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Parkers analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity (tachocline), bounded by a perfect conductor (radiative zone) on the one side, and by a highly diffusive medium (convective zone) supporting an $alpha$-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rate and frequency of dynamo modes is analytically derived. Graphic solution of the dispersion relations displays a somewhat unexpected, non-monotonic behaviour, the mathematical origin of which is elucidated. The dependence of the results on the parameter values (dynamo number and shear layer thickness) is investigated. The implications of this result for the solar dynamo problem are discussed.
We consider mean-field dynamo models with fluctuating alpha effect, both with and without shear. The alpha effect is chosen to be Gaussian white noise with zero mean and given covariance. We show analytically that the mean magnetic field does not gro
A quasi-linear theory is presented for how randomly forced, barotropic velocity fluctuations cause an exponentially-growing, large-scale (mean) magnetic dynamo in the presence of a uniform shear flow, $vec{U} = S x vec{e}_y$. It is a kinematic theory
The stellar parameters of RR Lyrae stars vary considerably over a pulsation cycle, and their determination is crucial for stellar modelling. We present a detailed spectroscopic analysis of the pulsating star RR Lyr, the prototype of its class, over a
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges throug
We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic t