Continuous Time Random Walk

The Continuous Time Random Walk (CTRW) provides a mathematical framework for the study of transport in heterogenous media. It is much more general than usual transport models based on (local) Ordinary Differential Equations, and in particular can handle transport in systems without characteristic scales (such as systems in a state of Self-Organised Criticality or SOC).

Motivation

Interestingly, the absence of local characteristic scales means that effective transport coefficients (the diffusivity etc.) become dependent on the system size, as is indeed suggested by experimental scaling laws for plasma confinement.

In the framework of transport in plasmas, it is believed that the presence of trapping regions (such as turbulent eddies, magnetic islands, internal transport barriers) may lead to sub-diffusion, whereas the occurrence of streamers and profile self-regulation (via turbulence) may lead to super-diffusion. The goal of the CTRW approach is to model the effective transport in the presence of these complex phenomena.