(Super) cosmological solution for the Kasner model

In the theory of supergravity (N=1), the supersymmetric version of general relativity, and for the Kasner cosmological model (Bianchi type I) we find a non-trivial solution (for the metric and spinor-vector) under the most simple assumption =₁₁ + ₂₂; ₁₂+₂₁=0 and for a special choosed gaugeN=1,N ^j=0, ₀=0. This method could be also applied to other cosmological metrics and extended to enlarged Grassmann basis.O. Obregón was partially supported by the Alexander von Humboldt Stiftung.     

High order symplectic integrators for perturbed Hamiltonian systems

A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(^p + ²²), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(^p +⁴²). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.     

Effect of perturbations on the stability of triangular points. In the restricted problem of three bodies with variable mass

The effect of small perturbations and in the coriolis and the centrifugal forces respectively on the stability of the triangular points in the restricted problem of three bodies with variable mass has been studied. It is found that the range of stability of triangular points increases or decreases depending upon whether the perturbation point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line J₈–J₉=0 where J₈ and J₉ depend upon , the constant due to the variation in mass governed by Jeans' law.     

Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem

The location and the stability of the libration points in the restricted problem have been studied when small perturbation and are given to the Coriolis and the centrifugal forces respectively. It is seen that the pointsL ₄ andL ₅ form nearly equilateral triangles with the primaries and the pointsL ₁,L ₂,L ₃ remain collinear. It is further observed that for the pointsL ₄ andL ₅, the range of stability increases or decreases depending upon whether the point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line 36-19=0 and the stability of the collinear points is not influenced by the perturbations and they remain unstable.     

On the stability of equilibria of Hamiltonian systems near the main resonances

The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as ₂=2₁+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported.     

Estimation of the clear sky and the ground emissivity in Bahrain

The clear sky emissivity ₀ and the ground emissivity _g in Bahrain is studied. The study reveals that the annual value of ₀ is 0.88 ± 0.039 relating to the maximum and the minimum values in August and February, respectively. Meanwhile, the annual value of _g is 0.338 ± 0.228, where the maximum and the minimum values are in July and January, respectively. These two parameters are related to the transmittance factor .     

Nonlinear waves in a low-density plasma with a strong magnetic field

The nonlinear evolution of waves in a low-density plasma in a strong magnetic field is investigated on the basis of the Chew-Goldberger-Low approximation. The nonlinear effects are found to be essentially different for the magneto-acoustic and Alfvén modes. For the magnetic-acoustic mode, waveform distortion occurs at order ² (where is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order ^–1. For the Alfvén wave, modulation occurs at order ³ and shock formation over a time-scale of order ^–2. The nature of the waveform distortion is qualitatively different for the two modes.     

Time variation of the spectrum of Gyro-synchrotron emission from the Sun

The emission spectra and their time variations of gyro-synchrotron emission from an ensemble of energetic electrons are computed for some initial power-law distributions of the electron energies N()d= ^– with =2 or 4. The spectra and decay curves of the emission are compared with solar microwave bursts in order to separately estimate the magnetic field H and . From a limited number of observations, we have 3 and H 10³ gauss for the microwave impulsive bursts, and 2 and H (500–1000) gauss for the microwave type-IV bursts.     

Stability criteria in many-body systems

An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters ^ki _li {i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters ²³ and ₃₂. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters ²³ and ₃₂ for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of ²³ and ₃₂.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the ²³, ₃₂ plane and show the results agree well with the ²³, ₃₂ analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems.     

Near-infrared observations of the peculiar binary system epsilon Aurigae

Near-infrared photometric and low-resolution spectroscopic observations of Aurigae at two phases during the current eclipse are presented. The eclipse depths are found to be wavelength-independent in the infrared right up to 2.5 m. There is no infrared excess at wavelengths shorter than 2.5 m. The light absorbing particles in the eclipsing body must be larger than 10 m in size.     

Masses of macroscopic quark configurations in metric and dynamic theories of gravitation

Within the bounds of the general relativity and in gravidynamics, spherically-symmetric configurations are considered with the limit equation of state (P = ( - 4B)/3) and with the density increasing to the center. It is shown that unlike GR, where the existence of strange stars only is permissible (u-, d-, s-quarks), in the consistent dynamic theory of gravitation the existence ofstable configuration withr ^–2 (quark star) is possible with a bag out of quark-gluon plasma which includes all possible quark flavors (u, d, s, c, b, t, .. .). The total mass of such a compact object with the bag of the radius of 10 km (whose surface consists of the strange self-bound matter) must be 6 - 7M .     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

Stimulated comption effect in very compact radio sources

Expressions for the stimulated Compton effect are derived that are complete to order /ge/, where is the photon energy in the laboratory system, and =m ₀ C ² is the electron energy. Explicit formulas are given for the energy flow between a relativistic electron and a radiation field that obeys a power law so that the number of photons is proportional to ^–m–1. The amount of energy gained by an electron per second is then numerically calculated for conditions suggested by very compact radio sources as a function of the width of the spectrum, the spectral index, and the electron energy.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Absolute and relative amplitudes of variations in radius of classical cepheids

On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).     

Simple derivation of Symplectic Integrators with First Order Correctors

In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(h ⁶)+(² h ²), where is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(h ⁶)+(² h ⁴).This revised version was published online in October 2005 with corrections to the Cover Date.     

On the origin of the metagalaxy

An attempt is made to explain two properties of the metagalaxy: its expansion and the absence of causal connection of its distant regions during a large part of its initial history. It is postulated that the gravitating matter was born from the cosmological field, i.e., a medium with equation of statep=–.It is shown that such a postulate explains the expansion of metagalaxy and leads to a correct estimate of the entropy per baryon. The problem of causal connection can also be solved on this basis.     

Line formation in spherical media with partial frequency redistribution

Lines formed in a differentially expanding atmosphere have been calculated by using the angle averaged redistribution functionR _I (Hummer, 1962). We have compared these lines, in a few cases, with those formed by complete redistribution in the observer's frame of reference. We have considered an atmosphere whose ratios of inner to outer radii are 2 and 10, and it is assumed that the gas in the atmosphere is expanding uniformly with a maximum velocity of 3 mean thermal units. We have presented lines formed in spherical symmetry and those obtained by integrating over the apparent disc. Three types of physical situations are considered with a 2-level atom with non-LTE approximation (1) =10^–4, =10^–4, (2) =10^–4, =0 and (3) ==0, where is the probability per scatter that a photon is destroyed by collisional de-excitation, and is the ratioKc/Kl of absorption in the continuum per unit frequency interval to that in the line centre.It is found that there are noticeable differences between the profiles formed by partial redistribution (PRD) and complete redistribution (CRD). The profiles integrated over the stellar disc from the first type of the media are box type with flat top, which are similar to those observed in WC stars and those from the second type of media show emission peaks on red and blue sides with emission on the red side larger than the one on the blue side. The profiles from the third type of media with pure scattering, show some emission on the red side and deep absorption on the blue side. Large geometrical extensions of the atmosphere and higher gas velocities seem to enhance these two effects.     

A new microwave/X-ray diagnostic for the thermal phase of solar flares

We have observed 10 solar bursts during the thermal phase using the Haystack radio telescope at 22 GHz. We show that these high frequency flux observations, when compared with soft X-ray band fluxes, give useful information about the temperature profile in the flare loops. The microwave and X-ray band fluxes provide determinations of the maximum loop temperature, the total emission measure, and the index of the differential emission measure (q(T)/T = cT^–1). The special case of an isothermal loop ( = ) has been considered previously by Thomas et al. (1985), and we confirm their diagnostic calculations for the GOES X-ray bands, but find that the flare loops we observed departed significantly from the isothermal regime. Our results ( = 1–3.5) imply that, during the late phases of flares, condensation cooling ( 3.5) competes with radiative cooling ( 1.5). Further, our results appear to be in good agreement with previous deductions from XUV rocket spectra ( 2–3).     

The libration of a satellite caused by the tidal field of its planet

The tidal field caused by the second order zonal harmonic of the gravitational field of a planet is discussed according to the fernwirkungsgesetz (principle of local action) of Weyl (1921) introducing an accurate and simple form of the gravitational potential of the planet in elliptic coordinates. It is seen that the tidal field can be described at each point as a small rotation of the local canonical frame which causes a libration and a precession of the axis of rotation of the satellites of the planet. It is also shown that at each point P, is one third of the angle between the line of force through P and the line from P to the center of mass of the planet. All the formulae obtained, to compute and , are in closed form.     

The Tokyo PMC catalog 85

The catalog of positions of 1007 stars (792 FK4 and FK4S stars, 57 OB stars, 49 NPZT stars, and 109 SAO stars) is presented. They were observed during the period from December 1984 to September 1985 with the Tokyo Photoelectric Meridian Circle (Tokyo PMC). The positions in the catalog are referred to the equinox and equator of J2000, and are based on the FK4 system. The internal errors of a single observation were estimated to be ( cos, )=(0.16, 0.19), whereas the mean internal errors of the catalog positions were (0.08, 0.08) for FK4 stars and (0.09, 0.11) for FK4S stars. A comparison of the positions of the FK4 stars in the present catalog with those of the FK4 catalog shows significant differences cos and in some declination zones. Some of those differences are commonly found in other recent catalogs. Thus they may be considered to be real systematic errors in the FK4 system. Neither significant magnitude nor color equations exist in the Tokyo PMC 85 catalog.