Limit shocks of relativistic magnetohydrodynamics

In this paper we show that switch-on and switch-off shocks are allowed by the shock equations of relativistic MHD and have similar properties to their Newtonian counterparts. Just like in Newtonian MHD they are limits of fast and slow shock solutions and as such they may be classified as weakly evolutionary shocks.     

On the relativistic formulation of matter

A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are otherwise different in general relativity.     

Coupled-channel calculation for cross section of fusion and barrier distribution of ${}^{16,17,18}\mbox{O} + {}^{16}\mbox{O}$ reactions

In this work, the effect of multi-phonon excitation on heavy-ion fusion reactions has been studied and fusion barrier distributions of energy intervals near and below the Coulomb barrier have been studied for ^16,17,18O + ¹⁶O reactions. The structure and deformation of nuclear projectiles have been studied. Given the adaptation of computations to experimental data, our calculations predict the behavior of reactions in intervals of energy in which experimental measurements are not available. In addition the S-factor for these reactions has been calculated. The results showed that the structure and deformation of a nuclear projectile are important factors. The S-factor, obtained in the coupled-channel calculations for the \({}^{16}\mbox{O} + {}^{16}\mbox{O}\), \({}^{17}\mbox{O} +{}^{16}\mbox{O}\) and \({}^{18}\mbox{O} +{}^{16}\mbox{O}\) reactions, showed good agreement with the experimental data and had a maximum value at an energy near 5, 4.5 and 4 MeV, respectively.     

The magnetohydrodynamics of black-hole accretion

The solution of basic flow equations of perfect magnetofluid in the fixed background of Kerr space-time has been obtained. We assume that magnetofluid (test) flow around a Kerr black hole is stationary and axisymmetric. A particular solution exhibits the property that flow lines lie on circles of constant radius. In addition, it is found that magnetofluid is endowed with frozen-in magnetic field-i.e., that it moves with the material.     

The magnetohydrodynamics of stellar structures

The equation governing the equilibrium of a centrally-symmetric, self-gravitating distribution of matter is obtained by assuming that matter is described by magnetofluid and it is shown that the equation of stellar structure described by an ideal fluid is recovered when magnetic fieldh is vanishing     

The general analytical expression for computation of generalized relativistic Fermi-Dirac functions

In this paper, general sufficiently analytical formulae are developed for the arbitrary order generalized relativistic Fermi-Dirac (FD) functions. Analytical assessment of relativistic FD function is very important for various fields of physics especially in the theory of relativistic nondegenerate and degenerate electron gas systems. One of the more appropriate and correct approximations is based on a binomial expansion method and incomplete Gamma functions that have been used in the calculations of the generalized relativistic FD functions. Note that, the established expression in special cases of specific values of parameters becomes the evaluation formulae of other type FD functions. Calculation results of the generalized relativistic FD functions are compared with the other approximations methods and available numerical approaches and demonstrated satisfactory agreement.     

Quantum scattering of KCl with He/para-$\mbox{H}_{2}$: potential energy surface and rate coefficients at low temperature

We present new two- and four-dimensional potential energy surfaces for the KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-He and KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-para-H₂ systems calculated with the internuclear distances of KCl and H₂ frozen at their experimental minimum energy. The CCSD(T) level of theory with aug-cc-pVQZ/AQZP basis sets is used. The potential surfaces present well depths of about \(78~\mbox{cm}^{-1}\) and \(235~\mbox{cm}^{-1}\) below the dissociation limit of the above interacting systems respectively. With these potential surfaces, cross sections are obtained in the close coupling scheme and rate coefficients inferred by averaging the cross sections over a Maxwell-Boltzmann velocity distribution for temperature below 50 K. A propensity towards \(\Delta J = 1\) transitions is observed.     

The dielectric analogue of magnetohydrodynamics

Almost half a century after Alfvén first conceived of the science of magnetohydrodynamics, it is still possible to trace his intuitive thinking to explore physical processes heretofore not considered. The ideas of magnetohydrodynamics (applicable to conducting fluids) can be transferred almost intact to purely dielectric fluids, such that we can arrive at a generalized concept applicable toany fluid-conducting or dielectric. In this sense, Alfvén's conception of magnetohydrodynamics may be ideationally even more profound than it has been thought to be so far.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Statefinder diagnostic for Born-Infeld type dark energy model with V_{0}e^{-\beta\varphi^{2}} potential

We investigate in this paper the dynamics of Born-Infeld (B-I) type dark energy model with scalar potential $V_{0}e^{-\beta\varphi^{2}}$ , and consider the new statefinder diagnostic to differentiate B-I type dark energy model from LCDM which corresponds to statefinder pair {r,s}={1,0}. We study the existence of attractor solution in this model and the evolving trajectory of r?s in our model with this scalar potential. It is numerically shown that the evolving trajectory of r?s is quite different from those of other dark energy models.     

Galaxy rotation curves: the effect of $\vec{j} \times\vec{B}$ force

Using the Galaxy as an example, we study the effect of [(j)\vec] ×[(B)\vec]\vec{j} \times \vec{B} force on the rotational curves of gas and plasma in galaxies. Acceptable model for the galactic magnetic field and plausible physical parameters are used to fit the flat rotational curve for gas and plasma based on the observed baryonic (visible) matter distribution and [(j)\vec] ×[(B)\vec]\vec{j} \times\vec{B} force term in the static MHD equation of motion. We also study the effects of varied strength of the magnetic field, its pitch angle and length scale on the rotational curves. We show that [(j)\vec] ×[(B)\vec]\vec{j} \times\vec{B} force does not play an important role on the plasma dynamics in the intermediate range of distances 6–12 kpc from the centre, whilst the effect is sizable for larger r (r≥15 kpc), where it is the most crucial.     

Stability of general relativistic Miyamoto–Nagai galaxies

The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well-known Miyamoto–Nagai model that represents well a thick galactic disc. The stability of the disc is investigated under a general first-order perturbation keeping the space–time metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disc. We find that flat galaxies have more non-stable modes than the thick ones, i.e. flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.     

A mathematical solution of general relativistic binary systems

A mathematical solution for general relativistic binary systems is obtained. A conclusion concerning the black hole in some binary systems is deduced from the mathematical solution.     

The magnetohydrodynamics of black hole accretion

The entropy accretion rate of perfect thermodynamic magnetofluid (test) flow is obtianed in the framework of Kerr space-time. Accretion by a moving black hole is also investigated, and it is shown that the moving black hole is able to focus the magnetofluid flow lines.     

Lissajous motion near Lagrangian point $$ L_{2} $$ in radial solar sail

An attempt was made to study the dynamics close to the collinear libration point \( L_{2} \) of the radial solar sail circular-restricted three-body problem (RSCRTBP) in the Sun–Jupiter System, where the third massless body is a solar sail. We analyse the qausi-periodic (Lissajous solutions) orbits about the libration point \( L_{2} \). The Lindstedt–Poincaré approximation for the qausi-periodic orbits was used for numerical simulations. We utilized linear quadratic regulator (LQR) to stabilize the full nonlinear model, and linear state-feedback controller was designed to stabilize the trajectory.     

A general relativistic effect in quasi-spherical objects as the possible origin of relativistic jets

Based on recently reported results, we present arguments indicating that sign changes in proper acceleration of test particles on the symmetry axis and close to the r=2M surface of quasi-spherical objects—related to the quadrupole moment of the source—might be at the origin of relativistic jets of quasars and micro-quasars.     

Treatment of pulsating white dwarfs including general relativistic effects

In this paper, pulsating white dwarfs are treated via general relativity. Numerical integration of Einstein's equations was used to find equilibrium white dwarfs models and the fundamental periods of small oscillations about these equilibrium models. In these calculations account was taken of coulomb, Thomas-Fermi, and exchange interactions as well as ion zero point energies. It is shown that general relativity makes not just a quantitative difference in the results but a qualitative differences; pure C¹² models which are stable in Newtonian mechanics can be unstable against collapse (at a central density of 3×10¹⁰ g/cm³) when general relativity is taken into account. The collapsing model may become a neutron star or may continue towards the Schwarzschild radius.More realistic white dwarf models with carbon burning products at the center, also were studied. For these models, the density at which the star becomes unstable against collapse due to electron capture (3×10⁹ g/cm³) was found to be lower than the density at which general relativistic instability occurs.     

Rotational cross sections and rate coefficients of $\mathrm{CP}(\mathrm{X}^{2}\varSigma ^{+})$ induced by its collision with He(1S)$\mathrm{He}(^{1}S)$ at low temperature

The potential energy surface (PES) for the \(\mathrm{CP}(\mathrm{X}^{2}\varSigma^{+})\)-\(\mathrm{He}(^{1}S)\) complex has been calculated at the RCCSD(T)-F12/VTZ-F12 level of theory. The analytic fit of the PES was obtained by using global analytical method. The fitted PES was used subsequently in the close-coupling approach for the computation of the state-to-state collisional excitation cross sections of the fine-structure levels of the CP-He complex. Collision energies were taken up to 1500 cm^?1 and they yield after thermal averaging, state-to-state rate coefficients up to 200 K. The propensity rules between the lowest fine-structure levels were studied. These rules show, on one hand, a strong propensity in favour of even \(\Delta N\) transitions, and the other hand, that cross sections and collisional rate coefficients for \(\Delta j =\Delta N\) transitions are larger than those for \(\Delta j\neq \Delta N\) transitions.