Environment-dependent continuous time random walk |
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Authors: | Lin Fang and Bao Jing-Dong |
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Institution: | College of Physical Science and Technology, Sichuan University, Chengdu 610064, China; Department of Physics, Beijing Normal University, Beijing 100875, China |
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Abstract: | A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory: the jumping distance and the waiting time, are replaced by two new ones: the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement <x2(t)>~tα is realized numerically and analysed theoretically, where the value of the power index α is in a region of 0 < α < 2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events. |
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Keywords: | continuous time random walk environment-dependent rare-though-dominate events anomalous diffusion |
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