Model of anomalous transport with backreacting localized perturbations

Abstract

MANY problems involving transport in physics, astrophysics and biology can be described in terms of a discrepancy between the experimentally observed flux of a quantity U and that predicted by elementary diffusion theory: this is known as anomalous transport. In such cases, there is often evidence for discrete structures or processes, spatially localized at fixed sites within the system, which can enhance the transport by giving rise to intermittent percolating pathways across the system ; examples include Kelvin–Helmholtz vortices in astrophysical accretion disks, island structures in plasma magnetic turbulence and enzymatic processes at the interfaces of cells. Such structures may themselves depend on U. To study the nonlinear elementary processes operating in these systems, we introduce a general model comprising localized structures coupled by two sets of variables: the transported quantity {U_i}, and a measure {δ_i} of the influence of each structure on the diffusion of U. The model is related to, but distinct from, cellular automata, which use only one set of coupling variables. We study the evolution of this model using anomalous transport in a turbulent magnetic plasma as an example. We believe that this model could provide a basis for studying the behaviour of a wide range of nonlinear systems.