Plasma Flows in Solar Filaments as Electromagnetically Driven Vortical Flows

Electromagnetic expulsion acts on a body suspended in a conducting fluid or plasma, which is subject to the influence of electric and magnetic fields. Physically, the effect is a magnetohydrodynamic analogue of the buoyancy (Archimedean) force, which is caused by the nonequal electric conductivities inside and outside the body. It is suggested that electromagnetic expulsion can drive the observed plasma counter-streaming flows in solar filaments. Exact analytical solutions and scaling arguments for a characteristic plasma flow speed are reviewed, and their applicability in the limit of large magnetic Reynolds numbers, relevant in the solar corona, is discussed.

New Optical Soliton Solutions to the Fractional Hyperbolic Nonlinear Schrödinger Equation

This paper is aimed at investigating the soliton solutions of the hyperbolic nonlinear Schrödinger equation. Exact analytical solutions of the model are acquired through applying an integration method, namely, the Sine-Gordon method. It is observed that the method is able to efficiently determine the exact solutions for this equation. Graphical simulations corresponding to some of the results obtained in the paper are also drawn. These results can help us better understand the behavior and performance of this model. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.

Dirac Particle in the Coulomb Field on the Background of Hyperbolic Lobachevsky Model

The known systems of radial equations describing the relativistic hydrogen atom on the base of the Dirac equation in Lobachevsky hyperbolic space is solved. The relevant 2-nd order differential equation has six regular singular points, its solutions of Frobenius type are constructed explicitly. To produce the quantization rule for energy values we have used the known condition for determination of the transcendental Frobenius solutions. This defines the energy spectrum which is physically interpretable and similar to the spectrum arising for the scalar Klein-Fock-Gordon equation in Lobachevsky space. In the present paper, exact analytical solutions referring to this spectrum are constructed. Convergence of the series involved is proved analytically and numerically. Squared integrability of the solutions is demonstrated numerically. It is shown that the spectrum coincides precisely with that previously found within the semi-classical approximation.

Dynamics of Hyperbolically Symmetric Fluids

We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative, and the central region cannot be attained by any fluid element. We describe this inner region by a vacuum cavity around the center. By assuming a causal transport equation some interesting thermodynamical properties of these fluids are found. Several exact analytical solutions, which evolve in the quasi–homologous regime and satisfy the vanishing complexity factor condition, are exhibited.

Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body

Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed. All result of the paper is based on the Fourier’s theory of heat conduction in solid bodies. Examples illustrate the applications of the developed method

Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

A mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.

Velocity Dependence and Tracer Dispersion in Newtonian Fluids Undergoing Creeping Flow

The dynamics of tracer particles in a viscous Newtonian fluid is studied analytically and numerically through channels of varying thickness for fluids undergoing creeping flow. Exact analytical solutions of mass conservation equations of tracer particles including consideration for pressure forces are obtained. Results of the analysis indicates that Stokes velocity is an indispensable parameter and is dependent on parameters such as channel thickness (height), viscosity of the fluid, pressure gradient driven the fluid and Reynolds number corresponding to the channel thickness. The accuracy of the solution obtained is verified by comparing its velocity profiles with those obtained from finite-element-based numerical simulation studies.