17.11.21 - Felix Höfling "Diffusion in complex materials: friction in liquids and a generalised master equation"

Diffusion in complex materials: friction in liquids and a generalised master equation

Friction in liquids arises from conservative forces between molecules and atoms and, even in simple liquids, must not be thought of as a single constant;rather it is a function of the temporal resolution of the experiment. As a
consequence, the effective dynamics of single molecules and solutes is non-Markovian, being one essential ingredient to vitrification mechanisms and viscoelasticity of soft materials. Based on high-precision simulations of three prototypical liquids, including water, we have obtained frequency-resolved friction data from atomistic to hydrodynamic scales [1]. I will discuss the abrupt emergence of friction at the atomistic scale, persistent correlations of Brownian forces, and the status of the generalised Stokes-Einstein relation that links single-molecule and collective responses.

In the second part, I will introduce a generalised master equation (GME) for non-Markovian jump processes that results from coarse-graining of diffusion in partitioned spaces [2]. The spatial domains can differ with respect to their
diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. This is motivated by a range of biological applications related to the transport of
molecules in cells, but finds also use in other fields. The approach is applied to target search problems in a two-domain model, yielding first-passage time (FPT) densities and an effective, scale-dependent reaction rate constant.

References:

[1] A. V. Straube, B. G. Kowalik, R. R. Netz, and F. Höfling, Commun. Phys. 3, 126 (2020).
[2] D. Frömberg and F. Höfling, J. Phys. A: Math. Theor. 54, 215601 (2021).

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