Related papers: A fast dynamo on the three-torus
Chicone et al [CMP (1995)] have shown that, kinematic fast dynamos in diffusive media, could exist only on a closed, 2D Riemannian manifold of constant negative curvature. This report, shows that their result cannot be extended to…
Analytical solution of first order torsion ${\alpha}$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while…
We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary…
We study the three-dimensional spontaneous flow transition of an active nematic in an infinite slab geometry using a combination of numerics and analytics. We show that it is determined by the interplay of two eigenmodes -- called S- and…
We consider the kinematic dynamo equations for a passive vector in $\mathcal{M} \times \mathbb{T} \subseteq \mathbb{R}^2 \times \mathbb{T}$ describing the evolution of a magnetic field with resistivity $\varepsilon>0$, that is transported…
Earlier Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP (1982)}] have computed the eigenvalue of a uniform stretching torus transformation which result on the first Riemann metric solution of the dynamo action problem. Recently some…
This paper provides a functional analytic approach to differential equations on Banach space with slowly evolving parameters. We develop a Fenichel-like theory for attracting subsets of critical manifolds via a Lyapunov-Perron method. This…
We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of magnetic field…
Recently Tang and Boozer [{\textbf{Phys. Plasmas (2000)}}], have investigated the anisotropies in magnetic field dynamo evolution, from local Lyapunov exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux tubes…
In this work, we report analytical results on transverse domain wall (TDW) statics and field-driven dynamics in quasi one-dimensional biaxial nanowires under arbitrary uniform transverse magnetic fields (TMFs) based on the…
If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that classical linearized stability theorem does not apply to it.…
The axisymmetric kinematic dynamo problem is reconsidered and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions, i.e. we assume a…
Modifications on a recently introduced fast dynamo operator by Chiconne et al [Comm Math Phys 173, 379 (1995)] in compact 3D Riemannian manifolds allows us to shown that slow dynamos are Lagrangean stable, in the sense that the sectional…
We consider kinematic dynamo action in rapidly rotating Boussinesq convection just above onset. The velocity is constrained to have either a square or a hexagonal pattern. For the square pattern, large-scale dynamo action is observed at…
A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by P. Hartman in 1960 for operators on finite-dimensional…
We combine simulations with new analyses that overcome previous pitfalls to explicate how nonhelical mean-field dynamos grow and saturate in unstratified, magnetorotationally driven turbulence. Shear of the mean radial magnetic field…
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the…
The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method,…
We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier-Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping…
The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding…