Related papers: The spherically symmetric alpha2-dynamo and some o…
The spectrum of the spherically symmetric alpha-2 dynamo is studied in the case of idealized boundary conditions. Starting from the exact analytical solutions of models with constant alpha-profiles a perturbation theory and a Galerkin…
The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order…
The spectral branching behavior of the 2x2 operator matrix of the magneto-hydrodynamic alpha^2-dynamo is analyzed numerically. Some qualitative aspects of level crossings are briefly discussed with the help of a simple toy model which is…
The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the J-symmetry, an operator…
It is shown that the alpha^2-dynamo of Magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric Quantum Mechanics are closely related as spectral problems in Krein spaces. For the…
The question is answered whether kinematic alpha^2-shell-dynamos are able to produce a cyclic activity or not. The alpha-effect is allowed to be latitudinally inhomogeneous and/or anisotropic, but it is assumed as radially uniform in the…
Until recently, the existence of oscillatory mean-field dynamos of the alpha^2-type with spherically symmetric and isotropic alpha was an open question. We find such dynamos by means of an evolutionary strategy, and we illustrate the…
The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial…
In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it was shown that a simple mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha can exhibit a number of features which are typical…
A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac…
We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and…
Kinney et al [PPL \textbf{1},(1994)] have investigated plasma filamentary structure dynamics. More recently, Wilkin et al [Phys Rev Lett \textbf{99}:134501,(2007)] have shown that kinetic energy spectrum of magnetic structures in…
The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\alpha =(i \nabla + A)^2 + \alpha\delta$ in $L^2(R^2)$ with a $\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\Sigma$ are studied. Here…
We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic $\alpha$--quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
We discuss operators of the type $H = -\Delta + V(x) - \alpha \delta(x-\Sigma)$ with an attractive interaction, $\alpha>0$, in $L^2(\mathbb{R}^3)$, where $\Sigma$ is an infinite surface, asymptotically planar and smooth outside a compact,…
We construct supersymmetric quantum mechanics in terms of two real supercharges on noncommutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two and three dimensional noncommutative superoscillators. We further…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on pseudosphere and compare their spectra and the sets of…
We demonstrate that dynamical symmetry plays a crucial role in determining the structure of the eigenspectra of spinor Bose-Einstein condensates (BECs). In particular, the eigenspectra of spin- 1 and spin-2 BECs in the single-mode…