Phase transition in K2Cd2(SO4)3: Order parameter and microscopic distortions

The transition from P2₁3(T ⁴) to P2₁2₁2₁(D ₂ ⁴ ) in the langbeinite K₂Cd₂(SO₄)₃ has been analyzed using group theoretical methods and previously published structural data above and below the transition. We find that because the transition is strongly first-order, the primary-order parameter has relatively large values at the transition temperature, and higher order terms which involve the order parameter, the strain, and the coupling of the two must be included in the Landau expansion for the free energy. Complex displacements occur at the transition for all atoms of the unit cell, but these displacements can be resolved into contributions which can be shown from symmetry considerations to transform as the _{2 3} irrep of P2 ₁ 3(T ⁴) as well as contributions from symmetry-preserving displacements which transform under the irrep ₁. Therefore, the transition is not a simple one and involves sulfate rotations and cadmium and potassium ion displacements.     

Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

Multifrequency behayiour of the dwarf nova SS Cygni

Several years of coordinated multifrequency observations of the dwarf nova SS Cygni have been performed in order to study the accretion behaviour of this system in particular, and in general to clarify this crucial problem for the cataclysmic variables.From IUE measurements, together with those from optical and IR ground based telescopes, we have found orbital modulations in the continuum and in the equivalent widths of the emission lines. During quiescent phases the behaviour of SS Cygni are dependent on the type of the preceding outburst (long-type or short-type).In this paper we will discuss the physical implications one can derive from these results.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.Based on the observations performed with IUE (VILSPA) satellite, and with the telescopes of the Loiano and Roque de los Muchachos Observatories.     

Astron observations of the Rapid Burster MXB 1730-335 and constraints on burster parameters from spectra of trailing bursts

We report on eight X-ray bursts detected by ASTRON from the Rapid Burster (RB) on 13 and 28 April and 16 August, 1983. Six of them (trailing bursts), with durations of 1.5–2 min, rise times of 5–10 s and intervals of 1–1.5 hours, exhibit spectral softening during the burst decay and may be related to the type I bursts. Two of the bursts (triangle bursts) observed on 28 April at interval of 28 min with much longer rise times (30–50 s) and longer durations (3 min), do not show distinct spectral softening. Persistent flux from RB on 16 August was estimated asF _p(2.0–2.4)×10^–9 erg cm^–2 s^–1. Spectral evolution of two trailing bursts was investigated by fitting their spectra in consecutive time intervals with the blackbody (BB), isothermal scattering photosphere (SP) and thermal bremsstrahlung (TB) models. Around the burst maxima the SP model fits the data best whereas in the burst tails the TB model is generally better. The BB model is worse than at least one of the two others. Interpretation of the burst spectra in terms of the BB radiation leads to improbably small neutron star mass and radius (M<0.86M ,R _NS<5 km) if the peak luminosity does not exceed the Eddington limit. Interpretation of the spectra around the burst maxima (3–15 s from the burst onset) in terms of an isothermal SP yields reasonable constraints onM,R _NS, and distanceD. For instance, for the hydrogen photosphere we obtainedM=(1.0–2.1)M R _NS=(7.1–16.4) km ifD=11 kpc. If one postulatesM=1.4M , thenD=(8.5–13) kpc for hydrogen photosphere; if, besides,D=11 kpc, thenR _NS=(8.1–13.3) km. It follows also from the SP-interpretation that the photosphere radius may increase up to 20–30 km in maxima of the trailing bursts when the luminosity becomes close to the Eddington luminosity.     

Experimental investigation of the elastic modulus of a fractal system—A model of fractured rocks

The elastic properties of a physical model representing a damaged rock matrix were studied using a square lattice deformed under tensile stress. The elastic modulusM of such a system varies in agreement with percolation theory as|x–x _c | ^f , wherex is the damage parameter andx _c the threshold value of the damage parameter,f3.6. Atxx _c the scale dependence ofM can be expressed asML ^–f/v , whereL is the size of the sample andv the correlation exponent in percolation theory.The experimental results are of interest in assessing elastic properties in earthquake focal zones and fault zones in general.     

Intercomparison of measurements of stratospheric hydrogen fluoride

Observations of the vertical profile of hydrogen fluoride (HF) vapor in the stratosphere and of the vertical column amounts of HF above certain altitudes were made using a variety of spectroscopic instruments in the 1982 and 1983 Balloon Intercomparison Campaigns. Both emission instruments working in the far infrared spectral region and absorption instruments using solar occultation in the 2.5m region were employed. No systematic differences were seen in results from the two spectral regions. A mean profile from 20–45 km is presented, with uncertainties ranging from 20% to 50%. Total columns measured from ground and from 12 km are consistent with the profile if the mixing ratio for HF is small in the tropophere and low stratosphere.     

Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

The use of analytical solutions of the diffusion equation for footprint prediction is explored. Quantitative information about the footprint, i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.     

X-ray of gamma-ray bursts observable by HEAO-B

On grounds of Mazetset al. (1980a) conclusion that all gamma-ray bursts recorded were emitted at the distance 1 kpc from the Sun it is shown that bursts from the Galaxy and from another galaxies may be observable byEinstein Observatory (HEAO-B). The HEAO-B observing programs are considered and the numbers of possibly recorded events are estimated. It is concluded that the important information about sources of gamma-bursts may be obtained in this way.     

Periodic orbits around an oblate spheroid

The general properties of certain differential systems are used to prove the existence of periodic orbits for a particle around an oblate spheroid.In a fixed frame, there are periodic orbits only fori=0 andi near /2. Furthermore, the generating orbits are circles.In a rotating frame, there are three families of orbits: first a family of periodic orbits in the vicinity of the critical inclination; secondly a family of periodic orbits in the equatorial plane with 0<e<1; thirdly a family of periodic orbits for any value of the inclination ife=0.