Related papers: Ill-posedness of the mean-field dynamo equations w…
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…
We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the…
It is shown, that the saturated $\alpha$-effect taken from the nonlinear dynamo equations for the thin disk can still produce exponentially growing magnetic field in the case, when this field does not feed back on the $\alpha$. For negative…
Using a rotating flat layer heated from below as an example, we consider effects which lead to stabilizing an exponentially growing magnetic field in magnetostrophic convection in transition from the kinematic dynamo to the full non-linear…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for…
We present numerical simulations of driven magnetohydrodynamic (MHD) turbulence with weak/moderate imposed magnetic fields. The main goal is to clarify dynamics of magnetic field growth. We also investigate the effects of the imposed…
Motivated both by considerations of the generation of large-scale astrophysical magnetic fields and by potential problems with mean magnetic field generation by turbulent convection, we investigate the mean electromotive force (emf)…
The turbulent dynamo effect, which describes the generation of magnetic fields in astrophysical objects, is described by the dynamo equation. This, in the kinematic (linear) approximation gives an unbounded exponential growth of the long…
We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean…
We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative…
Understanding large scale magnetic field growth in turbulent plasmas in the magnetohydrodynamic limit is a goal of magnetic dynamo theory. In particular, assessing how well large scale helical field growth and saturation in simulations…
We generalize the mean field magnetic dynamo to include local evolution of the mean vorticity in addition to the mean magnetic field. The coupled equations exhibit a general mean field dynamo instability that enables the transfer of…
Stratified disks with strong horizontal magnetic fields are susceptible to magnetic buoyancy instability (MBI). Modifying the magnetic field and gas distributions, this can play an important role in galactic evolution. The MBI and the…
To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the…
The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable…
Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The…
We study the nonlinear evolution of the magnetic buoyancy instability in rotating and non-rotating gas layers using numerical solutions of non-ideal, isothermal MHD equations. The unstable magnetic field is either imposed through the…
We analyze the electromotive force (EMF) terms and basic assumptions of the linear and nonlinear dynamo theories in our three-dimensional (3D) numerical model of the Parker instability with cosmic rays and shear in a galactic disk. We also…
It is well--known that when magnetic monopoles are introduced in plasma equations the propagation of electromagnetic waves is modified. This occurs because of Maxwell equations acquire a symmetrical structure due to the existence of…
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear…