- Access by Xinjiang University
Correlated random walk in continuous space
Phys. Rev. E 54, 58 – Published 1 July, 1996
DOI: https://doi.org/10.1103/PhysRevE.54.58
Abstract
We present a model for diffusion with correlated motion in continuous space. Correlation is implied as the retention of the directional memory of the moving particle between successive scattering events. We use a model borrowed from the field of polymers, based on a scattering angle θ, which is analogous to the bond angle between two monomers in a chain molecule. We monitor via Monte Carlo computer simulations the usual random walk properties, such as the mean-square displacement, the number of sites visited (where the underlying continuous space is binned in boxes), etc., for two-dimensional spaces, as a function of time, and the correlation parameter. This type of motion belongs asymptotically to the same class as the regular random walk. For short times one observes a crossover that is strongly dependent on the correlation parameter in a scaling form, which is calculated numerically. © 1996 The American Physical Society.
References (9)
- V. Lottner, J. W. Haus, A. Heim and K. W. Kehr, J. Phys. Chem. Solids 40, 557 (1979).
- A. Dafano and G. Jacucci, Phys. Rev. Lett. 39, 950 (1977); J. Nucl. Matter 69/70, 549 (1978).
- P. Argyrakis and R. Kopelman, Chem. Phys. 57, 29 (1981); ibid. 78, 251 (1983).
- M. N. Barber and B. W. Ninham, Random and Restricted Walks: Theory and Applications (Gordon and Breach, New York, 1970).
- K. W. Kehr and P. Argyrakis, J. Chem. Phys. 84, 5816 (1986).
- P. Argyrakis and K. W. Kehr, J. Stat. Phys. 63, 399 (1991); J. Chem. Phys. 97, 2718 (1992) P. Argyrakis and R. Kopelman, ibid. 84, 1047 (1986).
- P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969).
- G. H. Weiss and R. J. Rubin, Adv. Chem. Phys. 52, 363 (1983).
- F. S. Henyey and V. Seshadri, J. Chem. Phys. 76, 5530 (1982).