Related papers: A Solvable Model for Nonlinear Mean Field Dynamo
The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the…
We consider the model of a transverse vector (e.g. magnetic) field with the most general form of the nonlinearity, known as the ${\cal A}$ model, passively advected by a strongly compressible turbulent flow, governed by the randomly stirred…
Using direct simulations of hydromagnetic turbulence driven by random polarized waves it is shown that dynamo action is possible over a wide range of magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions are being…
We study the N-dependence of the thermodynamical variables and the dynamical behavior of the well-known Hamiltonian Mean Field model. Microcanonical analysis revealed a thermodynamic limit which defers from the a priory traditional…
In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…
We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…
Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in presence of a background linear shear flow. Key techniques involved here are same as in our earlier work…
In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process…
We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating ABC-flow…
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory…
Large-scale magnetic fields are relevant for a number of dynamical processes in accretion disks, including driving turbulence, reconnection events, and launching outflows. Numerical simulations have indicated that the initial strengths and…
Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is…
We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local…
Mean field dynamo theory is a leading candidate to explain the observed large scale magnetic fields of galaxies and stars. However, controversy arises over the extent of premature quenching by the backreaction of the growing field. We…
A two-dimensional mean field dynamo model is solved where magnetic helicity conservation is fully included. The model has a negative radial velocity gradient giving rise to equatorward migration of magnetic activity patterns. In addition…
A numerical study of dynamos in rotating convecting plane layers is presented which focuses on magnetic energies and dissipation rates, and the generation of mean fields (where the mean is taken over horizontal planes). The scaling of the…
Fluctuation dynamos are generic to astrophysical systems. The only analytical model of the fluctuation dynamo is Kazantsev model which assumes a delta-correlated in time velocity field. We derive a generalized model of fluctuation dynamo…
The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was…
This work investigates a passive vector field which is transported and stretched by a divergence-free Gaussian velocity field, delta-correlated in time and poorly correlated in space (spatially nonsmooth). Although the advection of a scalar…
Some recent results and open issues in magnetic dynamo theory are addressed. The distinction between small-scale and mean-field dynamo (MFD) action in forced turbulent flows is emphasized. Though useful, the MFD has been controversial. This…