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A3: Coarse-graining frequency-dependent phenomena and memory in colloidal systems

The goal of this project is to develop coarse-graining schemes for systems where the separation of time scales is incomplete and memory effects become important. We develop and test these schemes using colloids in simple or complex fluids as an example. In the first funding period, we have considered dilute systems of one or two colloids in simple fluids and developed an iterative method to determine memory kernels. In the next funding period, we plan to consider many-particle-effects, include charges, and also consider driven nonequilibrium and active systems. In the new mathematical work-packages we will analyze rigorously the inverse problem of determining appropriate memory kernels for the generalized Langevin equation.

Fluctuation–dissipation relations far from equilibrium: a case study
Gerhard Jung, Friederike Schmid
Soft Matter 17 (26), 6413-6425 (2021);

Introducing Memory in Coarse-Grained Molecular Simulations
Viktor Klippenstein, Madhusmita Tripathy, Gerhard Jung, Friederike Schmid, Nico F. A. van der Vegt
The Journal of Physical Chemistry B 125 (19), 4931-4954 (2021);

Mathematical analysis of some iterative methods for the reconstruction of memory kernels
Martin Hanke
ETNA - Electronic Transactions on Numerical Analysis 54, 483-498 (2021);

Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
N Bockius, J Shea, G Jung, F Schmid, M Hanke
Journal of Physics: Condensed Matter 33 (21), 214003 (2021);

Frequency-Dependent Dielectric Polarizability of Flexible Polyelectrolytes in Electrolyte Solution: A Dissipative Particle Dynamics Simulation
Gerhard Jung, Sebastian Kasper, Friederike Schmid
Journal of The Electrochemical Society 166 (9), B3194-B3202 (2019);

Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models
Gerhard Jung, Martin Hanke, Friederike Schmid
Soft Matter 14 (46), 9368-9382 (2018);

Frequency-dependent hydrodynamic interaction between two solid spheres
Gerhard Jung, Friederike Schmid
Physics of Fluids 29 (12), 126101 (2017);

Iterative Reconstruction of Memory Kernels
Gerhard Jung, Martin Hanke, Friederike Schmid
Journal of Chemical Theory and Computation 13 (6), 2481-2488 (2017);

In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely, the memory kernel, from equilibrium all-atom simulations. In this article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and discretization effects. Furthermore, we also propose a new numerical integrator for generalized Langevin equations that is significantly more accurate than the more commonly used generalization of the velocity Verlet integrator. We demonstrate the performance of the above-described methods using the example of backflow-induced memory in the Brownian diffusion of a single colloid. For this system, we are able to reconstruct realistic coarse-grained dynamics with time steps about 200 times larger than those used in the original molecular dynamics simulations.

Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions
Gerhard Jung, Friederike Schmid
The Journal of Chemical Physics 144 (20), 204104 (2016);

Exact values for bulk and shear viscosity are important to characterize a fluid, and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics simulations of steady-state systems with periodic boundary conditions — one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics fluid.

Flows and mixing in channels with misaligned superhydrophobic walls
Tatiana V. Nizkaya, Evgeny S. Asmolov, Jiajia Zhou, Friederike Schmid, Olga I. Vinogradova
Physical Review E 91 (3), (2015);


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