Numerical solution of the dam failure problem by the random choice method

A numerical solution of the dam failure problem as described by the one-dimensional shallow water equations is presented. The construction of the solution is based on the random choice method consisting in the superposition of locally theoretical solutions and sampling techniques. The search of the optimal sampling is performed through the application of the random choice method to the scalar wave equation. The dam failure problem is then solved and a comparison with the theoretical solution is presented. It is shown that the random choice method computes the bore with almost infinite resolution, represents exactly the constant state behind it and calculates the depression wave with great accuracy.     

Far-infrared brightness temperature of Saturn's disk and rings

We present far-infrared observations of Saturn in the wavelength band 76–116 μm, using a balloon-borne 75-cm telescope launched on 10 December 1980 from Hyderabad, India, when B′, the Saturnicentric latitude of the Sun, was 4°.3. Normalizing with respect to Jupiter, we find the average brightness temperature of the disk-ring system to be 90 ± 3° K. Correcting for the contribution from rings using experimental information on the brightness temperature of rings at 20 μm, we find T_D, the brightness temperature of the disk, to be 96.9 ± 3.5° K. The systematic errors and the correction for the ring contribution are small for our observations. We, therefore, make use of our estimate of T_D and earlier observations of Saturn when contribution from the rings was large and find that for wavelengths greater than 50 μm, there is a small reduction in the ring brightness temperature as compared to that at 20 μm.     

A search for energetic neutrons emitted during solar flares

On the basis of solar flare forecasts, balloon flights were made from Hyderabad, India (vertical geomagnetic threshold rigidity of 16.9 GV), to detect the possible emission of high energy neutrons during solar flares. The detector comprised of a central plastic scintillator, completely surrounded by an anticoincidence plastic scintillator shield. The instrument responds to neutrons of about 15–150 MeV and gamma rays of about 5–30 MeV with about the same efficiency. The detector was flown to an atmospheric depth of 25 g cm^-2 on February 26, 1969; while the balloon was at ceiling a flare of importance 2B and one of 1N occurred. No perceptible flare associated increase in the counting rate was observed. Using the observed counting rates, an upper limit of 1.2 × 10^-2 neutrons cm^-2 sec^-1 is obtained for the first time for a flare of importance 2B for neutrons of energy 15–150 MeV. The corresponding upper limit for gamma rays of energy 5–30 MeV is found to be 10^-2 photons cm^-2 sec^-1. The neutron flux limits are compared with the recent calculations of Lingenfelter.     

The energy spectrum of cosmic ray electrons between 10 and 1000 GeV

Measurements made by the Bombay Group on the fluxes of cosmic ray electrons in the energy range 10–1000 GeV have been compared with those of other workers in the same energy domain with a view to understand the present confused situation on the existing observations at these high energies. Such an analysis clearly brings out the current situation in its true perspective and highlights the care and emphasis to be placed on future experimentation in this important field.     

Transit or occultation?

Published discussions of photometric observations of VZ Hya and CM Lac disagree as to whether the deeper eclipses are transits or occultations. The evolutionary histories of these systems are critically dependent on a resolution of the disagreement. The luminosity ratio of the components of VZ Hya, inferred from spectrograms, shows unequivocally that the deeper eclipse is a transit. The case of CM Lac is less definitive. While the photometric observations favor primary minimum as a transit, the ratio of the radii is close to unity, and neither the spectrograms nor the photometry leads to an unequivocal result. Some confusion in notation appearing in a discussion of the components of EI Cep is noted. In each of the three cases the observational evidence favors a straightforward evolutionary interpretation in which the more massive star is the larger.     

Correlating fracture trends and hydraulic head using semivariogram cloud analysis

Fracture trends (defined as kilometer-scale linear features interpolated between field observations of fractures along their strikes) often have a dominant orientation. Finding a correlation between this orientation and hydraulic data could shed light on their hydraulic influence. A significant correlation between head residuals from first-order regional drift and the orientation of 2- to 4-km-long fracture trends was found in a study site in the Negev, Israel, using the semivariogram cloud analysis. Correlation of head residuals rather than the head itself implies that the orientation of the fracture trends controls the anisotropy and heterogeneity at this scale, mainly because the fracture trends define the orientation of blocks, which differ in their hydraulic properties. Preferential transmissive pathways are probably shorter than the full extent of the fracture trends, causing a relatively high head difference along the trends on the 2- to 4-km scale. Fracture trend density and additional data from short-range hydraulic tests helped characterize two blocks separated by a fault zone. The identification of hydraulic features on a kilometer scale is necessary for better modeling of regional ground water flow and transport. Hydraulic tests at this scale are not feasible, thereby rendering combined analyses of head and structural data, such as the one presented here, essential.     

Compositional effects on element partitioning between Mg-silicate perovskite and silicate melts

High-pressure melting experiments were performed at ~26 GPa and ~2,200–2,400°C on synthetic peridotite compositions with varying FeO and Al₂O₃ contents and on a synthetic CI chondrite analogue composition. Peridotite liquids show a crystallisation sequence of ferropericlase (Fp) followed down temperature by Mg-silicate perovskite (MgPv) + Fp, which contrasts a sequence of MgPv followed by MgPv + Fp observed in the chondritic composition. The difference in crystallisation sequence is a consequence of the different bulk Mg/Si ratios. MgPv/melt partition coefficients for major, minor and trace elements were determined by electron microprobe and secondary ion mass spectrometry. Partition coefficients of tri- and tetravalent elements increase with increasing Al concentration in MgPv. A lattice strain model indicates that Al³⁺ substitutes predominantly onto the Si-site in MgPv, whereas most elements substitute onto the Mg-site, which is consistent with a charge-compensating coupled substitution mechanism. MgPv/melt partition coefficients for Mg (D_Mg) and Si (D_Si) are related to the melt Mg/Si ratio such that D_Si becomes lower than D_Mg at low Mg/Si melt ratios. We use a crystal fractionation model, based on upper mantle refractory lithophile element ratios, to constrain the amount of MgPv and Ca-silicate perovskite (CaPv) that could have fractionated during a Hadean magma ocean event and could still be present as a chemically distinct heterogeneity in the lower mantle today. We show that a fractionated crystal pile composed of 96% MgPv and 4% CaPv could comprise up to 13 wt% of the entire mantle.