TY  - JOUR
A1  - Vahabi, Mahsa
A1  - Schulz, Johannes H. P.
A1  - Shokri, Babak
A1  - Metzler, Ralf
T1  - Area coverage of radial Levy flights with periodic boundary conditions
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We consider the area coverage of radial Levy flights in a finite square area with periodic boundary conditions. From simulations we show how the fractal path dimension d(f) and thus the degree of area coverage depends on the number of steps of the trajectory, the size of the area, and the resolution of the applied box counting algorithm. For sufficiently long trajectories and not too high resolution, the fractal dimension returned by the box counting method equals two, and in that sense the Levy flight fully covers the area. Otherwise, the determined fractal dimension equals the stable index of the distribution of jump lengths of the Levy flight. We provide mathematical expressions for the turnover between these two scaling regimes. As complementary methods to analyze confined Levy flights we investigate fractional order moments of the position for which we also provide scaling arguments. Finally, we study the time evolution of the probability density function and the first passage time density of Levy flights in a square area. Our findings are of interest for a general understanding of Levy flights as well as for the analysis of recorded trajectories of animals searching for food or for human motion patterns.
Y1  - 2013
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/35074
SN  - 1539-3755
VL  - 87
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -