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.     

Collapse and explosion in a rotating star

The collapse, bounce, shock wave and expansion of the envelope of a rotating star have been analysed in the adiabatic approximation using the particle-in-cell method. The bounce takes place first in the equatorial plane and a shock wave arises there which shortly afterwards crosses the surface of the star. In the envelope, and to a less extent in the remainder of the star, there is a fast and lasting meridional motion the direction of which changes. As a consequence of the fast meridional motion in the envelope, mass and angular momentum are transported towards the axis of rotation. If the initial star rotates fast enough this will cause a secondary radial expansion in the polar region and a mass ejection. These motions reduce the strong anisotropy caused originally by the equatorial expansion. Strong whirls may arise along the axis of rotation. In the remainder of the star the meridional motion becomes supersonic. The temperature in the envelope depends to a high degree on the choice of the equation of state. Massloss is proportional to the energy initially added. The final loss of angular momentum and of energy is quite large, both losses being about 25%.     

Response of Rigid Rotators to Gravitational Radiation

The response of an axially symmetric rigid rotator to incident gravitational radiation is discussed for particular states of free rotator motion using generalized EULERian equations, and assuming wavelengths large compared with the rotator dimensions. First, if coincident initially, the rotation and the symmetry axes slightly differ after exposed to a radiation flux which has suitable polarization and propagates perpendicular to the rotation axis. Secondly, the angular velocity of a rotation perpendicular to the symmetry axis is changed in a wave field propagating in the direction of the rotation axis (BRAGINSKI-rotator). — For highly monochromatic resonance radiation with wave frequencies equal to the rotation frequency (in the first case) or twice the rotation frequency (second case), the response is sufficiently large to have some interest for future experiments.     

Tidal effects of the galaxy on a globular cluster

Tidal effects of a Schmidt (1965) model galaxy on a typical globular cluster moving in an orbit along the axis of symmetry of the spheroid is studied under the impulsive approximation. Ann-body simulation is made for comparison. Results show that in both cases, a high concentration cluster gains enough energy to be totally dissolved within a distance of 2 kpc. A significant mass loss occurs as the cluster approaches the Roche distance.     

Rotating self-gravitating fluid spheroid with a magnetic field

The equilibrium of a self-gravitating fluid spheroid is examined in the presence of a rotation and a poloidal magnetic field. It is shown that ‘true equilibrium’ allows only rigid rotation for a spheroid of a small eccentricity.     

An explosion model in magne to gasdynamics

By taking into account the interaction with magnetic field, in an axially symmetric inhomogeneous medium and assuming Gaussian density profile in radial direction instead of the cusped exponential law, a point explosion has been investigated by generalising the method suggested by Laumbach and Probstein (1969). The shock envelope becomes increasingly elongated along the axis of rotation, until it finally breaks through into the intergalactic space before it can spread considerably in equatorial directions as in ordinary gasdynamics. A comparison has been made between our results and those obtained in ordinary gasdynamics.Explosion models of double radio sources and related objects are suggested.     

Large Meteoroid Fragmentation: Modeling the Interaction of the Chelyabinsk Meteoroid with the Atmosphere

The interaction between a large meteoroid and the atmosphere is modeled as its destruction into a cloud of fragments and vapors moving with a common shock wave. Under the action of aerodynamic forces the shape of this cloud is deformed—it is expanded in the direction transverse to the motion and compressed in the longitudinal direction. With allowance for the pressure distribution over the surface of a body varying its shape (it is assumed that the sphere is transformed into a flattened spheroid), the relation for the rate of increase in the midsection radius of a fragmented meteoroid has been obtained. This rate significantly depends on the degree of the meteoroid flattening which leads to a significantly smaller increase in the transverse size of the meteoroid along the trajectory as compared to similar models used in the literature where the influence of the body shape was not considered. The proposed model also takes into account the change in the density of the cloud of fragments due to an increase in gaps between them. An approximate analytical solution of equations of the physical theory of meteors with drag and heat transfer coefficients varying along the trajectory has been obtained for a fragmented meteoroid. The interaction of the Chelyabinsk meteoroid with the atmosphere is modeled and the solution obtained for the energy release curve is compared with the observational data.     

The equilibrium configuration of rapid rotating compact stars and some gravitational effects

In this paper, the equilibrium configurations of rapid rotating compact stars and some gravitational effects are studied within the general relativity by use of the Harrison-Wheeler equation of state and by the self-consistent field method. Numerical calculations show that the equilibrium configuration of a rotating star is a spheroid. For large spin velocities, say, ω > 3.0 × 10² sec⁻¹ the eccentricity and mass increase very rapidly as the angular velocity increases, for the critical angular velocity of the rotating star, the eccentricity is about 0.7, the increase in mass is about 10–35%. The difference of the gravitational redshifts at the surface of the star caused by rotation, and the difference of the light bending when the beam moves in the direction of rotation or in the opposite direction are obvious.     

Preferred orientation distribution of shock‐induced planar microstructures in quartz and feldspar

Shocked quartz and feldspar grains commonly exhibit planar microstructures, such as planar fractures, planar deformation features, and possibly microtwins, which are considered to have formed by shock metamorphism. Their orientation and frequency are typically reported to be randomly distributed across a sample. The goal of this study is to investigate whether such microstructures are completely random within a given sample, or whether their orientation might also retain information on the direction of the local shock wave propagation. For this work, we selected samples of shatter cones, which were cut normal to the striated surface and the striation direction, from three impact structures (Keurusselkä, Finland, and Charlevoix and Manicouagan, Canada). These samples show different stages of pre‐impact tectonic deformation. Additionally, we investigated several shocked granite samples, selected at different depths along the drill core recovered during the joint IODP‐ICDP Chicxulub Expedition 364 (Mexico). In this case, thin sections were cut along two orthogonal directions, one parallel and one normal to the drill core axis. All the results refer to optical microscopy and universal‐stage analyses performed on petrographic thin sections. Our results show that such shock‐related microstructures do have a preferred orientation, but also that relating their orientation with the possible shock wave propagation is quite challenging and potentially impossible. This is largely due to the lack of dedicated experiments to provide a key to interpret the observed preferred orientation and to the lack of information on postimpact orientation modifications, especially in the case of the drill core samples.     

Magnetorotational supernovae. Magnetorotational instability. Jet formation

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×10⁵¹ erg.     

Modelling of self-similar cylindrical shock wave in radiating magnetogasdynamics,I

Self-similar flows of a perfect gas behind a cylindrical blast wave with radiation heat flux in the presence of an azimuthal magnetic field have been investigated. The effects of radiation flux and magnetic field together on the other flow variables have been studied in the region of interest. The magnetic field and density distribution vary as an inverse power of radial distance from the axis of symmetry. The electrical conductivity of the gas is taken to be infinite. The total energy of the flow between the inner expanding surface and the shock is assumed to be constant. We also have supposed the gas to be grey and opaque and the shock to be transparent and isothermal.     

Contraction of near-Earth satellite orbits using uniformly regular KS canonical elements in an oblate atmosphere with density scale height variation with altitude

A new non-singular analytical theory for the contraction of near-Earth satellite orbits under the influence of air drag is developed in terms of uniformly regular Kustaanheimo and Stiefel (KS) canonical elements using an oblate atmosphere with variation of density scale height with altitude. The series expansions include up to fourth power in terms of eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. It is observed that the analytically computed values of the semi-major axis and eccentricity are consistent with the numerically integrated values up to 500 revolutions over a wide range of the drag-perturbed orbital parameters. The theory can be effectively used for re-entry of near-Earth objects.     

Multiple resonance in one problem of the stability of the motion of a satellite relative to the center of mass

We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities.     

Hypersonic beam driven by high-energy particles in extragalactic radio sources

A mechanism is proposed for the formation of collimated beams in radio galaxies. The collimated flows which are non-thermally driven by high energy particles and magneto-hydrodynamic (MHD) waves are presented. The galactic nucleus surrounded by a cool gas is investigated. The cool gas accretes onto the nucleus and the accretion matter can confine the wave zone around the nucleus in which the high energy particles are completely locked to the MHD waves. When a quasi-radial magnetic field is embedded in the accretion flow, the MHD wave packets are collimated into the direction of symmetry axis of the galactic nuclear disc. The fluid around the nucleus is considered to be accelerated and heated by the MHD waves and ejected along the axis.A complete set of hydrodynamic equations which contain the energy transfers of high energy particles and MHD waves is presented. One-dimensional flows which are in pressure equilibrium with the surrounding accretion matter are calculated. When the energy density of the MHD waves is higher than that of the thermal energy, the fluid flow is strongly collimated in a narrow beam. When the MHD waves are strongly damped by the resistivity of the fluid at the great distance from the galactic centre, the collimated beam broadly reexpands. On the basis of the collimated beams driven by high energy particles, the radio morphology of the double radio sources is discussed.     

Observation of a tilt of Titan's middle-atmospheric superrotation

Maps of isotherms on surfaces of constant pressure in Titan's middle atmosphere encircle the poles but show an offset, implying that the mean zonal flow has an axis of symmetry that is tilted relative to the spin axis of the solid body. The effect is seen in both hemispheres around a consistent axis. Periodogram analysis of the temperature field shows that wavenumber one, the signal corresponding to the spin tilt, is the strongest wave component. We conjecture that the tilt of the atmospheric spin is due to a feedback between the flow and the solar heating. The spin adjusts itself to align the spin equator with the direction toward the Sun, and thereby maximizes the efficiency with which the meridional circulation pumps angular momentum upward to generate superrotation.     

Formation of bipolar flow by the stellar wind embeded in molecular disk

The interaction of the isotropic stellar wind with the rotating isothermal cloud surrounding the young star is investigated. The density distribution of the cloud is taken as that for the equilibrium state of the rotating isothermal cloud modified by adding the rarefied interstellar gas in the polar region. The development of the shock envelope and the structure of the shell induced by the stellar wind are obtained. It is shown that the envelope of the shock front elongates and opens to the polar direction with half opening angle of about 20 degrees resulting the bipolar flow which is able to reproduce well the observed properties for the outflow in the bipolar sources.     

Similarity solutions for an axially symmetric explosion model in magnetogasdynamics. I

Similarity solutions, for a point explosion in a spheroid with axially symmetric density distribution obeying power laws in the presence of magnetic field, are obtained. A new technique suggested by Bhowmick (1978) has been utilised to study the character of flow variables behind the shock front in an axisymmetric model. The total energy of the wave is constant.     

Prediction of satellite orbits contraction due to diurnally varying oblate atmosphere and altitude-dependent scale height using KS canonical elements

A new non-singular analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of uniformly regular KS canonical elements. Diurnally varying oblate atmosphere is considered with variation in density scale height dependent on altitude. The series expansion method is utilized to generate the analytical solutions and terms up to fourth-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere) are retained. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The important drag perturbed orbital parameters: semi-major axis and eccentricity are obtained up to 500 revolutions, with the present analytical theory and by numerical integration over a wide range of perigee height, eccentricity and inclination. The differences between the two are found to be very less. A comparison between the theories generated with terms up to third- and fourth-order terms in c and e shows an improvement in the computation of the orbital parameters semi-major axis and eccentricity, up to 9%. The theory can be effectively used for the re-entry of the near-Earth objects, which mainly decay due to atmospheric drag.     

Analytical orbit predictions with air drag using KS uniformly regular canonical elements

A new nonsingular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed for long term motion in terms of the KS uniformly regular canonical elements by a series expansion method, by assuming the atmosphere to be symmetrically spherical with constant density scale height. The series expansions include up to third order terms in eccentricity. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semi major axis and eccentricity up to 1000 revolutions, obtained with the present solution, with KS elements analytical solution and Cook, King-Hele and Walker's theory with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination.     

Some cosmological models with spin and torsion,I

The Einstein-Cartan theory, which is a slight modification of the general theory of relativity, is almost indistinguishable in its practical consequences from the latter theory. A characteristic spin-spin repulsive interaction which is of some importance at ultraheavy densities, prevents the singularities occurring in the Einstein-Cartan treatment. It is shown how this mechanism of preventing the singularity applies to cosmological models in which the spins of matter are aligned along some symmetry axis. Some exact solutions without singularities of the relevant set of equations are obtained.