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Directed random walks in continuous space.

Sheng-You Huang1, Xian-Wu Zou, Zhun-Zhi Jin

  • 1Department of Physics, Wuhan University, Wuhan 430072, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

Directed random walks in 2D space exhibit ballistic motion characteristics. Researchers observed a crossover from random to ballistic behavior, dependent on direction, impacting diffusion dynamics.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Understanding diffusion with directed motion is crucial in various physical phenomena.
  • Continuous directed random walks provide a model for such complex transport processes.

Purpose of the Study:

  • To investigate diffusion with directed motion in a two-dimensional continuous space.
  • To analyze the average square end-to-end distance and return probability for directed random walks.
  • To study the crossover behavior from random to ballistic motion and its dependence on direction.

Main Methods:

  • Utilized the model of continuous directed random walks.
  • Calculated the average square end-to-end distance .
  • Investigated the return probability P00(t).

Main Results:

  • Directed random walks asymptotically belong to the ballistic motion class (nu=1.0).
  • Observed a short-time crossover from purely random walks (nu=0.5) to ballistic motion (nu=1.0).
  • Established a scaling relation approximately tf(t/theta(-2)) and a similar scaling for return probability.

Conclusions:

  • The study confirms that directed motion in 2D continuous space leads to ballistic-like diffusion.
  • The crossover dynamics are influenced by the direction parameter, revealing a transition in walk behavior.
  • Scaling relations were identified for both end-to-end distance and return probability, unifying the observed phenomena.

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