B1: Inverse problems in coarse-grained particle simulations

Coarse-graining (CG) is an indispensable tool in computational materials science, but the associated upscaling and downscaling processes have to be designed with great care. Each of these interscale transfers comes with important inverse problems to be solved, most of which are ill-posed or ill-conditioned. In this project, we apply rigorous techniques from the mathematical field of inverse and ill-posed problems to provide a mathematically rigorous foundation of existing and/or new upscaling processes. Furthermore, we develop novel CG algorithms in which one can incorporate thermodynamic constraints in a more natural way.

Iterative integral equation methods for structural coarse-graining
Marvin P. Bernhardt, Martin Hanke, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (8), 084118 (2021);
doi:10.1063/5.0038633

Application of the 2PT model to understanding entropy change in molecular coarse-graining
Marvin P. Bernhardt, Marco Dallavalle, Nico F. A. Van der Vegt
Soft Materials 18 (2-3), 274-289 (2020);
doi:10.1080/1539445x.2020.1737118

A generalized Newton iteration for computing the solution of the inverse Henderson problem
Fabrice Delbary, Martin Hanke, Dmitry Ivanizki
Inverse Problems in Science and Engineering, 1-25 (2020);
doi:10.1080/17415977.2019.1710504

A note on the uniqueness result for the inverse Henderson problem
F. Frommer, M. Hanke, S. Jansen
Journal of Mathematical Physics 60 (9), 093303 (2019);
Highlighted on Scilight, see https://aip.scitation.org/doi/10.1063/1.5134789
doi:10.1063/1.5112137

↓ Show Abstract↑ Hide Abstract The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974 Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here we provide a rigorous proof of a slightly more general version of the latter statement using Georgii's variant of the Gibbs variational principle.

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures
David Rosenberger and Nico F. A. van der Vegt
Phys. Rev. E 99, 053308 (2019);
doi:10.1103/PhysRevE.99.053308

Transferability of Local Density-Assisted Implicit Solvation Models for Homogeneous Fluid Mixtures
David Rosenberger, Tanmoy Sanyal, M. Scott Shell, and Nico F. A. van der Vegt
J. Chem. Theory Comp 15, 2881-2895 (2019);
doi:10.1021/acs.jctc.8b01170

Cosolute effects on polymer hydration drive hydrophobic collapse
Divya Nayar and Nico F. A. van der Vegt
J. Phys. Chem. B 122, 3587-3595 (2018);
doi:10.1021/acs.jpcb.7b10780

Addressing the temperature transferability of structure based coarse graining models
David Rosenberger and Nico F. A. van der Vegt
Phys.Chem.Chem.Phys 20, 6617-6628 (2018);
doi:10.1039/c7cp08246k

The Hydrophobic Effect and the Role of Cosolvents
Nico F. A. van der Vegt, Divya Nayar
The Journal of Physical Chemistry B 121 (43), 9986-9998 (2017);
doi:10.1021/acs.jpcb.7b06453

Molecular origin of urea driven hydrophobic polymer collapse and unfolding depending on side chain chemistry
Divya Nayar, Angelina Folberth, Nico F. A. van der Vegt
Physical Chemistry Chemical Physics 19 (28), 18156-18161 (2017);
doi:10.1039/c7cp01743j

Fréchet differentiability of molecular distribution functions I. $$L^\infty $$ L ∞ analysis
Martin Hanke
Letters in Mathematical Physics 108 (2), 285-306 (2017);
doi:10.1007/s11005-017-1009-0

Well-Posedness of the Iterative Boltzmann Inversion
Martin Hanke
Journal of Statistical Physics 170 (3), 536-553 (2017);
doi:10.1007/s10955-017-1944-2

An inverse problem in statistical mechanics
Martin Hanke
in Oberwolfach Reports, Editor: Gerhard Huisken, Chapter Report No. 08/2017, EMS, Zürich, Series: Oberwolfach Reports , Vol. 14 (2017);
doi:10.4171/OWR/2017/8

Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer
Francisco Rodríguez-Ropero, Philipp Rötzscher, Nico F. A. van der Vegt
The Journal of Physical Chemistry B 120 (34), 8757-8767 (2016);
doi:10.1021/acs.jpcb.6b04100

Study of Hydrophobic Clustering in Partially Sulfonated Polystyrene Solutions with a Systematic Coarse-Grained Model
Ran Zhang, Nico F. A. van der Vegt
Macromolecules 49 (19), 7571-7580 (2016);
doi:10.1021/acs.macromol.6b01132

Comparison of iterative inverse coarse-graining methods
David Rosenberger, Martin Hanke, Nico F.A. van der Vegt
The European Physical Journal Special Topics 225 (8-9), 1323-1345 (2016);
doi:10.1140/epjst/e2016-60120-1

Mechanism of Polymer Collapse in Miscible Good Solvents
Francisco Rodríguez-Ropero, Timir Hajari, Nico F. A. van der Vegt
The Journal of Physical Chemistry B 119 (51), 15780-15788 (2015);
doi:10.1021/acs.jpcb.5b10684

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
hankeIjI@oizfiEmathematik.uni-mainz.de
http://www.mathematik.uni-mainz.de/Members/hanke

Prof. Dr. Nico van der Vegt
Institut für Physikalische Chemie
Technische Universität Darmstadt
Alarich-Weiss-Straße 10
D-64287 Darmstadt
Tel: +49 6151 16 4356
Fax: +49 6151 16 2048
vandervegtylgdRBxSzy@vCcsi.tu-darmstadt.de
http://www.cpc.tu-darmstadt.de/cpc/