TY  - JOUR
A1  - Padash, Amin
A1  - Sandev, Trifce
A1  - Kantz, Holger
A1  - Metzler, Ralf
A1  - Chechkin, Aleksei
T1  - Asymmetric Levy flights are more efficient in random search
T2  - Fractal and fractional
N2  - We study the first-arrival (first-hitting) dynamics and efficiency of a one-dimensional random search model performing asymmetric Levy flights by leveraging the Fokker-Planck equation with a delta-sink and an asymmetric space-fractional derivative operator with stable index alpha and asymmetry (skewness) parameter beta. 

We find exact analytical results for the probability density of first-arrival times and the search efficiency, and we analyse their behaviour within the limits of short and long times. 
We find that when the starting point of the searcher is to the right of the target, random search by Brownian motion is more efficient than Levy flights with beta <= 0 (with a rightward bias) for short initial distances, while for beta>0 (with a leftward bias) Levy flights with alpha -> 1 are more efficient. 

When increasing the initial distance of the searcher to the target, Levy flight search (except for alpha=1 with beta=0) is more efficient than the Brownian search. Moreover, the asymmetry in jumps leads to essentially higher efficiency of the Levy search compared to symmetric Levy flights at both short and long distances, and the effect is more pronounced for stable indices alpha close to unity.
KW  - asymmetric Levy flights
KW  - first-arrival density
KW  - search efficiency
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/63740
SN  - 2504-3110
VL  - 6
IS  - 5
PB  - MDPI
CY  - Basel
ER  -