Singular value decomposition for the 2D fan-beam Radon transform of tensor fields

In this article we study the fan-beam Radon transform ${\cal D}_m$ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2\pi)\times[0,2\pi)).$ The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor fields on the disc $\mathbb D$ was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator ${\cal D}_m$ was obtained. The inversion formula for the fan-beam tensor transform ${\cal D}_m$ follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.Comment: LaTeX, 37 pages with 5 figure

A Solvable Model for Nonlinear Mean Field Dynamo

We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity field is Gaussian and white in time (the Kazantsev-Kraichnan ensemble), while the regular part describing the back reaction of the magnetic field is chosen from balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.Comment: 6 page

The Adler DD-function for N=1{\cal N}=1 SQCD regularized by higher covariant derivatives in the three-loop approximation

We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the $D$-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for ${\cal N}=1$ SQCD is found in this scheme to the order $O(\alpha_s^2)$. The problem of scheme-dependence of the $D$-function and the NSVZ-like equation is briefly discussed.Comment: 25 pages, 2 figures; the version accepted for publication in Nuclear Physics

On the possible origin of meteoroid generating asteroid orbits

A mechanism to replenish the Apollo and Amor groups by resonant asteroid-orbit transformation is suggested. The method of this mechanism and the results obtained are discussed