@article{PalyulinMetzler2012,
  author    = {Palyulin, Vladimir V. and Metzler, Ralf},
  title     = {How a finite potential barrier decreases the mean first-passage time},
  series = {Journal of statistical mechanics: theory and experiment},
  journal   = {Journal of statistical mechanics: theory and experiment},
  number    = {1},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/2012/03/L03001},
  pages     = {10},
  year      = {2012},
  abstract  = {We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.},
  language  = {en}
}
@article{PalyulinChechkinMetzler2014,
  author    = {Palyulin, Vladimir V. and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias},
  series = {Journal of statistical mechanics: theory and experiment},
  journal   = {Journal of statistical mechanics: theory and experiment},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/2014/11/P11031},
  pages     = {32},
  year      = {2014},
  abstract  = {Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.},
  language  = {en}
}