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Numerical Simulation of Anomalous Diffusion in Levy Random Walk Processes by Monte Carlo Method

Anita Sharma

Abstract


We have simulated the nonlinear behaviour of mean square displacement <r2>, with time based on Levy random walk model. By analysing different prospects, we came to the conclusion that, Levy random walk with continuous step length distribution gives rise to <r2> which behaves nonlinearly with time. This is only observable, when time average is taken and ensemble average does not lead to any nonlinearity. It also indicated the non-ergodic property of Levy distribution.

Keywords


Anomalous diffusion, Levy flight, random walk, ergodicity, Monte Carlo method, Levy distribution, Gaussian distribution

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References


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