Related papers: A Solvable Model for Nonlinear Mean Field Dynamo
We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the meanfield limit of these models manifests multistable parameter regions of coexisting steady states…
We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to…
We propose a two fluid theory to model a dilute polymer solution assuming that it consists of two phases, polymer and solvent, with two distinct macroscopic velocities. The solvent phase velocity is governed by the macroscopic Navier-Stokes…
We investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh-B\'enard convection using direct numerical simulations. The kinetic and magnetic energies are divided into…
We analyze the Markov property of solutions to the compressible Navier--Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem.…
Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…
We report an extensive numerical study of the small-scale turbulent dynamo at large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy…
Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field dynamos. Here, a mean field dynamo in cosmic scales on a Riemannian spatial…
A method is proposed for computing coefficients in the Kazantsev equation of small-scale dynamo for the full spectrum of hydromagnetic turbulence comprising the inertial range together with the range of viscous dissipation. The dynamo…
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part,…
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of turbulent dynamo, and study the dynamo process…
In turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the…
We investigate mean field game systems under invariance conditions for the state space, otherwise called {\it viability conditions} for the controlled dynamics. First we analyze separately the Hamilton-Jacobi and the Fokker-Planck…
We derive the exact solution of the Boltzmann kinetic equation for the three-dimensional Lorentz model in the presence of a constant and uniform magnetic field. The velocity distribution of the electrons reduces exponentially fast to its…
In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for…
Jetted astrophysical phenomena with black hole (BH) engines, including binary mergers, jetted tidal disruption events, and X-ray binaries, require a large-scale vertical magnetic field for efficient jet formation. However, a dynamo…
A rigorous theory for the generation of a large-scale magnetic field by random non-helically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low Rm and weak shear. The…
The small-scale dynamo is a process by which turbulent kinetic energy is converted into magnetic energy, and thus is expected to depend crucially on the nature of turbulence. In this work, we present a model for the small-scale dynamo that…
We introduce $\infty$-dimensional versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the…
The small-scale kinematic dynamo in a two-dimensional chaotic flow is studied. The analytic approach is developed in framework of the Kraichnan-Kazantsev model. It is shown that the growth of magnetic field $\bm{B}$ fluctuations stops at…