The 2-D lattice theory of Flower Constellations

The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a $2\times 2$ 2 × 2 lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the $J_2$ J 2 effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.     

Rotating perfect fluids in general relativity

The field equations and the equation of motion for perfect fluids in axially-symmetric-cylindrical coordinates are presented. For rigidly rotating perfect fluid with constant pressure, exact solutions are obtained in symmetric case and axially-symmetric case as well.     

Inhomogeneous perfect fluid cosmologies in (4+1) dimensions

Exact solutions are obtained in (4+1) dimensions for plane symmetric and cylindrically symmetric inhomogeneous spacetimes. In the former case the three space depends on time only while the metric corresponding to the extra dimension is dependent on space as well as time coordinates. The cylindrically symmetric nonstatic solutions for the perfect fluid have no singularity near the axis, but show big bang type of singularity in the finite past. One of the classes of such solutions satisfies the barotropic equation of state of the form =p. Static solutions with cylindrically symmetric solutions are also obtained in 5 dimensions.     

Static wormhole solutions in f(R) gravity

In this work, we study static spherically symmetric wormhole solutions in f(R) gravity. We explore wormhole solutions for anisotropic and isotropic fluids as well as barotropic equation of state with radial pressure. The behavior of weak and null energy conditions is investigated in each case. It is found that these energy conditions are violated for both the anisotropic and isotropic case but are satisfied for barotropic fluids in particular regions. This confirms the existence of wormholes obeying the energy conditions in these regions.     

Regions of stability in rotational dynamics

We investigate the rotational dynamics of a triaxial planet moving on a Keplerian orbit around its star. The dynamics is ruled by several parameters, like the eccentricity, the obliquity, the non-principal rotation, the angular momentum, etc. We consider two specific cases in which the planet is symmetric or asymmetric, according to whether two moments of inertia coincide or differs from each other. We study the dynamics by constructing maps of dynamical stability based on the computation of the maximum Lyapunov characteristic number versus some typical parameters. The results show that only specific resonances appear in the symmetric case, while the asymmetric case shows a much richer phenomenology.     

Modelling the magnetic field and differential rotation effects for the vicinity of the base of convective zone in the Sun

In this work, some numerical solutions of magnetohydrodynamics equations are investigated in the presence of differential rotation with the use of previously developed algorithm. This algorithm includes the thin shell approximation and a special separation of variables which were used to obtain the radial and latitudinal variations of physical parameters in spherical coordinates. The magnetic field profile is chosen to produce comparable magnetic fluxes found in previous works. The sphericity and density shape parameters relevant to model is determined by using two different known differential rotation profiles. It is found that the shape of variations in physical parameters is strongly dependent to magnetic field profile and there is a considerable change in density with respect to reference model. It is as well shown that the spherical symmetric distributions of physical parameters are broken for the region of study.     

Observations of asteroid occultations by the trailed-image method

The method of trailed CCD images for observations of asteroid occultations is described. This method was used to observe 9 asteroid occupations at the Lisnyky observational station in 2006 with the telescope AZT-8 (D= 0.7m and F= 2.8m) equipped by the CCD ST-8 XME. In the case of occultation of the star TYC 0587-00209-1U by the asteroid 76 Freia in November 4, 2006, the distance between the asteroid center and the star, as well as the time of asteroid occultation were determined. The size of asteroid 76 Freia is determined assuming that its shape is spherically symmetric. In other cases, the minimal distances between the asteroid center and the star are determined. The method makes it possible to observe asteroid occultations with high time resolution.     

Prediction of the in-situ dust measurements of the stardust mission to comet 81P⧸Wild 2

We predict the amount of cometary, interplanetary, and interstellar cosmic dust that is to be measured by the Cometary and Interstellar Dust Analyzer (CIDA) and the aerogel collector on board the Stardust spacecraft during its fly-by of comet P⧸Wild 2 and during the interplanetary cruise phase. We give the dust flux on the spacecraft during the encounter with the comet using both, a radially symmetric and an axially symmetric coma model. At closest approach, we predict a total dust flux of 10⁶⁰ m⁻² s⁻¹ for the radially symmetric case and 10⁶⁵ m⁻² s⁻¹ for the axially symmetric case. This prediction is based on an observation of the comet at a heliocentric distance of 1.7 AU. We reproduce the measurements of the Giotto and VEGA missions to comet P⧸Halley using the same model as for the Stardust predictions. The planned measurements of interstellar dust by Stardust have been triggered by the discovery of interstellar dust impacts in the data collected by the Ulysses and Galileo dust detector. Using the Ulysses and Galileo measurements we predict that 25 interstellar particles, mainly with masses of about 10⁻¹² g, will hit the target of the CIDA experiment. The interstellar side of the aerogel collector will contain 120 interstellar particles, 40 of which with sizes greater than 1 μm. Furthermore, we investigate the contamination of the CIDA and collector measurements by interplanetary particles during the cruise phase.     

Epicyclic Frequencies Derived From The Effective Potential: Simple And Practical Formulae

We present and discuss a short and simple derivation of orbital epicyclic frequencies for circular geodesic orbits in stationary and axially symmetric spacetimes. Such spacetimes include as special cases analytically known black hole Kerr and Schwarzschild spacetimes, as well as the analytic Hartle-Thorne spacetime and all numerically constructed spacetimes relevant for rotating neutron stars. Our derivation follows directly from energy and angular momentum conservation and it uses the concept of the effective potential. It has never been published, except for a few special cases, but it has already become a part of the common knowledge in the field.     

Families of Asymmetric Periodic Orbits in the Restricted Three-body Problem

This paper studies the asymmetric solutions of the restricted planar problem of three bodies, two of which are finite, moving in circular orbits around their center of masses, while the third is infinitesimal. We explore, numerically, the families of asymmetric simple-periodic orbits which bifurcate from the basic families of symmetric periodic solutions f, g, h, i, l and m, as well as the asymmetric ones associated with the families c, a and b which emanate from the collinear equilibrium points L ₁, L ₂ and L ₃ correspondingly. The evolution of these asymmetric families covering the entire range of the mass parameter of the problem is presented. We found that some symmetric families have only one bifurcating asymmetric family, others have infinity number of asymmetric families associated with them and others have not branching asymmetric families at all, as the mass parameter varies. The network of the symmetric families and the branching asymmetric families from them when the primaries are equal, when the left primary body is three times bigger than the right one and for the Earth–Moon case, is presented. Minimum and maximum values of the mass parameter of the series of critical symmetric periodic orbits are given. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, we regularize the equations of motion of the problem using the Levi-Civita transformations.     

On the equilibrium of a cylindrical plasma supported horizontally by magnetic fields in uniform gravity

We consider the mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity. This configuration is what may be expected if a quiescent prominence were to condense in a region initially filled with a uniform magnetic field. A set of exact solutions describing the equilibrium situation is presented. Although the plasma distribution is assumed to be cylindrically symmetric to obtain tractibility of the problem, exact force balance between plasma pressure, the Lorentz force and gravity is achieved everywhere in space. The set of solutions covers a particular case of a uniform temperature as well as cases where the temperature rises from zero at the center of the plasma cylinder to rapidly reach a constant asymptotic value outside the cylinder. The physical properties of these solutions are described. A suggestion is made for future development, based on the present work, to construct a prominence model in which the requirements of both mechanical and radiative equilibrium are satisfied.     

Non-Spherical Sources of Strong Gravitational Fields Out of Hydrostatic Equilibrium

We describe the departure from equilibrium of matter distributions representing sources for a class of Weyl metric. It is shown that, for extremely high gravitational fields, slight deviations from spherical symmetry may weaken its tendency to a catastrophic collapse. For critical values of surface gravitational potential, in contrast with the exactly spherically symmetric case, the speed of entering the collapse regime decreases substantially, at least for specific cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies on metric–decimetric Type II bursts in relation to soft X-ray flares

The relationship between metric type II radio bursts and soft X-ray (SXR) flares is studied. Type II bursts are highly associated with SXR flares. The duration and drift rate of type II bursts are found to depend on the duration, asymmetry in duration (ratio of rise time to duration), as well as on the peak flux of SXR bursts. Important results obtained are: (i) the durations of type II bursts are linearly correlated with the durations of associated SXR bursts in case of long-lived events (duration >40 min), whereas in short-lived flares such a correlation is not found, (ii) the durations of type II bursts do not depend upon the SXR peak flux, (iii) more durable type II radio bursts are correlated with more symmetric SXR bursts, (iv) average drift rates of type II bursts are larger in the events associated with more powerful and more symmetric SXR bursts.     

Undamped oscillations of collisionless stellar systems: Spheres,spheroids and discs

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed     

Retrograde Orbits in Ring Configurations of N Bodies

New families of simple, double and triple periodic symmetric retrograde orbits in various ring configurations are presented in this paper, providing new information on the dynamic behavior of such many-body systems. The evolution of the characteristic curves and of their orbits-members is discussed as well as their most prominent qualitative aspects. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cellinoid Shape Model for Asteroids

The ellipsoid shape model plays an important role in physical research on asteroids. However, its symmetric structure cannot practically simulate real asteroids. This article applies a general shape model, named the cellinoid, instead of the ellipsoid model to simulate the asymmetric shape of asteroids. The cellinoid shape model consists of eight octants of ellipsoids having different semi-axes, with the constraint that adjacent octants must have two equal semi-axes in common. Totally, the shape of the cellinoid model is controlled by six parameters, not three as in the case of the shape of the ellipsoid. Using this shape model, the brightness of asteroids observed from the Earth can be fitted numerically by the surface triangularization of the cellinoid. The Levenberg–Marquardt algorithm is also employed here to solve a nonlinear minimization problem. Owing to the asymmetric shape of the cellinoid, the physical parameters of asteroids, such as the rotation period and pole orientation, can be fitted more accurately than in the case of the ellipsoid model. Finally, this is confirmed numerically by applying the shape to both synthetic light curves and real light curves of asteroids. Additionally, the center of mass and moment of inertia of the cellinoid are analyzed explicitly.     

Kantowski–Sachs bulk viscous string cosmological model in Brans–Dicke theory of gravitation

This paper deals with the collapse and expansion of relativistic anisotropic self-gravitating source. The field equations for non-radiating and non-static plane symmetric anisotropic source have been evaluated. The non-radiating property of the fluid leads to evaluation of the metric functions. We have classified the dynamical behavior of gravitational source as expansion and collapse. The collapse in this case leads to the final stage without the formation of apparent horizons while such horizons exists in case of spherical anisotropic source. The matching of interior and exterior regions provides the continuity of masses over the boundary surface.     

Models of forbidden line emission profiles from axisymmetric stellar winds

A number of strong infrared forbidden lines have been observed in several evolved Wolf–Rayet (WR) star winds, and these are important for deriving metal abundances and testing stellar evolution models. In addition, because these optically thin lines form at large radius in the wind, their resolved profiles carry an imprint of the asymptotic structure of the wind flow. This work presents model forbidden line profile shapes formed in axisymmetric winds. It is well known that an optically thin emission line formed in a spherical wind expanding at constant velocity yields a flat-topped emission profile shape. Simulated forbidden lines are produced for a model stellar wind with an axisymmetric density distribution that treats the latitudinal ionization self-consistently and examines the influence of the ion stage on the profile shape. The resulting line profiles are symmetric about line centre. Within a given atomic species, profile shapes can vary between centrally peaked, doubly peaked, and approximately flat-topped in appearance depending on the ion stage (relative to the dominant ion) and viewing inclination. Although application to WR star winds is emphasized, the concepts are also relevant to other classes of hot stars such as luminous blue variables and Be/B[e] stars.     

Keplerian periodic orbits in the isosceles problem

The planar isosceles three-body problem where the two symmetric bodies have small masses is considered as a perturbation of the Kepler problem. We prove that the circular orbits can be continued to saddle orbits of the Isosceles problem. This continuation is not possible in the elliptic case. Their perturbed orbits tend to a continued circular one or approach a triple collision. The basic tool used is the study of the Poincaré maps associated with the periodic solutions. This revised version was published online in July 2006 with corrections to the Cover Date.