Author(s): Huang SY, Zou XW, Jin ZZ
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Abstract The investigation on diffusion with directed motion in a two-dimensional continuous space is completed by using the model of the continuous directed random walks. The average square end-to-end distance approximately t(2nu) is calculated. The results show that this type of walks belongs asymptotically to the same class (nu=1.0) as the ballistic motions. For short time, we observe a crossover from purely random walks (nu=0.5) to ballistic motions (nu=1.0). The dependence of the crossover on the direction parameter theta is studied. There exists a scaling relation of the form approximately tf(t/theta(-2)). The return probability P00(t) is also investigated and the scaling form similar to is obtained.
This article was published in Phys Rev E Stat Nonlin Soft Matter Phys and referenced in Journal of Computer Science & Systems Biology