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Publications 2019

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);
doi:10.1063/1.5112137

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.

Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules
Stefan Jaschonek, Ken Schäfer, Gregor Diezemann
The Journal of Physical Chemistry B 123 (22), 4688-4694 (2019);
doi:10.1021/acs.jpcb.9b02676

Temperature dependent mechanical unfolding of calixarene nanocapsules studied by molecular dynamics simulations
Takashi Kato, Ken Schäfer, Stefan Jaschonek, Jürgen Gauss, Gregor Diezemann
The Journal of Chemical Physics 151 (4), 045102 (2019);
doi:10.1063/1.5111717

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

Conditional reversible work coarse-grained models with explicit electrostatics - An application to butylmethylimidazolium ionic liquids
Gregor Deichmann and Nico F. A. van der Vegt
J. Chem. Theory Comp. 15, 1187-1198 (2019);
doi:10.1021/acs.jctc.8b00881

Phase equilibria modeling with systematically coarse-grained models - A comparative study on state point transferability
Gregor Deichmann, Marco Dallavalle, David Rosenberger and Nico F. A. van der Vegt
J. Phys. Chem. B 123, 504-515 (2019);
doi:10.1021/acs.jpcb.8b07320

Polydispersity Effects on Interpenetration in Compressed Brushes
Leonid I. Klushin, Alexander M. Skvortsov, Shuanhu Qi, Torsten Kreer, Friederike Schmid
Macromolecules 52 (4), 1810-1820 (2019);
doi:10.1021/acs.macromol.8b02361

How ill-defined constituents produce well-defined nanoparticles: Effect of polymer dispersity on the uniformity of copolymeric micelles
Sriteja Mantha, Shuanhu Qi, Matthias Barz, Friederike Schmid
Physical Review Materials 3 (2), (2019);
doi:10.1103/physrevmaterials.3.026002

An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions
A. Chertock, A. Kurganov, M. Lukacova-Medvidova, S. Nur Oezcan
Kinetic and Related Models 12 (1), 195–216 (2019);
URL: http://aimsciences.org//article/doi/10.3934/krm.2019009
doi:10.3934/krm.2019009

In this paper, we study two-dimensional multiscale chemotaxis models based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator which describes the velocity change of the cells. The parabolic scaling yields a non-dimensional kinetic model with a small parameter, which represents the mean free path of the cells. We propose a new asymptotic preserving numerical scheme that reflects the convergence of the studied micro-macro model to its macroscopic counterpart-the Patlak-Keller-Segel system-in the singular limit. The method is based on the operator splitting strategy and a suitable combination of the higher-order implicit and explicit time discretizations. In particular, we use the so-called even-odd decoupling and approximate the stiff terms arising in the singular limit implicitly. We prove that the resulting scheme satisfies the asymptotic preserving property. More precisely, it yields a consistent approximation of the Patlak-Keller-Segel system as the mean-free path tends to 0. The derived asymptotic preserving method is used to get better insight to the blowup behavior of two-dimensional kinetic chemotaxis model.

Energy-stable linear schemes for polymer-solvent phase field models
P. Strasser, G. Tierra, B. Dünweg, M. Lukacova-Medvidova
Comp. Math. Appl. 77 (1), 125-143 (2019);
URL: https://www.sciencedirect.com/science/article/pii/S0898122118305303?via%3Dihub
doi:https://doi.org/10.1016/j.camwa.2018.09.018

We present new linear energy-stable numerical schemes for numerical simulation of complex polymer–solvent mixtures. The mathematical model proposed by Zhou et al. (2006) consists of the Cahn–Hilliard equation which describes dynamics of the interface that separates polymer and solvent and the Oldroyd-B equations for the hydrodynamics of polymeric mixtures. The model is thermodynamically consistent and dissipates free energy. Our main goal in this paper is to derive numerical schemes for the polymer–solvent mixture model that are energy dissipative and efficient in time. To this end we will propose several problem-suited time discretizations yielding linear schemes and discuss their properties.

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