Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 60: Anomalous Diffusion (joint session DY/BP)

DY 60.3: Talk

Thursday, March 15, 2018, 10:30–10:45, BH-N 334

First-passage properties of Gaussian interfaces — •Markus Gross — MPI-IS Stuttgart / Uni Stuttgart

Fluctuating interfaces are relevant in various circumstances, such as liquid phase separation, nanofluidics, or surface growth. An effective description of the interfacial dynamics is provided by the Edwards-Wilkinson and the stochastic Mullins-Herring equations, corresponding to non-conserved and conserved dynamics. Despite the Gaussian nature of these models, their first-passage properties are highly nontrivial due to the presence of long-range correlations along the interface. We study here the full spatio-temporal evolution of an interface until it reaches a given maximum height for the first time. Analytical predictions, obtained within weak-noise theory, are contrasted to results of numerical Langevin simulations of the first-passage problem. It is shown the averaged profile shape is accurately captured by weak-noise theory, but the time evolution (specifically, the dynamic exponent) is not. The latter can instead be accounted for within a reduced model based on a fractional Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches an absorbing boundary.

References: M. Gross, arXiv:1708.03466, 1708.03467