Computer simulation study of the Levy flight process

Abstract

Abstract. Random walk simulation of the Levy flight shows a linear relation between the mean square displacement <r 2 > and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (l m ) affects the diffusion coefficient, even though it remains constant for l m greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results are also implied that the movement of a levy flight particle is similar to the case the particle moves in each time step with an average length of jumping <l>. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use time average instead of ensemble average. The difference between time average and ensemble average results points that the Levy distribution may be a non-ergodic distribution.

The Method for Magnetic Hyperthermia Based on Particle Swarm Optimization Algorithm with Levy Flight

“…10 On the basis of the PSO algorithm, the random Levy°ight mechanism is introduced to adjust the particle trajectory, which not only helps to get out of the local optimum, but also gets better convergence when the particles are in the vicinity of global optimum. 3 Its main function is that when the particles move in a small range near the local optimum, the jump of a large step can be given out. In the space of d dimension, the formula for the velocity and the position x of the particle at the time of t is improved:…”

Cooperative search with autonomous vehicles in a 3D aquatic testbed

“…These applications are best modeled with a destructive target scheme in which targets may only be found once. Previous studies have found the use of Lévy flights to be an efficient strategy for finding sparse targets in a two-dimensional environment [10], [11], [12], [13], [14], [15], and more recent results suggest that this may apply in three dimensions as well [21]. In what follows, we simulate and implement several methods for target search using aquatic vehicles that follow Lévy flights.…”

“…By restricting ourselves to primitive devices, we provide a proof-of-concept demonstration of how such vehicles may effectively perform search functions even under severe control and buoyancy limitations. We use our testbed implementation to investigate three-dimensional search strategies for single and multiple vehicles, extending existing two-dimensional search algorithms [10], [11], [12], [13], [14], [15]. The strategies are based on Lévy flights, in which path directions are chosen uniformly at random but with a path length sampled from a power-law distribution, offering the possibility of occasional long-distance motion.…”

Research and simulation on Levy flight model for DTN

“…Levy Flight is a special kind of random walk model [9][10][11][12][13][14][15][16][17], which was named after French mathematician Paul Pierre Levy in 1937. There are many natural and artificial facts that can be described by Levy Flight, such as fluid dynamics, earthquake analysis, etc.…”