@article{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  volume    = {16},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  number    = {13},
  publisher = {RSC Publications},
  address   = {Cambridge},
  issn      = {1463-9084},
  doi       = {10.1039/C3CP55160A},
  pages     = {6118 -- 6128},
  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}
}
@article{SandevMetzlerTomovski2014,
  author    = {Sandev, Trifce and Metzler, Ralf and Tomovski, Zivorad},
  title     = {Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise},
  series = {Journal of mathematical physics},
  volume    = {55},
  journal   = {Journal of mathematical physics},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4863478},
  pages     = {23},
  year      = {2014},
  abstract  = {We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.},
  language  = {en}
}