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.

The Hydrophobic Effect and the Role of Cosolvents

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

Physical Chemistry Chemical Physics 19 (28), 18156-18161 (2017);
doi:10.1039/c7cp01743j

Well-Posedness of the Iterative Boltzmann Inversion

Journal of Statistical Physics, (2017);
doi:10.1007/s10955-017-1944-2

Fréchet differentiability of molecular distribution functions II: the Ursell function

Letters in Mathematical Physics, (2017);
doi:10.1007/s11005-017-1010-7

Fréchet differentiability of molecular distribution functions I. $$L^\infty$$ L ∞ analysis

Letters in Mathematical Physics, (2017);
doi:10.1007/s11005-017-1009-0

An inverse problem in statistical mechanics

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

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

Macromolecules 49 (19), 7571-7580 (2016);
doi:10.1021/acs.macromol.6b01132

Comparison of iterative inverse coarse-graining methods

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

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
• hankeWxGuD-a_@Bmathematik.uni-mainz.de
• http://www.mathematik.uni-mainz.de/Members/hanke
• Prof. Dr. Nico van der Vegt
• Institut für Physikalische Chemie