Magnetic Quenching of Turbulent Diffusivity: Reconciling Mixing-length Theory Estimates with Kinematic Dynamo Models of the Solar Cycle

The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric-average of the dynamically quenched diffusivity. Here, we provide an analytic fit to the dynamically quenched diffusivity profile, which can be used in kinematic dynamo simulations. Having successfully reconciled the mixing-length theory estimated diffusivity profile with kinematic dynamo models, we argue that they remain a viable tool for understanding the solar magnetic cycle.Comment: Submitted to ApJ

Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, that can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.Comment: 19 pages, 6 figures, RevTeX. Physical Review X, at pres

Investigating the in-/through-plane effective diffusivities of dry and partially-saturated gas diffusion layers

In this study, the effective oxygen diffusivity in the dry or partially-saturated gas diffusion layer (GDL) is numerically investigated by an oxygen diffusion model in GDLs reconstructed by a stochastic method. The predicted effective diffusivity in dry GDLs is compared with various diffusivity models from literatures. Reasonable agreements with other models were obtained. The effect of the PTFE loading in the dry Toray carbon paper is also investigated and compared with recent experimental data. It is found that the effective diffusivity becomes lower under higher PTFE loading due to the decreased pore volume, as expected. The relative effective oxygen diffusivity in partially-saturated GDLs is calculated using the two-phase volume of fluid (VOF) model and an oxygen diffusion model. The effects of different local water profiles and porosity distribution on the effective oxygen diffusivity in both the through-plane (TP) and in-plane (IP) directions are investigated and compared with a lattice Boltzmann model and experimental data. The present results are in good agreement with other studies. It is found that local water profile has significant impacts on the effective diffusivity in partially-saturated GDLs and the diffusivity in the TP direction is more sensitive to the water distribution than the IP direction

Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution

Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium distribution is a generalization of the Boltzmann distribution. This generalized Boltzmann distribution involves an effective potential which is a function of coordinate dependent diffusivity. We discuss various implications of the existence of this generalized Boltzmann distribution for equilibrium of systems with coordinate dependent diffusivity and damping.Comment: 11 pages, 1 figur