TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
JF  - Journal of statistical mechanics: theory and experiment
N2  - 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.
KW  - driven diffusive systems (theory)
KW  - fluctuations (theory)
KW  - stochastic processes (theory)
KW  - diffusion
Y1  - 2014
U6  - https://doi.org/10.1088/1742-5468/2014/11/P11031
SN  - 1742-5468
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Metzler, Ralf
T1  - Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.
KW  - first passage
KW  - anomalous diffusion
KW  - potential landscape
KW  - polymer translocation
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/3/032002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 3
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -