@misc{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaž and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402109},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}
@misc{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].},
  language  = {en}
}