to prepare them for a possible career in the area of theoretical Materials Sciences 2) to ensure common standards in the education of all graduate students in the TRR 146 by means of a well structured supervision and management program, 3) to establish and strengthen links within the TRR 146 already at the level of graduate students and young postdoctoral researchers. Special emphasis is placed on promoting exchange between groups within and outside of the TRR […]

Project B2: Many-body effects and optimized mapping schemes for systematic coarse-graining The first goal of the B2 project is to provide the consortium with a platform for systematic coarse-graining via the open-source software package “Versatile Object-oriented Toolkit for Coarse-graining Applications” (VOTCA). Projects requiring swift parameterizations of coarse-grained models have already benefited from using this toolkit. The second goal is the development of coarse-grained potentials that capture more accurately many-body effects, by going beyond standard pair-wise interactions. To this end, we develop and test various coarse-graining strategies based on short-range three-body, local-density-dependent, and local-conformation-dependent potentials. Further, we devise optimized mapping schemes for coarse-grained representations using machine-learning techniques: In the previous funding period, we trained artificial neural networks for structural coarse-graining, and kernel-based methods to develop a general model for three-body potentials. Building upon our previous research, we will advance our coarse-graining strategies to better reproduce conformational details and dynamics, and also […]