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This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
Exact soliton solutions of a modified Landau-Lifshitz equation for the magnetization of conducting ferromagnet in the presence of a spin-polarized current are obtained by means of inverse scattering transformation. From the analytical…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
A techniques, describing electron dynamics for magnetic models closed to cyclical accelerators, is developed and applied to the analysis of electromagnetic radiation emitted by charged particles. Formulas for the angular characteristics of…
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supersymmetric transformations will be used to obtain new…
Basing on self-consistent solution of non-linear GL-equations, the phase boundary is found, which divides the regions of I- and II-order phase transitions of a superconducting cylinder in magnetic field to normal state. This boundary is a…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
An efficient method has been developed for solving the inverse problem of Doppler-Zeeman mapping of magnetic, chemically peculiar stars. A regularized iteration method is used to simultaneously solve the integral equations for the Stokes I,…
This paper presents an overview of the radiative transfer problem of calculating the spectral line intensity and polarization that emerges from a (generally magnetized) astrophysical plasma composed of atoms and molecules whose excitation…
We explore the applicability of the transcorrelated method to the elements in the second row of the periodic table. We use transcorrelated Hamiltonians in conjunction with full configuration interaction quantum Monte Carlo and coupled…
A single spherical antenna is capable of measuring the direction and polarization of a gravitational wave. It is possible to solve the inverse problem using only linear algebra even in the presence of noise. The simplicity of this solution…
We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…
This paper examines the radiative transfer of synchrotron radiation in the presence of a magnetic field configuration resulting from the compression of a highly disordered magnetic field. It is shown that, provided Faraday rotation and…
We employ synthetic observations obtained with MHD simulations to study how to trace the distribution of turbulent magnetic fields using the synchrotron polarization gradient techniques suggested by Lazarian \& Yuen (2018). Both synchrotron…
The exact solution to the Einstein equations that represents a static axially symmetric source deformed by an internal quadrupole is considered. By using the Poincare section method we numerically study the geodesic motion of test…
Semi-Lagrangian solvers for the Vlasov system offer noiseless solutions compared to Lagrangian particle methods and can handle larger time steps compared to Eulerian methods. In order to reduce the computational complexity of the…
We predict the limit cycle solution for a ring-shape bosonic condensate of exciton-polaritons confined in an optically induced rotating trap. The limit cycle manifests itself with polarization oscillations on a characteristic timescale of…
Motivated by experimental developments in non-Kramers spin ice materials and the unclear role of disorder therein, we study the impact of random transverse fields on the dynamics of correlated magnetic systems. We model the effect of…
A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using…
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to…