The Non-isotropic Of The Levy Walk And It’s Dynamics Simulation

Recently the study on anomalous diffusion is one of the hot spots in math and physics. Levy walk is connected with our lives closely. This text is composed of five chapters. The opening chapter gives a brief overview of Levy walk and some formulas about our work. In the second chapter we study Levy walk which is under the influence of local time. Two cases (1<λ<2, and 2<λ) are considered in these parts. By the theory results of propagator; we calculate the simulated images of the the propagator function from tracks of particles. The theory result is consistent with simulation results. In chapter three the tempered Levy walk is studied; we obtain the ensemble average which is shown by Mittag-leffler function; and the ensemble average changing with the index α;λ and the time of observation is shown in the text. In chapter three we learn the Non-isotropic of the Levy walk; in this part we discuss the power index of λ and A and obtain the relation between the ensemble average and λ and λ; in addition the propagator is shown by the Gaussian distribution and the Levy stable distribution. It’s easy to find the different trend of the propagator between X and Y from the propagator figure. In the last chapter we sum up the results and point out the defect of the paper.