Dynamics of a rigid rod in a disordered medium with long-range spatial correlation

We investigate the diffusion of a rigid rodlike object in a two-dimensional disordered host medium, which consists of static pointlike sources of force. The points are distributed with long-range spatial correlation and interact with the rod via a repulsive potential. The time dependence of the rod's center-of-mass mean-squared displacement and its rotational mean-squared displacement are obtained for various degrees of long-range spatial correlation and rod's lengths. These transport characteristics are compared to those obtained in previous studies for the case of homogeneous distribution of force points. It is shown that existence of long-range correlation among force points makes the center of mass diffusion anomalous.

Figure 1

(a) A sample of anticorrelated distribution of obstacles with Hurst exponent $H=0.2$. (b) A correlated sample with $H=0.7$. In both figures the number density is $\rho =0.06$.

Figure 2

Time series of rod's kinetic (top) and potential (bottom) energies. The rod's length is $L_{\mathrm{rod}}=29$ and its total energy is $E=1$. The medium is characterized with $H=0.2$ and $\rho =0.006$.

Figure 3

(a) Positional mean-squared displacement and (b) angular mean-squared displacement of CM in a medium with Hurst exponent $H=0.2$ and $\rho =0.006$ for various $L_{\mathrm{rod}}$.

Figure 4

(a) Angular mean-squared displacement for a rod of length $L=21$ in a correlated medium with $H=0.3$ for various densities. (b) Angular mean-squared displacement in a dense medium characterized by density $\rho =0.019$ and the Hurst exponent $H=0.3$ for various rod's length.

Figure 5

(a) Mean-squared displacement of CM, and (b) angular mean-squared displacement in a medium characterized by the Hurst exponent $H=0.7$ and $\rho =0.006$.

Figure 6

Dependence of diffusion scaling exponent $\delta$ on the Hurst exponent $H$ for two media of obstacle densities $\rho =0.006$ and $\rho =0.01$.

Figure 7

Dependence of diffusion scaling exponent $\delta$ on the obstacles density for a medium characterized by $\rho$ for $H=0.2$.

Figure 8

(a) Mean-squared displacement of CM, and (b) angular mean-squared displacement in an uncorrelated media with densities $\rho =0.02$ and $\rho =0.03$.