An axially symmetric explosion model in magnetogasdynamics: II

A method using Eulerian coordinate system is developed under a local radiality assumption to study a point explosion in a spheroid with axially symmetric exponential density distribution, including the effect of azimuthal magnetic field.     

Axially symmetric explosion in magnetogasdynamics

A point explosion in a spheroid with axially symmetric exponential density distribution is investigated by generalizing the method of Laumbach and Probstein to include the effects of a magnetic field. It is shown that the shock velocity decreases and tends to zero. Also, the elongation of the shock envelope along the axis of symmetry is much reduced and the blowout of the shock wave is removed on account of the magnetic field.     

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.     

Non-similarity solutions for cylindrical shock waves in radiative magnetogasdynamics,I

The propagation of radiative-magnetogasdynamic cylindrical shock waves in an exponentially increasing medium is investigated. The shock wave moves with variable velocity and the total energy of the wave is also variable. The transformations in terms of , as given in the text, is necessarily a non-similarity one.     

An explosion with cylindrical symmetry in magnetogasdynamics

The propagation of magnetogasdynamic cylindrical shock waves in an exponentially increasing medium including the effects of the azimuthal magnetic field, is investigated. The shock wave moves with variable velocity and the total energy of the wave is variable. It is shown that the magnetic field has its significant effect on the pressure flow velocity and the inner expanding vacuum region.     

Report on the dynamical evolution of an axially symmetric quasar model

The role of the angular momentum in the regular or chaotic character of motion in an axially symmetric quasar model is examined. It is found that, for a given value of the critical angular momentumL _zc , there are two values of the mass of the nucleusM _n for which transition from regular to chaotic motion occurs. The [L _zc – M _n ] relationship shows a linear dependence for the time independent model and an exponential dependence for the evolving model. Both cases are explained using theoretical arguments together with some numerical evidence. The evolution of the orbits is studied, as mass is transported from the disk to the nucleus. The results are compared with the outcomes derived for galactic models with massive nuclei.     

Analytical solutions of cylindrical shock waves in magnetogasdynamics,I

The C.C.W. method has been used to investigate the propagation of converging and diverging cylindrical shock waves in a non-uniform medium under the influence of a magnetic field of constant strength. A comparison has also been made between the two types of cylindrical shock waves, simultaneously for both weak and strong cases of the magnetic field. Density distribution is assumed to be _o = r ^–, where is the density at the axis of symmetry and a constant. The analytical expressions for shock velocity and shock strength as well as the pressure, the density, and the particle velocity just behind the shock front have been derived for both the cases.     

Exact analytic solutions for the rotation of an axially symmetric rigid body subjected to a constant torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.     

Five-dimensional axially symmetric string cosmological model in Lyra manifold

In this paper we constructed five dimensional axially symmetric cosmological model generated by a cloud of strings with particles attached to them in Lyra manifold. Out of the two different cases obtained one case leads to the five dimensional vacuum universe in general theory of relativity while the other case yields a string cosmological model in Lyra manifold. In the cosmic string model we observed that the sum of tension density and rest energy density of strings vanishes and this model is also inflationary.     

On stationary axially symmetric solutions of a scalar-tensor theory of gravitation

In this paper we obtain the general axially symmetric space-times in scalar-tensor theory of gravitation proposed by Sáez and Ballester. The only possible solutions of these space-times in this theory are dust solutions. One of the obtained solutions here has a similar considerations to Van Stockum dust solution. A detailed study of geometric and kinematical properties of the obtained solutions are carried out. Furthermore, closed timelike curves are present in these solutions.     

Similarity parameters for converging shock waves in non-ideal magnetogasdynamics by Landau-Stanyukovich rule

In present paper, I have studied second-kind self-similar solutions of converging cylindrical shock wave in non-ideal magnetogasdynamics. Two trial functions suggested by Singh et al. and the shooting method of Landau–Stanyukovich are used to determine the similarity exponent α for different values of specific heat ratio γ and the parameter k, where k∈(0,1] and internal volume $\tilde{b}$ in non-ideal magnetogasdynamics.     

Self-similar solutions for the blast wave problem in magnetogasdynamics,II

The problem of explosion along a line in a gas cloud in the presence of transverse magnetic field has been considered. Similarity solutions of the adiabatic motion of a gas behind an infinitely strong cylindrical shock wave propagating into an infinitely conducting medium at rest is obtained. Shock radius varies exponentially with time and density is inversely proportional to fourth power of shock radius just ahead of the shock front.     

Degeneracy of semi-analytic solution for axially symmetric lens equations

We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when   r /ξ₀≪ 1  and ξ₀ is the scalelength of the density profile. At the strong lensing regime, which is mostly constrained by the inner part of the mass density profile, we assume ρ∝ r ^α.
A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c ₁ and the total mass M . We apply our semi-analytical model to show how the solutions of the axially symmetric lens equations are degenerated in respect to the parameters α and c ₁.
In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed.
Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter  α=[−2.0, −1.0]  .     

Axially symmetric explosion in a spheroid

The method of Laumbach and Probstein is applied to a point explosion in a spheroid with exponential density distribution. It is shown that the shock wave propagates strongly along the direction of symmetry axis and the envelope of the shock front elongates to the same direction. The rate of elongation of the shock envelope increases with the eccentricity of the spheroid and finally the blowout of the shock wave along the polar axis occurs when the eccentricity exceeds some critical value. It is suggested that such a blowout of the shock may be connected with some galactic outburst having axial symmetry.     

A method of computing the gravitational field of an axially symmetric flat galaxy

A method has been developed for computing the gravitational force field of an axially symmetric flat galaxy from its surface mass density. The method is simple to program, fast, and accurate. An inversion formula is derived that allows computation of surface density from rotation curves by use of any method that converts density to force. The method is compared with a method of Clutton-Brock that utilizes Hankel transforms of Laguerre functions.     

On static and spherically symmetric solutions of Starobinsky model

We investigate the problem of static and spherically symmetric solutions in the Starobinsky gravity model.By extending the Lichnerowicz and Israel theorems, William Nelson has demonstrated that the Schwarzschild solution is the unique static, spherically symmetric and asymptotically flat black hole solution in the Starobinsky model.However, Hong Lüet al.find that there are sign errors in the proof of Nelson.This raises the problem of whether Nelson's proof is correct or not.In order to answer this question, we explore the corresponding solutions by using the Taylor series expansion method.We find that Nelson's conclusion is indeed correct despite the flaw in the proof.     

On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field

The projection of an axially symmetric satellite's orbit on a plane perpendicular to the rotation axis (z=const.) is given by the second-order differential equation. $$\frac{{y''}}{{1 + y'^2 }} = \bar \Psi _y - y'\bar \Psi _{x,}$$ where the prime denotes the derivative with respect tox and \(\bar \Psi (x,y)\) is a known function. Two integrability cases have been investigated and it has been shown that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the calssical plane eikonal equation of geometric optics.