Area coverage of radial Levy flights with periodic boundary conditions

Abstract

We consider the time evolution of two-dimensional Levy flights in a finite area with periodic boundary conditions. From simulations we show that the fractal path dimension d_f and thus the degree of area coverage grows in time until it reaches the saturation value d_f=2 at sufficiently long times. We also investigate the time evolution of the probability density function and associated moments in these boundary conditions. Finally we consider the mean first passage time as function of the stable index. Our findings are of interest to assess the ergodic behavior of Levy flights, to estimate their efficiency as stochastic search mechanisms and to discriminate them from other types of search processes.

7 pages, 8 figures, RevTeX

References in corpus (7)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Fractional Laplacian in Bounded Domains
• Leapover lengths and first passage time statistics for Lévy flights
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions

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