# 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

Soft Matter 17 (26),
6413-6425
(2021);

doi:10.1039/d1sm00521a

Introducing Memory in Coarse-Grained Molecular Simulations

The Journal of Physical Chemistry B 125 (19),
4931-4954
(2021);

doi:10.1021/acs.jpcb.1c01120

Mathematical analysis of some iterative methods for the reconstruction of memory kernels

ETNA - Electronic Transactions on Numerical Analysis 54,
483-498
(2021);

doi:10.1553/etna_vol54s483

Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations

Journal of Physics: Condensed Matter 33 (21),
214003
(2021);

doi:10.1088/1361-648x/abe6df

Frequency-Dependent Dielectric Polarizability of Flexible Polyelectrolytes in Electrolyte Solution: A Dissipative Particle Dynamics Simulation

Journal of The Electrochemical Society 166 (9),
B3194-B3202
(2019);

doi:10.1149/2.0231909jes

Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models

Soft Matter 14 (46),
9368-9382
(2018);

doi:10.1039/c8sm01817k

Frequency-dependent hydrodynamic interaction between two solid spheres

Physics of Fluids 29 (12),
126101
(2017);

doi:10.1063/1.5001565

Iterative Reconstruction of Memory Kernels

Journal of Chemical Theory and Computation 13 (6),
2481-2488
(2017);

doi:10.1021/acs.jctc.7b00274

Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions

The Journal of Chemical Physics 144 (20),
204104
(2016);

doi:10.1063/1.4950760

Flows and mixing in channels with misaligned superhydrophobic walls

Physical Review E 91 (3),
(2015);

doi:10.1103/physreve.91.033020

## Contact

- Prof. Dr. Martin Hanke-Bourgeois
- Institut für Mathematik
- Universität Mainz
- Staudingerweg 9
- D-55128 Mainz
- Tel: +49 6131 39 22528
- Fax: +49 6131 39 23331
- hanketuFzZYT@gmathematik.uni-mainz.de
- http://www.mathematik.uni-mainz.de/Members/hanke

- Prof. Dr. Friederike Schmid
- Institut für Physik
- Universität Mainz
- Staudingerweg 9
- D-55128 Mainz
- Tel: +49 6131 3920365
- Fax: +49 5131 3920496
- Sekr: +49 6131 3920495
- friederike.schmidRWMYBM@JVtYHSpuni-mainz.de
- https://www.komet1.physik.uni-mainz.de/people/friederike-schmid/