Central configurations of four bodies with one inferior mass

The number of equivalence classes of central configurations (abbr. c.c.) in the planar 4-body problem with three arbitrary and a fourth small mass is investigated. These c.c. are derived according to their generic origin in the 3-body problem. It is shown that each 3-body collinear c.c. generates exactly 2 non-collinear c.c. (besides 4 collinear ones) of 4 bodies with smallm ₄0; and that any 3-body equilateral triangle c.c. generates exactly 8 or 9 or 10 (depending onm ₁,m ₂,m ₃) planar 4-body c.c. withm ₄=0. Further, every one of these c.c. can be continued uniquely to sufficiently smallm ₄>0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable tom ₄>0.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.     

Theory of the local scale parameter method for EDM

The determination of a representative refractive index for the wave path is the main limitation of the attainable accuracy in electronic distance measurement. To overcome this limitation the length ratio method was initially proposed and later developed into the local scale parameter (LSP) method. In this paper, the mathematical model of the LSP method is derived for electro-optical distance measurement from first principles based on the physics of the atmospheric boundary layer. The model does not rely on standard atmospheres. It is shown that atmospheric temperatures and pressures must be observed at instrument stations but not at reflector stations. Appropriate LSP field procedures and the results of some field experiments are summarized. The method consistently produces accuracies of better than ±1 ppm. Use of the method is recommended for high precision (trilateration) networks, which need to be measured repeatedly and where absolute scale is not relevant.     

Diploptene: an indicator of terrigenous organic carbon in Washington coastal sediments

The pentacyclic triterpene 17 beta(H),21 beta(H)-hop-22(29)-ene (diploptene) occurs in sediments throughout the Columbia River drainage basin and off the southern coast of Washington state in concentrations comparable to long-chain plantwax n-alkanes. The same relationship is evident for diploptene and long-chain n-alkanes in soils from the Willamette Valley. Microorganisms indigenous to soils and soil erosion are indicated as the biological source and physical process, respectively, for diploptene in coastal sediments. Similarity between the stable carbon isotopic composition (delta 13CPDB) of diploptene isolated from soil in the Willamette Valley (-31.2 +/- 0.3%) and from sediments deposited throughout the Washington coastal environment (-31.2 +/- 0.5%) supports this argument. Values of delta for diploptene in river sediments are variable and 8-17% lighter, indicating that an additional biological source such as methane-oxidizing bacteria makes a significant contribution to the diploptene record in river sediments. Selective biodegradation resulting from a difference in the physicochemical association within eroded particles can explain the absence of the more-13C-depleted form of diploptene in Washington coastal sediments, but this mechanism remains unproven.     

Stable isotope (O and C) and pollen trends in eastern Lake Erie,evidence for a locally-induced climatic reversal of Younger Dryas age in the Great Lakes basin

A cool period from about 11000 to 10 500 BP (11 to 10.5 ka) is recognized in pollen records from the southern Great Lakes area by the return of Picea and Abies dominance and by the persistence of herbs. The area of cooling appears centred on the Upper Great Lakes. A high-resolution record (ca. 9 mm/y) from a borehole in eastern Lake Erie reveals, in the same time interval, this pollen anomaly, isotope evidence of meltwater presence (a — 3 per mil shift in ¹⁸O and a +1.1 per mil shift in ¹³C), increased sand, and reduced detrital calcite content, all suggesting concurrent cooling of Lake Erie. The onset of cooling is mainly attributed to the effect of enhanced meltwater inflow on the relatively large upstream Main Lake Algonquin during the first eastward discharge of glacial Lake Agassiz. Termination of the cooling coincides with drainage of Lake Algonquin, and is attributed to loss of its cooling effectiveness associated with a substantial reduction in its surface area. It is hypothesized that the cold extra inflow effectively prolonged the seasonal presence of lake ice and the period of spring overturn in Lake Algonquin. The deep mixing would have greatly increased the thermal conductive capacity of this extensive lake, causing suppression of summer surface lakewater temperatures and reduction of onshore growing-degree days. Alternatively, a rapid flow of meltwater, buoyed on sediment-charged (denser) lakewater, may have kept the lake surface cold in summer. Other factors such as wind-shifted pollen deposition and possible effects from the Younger Dryas North Atlantic cooling could have contributed to the Great Lakes climatic reversal, but further studies are needed to resolve their relative significance.Contribution to Climo Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate ProgramGeological Survey of Canada Contribution 58 890     

Differential unroofing within the central metasedimentary Belt of the Grenville Orogen: constraints from 40Ar/39Ar thermochronology

An ⁴⁰Ar/³⁹Ar thermochronological investigation of upper greenschist to granulite facies gneiss, amphibolite and marble was conducted in the Central Metasedimentary Belt (CMB), Ontario, to constrain its cooling history. Incremental ⁴⁰Ar/³⁹Ar release spectra indicate that substantial differential unroofing occurred in the CMB between 1000 and 600 Ma. A consistent pattern of significantly older hornblende and phlogopite ⁴⁰Ar/³Ar cooling ages on the southeast sides of major northeast striking shear zones is interpreted to reflect late displacement due to extensional deformation. Variations in hornblende ⁴⁰Ar/³⁹Ar age plateaus exceeding 200 Ma occur over distances less than 50 km with major age discontinuities occurring across the Robertson Lake shear zone and the Sharbot Lake mylonite zone which separate the Sharbot Lake terrane from the Elzevir and Frontenac terranes. Extensional displacements of up to 14 km are inferred between the Frontenac and Elzevir terranes of the CMB. No evidence for significant post argon-closure vertical displacement is indicated in the vicinity of the Perth Road mylonite within the Frontenac terrane. Variations of nearly 100 Ma in phlogopite ⁴⁰Ar/³⁹Ar plateau ages occur in undeformed marble on either side of the Bancroft Shear Zone. Phlogopites from sheared and mylonitized marble within the shear zone yield ⁴⁰Ar/³⁹Ar diffusional loss profiles, but have older geologically meaningless ages thought to reflect incorporation of excess argon. By 900 Ma, southeast directed extension was occurring throughout the CMB, possibly initiated along previous zones of compressional shearing. An easterly migration of active zones of extension is inferred, possibly related to an earlier, overall easterly migration of active zones of regional thrusting and easterly migration of an ancient subduction zone. The duration of extensional shearing is not well constrained, but must have ceased before 600 Ma as required by the deposition of overlying undeformed Cambrian and/or Ordovician sedimentary rocks.Contribution No. 481 from the Mineralogical Laboratory, University of Michigan     

Fractional Crystallization and Liquid Immiscibility Processes in the Alkaline-Carbonatite Complex of Juqui (So Paulo, Brazil)

The Juqui circular intrusion, which is Cretaceous in age (130–135Ma), crops out in the Precambrian gneissic basement in Brazilover an area of 14 km2. It consists of olivine clinopyroxen-itecumulates (with minor olivine gabbros) in the northeastern sector(74 vol.%), whereas ijolites-melteigites-urtites (4%) and nephelinesyenites with minor essexites and syenodiorites (21%) outlinesubannular concentric patterns with an Mg-carbonatite core (1%), in the southwestern part of the complex. Petrographical, bulk rock, and mineral compositional trendsindicate that the origin of the complex can be largely accountedfor by shallow-level fractional crystallization of a carbonatedbasanitic parental magma. Such a magma was generated deep inthe subcontinental lithosphere by low-degree partial meltingof a garnet-phlogopite peridotite source. Mass-balance calculations in agreement with field volume estimatespermit definition of several fractionation stages of the magmaticevolution under nearly closed-system conditions, with inwarddevelopment of zonally arranged side-wall cumulates. These stagesinvolved: (1) fractionation from basanite to essexite magma(liquid fraction F = 33–5%) by crystallization of olivineclinopyroxenite plus minor olivine alkali gabbro cumulates;(2) derivation of the least differentiated mafic nepheline syenite(F = 5–5 %) from essexitic magma by subtraction of a syenodioriteassemblage; (3) exsolution of a carbonatite liquid (5%) froma CO₂-enriched mafic nepheline syenite magma, which also underwentcontinuous fractionation giving rise to ijolite-melteigite-urtitecumulates. The proportion of cumulus clinopyroxene and biotiteand intercumulus nepheline and alkali feldspar in these lastrocks, as well as the absence of alkalis in carbonatite, maybe attributed, at least in part, to loss of alkali-rich hydrousfluids released during and after the unmixing formation of thetwo conjugate liquids. The KD values determined for Mg-carbonatite/nepheline syeniteare lower (1–4–2–9) for light rare earth elements(LREE) than for REE from Eu to Yb (4–6–7–8),in contrast to recent experimental results (Hamilton et al.,1989). A possible explanation is that Juquia Mg-carbonatiterepresents an alreadydifferentiated magma, which underwent extensivefractionation of LREE-enriched calcite. In this way, the highvariability of K₀ REE patterns observed in several alkaline-carbonatitecomplexes can also be accounted for. The remarkably constant initial ⁸⁷Sr/⁸⁶Sr ratios (mostly between0–7052 and 0–7057) support the interpretation ofthe intrusion as having been generated by fractrional crystallizationand liquid immiscibility from a common parental magma. Iligherisotopic ratios (0–7060–0–7078), found mainlyin dykes and in the border facies of the intrusion, may be dueto contamination by the gecissic basement.     

Computation of surface energies in an electrostatic point charge model: I. Theory

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and Ψ(x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy (γ ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy γ is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Computation of surface energies in an electrostatic point charge model: II. Application to zircon (ZrSiO4)

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and (x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy ( ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Seismic hazard monitoring in Kamchatka and its applications to the M = 6.6 earthquake of 6 October 1987

The earthquake of 6 October 1987 (M = 6.6), which occurred near the Shipunsky Cape, Kamchatka, was the largest crustal event in the vicinity of the main city of Kamchatka — Petropavlovsk-Kamchatsky — during the last three decades. It was followed by numerous aftershocks. This earthquake allowed us to test the effectiveness of the seismic hazard monitoring in Kamchatka, including the seismological, geodetic and hydrogeochemical surveys. The seismic survey provided the location and source nature of the main shock and aftershocks and the seismic environment of the main shock. The geodetic and hydrogeochemical surveys have yielded data on the response to earthquakes of the Earth's surface deformations, water level, and chemical elements concentration in the underground water. As a result, the following data were obtained:

u

The earthquake of 6 October had a seismic moment 4–10 E18 Nm, thrust type of faulting and the source volume of 20 × 20 × 10 km³. The maximum intensity was VI–VII (MSK-64 scale) and maximum acceleration 88 cm/s².

Before this event, a relative increase in the number of the upper mantle (depth more than 100 km) moderate magnitude earthquakes during 5 years and a one-year period of seismic quiescence for small shallow earthquakes, were recognized. Significant anomalies in HCO₃ and H₃BO₃ concentrations in the underground waters were observed in the wells a week before the main shock.

     

Fluid-rock interaction in the Mo-bearing Nebelstein greisen complex,Bohemian Massif (Austria)

Summary In the Nebelstein area, molybdenite-bearing greisens occur together with peraluminous leucogranites. In the compositional change of the granites to the greisens, there is an almost complete loss of Na, combined with a decrease in Ca, Mg, Sr, and Ti concentrations. The progressive alteration is reflected by lower homogenization temperatures and increasing salinity in aqueous fluid inclusions. The fluid regime prior to greisenization was water-dominated with low salt contents, while the early stage of the greisen development was characterized by a mixed fluid containing carbon dioxide and water. This was succeeded by a moderate saline aqueous fluid which caused the mineralization by exchange of metal ions for Na⁺(Ca²⁺, K⁺). A negative correlation between salt content in fluid inclusions and Na₂O concentrations in the bulk rocks supports this model. Mass balance calculations for this interaction yield a minimum fluid-rock ratio of approximately 2 : I. Greisenization took place at a minimum pressure of 180 MPa (1.8 kb) and in a temperature range between 200 and < 400 °C.

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Fluid-Gestein-Wechselwirkung in dem Molybdänit führenden Greisenkomplex Nebelstein, Böhmische Masse (Österreich)

Zusammenfassung Die Molybdänglanz führenden Greisengesteine des Nebelsteins sind an peraluminöse Granite gebunden. Bei der Alteration der Granite ist für den Übergang Biotitgranit zu Greisen eine weitestgehende Verarmung an Na zu beobachten, gleichzeitig nehmen auch die Gehalte an Ca, Mg, Sr und Ti ab. Die fortschreitende Greisenbildung dokumentiert sich in den wäßrigen Flüssigkeitseinschlüssen durch steigende Salinität bei sinkenden Homogenisierungstemperaturen. Die fluide Phase war vor der Greisenbildung H₂O dominiert und niedrig salinar. Der Beginn der Alterationsprozesse ist durch CO₂ und H₂O hältige Fluide gekennzeichnet. Danach folgt ein Anstieg der Salinität, der auf den Austausch von Metallchloridlösungen gegen Na⁺, K^- und Ca^2- zurückgeführt wird. Dies läßt sich durch eine negative Korrelation der Salinität in den Flüssigkeitseinschlüssen mit dem Na-Gehalt der Gesteine belegen. Daraus wurde die Volumsbeziehung der den Granit durchströmenden fluiden Phase relativ zum Gestein mit mindestens 2 : 1 abgeleitet. Die Mineralisation fand bei einem Minimaldruck von 1,8 kb in einem Temperaturbereich von 200 - < 400 °C statt.

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This paper was presented at the IGCP 291 Project Symposium Metamorphic Fluids and Mineral Deposits, ETH Zürich, March21–23,1991.