Quenched trap model on the extreme landscape: The rise of subdiffusion and non-Gaussian diffusion

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.

Motion of an active particle with dynamical disorder

We propose a model for investigating the motion of a single active particle in a heterogeneous environment where the heterogeneity may arise due to crowding, conformational fluctuations and/or slow rearrangement of the surroundings. Describing the active particle in terms of the Ornstein-Uhlenbeck process (OUP) and incorporating heterogeneity in a thermal bath using two separate models, namely "diffusing diffusivity" and "switching diffusion", we explore the essential dynamical properties of the particle for its one-dimensional motion. In addition, we show how the dynamical behavior is controlled by dynamical variables associated with active noise such as strength and persistence time. Our model is relevant in the context of single particle dynamics in a crowded environment, driven by activity.

Convergence to a Gaussian by Narrowing of Central Peak in Brownian yet Non-Gaussian Diffusion in Disordered Environments

In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.

Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model

We study a two state "jumping diffusivity" model for a Brownian process alternating between two different diffusion constants, D+>D-, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D-⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.