Brownian motors in variable-shape medium: Overdamped versus underdamped cases

Abstract

In this paper, we investigate the statistical behavior of Brownian particles in a deformable traveling-wave potential in the absence of external load. We model the deformation of the system by the modified Remoissenet-Peyrard on-site potential, which is distinguished by its sine-Gordon shape. We examine numerically the effect of the deformed on-site potential with traveling speeds on the transport properties in overdamped as well as underdamped Brownian particles. Using the Langevin Monte Carlo method, we show that the average velocity of Brownian particles is an increasing function of the shape parameter in the overdamped case, and a decreasing function of the shape parameter in the underdamped case. It is found that, in the overdamped case, the numerical behavior of the average velocity of Brownian particles validates its analytical results. In the presence of the deformable traveling-wave potential, for negative as well as positive values of the shape parameter, the underdamped case favors the transport properties in the medium. The average velocity needed to cross the potential barriers is lowest in the underdamped case. Moreover, the effective diffusion coefficient in both cases exhibits peaks, and the diffusion process enhancement is discussed for some values of the shape parameter. Finally, in the underdamped case, by using the Smoluchowski equation and the finite-element methods, we analyze the distribution of Brownian particles in the deformed system.