The generation of multidimensional autoregressive series by the herringbone method

The generation of isotropic artificial series in two or three dimensions by the autoregressive process is of considerable interest for the purpose of modeling environmental properties such as ore grade or reservoir porosity. The relations needed to produce bilateral symmetry using the one-sided autoregressive recursion equations have been attained on the square net and on the isometric lattice by an alternation procedure. In the case of the square net, the one-sided autoregressive (AR) process is alternated between the two diagonals of the net, while in three dimensions, the alternation takes place among the four body diagonals of the isometric cell.     

Compton effect interpretation of solar red shift

The hypothesis that the solar red shift is due to Compton scattering of solar radiation through the electrons in the solar atmosphere predicts a variation in magnitude of the red shift with position in good agreement with observation. Quasar red shifts may be similarly explained.     

Strontium isotope composition of runoff from a glaciated carbonate terrain

The relationship between subglacial chemical weathering processes and the Sr isotope composition of runoff from Robertson Glacier, Alberta, Canada, is investigated. This glacier rests on predominantly carbonate bedrock of Upper Devonian age, but silicate minerals are also present. The provenance of solute in meltwaters is found to vary systematically with solute concentration and, by inference, subglacial water residence time. In dilute waters, the principal process of solute acquisition is calcite dissolution fueled by protons derived from the dissolution of CO₂ and subsequent dissociation of carbonic acid. At higher solute concentrations, dolomite dissolution coupled to sulfide oxidation is more important. Sr concentration is found to increase with total solute concentration in two separate meltwater streams draining from the glacier, but ⁸⁷Sr/⁸⁶Sr only increases in the eastern melt stream. Carbonate and K-feldspar sources are shown to dominate the Sr content of the western stream, irrespective of concentration. They also dominate the Sr content of the eastern stream at low and intermediate concentrations, but at higher concentrations, muscovite (with high ⁸⁷Sr/⁸⁶Sr) is also an important Sr source. This reflects the outcrop of muscovite-bearing lithologies in the catchment of the eastern stream and an increase in the rate of weathering of K-silicates relative to that of carbonates as more concentrated solutions approach saturation with respect to carbonates. Nonstoichiometric release of ⁸⁷Sr/⁸⁶Sr and preferential release of Sr over K from freshly ground K-silicate surfaces may also occur. This may help to explain the radiogenic nature of runoff from distributed subglacial drainage systems, which are characterized by long water:rock contact times and water flow through environments in which crushing and grinding of bedrock are active processes.Although the exchangeable Sr in tills has higher ⁸⁷Sr/⁸⁶Sr than local carbonate bedrock, only the more concentrated meltwaters from the eastern stream display similarly high values. The most dilute waters, which probably transport the bulk of the dissolved Sr flux from the glacier, have ⁸⁷Sr/⁸⁶Sr characteristic of local carbonate bedrock. Thus, the results suggest that although enhanced weathering of silicate minerals containing radiogenic Sr (such as muscovite) does occur in glaciated carbonate terrains, it is unlikely to contribute to any enhanced flux of radiogenic Sr from glaciated continental surfaces to the oceans.     

Jets of moderate optical thickness from thick acceretion disks

The intense, super-Eddington, well-collimated radiation field generated by non-Keplerian accretion disks orbiting black holes can accelerate matter to high velocities. By using an energy balance argument which is both simple and physically appealing, we show that ordinary electron-proton plasmas can only reach relativistic gamma-factors up to 1.5. A light electron-positron plasma could be accelerated up to 5. The approach is valid if the optical depth along the accelerating funnel is significant, and the optical depth across the funnel is negligible. It is, therefore, appropriate for long, narrow funnels. Our method could easily be generalized to disk geometries other than the examples we give.     

Similarity method for modelling hydroelastic offshore platforms

Similarity methods provide a very powerful technique for modelling offshore platforms. Such methods are preferable for situations where the wave-structure interaction process is complex, and its modelling cannot be expressed by rigorous mathematical formulations.In modelling the interaction between waves and an offshore platform, the dynamic properties of the wave and structure must be considered together to determine the similitude parameters. The paper gives details of such an investigation using a frequency response function approach. Three different models, which are termed general, distorted and nondistorted Froudian models, are developed. From the general model, it was found that the velocity scales of the wave and structure could be treated differently. Internal and external force scales could also be different. It is observed then that a restrictive modelling criterion is used when the velocity scale of a structure is obtained from Froudian scale modelling. Furthermore, detailed scales for practical use are developed. The model parameters for an acrylic plastic tripod tower platform with length scales of 1/50 and 1/70 are given, and the accuracy involved among the three models determined for these scales. The sensitivity of the results to slight variations in thickness and Young's modulus are also discussed.     

Effects of the duration of exposure to mercuric chloride on the embryogenesis of the estuarine teleost, Fundulus heteroclitus

Embryos of Fundulus heteroclitus in the 4–8 cell stage were exposed nine Hg⁺⁺ (as mercuric chloride) concentrations from 0 to 100 μg/litre (ppb) for 32 days, 5 days, 2 days and 1 day. All but the chronically (32-day) exposed embryos were allowed to continue development in mercury-free water (20% S) after the exposure period to determine the effect of duration of exposure on three parameters of development. Ninety-six hour survival, total hatching success and per cent incidence of lateral spinal curvature were measured. Only embryos exposed to mercury for a single day showed a significant increase in survival in comparison with embryos exposed for a longer period of time after four days of development. Under all conditions of exposure, survival was reduced at concentrations greater than 40 ppb Hg⁺⁺. Hatching success of chronically exposed embryos was significantly reduced at concentrations greater than 10 ppb Hg⁺⁺. Significant increases in total hatchability were effected by reducing the duration of exposure to five days and one day. Of eleutheroembryos emerging following chronic exposure to mercury, increases in the incidence of lateral spinal curvature were noted at all concentrations above 20 ppb Hg⁺⁺. Significant reductions of this disorder were observed among eleutheroembryos exposed to mercury for 5 days, 2 days or 1 day. Of the three parameters measured, the incidence of lateral spinal curvature and the resulting VH₅₀ value gave a more sensitive evaluation of the embryotoxic effects of Hg⁺⁺ as mercuric chloride on the estuarine teleost, Fundulus heteroclitus.     

Stable isotope geochemistry and phase equilibria of coesite-bearing whiteschists,Dora Maira Massif,western Alps

Peak metamorphic temperatures for the coesite-pyrope-bearing whiteschists from the Dora Maira Massif, western Alps were determined with oxygen isotope thermometry. The ¹⁸O(smow) values of the quartz (after coesite) (¹⁸O=8.1 to 8.6, n=6), phengite (6.2 to 6.4, n=3), kyanite (6.1, n=2), garnet (5.5 to 5.8, n=9), ellenbergerite (6.3, n=1) and rutile (3.3 to 3.6, n=3) reflect isotopic equilibrium. Temperature estimates based on quartz-garnet-rutile fractionation are 700–750 °C. Minimum pressures are 31–32 kb based on the pressure-sensitive reaction pyrope + coesite = kyanite + enstatite. In order to stabilize pyrope and coesite by the temperature-sensitive dehydration reaction talc+kyanite=pyrope+coesite+H₂O, the a(H₂O) must be reduced to 0.4–0.75 at 700–750 °C. The reduced a(H₂O) cannot be due to dilution by CO₂, as pyrope is not stable at X(CO₂)>0.02 (T=750 °C; P=30 kb). In the absence of a more exotic fluid diluent (e.g. CH₄ or N₂), a melt phase is required. Granite solidus temperatures are 680 °C/30 kb at a(H₂O)=1.0 and are calculated to be 70°C higher at a(H₂O)=0.7, consistent with this hypothesis. Kyanite-jadeite-quartz bands may represent a relict melt phase. Peak P-T-f(H₂O) estimates for the whiteschist are 34±2 kb, 700–750 °C and 0.4–0.75. The oxygen isotope fractionation between quartz (¹⁸O=11.6) and garnet (¹⁸O=8.7) in the surrounding orthognesiss is identical to that in the coesitebearing unit, suggesting that the two units shared a common, final metamorphic history. Hydrogen isotope measurements were made on primary talc and phengite (D(_SMOW)=-27 to-32), on secondary talc and chlorite rite after pyrope (D=-39 to -44) and on the surrounding biotite (D=-64) and phengite (D=-44) gneiss. All phases appear to be in nearequilibrium. The very high D values for the primary hydrous phases is consistent with an initial oceanicderived/connate fluid source. The fluid source for the retrograde talc+chlorite after pyrope may be fluids evolved locally during retrograde melt crystallization. The similar D, but dissimilar ¹⁸O values of the coesite bearing whiteschists and hosting orthogneiss suggest that the two were in hydrogen isotope equilibrium, but not oxygen isotope equilibrium. The unusual hydrogen and oxygen isotope compositions of the coesite-bearing unit can be explained as the result of metasomatism from slab-derived fluids at depth.     

Reversible Markov grain sequences in granite

A key feature of an ideal granite is the occurrence of grain sequences which are reversible Markov chains. This property was tested using a ² test on a 2 × 6 contingency table consisting of reversible grain pairs for microcline, plagioclase, quartz, and biotite, and on a 2 × 12 contingency table consisting of reversible grain triads. All 28 samples examined from the Pacolet Mills pluton, South Carolina, passed the ² test for grain pairs, and all but three of these passed the ² test for grain triads. The coefficients of the reversibility matrix were examined for statistical significance after normalization, using a logarithmic transformation. For all three phases of the Pacolet Mills pluton, the average coefficients were in the range 1.08–0.89. Elevated and depressed values of these coefficients suggested possible differences among the three phases of the granite in their crystallization paths.     

A method for determining the reversibility of a Markov sequence

This paper describes, given a tally matrix with strictly positive entries, a method to determine whether the associated Markov process is reversible, and (for reversible Markov processes) methods to compute the reversibility matrix from the tally matrix. If the tally matrixN is symmetric, then it is shown that the Markov process must be reversible and the reversibility matrixC equalss (R ^–1NR^–1), whereR is the diagonal matrix whosei ^th diagonal entry is the sum of the entries of thei ^th row ofN (for everyi) ands denotes the sum of all the entries ofN. Because a symmetric tally matrix is of special importance in applications, a ² test is proposed for determining, in the presence of experimental errors, whether such a matrix is symmetric.