Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

Abstract

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.

16 pages, 13 figures, RevTeX

References in corpus (16)

• Theoretical perspective on the glass transition and amorphous materials
• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Correlated continuous time random walks
• Occupation Time Statistics in the Quenched Trap Model
• Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
• Aging Scaled Brownian Motion
• Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises
• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes

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• Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation
• Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics