Related papers: Asymptotic Solutions for Mean-Field Slab Dynamos
We carried out global three-dimensional magneto-hydrodynamic simulations of dynamo activities in galactic gaseous disks without assuming equatorial symmetry. Numerical results indicate the growth of azimuthal magnetic fields non-symmetric…
Large-scale magnetic fields in stars and galaxies are thought to arise by mean-field dynamo action due to the combined influence of both helical turbulence and shear. Those systems are also highly conducting and the turbulence therein leads…
We consider the generation of magnetic field by a turbulent flow. For the linear induction equation (i.e. the kinematic dynamo problem), we show that the statistical moments of the magnetic field display multiscaling and in particular…
Galaxies are observed to host magnetic fields with a typical total strength of around 15microgauss. A coherent large-scale field constitutes up to a few microgauss of the total, while the rest is built from strong magnetic fluctuations over…
Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and…
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote…
The drift-Alfven instabilities in the magnetic field aligned (parallel) sheared flow of a finite beta plasma with comparable inhomogeneous ion temperature and homogeneous electron temperature are examined. The development of instabilities…
Using recent results on the operation of turbulent dynamos, we show that a turbulent dynamo can amplify a large scale magnetic field in the envelopes of asymptotic giant branch (AGB) stars. We propose that a slow rotation of the AGB…
We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect,…
The first results of the solar dynamo model that allows for the diamagnetic effect of inhomogeneous turbulence and the nonlocal alpha-effect due to the rise of magnetic loops are discussed. The nonlocal alpha-effect is not subject to the…
We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivation of the guiding-center approximation in the general three…
This paper is devoted to the construction of semiclassical spectrum and efficient (simple to implement) explicit semiclassical asymptotic eigenfunctions of the Dirac operator for relatively high-energy bound states in graphene in magnetic…
We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $\alpha$ effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale non-axisymmetric magnetic fields on the Sun.…
Aims. We investigate the cosmological evolution of large- and small-scale magnetic fields in galaxies in the light of present models of formation and evolution of galaxies. Methods. We use the dynamo theory to derive the timescales of…
Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $\alpha$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of…
Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than…
We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…
In this paper we consider spiral wave solutions of a general class of $\lambda-\omega$ systems with a small parameter $q$ and we prove that the asymptotic wavenumber of the spirals is a $\mathcal{C}^{\infty}$-flat function of the…