Anomalous transport in cellular flows: The role of initial conditions and aging

TL;DR

This study investigates how initial conditions influence subdiffusive transport and aging in cellular flows, revealing that subdiffusion is prominent only when particles start at cell borders and exhibits unique aging behaviors.

Contribution

The paper demonstrates that initial conditions critically affect subdiffusive behavior and aging in cellular flows, highlighting differences from classical CTRW models.

Findings

Subdiffusion occurs mainly when particles start at cell borders.

Aging properties are significant and reflected in the mean squared displacement.

Behavior differs from classical CTRW models with no trapped state dynamics.

Abstract

We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show subdiffusion. We have performed extensive numerical simulations of the systems under different initial conditions, and show that the pure intermediate-time subdiffusion regime is only evident when the particles start at the border between different cells, i.e. at the separatrix, and is less pronounced or absent for other initial conditions. The motion moreover shows quite peculiar aging properties which are also mirrored in the behavior of the time-averaged mean squared displacement for single trajectories. This kind of behavior is due to the complex motion of tracers trapped inside the cell, and is absent in classical models based on continuous time random walks (CTRW) with no dynamics in the trapped state.