C. Tojo et P. Argyrakis, CORRELATED RANDOM-WALK IN CONTINUOUS SPACE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(1), 1996, pp. 58-63
We present a model for diffusion with correlated motion in continuous
space. Correlation is implied as the retention of the directional memo
ry of the moving particle between successive scattering events. We use
a model borrowed from the field of polymers, based on a scattering an
gle theta, which is analogous to the bond angle between two monomers i
n a chain molecule. We monitor via Monte Carlo computer simulations th
e usual random walk properties, such as the mean-square displacement,
the number of sites visited (where the underlying continous space is b
inned in boxes), etc., for two-dimensional spaces, as a function of ti
me, and the correlation parameter. This type of motion belongs asympto
tically 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.