On the self-consistent model of an axisymmetric radio pulsar magnetosphere

We consider a model of axisymmetric neutron star magnetospheres. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the stream equation describing the magnetic field structure is linear both in the open and closed regions; the main problem is matching the solutions along the separatrix. We demonstrate that it is the stability condition on the separatrix that allows us to obtain a unique solution of the problem. In particular, the zero point of magnetic field is shown to be located near the light cylinder. Moreover, the hypothesis of the existence of the non-linear Ohm's Law, connecting the potential drop in the pair creation region and the longitudinal electric current flowing in the magnetosphere, is confirmed.     

Nonlinear Kelvin-Helmholtz magnetohydrodynamic instability of a rotating plasma

Nonlinear analysis for Kelvin-Helmholtz instability of an incompressible, inviscid, rotating fluid with infinite conductivity in the presence of gravity and surface tension has been discussed. The unperturbed magnetic field on two sides of the interface is taken to be uniform. The nonlinear Schrödinger equation for the time variation of amplitude of small perturbations with wave number around the neutral stability is derived. It is found that stability of a magnetised K-H rotating configuration depends on the density ratio, surface tension, and discontinuity of velocity and magnetic field. The effect of an aligned magnetic field and rotation on the non-linear instability of a rotating conducting plasma has been discussed in certain important limiting cases.     

Gravitational stability of dark energy in galaxies and clusters of galaxies

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.     

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker–Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.     

The effect of perturbations in coriolis and centrifugal forces on the nonlinear stability of equilibrium points in the restricted problem of three bodies

Celestial Mechanics and Dynamical Astronomy - The non-linear stability of the equilibrium points in the restricted problem has been studied when small perturbations ε and ε′ are...     

Effects of gyroviscosity and hall currents on the stability of a stratified rotating self-gravitating plasma

Instability in a horizontal layer of a stratified rotating self-gravitating plasma is studied to include simultaneously the effects of Hall currents and the finiteness of the ion Larmor radius. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of the unstable perturbations decreases with both coriolis forces and gyroviscous effects. The influence of the effects of gyroviscosity as well as of Coriolis forces is consequently stabilizing. Hall currents are found to have a destabilizing influence as the growth rate is found to increase with this effect.     

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z _f≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.     

Kink instability of relativistic force-free jets

A non-linear equation is found that describes helical equilibrium of relativistic force-free flows. Linear stability of the axisymmetrical jet with respect to helical perturbations is investigated. The growth rate of the kink instability is found.     

Effects of small external forces on the planar oscillation of a cable connected satellites system

The effects of small external dissipative and disturbing forces on the non-linear planar oscillation of a cable connected satellites system in the central gravitational field of earth have been studied. Typical non-linear oscillation's phenomena arizing from the aforesaid external forces are shown to take place. The presence of these forces enables the application of asymptotic methods of the theory of non-linear oscillations due to Bogoliubov and Mitropolsky to the equation characterizing the non-linear oscillation of the system.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

Thermodynamic study of non-linear electrodynamics in loop quantum cosmology

In this work, we have discussed the Maxwell’s electrodynamics in non-linear forms in FRW universe. The energy density and pressure for non-linear electrodynamics have been written in the electro-magnetic universe. The Einstein’s field equations for flat FRW model in loop quantum cosmology have been considered if the universe is filled with the matter and electro-magnetic field. We separately assumed the magnetic universe and electric universe. The interaction between matter and magnetic field have been considered in one section and for some particular form of interaction term, we have found the solutions of magnetic field and the energy density of matter. We have also considered the interaction between the matter and electric field and another form of interaction term has been chosen to solve the field equations. The validity of generalized second law of thermodynamics has been investigated on apparent and event horizons using Gibb’s law and the first law of thermodynamics for magnetic and electric universe separately.     

Quasi-viscous accretion flow – I. Equilibrium conditions and asymptotic behaviour

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the α-viscosity parameter. This method reduces the problem of solving a second-order non-linear differential equation (Navier–Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this 'quasi-viscous' flow are saddle points and spirals. On large spatial scales of the disc, where a linearized and radially propagating time-dependent perturbation is known to cause a secular instability, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length-scale has been defined for the full spatial extent over which the accretion process would be viable.     

The relation between magnetic and gas arms in spiral galaxies

The intriguing question of the origin of the arm-like magnetic structures seen between the optical spiral arms of certain spiral galaxies is addressed. Using a two-dimensional approximation to the non-linear disc dynamo equation, it is shown that gas streaming along the arms may produce such a field configuration. Another possibility is a spiral modulation of the turbulent diffusivity, associated with an enhancement of turbulence in the interstellar medium within the arms. The effects of a similar modulation of the alpha-effect are also examined. Finally, the consequences of a non-linear feedback of the large-scale field on the turbulent diffusivity ('η-quenching') are briefly discussed.     

Radial periodic perturbations of the Kepler problem

We consider radial periodic perturbations of a central force field and prove the existence of rotating periodic solutions, whose orbits are nearly circular. The proof is mainly based on the Implicit Function Theorem, and it permits to handle some small perturbations involving the velocity, as well. Our results apply, in particular, to the classical Kepler problem.     

Magnetic field variations of the SI in the magnetosphere and correlated effects in interplanetary space

Explorer 26 magnetic field data in the magnetospheric region of L=3?6 and LT 1100–1500 hr with geomagnetic latitude range ?6° to 27° have been analyzed for studying nineteen SI and SC events. Most of the SI events observed in the magnetosphere at less than 15° geomagnetic latitude are compressional with magnetic perturbations along the ambient field. Elliptic polarizations with magnetic field variations in all three components have been observed between 10° and 27° geomagnetic latitude. Polarization directions have been shown to have similar patterns to those observed in the surface magnetic field data. Afternoon LT zone data in the magnetosphere indicate polarization patterns in general agreement with the results of Wilson and Sugiura (1961) obtained earlier from surface observations. The SI/SC perturbations are also qualitatively shown to be related to changes in the interplanetary magnetic field observed beyond 1 a.u.     

Duality rotations and type D solutions of Einstein-Born-Infeld theory

Within the non-linear electrodynamics of Born-Infeld type, constrained by the condition that admits the freedom of the duality rotations the explicit type D solutions, which generalize the charged Taub-NUT metric with cosmological constant, are constructed. The obtained type D solution exhausts all solutions within the considered class, assumed that the real eigenvectors of the electromagnetic field are aligned along the geodesic and shear-free principa null directions.     

Massive scalar field interacting with viscous fluid distribution in cosmological models

The study of Einstein's field equations describing Robertson-Walker cosmological models with massive scalar field and viscous fluid representing the matter has been made. The problem has been investigated with and without the source density in the wave equation. Corresponding exact solutions of the field equations have been obtained under different physical equations of state: namely, (i) dust distribution, (ii) Zeldovich fluid distribution, (iii) disordered distribution of radiation subject to physically realistic conditions. The physical interpretations of the physically realistic solutions has been investigated. It has been found that physically realistic solutions has been obtained for closed cosmological models only.     

Stationary incompressible MHD perturbationsgenerated by a current source in a moving plasma

We consider the inductive interaction between a conducting body and a magnetizedincompressible plasma in relative uniform motion, which has application to the Io–Jupitersystem, for example. An incompressible plasma only supports one mode of propagation, namelythe Alfvén mode. In the case of free oscillations, this mode propagates the perturbations in themagnetic field and in the plasma velocity unattenuated along the direction of the backgroundfield, while the plasma pressure balances the magnetic pressure. The situation changes in thepresence of source currents and in a flowing plasma. In particular, the parallel plasma vorticityand parallel plasma current are propagated unattenuated along the familiar Alfvéncharacteristics, while the field and velocity perturbations suffer Laplacian decay in the near field.We study these perturbations in the frame of the body and compare them to the case of no sourceterms.     

Generation of magnetosonic waves and formation of structures in galaxies

We study the generation of magnetosonic waves in galactic gaseous discs taking account of the magnetic field, differential rotation and self-gravity. The special case of perturbations is considered with the wavevector perpendicular to the magnetic field. The necessary condition of the amplification of seed perturbations is the presence of differential rotation and non-vanishing radial component of the magnetic field that can easily be satisfied in galactic discs. Differential rotation stretches the azimuthal field from the radial one and, therefore, we consider the generation of waves on the time-dependent background magnetic field. Basically, an amplification is rather efficient, and seed perturbations become non-linear already after several rotation periods for a wide range of wavelength. The generated magnetosonic waves can be either non-oscillatory or oscillatory depending on the parameters of gas. If perturbations are Jeans stable, then typically non-oscillatory waves are amplified. However, interplay between self-gravity, magnetic field and rotational shear can change qualitatively the classical Jeans instability, so that the latter becomes oscillatory and tends to be suppressed in galaxies.     

The growth of density perturbations in the Lemaître universe

The rate of growth of density perturbations in certain Lemaître universes has been investigated using the differential equation derived by Bonnor. The perturbations that must be postulated at decoupling are not significantly different from those required in the conventional zero-pressure Friedmann-Lemaître models.