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 (20)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Forecast and Control of Epidemics in a Globalized World
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Fractional Laplacian in Bounded Domains
• Optimal target search on a fast folding polymer chain with volume exchange
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Leapover lengths and first passage time statistics for Lévy flights
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
• Lévy flights in a steep potential well
• Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field
• Levy--Brownian motion on finite intervals: Mean first passage time analysis
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Power-law tail distributions and nonergodicity
• Multi-scaling properties of truncated Levy flights

Cited by in corpus (11)

• Lévy flights versus Lévy walks in bounded domains
• Optimization of random search processes in the presence of an external bias
• Long-range correlations and fractal dynamics in C. elegans: changes with aging and stress
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Ergodic property of random diffusivity system with trapping events
• Underdamped stochastic harmonic oscillator
• Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
• Langevin picture of anomalous diffusion processes in expanding medium
• Stationary states in 2D systems driven by bi-variate Lévy noises
• Escape from bounded domains driven by multi-variate $\alpha$-stable noises
• Taming Lévy flights in confined crowded geometries