Propagation of plane relativistic shock waves in a slowly moving medium

Similarity solutions for the propagation of plane relativistic shock waves in a slowly moving medium, where the nucleon number density obeys an exponential law ofx/t, is obtained in this paper. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium.     

Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Propagation of plane relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of plane relativistic shock waves in the presence of a transverse magnetic field for the medium, where the nucleon number density obeys a power law of distance from the plane of explosion. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Propagation of plane relativistic shock waves

Similarity solutions for propagation of plane shock waves in a relativistic gas, where the nucleon number density varies linearly as distance from its edge at near vacuum is obtained. The shock front moves with constant speed and the solutions are applicable only to an isothermal medium or cold gas.     

The equation of polarization transfer in an inhomogeneous magnetized plasma

Following the formalism on the polarization transfer equation presented recently by the same authors, solutions to this transfer equation under several special cases of interest are discussed in this paper. Analytic solutions for the Stokes parameters for several special cases of interest are given, and numerical solutions to these parameters for arbitrary propagation direction and two types of inhomogeneity of the medium are presented.     

Critical properties of spherically symmetric accretion in a fractal medium

Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than it is for a continuum, and in the former case the static sonic condition is met on relatively larger length scales. The dynamic approach also shows that there is a remarkable closeness between an equation  of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. The stationary inflow solutions of a fractal medium are as much stable under the influence of linearized perturbations as they are for the fluid continuum.     

Dynamical friction and formation of structures: Some cosmological and cosmogonical aspects

The influence of dynamical friction on peculiar velocities in a two-component medium is considered. One of the components is assumed to consist of heavy particles with small gravitational interactions and the other is assumed uniform and its particles of much less weight. Here the solutions for the stationary as well as for the cosmologically expanding medium are obtained. These solutions illustrate the possibility for clusters of galaxies to have super-low velocities. It is emphasized that the presence of two components leads to the formation of individual strings and general string structure in one of the component. A string-like structure of the Universe becomes inevitable in the case when an initial perturbations spectrum has a specific scale, and falls down abruptly for larger and smaller distances. Such a picture of the formation of large-scale structure of the Universe is similar to the formation of particle tracks in the Wilson chamber, where tracks are the observational clusters of galaxies, and ‘particles’ are invisible perturbations in the second (neutrino?) component.     

Energy albedo for multiregion slabs

An asymptotic solution for the equation of radiative transfer in an inhomogeneous medium was obtained on the basis of the corresponding solutions for homogeneous sub-layers in the slowing down region. Function relations between the reflection and transmission coefficients for the whole slab and those of the sublayers are given. The invariant embedding concepts are used to get the reflection and transmission coefficients for the sub-layers. We assumed different models for the slowing-down kernels. Laplace transform was used to transform the Boltzmann equation to one velocity approximation with re-scaled mean-free path and single-scattering albedo. Numerical results are given for energy albedo as a function of the mass number of the host medium.     

The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting half-space

The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting medium described by tensor constitutive parameters is studied. Starting from the Maxwell-Minkowski equations the wave solutions in the laboratory frame, the modified law of refraction and the reflecton and the transmission coefficients are obtained both for incidentE- andH-waves, corresponding to the two specific orientations of the plane of incidence relative to the direction of motion of the medium. The reflection and the transmission coefficients for a moving conducting medium do not, in general, add to unity resulting in the possibility of energy transference between the moving medium and the transmitted wave. Further the various reflection and transmission characteristics are modified in an interesting manner due to the finite conductivity, the anisotropy and the motion of the medium. Numerical results for the reflection and the transmission coefficients are presented for a range of the parameters characterizing the anisotropy and the velocity of the moving medium.     

Unsteady MHD free-convection flows on a porous plate with time-dependent heating in a rotating medium

The three-dimensional unsteady free-convection flows of a viscous fluid near a porous infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green function of the problem is determined and exact solutions are obtained for special cases of the impulsive and the accelerated heating effect for an arbitrary Prandtl number. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layers are discussed.     

Self-similar magnetogasdynamic cylindrical shock waves,I

Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.     

Properties of dispersive Alfvén waves: 3. Hydrodynamics (Very Low,Intermediate, and Low Density Plasmas)

The behavior of dispersive Alfvén waves (DAWs), including inertial and kinetic Alfvén waves, in astrophysical plasmas of very low, intermediate, and low pressure is investigated in the hydrodynamic approximation. New full solutions are obtained. Our results are analyzed and compared with those from the kinetic approach. It is shown that one general solution for the DAWs in plasmas of very low, intermediate, and low pressure can be obtained in the framework of the hydrodynamic approach, as opposed to the kinetic one. In the very low damping region, the kinetic and hydrodynamic solutions agree very well; but there are parameter regions where the solutions are essentially different. The influence of the astrophysical medium parameters on the DAW behavior and properties is analyzed. All main wave characteristics—the dispersion, damping, polarization, density perturbations, and charge density perturbations—are obtained, whose the consideration is very important for the observation and detection of these waves, as well as for a more correct understanding of their behavior and role in various astrophysical processes taking place in the cosmic medium.     

Effects of stepwise variation of single-scattering albedo on reflectivity and transmissivity of a linear-anisotropically scattering slab

Unsteady free-convection flows near an infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green's function of the problem is determined and exact solutions are obtained for special cases of the time-dependent heating effect. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layer are determined, and the structure of the thermal wave trains is discussed.Formerly Kulshrestha.     

Free and forced convection flow through a porous medium near the leading edge

Locally similar solutions of the combined free and forced convection flow in a semi-infinite vertical porous medium are obtained by a perturbation method. The solutions, obtained near the leading edge of the plate, are discussed in comparison with the numerical results obtained by Raptis and Perdikis (1988).     

Plane relativistic shock waves at the edge of a gas

Similarity solutions for propagation of plane relativistic shock waves through a medium of decreasing nucleon density and approaching the edge of the gas as well as for the subsequent motion of the gas after the shock front arrives at the vacuous boundary are studied in this paper. The medium in the pre-disturbed stage is assumed cold and in the disturbed stage its equation of state is taken as that of a photonic gas.     

An isothermal shock wave in a perfectly-conducting and non-homogeneous stellar interior

In the present paper, we have obtained some exact analytic self-similar solutions for a zero-temperature gradient behind a magnetogasdynamic shock wave produced by stellar explosions. The initial density of the medium is taken to vary as some power of the distance from the point of explosion. The solutions are obtained for the cases when the energy of the shocked gas is constant, the energy is varying, and the shock velocity is constant. General solutions are also obtained. We have also analytically obtained the position of the singular surface behind the shock wave.     

Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid

We study the unsteady free-convection flow near a moving infinite flat plate in a totating medium by imposing a time-dependent perturbation on a constant plate temperature. The temperatures involved are assumed to be very large so that radiative heat transfer is significant, which renders the problem very nonlinear even on the assumption of a differential approximation for the radiative flux. When the perturbation is small, the transient flow is tackled by the Laplace transform technique. Complete first-order solutions are deduced for an impulsive motion.     

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.     

Similarity solutions for a stellar line explosion

Similarity solutions for line explosion in a non-uniform self-gravitating medium including the effects of magnetic field radiation flux and neglecting the radiation pressure and energy are investigated. Gas is assumed to be grey and opaque and the shock to be transparent and isothermal.     

A self-similar flow behind a spherical shock wave with thermal radiation,I

Similarity solutions, for one-dimensional unsteady flow of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling, are investigated. The shock ahead of the point of explosion or piston is propagating into a transparent medium at rest with non-uniform density. The total energy of the wave is assumed to be time dependent obeying a power law.