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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.

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics
Sebastian Kloth, Marvin P Bernhardt, Nico F A van der Vegt, Michael Vogel
Journal of Physics: Condensed Matter33 (20),204002 (2021);

An interplay of excluded-volume and polymer–(co)solvent attractive interactions regulates polymer collapse in mixed solvents
Swaminath Bharadwaj, Divya Nayar, Cahit Dalgicdir, Nico F. A. van der Vegt
The Journal of Chemical Physics154 (13),134903 (2021);

Iterative integral equation methods for structural coarse-graining
Marvin P. Bernhardt, Martin Hanke, Nico F. A. van der Vegt
The Journal of Chemical Physics154 (8),084118 (2021);

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 Materials18 (2-3),274-289 (2020);

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);

Does Preferential Adsorption Drive Cononsolvency?
Swaminath Bharadwaj, Nico F. A. van der Vegt
Macromolecules52 (11),4131-4138 (2019);

A note on the uniqueness result for the inverse Henderson problem
F. Frommer, M. Hanke, S. Jansen
Journal of Mathematical Physics60 (9),093303 (2019);
Highlighted on Scilight, see https://aip.scitation.org/doi/10.1063/1.5134789

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. E99,053308 (2019);

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 Comp15,2881-2895 (2019);

Cosolute effects on polymer hydration drive hydrophobic collapse
Divya Nayar and Nico F. A. van der Vegt
J. Phys. Chem. B122,3587-3595 (2018);

Addressing the temperature transferability of structure based coarse graining models
David Rosenberger and Nico F. A. van der Vegt
Phys.Chem.Chem.Phys20,6617-6628 (2018);

The Hydrophobic Effect and the Role of Cosolvents
Nico F. A. van der Vegt, Divya Nayar
The Journal of Physical Chemistry B121 (43),9986-9998 (2017);

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 Physics19 (28),18156-18161 (2017);

Fréchet differentiability of molecular distribution functions I. $$L^\infty $$ L ∞ analysis
Martin Hanke
Letters in Mathematical Physics108 (2),285-306 (2017);

Well-Posedness of the Iterative Boltzmann Inversion
Martin Hanke
Journal of Statistical Physics170 (3),536-553 (2017);

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

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 B120 (34),8757-8767 (2016);

Study of Hydrophobic Clustering in Partially Sulfonated Polystyrene Solutions with a Systematic Coarse-Grained Model
Ran Zhang, Nico F. A. van der Vegt
Macromolecules49 (19),7571-7580 (2016);

Comparison of iterative inverse coarse-graining methods
David Rosenberger, Martin Hanke, Nico F.A. van der Vegt
The European Physical Journal Special Topics225 (8-9),1323-1345 (2016);

Mechanism of Polymer Collapse in Miscible Good Solvents
Francisco Rodríguez-Ropero, Timir Hajari, Nico F. A. van der Vegt
The Journal of Physical Chemistry B119 (51),15780-15788 (2015);


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