Rectification and Non-Gaussian Diffusion in Heterogeneous Media

Abstract

Abstract:We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and backward probabilities depend on the nature of the host medium, on local forces, and also on time. We have applied our results to two situations: diffusion in a disordered medium, and diffusion in a confined system. For such scenarios, we have shown that our theoretical predictions are in very good agreement with numerical results. Moreover, we have shown that the deviations from the Gaussian solution lead to the onset of rectification. Our predictions could be used to detect the presence of local forces and to characterize the intrinsic short-scale properties of the host medium-a problem of current interest in the study of micro-and nano-systems.

Subtle changes in crosslinking drive diverse anomalous transport characteristics in actin–microtubule networks

“…As shown in Fig. 5A, 34 (Δ ) for all conditions decreases from an initial absolute maximum ~(10) to a nearly timeindependent plateau of ~(1). However, the long-time plateau is significantly higher for the crosslinked networks relative the unlinked network, further evidenced by the time-average of 34 (Δ ) shown in the inset.…”

“…Single-particle tracking (SPT), often used to characterize particle diffusion in complex environments, can determine anomalous transport characteristics such as: subdiffusion, in which the mean-squared displacement (MSD) scales as ~Δ ! where < 1 23,[25][26][27] ; ergodicity-breaking, in which the time-averaged MSD differs from the ensemble-averaged MSD [28][29][30] ; and non-Gaussianity, in which the distribution of particle displacements deviates from the normal distribution consistent with Brownian motion [31][32][33][34][35][36] . While single particle tracking measures the motion of individual particles to measure transport properties, differential dynamic microscopy (DDM) extracts complementary information inaccessible to SPT by probing the ensemble scale.…”

“…3, the distributions for all networks are distinctly non-Gaussian, with significant broad tails for large displacements. This phenomenon is commonly seen in crowded media in both synthetic and biological systems, and is a hallmark of dynamic heterogeneity [32][33][34][35][36]45,46 . However, in these systems, non-Gaussian transport is often transient and reverts to Gaussian at long enough times [47][48][49] .…”

Subtle changes in crosslinking drive diverse anomalous transport characteristics in actin-microtubule networks

“…Single-particle tracking (SPT), often used to characterize particle diffusion in complex environments, can determine anomalous transport characteristics such as: subdiffusion, in which the mean-squared displacement (MSD) scales as ~Δ where < 1 23,[25][26][27] ; ergodicity-breaking, in which the time-averaged MSD differs from the ensemble-averaged MSD [28][29][30] ; and non-Gaussianity, in which the distribution of particle displacements deviates from the normal distribution consistent with Brownian motion [31][32][33][34][35][36] . While single particle tracking measures the motion of individual particles to measure transport properties, differential dynamic microscopy (DDM) extracts complementary information inaccessible to SPT by probing the ensemble scale.…”

Nonequilibrium Phenomena in Confined Systems

“…In the first contribution to this special issue [1], by P. Malgaretti, I. Pagonabarraga and J.M. Rubi, the authors focus on how local forces in heterogeneous media modify Brownian motion and leads to deviations in the Gaussian probability distribution of displacements typical of thermal motion.…”