Microscopic effects at fluid interfaces

Participants

Prof. Dr. Hans Wilhelm Alt
Prof. Dr. Michael Griebel
Dr. Marcel Arndt
Dr. Christiane Helzel
Dipl.-Phys. Lukas Jager
Prof. Dr. Rolf Krause
Dr. Marc Alexander Schweitzer

Description

Physical phenomena at interfaces between two or more fluids often happen on different length and time scales. The physical laws which cause the behavior at the interface can be quite different depending on the potentials which describe the interaction of the molecules. These microscopic effects can for example emerge on the macroscopic level as surface tension, diffusion or reaction processes. But the interaction of the macroscopic and the microscopic levels is still not fully understood.

The aim of this project is to clarify the connection of the different scales and to develop numerical methods which allow to include microscopic effects within a macroscopic model. To this end, we study the upscaling process from the microscopic to the macroscopic level by averaging, numerical homogenization and by statistical mechanics methods. Furthermore techniques are investigated which couple local models in different subdomains at different scales. Such local coupling methods can be gained by overlapping and non-overlapping domain decomposition techniques, where in one subdomain a macroscopic continuum model is derived whereas in the adjacent subdomain the atomistic model is kept. Thus boundary/coupling conditions between local models on different scales have to be developed. This way physical phenomena at interfaces can be simulated numerically taking also microscopic phenomena into account. Furthermore, in a similar fashion, implicit solvent models for the efficient numerical simulation of large molecules in water can be derived. Here we focus on an upscaling method inspired by a multigrid coarsening process and a mean-field approach using dimension-adaptive sparse grid integration.

References

[1]	H. W. Alt, The Entropy Principle for Fluid Interfaces, Preprint 2004.
[2]	H. W. Alt, L. Jager, Numerical Molecular Dynamics with Lennard-Jones Potential and the Computation of Macroscopic Quantities, 2004, in preparation.
[3]	M. Griebel, L. Jager, A Multiscale Minimization Technique for the Fast Determination of Low Energy Conformations of Biomolecules, in preparation.