@article{DzhanoevSokolov2017,
  author    = {Dzhanoev, Arsen R. and Sokolov, Igor M.},
  title     = {The effect of the junction model on the anomalous diffusion in the 3D comb structure},
  series = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  volume    = {106},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2017.12.001},
  pages     = {330 -- 336},
  year      = {2017},
  abstract  = {The diffusion in the comb structures is a popular model of geometrically induced anomalous diffusion. In the present work we concentrate on the diffusion along the backbone in a system where sidebranches are planes, and the diffusion thereon is anomalous and described by continuous time random walks (CTRW). We show that the mean squared displacement (MSD) in the backbone of the comb behaves differently depending on whether the waiting time periods in the sidebranches are reset after the step in the backbone is done (a rejuvenating junction model), or not (a non-rejuvenating junction model). In the rejuvenating case the subdiffusion in the sidebranches only changes the prefactor in the ultra-slow (logarithmic) diffusion along the backbone, while in the non-rejuvenating case the ultraslow, logarithmic subdiffusion is changed to a much faster power-law subdiffusion (with a logarithmic correction) as it was found earlier by Iomin and Mendez [25]. Moreover, in the first case the result does not change if the diffusion in the backbone is itself anomalous, while in the second case it does. Two of the special cases of the considered models (the non-rejuvenating junction under normal diffusion in the backbone, and rejuvenating junction for the same waiting time distribution in the sidebranches and in junction points) were also investigated within the approach based on the corresponding generalized Fokker-Planck equations. (c) 2017 Elsevier Ltd. All rights reserved.},
  language  = {en}
}
@article{KruesemannSchwarzlMetzler2016,
  author    = {Kruesemann, Henning and Schwarzl, Richard and Metzler, Ralf},
  title     = {Ageing Scher-Montroll Transport},
  series = {Transport in Porous Media},
  volume    = {115},
  journal   = {Transport in Porous Media},
  publisher = {Springer},
  address   = {New York},
  issn      = {0169-3913},
  doi       = {10.1007/s11242-016-0686-y},
  pages     = {327 -- 344},
  year      = {2016},
  abstract  = {We study the properties of ageing Scher-Montroll transport in terms of a biased subdiffusive continuous time random walk in which the waiting times between consecutive jumps of the charge carriers are distributed according to the power law probability with . As we show, the dynamical properties of the Scher-Montroll transport depend on the ageing time span between the initial preparation of the system and the start of the observation. The Scher-Montroll transport theory was originally shown to describe the photocurrent in amorphous solids in the presence of an external electric field, but it has since been used in many other fields of physical sciences, in particular also in the geophysical context for the description of the transport of tracer particles in subsurface aquifers. In the absence of ageing () the photocurrent of the classical Scher-Montroll model or the breakthrough curves in the groundwater context exhibit a crossover between two power law regimes in time with the scaling exponents and . In the presence of ageing a new power law regime and an initial plateau regime of the current emerge. We derive the different power law regimes and crossover times of the ageing Scher-Montroll transport and show excellent agreement with simulations of the process. Experimental data of ageing Scher-Montroll transport in polymeric semiconductors are shown to agree well with the predictions of our theory.},
  language  = {en}
}