Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Invariance and scaling properties in the distributions of contributing area and energy in drainage basins

The cumulative probability distributions for stream order, stream length, contributing area, and energy dissipation per unit length of channel are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be related to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability distributions is able to fit the observed frequency distributions, and their deviations from straight lines in a log-log plot.     

On the perturbation of the anomalistic period of a highly eccentric orbit satellite due to the zonal harmonics

In this note a simple formula is given for the perturbation of the anomalistic period of a highly eccentric orbit due to the zonal harmonics. This perturbation depends essentially only on the semi-major axisa, the eccentricitye (or pericentre radius r =a(1-e)) and the latitude of the pericentre.     

Compositional variation in Hg-bearing sphalerite from the polymetallic Eskay Creek deposit, British Columbia, Canada

The Eskay Creek, British Columbia, Canada, is a polymetallic, gold- and silver-rich, volcanic-hosted, massive sulfide deposit. The ore in the deposit is divided into subzones distinguished by mineralogy, texture, grade and metallurgical characteristics. This study presents the results of a mineralogical examination of three composite field samples, with emphasis on the chemistry of sphalerite. Sphalerite is associated with variable amounts of Hg-tetrahedrite and cinnabar, and an array of sulfides, sulphosalts and non-opaque minerals. Electron micro probe analyses of sphalerite in the three composite samples reveal wide variations in compositions. The Hg content in sphalerite in the three samples varies between 0.08 and 16.35 wt%, whereas the Fe content ranges from 0.33 to 2.29 wt%. The chemical formula of the sphalerite shows the compositional range (Zn_0.89–0.98Hg_0.01–0.09.Fe_0.005–0.02)S. Sphalerite exhibits an almost perfect substitution of Hg and Zn, as shown by the negative covariance between them. Sphalerite with the highest Hg contents tends to have the lowest Fe concentrations. The highest Hg contents in sphalerite are recorded in the samples with the highest bulk Hg concentrations and with the highest cinnabar contents.

The compositional variations of sphalerite are important because they can be used in mapping ore forming fluids and indicate possible temporal variations. Second, determination of the compositional variation of the sphalerite in the mine has metallurgical implications because the mineral is an important Zn source. The mineralogical data indicate that non-physical processes (e.g. pyrometallurgy) must be used to separate Hg from Zn concentrates, with direct environmental implications, that is, release of metals, such as Hg, into the environment during mining and processing.     

Pyrolysis-high resolution gas chromatography and pyrolysis gas chromatography-mass spectrometry of kerogens and kerogen precursors

A series of kerogens and kerogen precursors isolated from DSDP samples, oil shales and Recent algal mats have been examined by Curie point pyrolysis-high resolution gas chromatography and gas chromatography-mass spectrometry. This study has shown that the three main types of kerogens (marine, terrestrial and mixtures of both) can be characterized using these techniques. The marine (algal) kerogens yield principally aliphatic products and the terrestrial kerogens yield more aromatic and phenolic products with some n-alkanes and n-alkenes. The yields of n-alkanes and n-alkenes increase and phenols decrease with increasing geologic age, however, pyrolysis-GC cannot be used to characterize the influence of short term diagenesis on the kerogen structure.     

Nuclear and incommensurate magnetic structure of NaFeGe2O6 between 5?K and 298?K and new data on multiferroic NaFeSi2O6

The compound NaFeGe₂O₆ was grown synthetically as polycrystalline powder and as large single crystals suitable for X-ray and neutron-diffraction experiments to clarify the low temperature evolution of secondary structural parameters and to determine the low temperature magnetic spins structure. NaFeGe₂O₆ is isotypic to the clinopyroxene-type compound aegirine and adopts the typical HT-C2/c clinopyroxene structure down to 2.5?K. The Na-bearing M2 polyhedra were identified to show the largest volume expansion between 2.5?K and room temperature, while the GeO₄ tetrahedra behave as stiff units. Magnetic susceptibility measurements show a broad maximum around 33?K, which marks the onset of low-dimensional magnetic ordering. Below 12?K NaFeGe₂O₆ transforms to an incommensurately modulated magnetic spin state, with k?=?[0.323, 1.0, 0.080] and a helical order of spins within the M1-chains of FeO₆ octahedra. This is determined by neutron-diffraction experiments on a single crystal. Comparison of NaFeGe₂O₆ with NaFeSi₂O₆ is given and it is shown that the magnetic ordering in the latter compound, aegirine, also is complex and is best described by two different spin states, a commensurate one with C2??/c?? symmetry and an incommensurate one, best being described by a spin density wave, oriented within the (1 0 1) plane.     

Thermal expansion and high-temperature P21/c–C2/c phase transition in clinopyroxene-type LiFeGe2O6 and comparison to NaFe(Si,Ge)2O6

A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) Å, β = 108.844(6)°, V = 442.75(16) ų, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the $(\bar{1}\,0\,1) A synthetic clinopyroxene with composition LiFe³⁺Ge₂O₆, monoclinic s.g. P2₁/c, a = 9.8792(7), b = 8.8095(5), c = 5.3754(3) ?, β = 108.844(6)°, V = 442.75(16) ?³, has been studied by in situ low- and high-temperature single-crystal X-ray diffraction. The variation of lattice parameters and the intensity of the b-type reflections (h + k = 2n + 1, only present in the P-symmetry) with increasing temperature showed a displacive phase transition from space group P2₁/c to C2/c at a transition temperature T _tr = 789 K, first order in character, with a sudden volume increase of 1.6% and a decrease of β by 1° at the transition. This spontaneous dilatation is reversible, shows a limited hysteresis of ±10°C, and corresponds to the vanishing of the b-type reflections, thus indicating a symmetry increase to space group C2/c. Below T _tr an expansion is observed for all the cell parameters, while the β angle remained almost constant; at T > T _tr the thermal volume expansion is due to dilatation of the structure in the ([`1] 0 1)(\bar{1}\,0\,1) plane, mostly along [0 1 0], and pure shear in the (0 1 0) plane due to the decrease of β. From comparison with silicate analogues, the germanate clinopyroxenes are more expansible, while the P2₁/c expands more than the C2/c phase. The evolution of Q ² (calculated as the normalized intensity of b-type reflections) with T in the framework of the Landau theory has been done using a standard expression for a first order phase transition. We observe a jump of Q ₀² = 0.538(2) at T _tr, with T _c of 481(7) K, b/a = −2,290 K, and c/a = 3,192 K, and thus far from being tri-critical point. A closely related composition (LiFe³⁺Si₂O₆) shows an equivalent phase transition at 228 K, which is very close to the tri-critical point and 561 K cooler. This result indicates that a change in the composition of tetrahedral sites can have dramatic effects on the P2₁/c ↔ C2/c displacive phase transition in clinopyroxenes. The major changes observed in the evolution of the crystal structure with T are observed in the M2 polyhedron, with a volume decrease by ca. 13.3%, compared to ca. 1.3% observed in the M1 polyhedron. The tetrahedra behave as rigid units with neither a significant change of volume at T > T _tr (<1‰), nor a change of tilting of the basal plane. No change in coordination is observed at T > T _tr in the M2 polyhedron, which remains sixfold coordinated although a strong deformation of this polyhedron is observed. This deformation is related to a strong change by 51.4° at T _tr of the kinking angle (O3–O3–O3 angle) of the B-chain of tetrahedra, which switches from O-rotated to S-rotated [from 143.3(5)° to 194.7(6)°]. The A-chain is S-rotated at T < T _tr [206.8(5)° at 703 K] and extends by 12° at the transition.     

Wind-induced drift of objects at sea: The leeway field method

A method for conducting leeway field experiments to establish the drift properties of small objects (0.1-25 m) is described. The objective is to define a standardized and unambiguous procedure for condensing the drift properties down to a set of coefficients that may be incorporated into existing stochastic trajectory forecast models for drifting objects of concern to search and rescue operations and other activities involving vessels lost at sea such as containers with hazardous material.An operational definition of the slip or wind and wave-induced motion of a drifting object relative to the ambient current is proposed. This definition taken together with a strict adherence to a 10 m wind speed allows us to refer unambiguously to the leeway of a drifting object. We recommend that all objects if possible be studied using what we term the direct method, where the object’s leeway is studied directly using an attached current meter.We establish a minimum set of parameters that should be estimated for a drifting object for it to be included in the operational forecast models used for prediction of search areas for drifting objects.We divide drifting objects into four categories, depending on their size. For the smaller objects (less than 0.5 m), an indirect method of measuring the object’s motion relative to the ambient current must be used. For larger objects, direct measurement of the motion through the near-surface water masses is strongly recommended. Larger objects are categorized according to the ability to attach current meters and wind monitoring systems to them.The leeway field method proposed here is illustrated with results from field work where three objects were studied in their distress configuration; a 1:3.3 sized model of a 40-foot Shipping container, a World War II mine and a 220 l (55-gallon) oil drum.