Project A3: Coarse-graining frequency-dependent phenomena and memory in colloidal systems
The purpose of this project is to develop numerical strategies for dynamic coarse-graining in situations where the separation of time scales is incomplete and memory effects are important. This entails the reconstruction of coarse-grained dynamical equations that include memory (generalized Langevin equations, GLE), the efficient simulation of coarse-grained models with memory and the application to colloidal dispersions at equilibrium and non-equilibrium. This project is complementary to project A2, where related problems are addressed in the context of dynamic coarse-graining of molecular liquids.
In the second funding period, we have extended our previous work on iterative memory reconstruction for single colloids (first funding period) to systems containing multiple colloids, where pair memory effects must be taken into account. A benchmark simulation of 125 colloids in solution showed that a speedup of at least three orders of magnitude can be obtained by dynamic coarse-graining with memory while still capturing the correct dynamics.
In the mathematics subproject, we have then proceeded by a mathematical analysis of this iterative memory reconstruction method. Our analysis revealed the underlying cause why certain ad hoc adjustments (a “sliding time window”) had to be introduced in order to achieve convergence. Furthermore, we have investigated strategies to derive extended Markov models for coarse-grained systems with memory. We have developed a new algorithm which directly determines such Markov models from sampled autocorrelation data. The algorithm is based on the so-called Prony method for exponential interpolation and the “Positive Real Lemma” from control theory. It allows to set up Markov models with up to twenty extended variables. The memory kernel can be obtained as a side product, if necessary.
In the physics subproject, we have focussed on systems far from equilibrium. We have studied two different test cases: (i) A colloid that is driven through a fluid medium by an external force (active microrheology), and (ii) a passive colloid immersed in a bath of active Brownian particles. Contrary to a frequent assumption in the literature, the second fluctuation-dissipation theorem (2FDT) that relates the memory kernel with the correlations of the fluctuating “random” forces on the colloid turned out to always be exactly fulfilled even far from equilibrium. We have derived a general mathematical argument why the random forces must obey the 2FDT if the memory kernel is derived from a time correlation function via a so-called Volterra equation. On the other hand, the shape and the range of the memory kernel changes significantly far from equilibrium.
In the next funding period, we plan to further extend this work in three directions: First, on the mathematical side, we will further develop the algorithm for deriving extended Markovian schemes such that it can also be applied to higher dimensional problems with several coarse-grained particles.
Second, in joint work between mathematics and physics, we will explore and develop dynamic coarse-graining strategies in the presence of external potentials. In this case, the GLE also includes a conservative term. The challenge on the mathematical side is to account for such external forces when constructing the equivalent extended Markov model. The challenge on the physics side is to investigate the influence of external potentials on the memory kernel, in particular in the vicinity of boundaries.
Third, on the physical side, we plan to study situations with spatially varying memory kernel from a more general perspective. For example, we will consider colloidal systems in an active bath with time- and space-dependent activity level. In our current work, we have recovered the experimental observation that a passive colloid starts behaving like an active particle in an active bath. We will investigate whether memory kernels that vary in space and time can introduce additional effects.
Passive probe particle in an active bath: can we tell it is out of equilibrium?
Jeanine Shea, Gerhard Jung, Friederike Schmid
Soft Matter, 2022,18, 6965-6973, (2022)
see publication
Fluctuation–dissipation relations far from equilibrium: a case study
Gerhard Jung, Friederike Schmid
Soft Matter 17 (26), 6413-6425 (2021)
see publication
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 B125 (19), 4931-4954 (2021)
see publication
Mathematical analysis of some iterative methods for the reconstruction of memory kernels
Martin Hanke
ETNA - Electronic Transactions on Numerical Analysis 54, 483-498 (2021)
see publication
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)
see publication
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)
see publication
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)
see publication
Frequency-dependent hydrodynamic interaction between two solid spheres
Gerhard Jung, Friederike Schmid
Physics of Fluids 29 (12), 126101 (2017)
see publication
Iterative Reconstruction of Memory Kernels
Gerhard Jung, Martin Hanke, Friederike Schmid
Journal of Chemical Theory and Computation 13 (6), 2481-2488 (2017)
see publication
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)
see publication
Flows and mixing in channels with misaligned superhydrophobic walls
Tatiana V. Nizkaya, Evgeny S. Asmolov, Jiajia Zhou, Friederike Schmid, Olga I. Vinogradova
Physical Review E91 (3), (2015)
see publication