Trajectories of bodies in triple systems with moderate lifetimes

The general three-body problem with equal masses and zero initial velocities is considered. Sets of initial conditions for which the triple systems decay over comparatively short times, 10T _cr < T < 20T _cr, are distinguished (T _cr is the mean crossing time for a component of the system). These sets form distinct families of structures in the domain of the initial conditions. The properties of trajectories of the bodies within some of these structures are described. It is shown that the set of families is no more than countable. A new classification for families of trajectories in decaying triple systems is proposed. Some problems in classifying trajectories in the three-body problem that must be addressed in the future are formulated.     

The decay of triple systems

Numerical simulations have been carried out in the general three-body problem with equal masses with zero initial velocities, to investigate the distribution of the decay times T based on a representative sample of initial conditions. The distribution has a power-law character on long time scales, f(T) ∝ T ^?α , with α = 1.74. Over small times T < 30T _cr (T _cr is the mean crossing time for a component of the triple system), a series of local maxima separated by about 1.0T _cr is observed in the decay-time distribution. These local peaks correspond to zones of decay after one or a few triple encounters. Figures showing the arrangement of these zones in the domain of the initial conditions are presented.     

Quartz microstructures developed during non-steady state plastic flow at rapidly decaying stress and strain rate

Synseismic loading to very high stresses (>0.5 GPa) and subsequent creep during stress relaxation in the uppermost plastosphere at temperatures of ca. 300–350 °C, near the lower tip of an inferred once seismically active crustal scale fault, was proposed based on peculiar microstructures identified in rocks exposed over >100 km² in the Sesia Zone, European Western Alps. Here we discuss the conspicuous and highly heterogeneous microstructural record of quartz in disseminated small-scale shear zones. Sub-basal deformation lamellae and arrays of elongate subgrains on the TEM-scale indicate an early stage of glide-controlled deformation at high stresses. Distributed brittle failure is indicated by healed microcracks. Very fine-grained recrystallised aggregates with a pronounced crystallographic preferred orientation reflect intense plastic flow by dislocation creep. Locally, a fine-grained foam microstructure indicates a final stage of static grain growth at low differential stress. For the previously inferred peak stresses of about 0.5 GPa and given temperatures, initial strain rates on the order of 10⁻¹⁰ s⁻¹ are predicted by available flow laws for dislocation creep of quartz. We emphasise the importance of short-term non-steady state deformation in the uppermost plastosphere underlying seismically active upper crust. The related heterogeneous record of quartz is governed by the local stress history at constant temperature.     

Dark halos of wide triple systems of galaxies

A new class of metagalactic system—wide triple systems of galaxies with characteristic scale lengths of ～1 Mpc—are analyzed. Dynamical models of such systems are constructed, and the amount of dark mass contained in them is estimated. In principle, kinematic data for wide triplets allow two types of models: with individual galactic halos and with a common halo for the entire system. A choice between the two models can be made based on X-ray observations of these systems, which can determine whether clustering and hierarchical evolution continues on scales of ～1 Mpc or whether systems with such scale lengths are in a state of virial quasi-equilibrium.     

Finite element study of patterns of shear zones in granular bodies during plane strain compression

Numerical investigations of patterns of shear zones in granular bodies obtained during quasi-static plane strain compression tests were performed. The effect of a spatially correlated stochastic distribution of the initial void ratio and roughness of horizontal plates was analyzed. To describe a mechanical behavior of a cohesionless granular material during a monotonic deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. FE calculations were carried out with both initially dense and initially loose cohesionless sand. A Latin hypercube method was applied to generate Gaussian truncated random fields of initial void ratio in a granular specimen. A weak correlation of the initial void ratio in both directions and its large standard deviation were assumed for all specimens. The horizontal boundaries were either ideally smooth or very rough. The FE results show similar patterns of shear zones as compared to experiments.     

The Lyapunov exponents in the dynamics of triple star systems

The dynamics of weakly heirarchical triple stars with equal masses are considered. Full spectra of the Lyapunov exponents are found via numerical integration of the orbits, for various initial configurations of the systemin the planar problem and with initial conditions in the vicinity of the 2 : 1 resonance (i.e., with the initial ratios of the periods of the outer and inner binaries being close to 2 : 1). Dependences between the Lyapunov time and the disruption time of the systemare constructed for initial conditions near and far from resonance. The character of these relationships is different near and far from resonance, corresponding to two kinds of Hamiltonian intermittency. The trajectories “stick” to the regular component in phase space near resonance, while this effect is not dominant far from resonance. Analysis of the distributions of the disruption times of the triple systems for initial conditions near and far from resonance confirm these conclusions.     

Geochemistry and origin of the ore-forming fluids in hydrothermal-magmatic systems in tectonically active zones

Data on fluid inclusions and stable isotope compositions (O, H, C, and S) in minerals have been summarized for large-and middle-scale mesothermal gold deposits (Nezhdaninsk, Berezovsk, Kochkar’, Svetlinsk, Darasun, and Maisk), cassiterite-silicate-sulfide deposits of Sikhote Alin (Solnechnoe, Arsen’evsk, and Vysokogorsk), vein silver-base metal deposits in the Southern Verkhoyansk region (Prognoz and Kupol’noe), and epithermal copper-bismuth-silver-base metal deposits of the Karamazar district in Tajikistan (Kanimansur, Tary Ekan, and Zambarak). It is shown that ores precipitated from fluids with salinity varying from brines (up to 60 wt % NaCl equiv) to dilute fluids (1–3 wt % NaCl equiv). As a rule, fluids of different compositions entered the hydrothermal-magmatic system. A fluid mixture of H₂O-CO₂-NaCl±CH₄±N₂ predominated in the orogenic (mesothermal) gold-bearing hydrothermal systems, with deposition of the final-stage gold-bearing sulfosalts from aqueous-salt fluid. Brines played a significant role in the formation of cassiterite-silicate-sulfide and vein silver-base metal deposits. The brines often coexisted with a low-density vapor-rich fluid at the ore deposition site. The obtained data suggest a predominant magmatic component in the hydrothermal-magmatic systems, with a significant contribution of meteoric waters.     

Formation of low-mass X-ray novae with black holes from triple systems

We apply a population synthesis technique to study the formation and evolution of low-mass X-ray binaries with black holes, observed as X-ray novae, from hierarchical triple systems. A scenario is suggested in which an inner close binary system evolves into an X-ray system with a large mass ratio. The high rate of accretion onto the neutron star leads to a common envelope stage, which may result in the formation of a Thorne-Zytkow (TZ) object. During its evolution, the envelope of the TZ object expands, encompassing the third star. The recurrent common-envelope stage decreases the size of the orbit of the third star, leading to the formation of a lowmass X-ray nova with a black hole. The dynamical stability of triple systems automatically ensures that only lowmass X-ray novae form. We also consider the possible formation of an X-ray nova from a binary in the case of asymmetrical core collapse during a supernova explosion.     

Fracture systems in normal fault zones crosscutting sedimentary rocks,Northwest German Basin

Field studies of fracture systems associated with 58 normal fault zones crosscutting sedimentary rocks were performed in the Northwest German Basin. Fracture orientations, densities, apertures and lengths, as well as fault zone structural indices, were analysed separately for fault damage zones and host rocks. The results show a pronounced difference between carbonate and clastic rocks: mainly in carbonate rocks we found presence of clear damage zones, characterized by higher fracture densities than in the host rocks. While the maximum aperture is similar for both units, the percentage of fractures with large apertures is much higher in the damage zones than in the host rocks.Based on laboratory measurements of Young's moduli and field measurements of fracture densities, we calculate effective stiffnesses E_e, that is the Young's moduli of the in situ rock masses, within the normal fault zones. Compared with carbonate rocks, E_e computed for clastic-rock damage zones decreases significantly less due to lower fracture densities. We conclude that normal fault zones in carbonate rocks have more profound effects on enhancing permeability in fluid reservoirs than those in clastic rocks. The results are of great importance for modelling the hydromechanical behaviour of normal fault zones in subsurface fluid reservoirs.     

Major fracture zones of Morocco: The South Atlas and the Transalboran fault systems

Within the fracturai pattern of Morocco, 35–45° and 70–90° directions are predominant. Most of the faults originated already during the Upper Palaeozoic and were repeatedly reactivated, later on. Two of the large fracture systems are considered here.The South Atlas fault system (SAF) is composed of different faults with directions varying between 45–90°. They were not functionally connected to the southern hinge of the High Atlas until its Miocene uplift. Today, it seems to be inactive on the whole. Both the tectonic data and the facies distribution of Mesozoic strata contradict clearly the interpretation that the SAF is a huge wrench-fault or even the Mesozoic plate margin of Africa. The SW striking Transalboran fault system (TAF) is still active. It crosses Morocco from Melilla to Agadir, showing again singular faults which are unified to extended lineaments only in a few areas. The intervals between the faults are bridged by linear arrangements of earthquake hypocenters. Sinistral massflow within the deeper parts of the lithosphere seems to be compensated at the surface by movements along pre-existing faults. For the Moroccan segment of the TAF, a sinsitral displacement is testified at least since the Oligocene, while the northeastern segments from the Rif to Spain did not even originate until the Pliocene. This would mean that sinistral shear was transmitted from Africa into the accreted Alboran and Iberia blocks after the Miocene collision.

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Zusammenfassung Unter den großen Störungen Marokkos dominieren die Richtungen 35–45° und 70–90°. Sie wurden zumeist im Jungpaläozoikum angelegt und später wiederholt reaktiviert. Zwei der großen Bruchsysteme wurden näher untersucht:Die Südatlas-Störungszone (SAF) besteht aus unzusammenhängenden Brüchen unterschiedlichen Alters, deren Streichrichtung von 45–90° variiert. Diese wurden erst bei der miozänen Heraushebung des Hohen Atlas zu dessen südlichem Scharnier umfunktioniert. Heute sind nur wenige Störungen des Systems aktiv. Diese Befunde und ebenso die stratigraphisch-fazielle Entwicklung im Mesozoikum Marokkos verbieten, die SAF als bedeutende Lateralverschiebungszone oder gar als nördliche Plattengrenze Afrikas zu interpretieren.Das noch heute aktive, SW-streichende Transalboran-Störungssystem (TAF) setzt sich durch Marokko von Melilla bis Agadir fort. Es besteht an der Oberfläche ebenfals aus singulären Brüchen, die sich nur bereichsweise zu längeren Linien zusammenschließen. Zwischen den Störungen vermitteln linear angeordnete Herde rezenter Erdbeben: Sinistraler Massentransport an einer Tiefenstörung wird an der Oberfläche durch Teilbewegungen an präexistenten Störungen kompensiert. Während in Marokko südlich des Rifs sinistraler Versatz mindestens seit dem Oligozän nachgewiesen ist, entstand die TAF vom Rif bis nach Spanien erst im Pliozän. Die sinistrale Scherung tritt also erst nach der miozänen Kollision von Afrika aus auf die nunmehr akkretierten Mikroplatten- Alboran-Block und Iberia - über.

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Résumé Les grandes fractures du Maroc présentent les deux directions prédominantes de 35°-40° et 70°–90°. La plupart de ces fractures datent du Paléozoïque supérieur et ont été réactivées plusieurs fois au Mésozoïque et au Cénozoïque. Deux de ces grands systèmes de fractures sont considérés ici.L'accident sud-atlasien (SAF) est composé de fractures indépendantes d'âges divers dont la direction varie entre 45° et 90°. Ces fractures ne se sont connectées à la charnière du Haut Atlas qu'après le soulèvement miocène de celui-ci. Aujourd'hui, quelques failles seulement sont encore actives. Ces observations, ainsi que la distribution des faciès du Mésozoïque au Maroc sont en contradiction avec le modèle qui voit dans le SAF une grande zone de décrochement ou même la marge nord de la plaque africaine.L'accident transalboran (TAF), encore actif aujourd'hui, traverse le Maroc en direction sudouest de Mélilla à Agadir. Il est composé de failles discontinues, connectées entre elles seulement à quelques endroits. Les intervalles qui séparent ces failles sont jalonnés par des alignements rectilignes d'hypocentres de séismes récents. L'ensemble correspond à un décrochement sénestre profond compensé en surface par des mouvements le long de failles préexistantes. Ce décrochement sénestre, dans le segment du TAF situé au sud du Rif, s'est manifesté au moins depuis l'Oligocène, tandis que la partie qui s'étend du Rif à l'Espagne méridionale n'a été active qu'à partir du Pliocène. Ceci signifie que ce cisaillement sénestre ne s'est transmis de l'Afrique vers l'Europe qu'après l'accrétion, au Miocène, de la microplaque Alboran et du bloc ibérique.

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Criteria for the stability of triple systems and their application to observations of multiple stars

Criteria for stability of triple systems are studied and compared with the results of numerical simulations obtained for model triple systems and observed multiple stars. The results for the stability analyses using two new criteria—those of Aarseth and of Valtonen et al.—agree with the simulation results in 98% of cases. Thus, these criteria can be used to analyze the stability of systems for which direct modeling of their dynamical evolution is difficult (for example, because not all orbital parameters for their subsystems are known). The last published version of the “Multiple-Star Catalog” of Tokovinin is analyzed to search for systems that may be unstable according to the two new criteria. More detailed studies are carried out for the HD 284419 (T Tau) system. The parameters of the apparent motion method is used to obtain new orbital solutions for this system. The regions of dynamical stability of the system as functions of the orbital parameters are estimated. It is not possible to determine a unique solution for the orbit with the available data; for periods shorter than 300 yr and longer than 5500 yr, the probability of decay of the system on time scales less than 107 yr is high. This conclusion is supported by the application of the stability criteria, as well as direct modeling of the system’s dynamical evolution.     

The role and impact of freshwater–seawater mixing zones in the maturation of regional dolomite bodies within the proto Floridan Aquifer, USA

Palaeogene dolostones from the sub‐surface of Florida are ideal for the study of dolomite maturation because they record the early stages of a secondary dolomite overprint without destruction by later diagenetic overprints. Two distinct dolomite textures occur in the dolostones of the Upper Eocene Ocala and Lower Oligocene Suwannee limestones in west‐central Florida: a porous and permeable sucrosic dolomite and a less porous and relatively impermeable indurated non‐sucrosic dolomite. In both textures, the initial matrix dolomite is dully luminescent, whereas the secondary overprint is dominantly luminescent cement in the Suwannee and only neomorphic luminescent dolomite in the Ocala. The abundance of luminescent dolomite ranges from 2% to 38%, which translates to 1·6 km³ of material in the Suwannee and 13·5 km³ in the Ocala. Extrapolated trace‐element contents (Sr and Na) and δ¹⁸O values for the matrix and luminescent end‐members indicate a marine origin for the matrix dolomite in both units, and a freshwater–seawater mixing‐zone origin for the secondary luminescent dolomites. The δ¹⁸O values indicate that a saline, middle mixing‐zone environment overprinted the Suwannee but a more dilute mixing zone affected the Ocala. Fluid–fluid mixing models constrained by modern Floridan aquifer hydrochemistry and extrapolated ⁸⁷Sr/⁸⁶Sr values of the luminescent phases indicate that the mixing zones operated during the Late Miocene to Pliocene in the Ocala and affected the Suwannee in the Pliocene. The luminescent Suwannee mixing‐zone cement reduced porosity up to threefold and permeability up to 100‐fold, which converted many sucrosic dolomites to indurated dolomites. By contrast, the neomorphic luminescent Ocala dolomite did not have an appreciable impact on the maturations. Although freshwater–seawater mixing zones were not the sites of the initial dolomitization, the mixing‐zone environment did dramatically overprint and mature the regionally widespread dolomites of the Ocala and Suwannee limestones. This maturation occurred shortly after formation of the proto‐Floridan aquifer; the timing suggests the matrix dolomites were ‘ripe’ for alteration and that the only prerequisite for mixing‐zone dolomite is pre‐existing dolomite substrates to reduce kinetic barriers. In contrast to recent claims, the results of this study demonstrate that mixing zones can be effective in forming regionally significant amounts of secondary dolomite and influencing the petrophysical maturation of dolomite bodies.     

Marginal-water application in arid zones

The intensified efforts to improve agricultural economy in arid zones is associated with increased demand for water. Scarcity of potable water has hightened the importance of marginal water in dry regions. Marginal water includes saline water, wastewater, and runoff water. These water sources differ in location in regards to the application site, quality, quantity, and stability of supply. Previous experience proved that each of the above alternative water sources can be used separately or in combination, for the economic benefit of the farmers.     

Deep fluids in subduction zones

The fluid inclusions preserved in high and ultrahigh pressure rocks provide direct information on the compositions of fluid phases evolved during subduction zone metamorphism, and on fluid–rock interactions occurring in such deep environments. Recent experiments and petrologic studies of eclogite–facies rocks demonstrate that stability of a number of hydrous phases in all rock systems allows fluid transport into the mantle sources of arc magmas, as well as into much deeper levels of the Earth's mantle. In eclogite–facies rocks, the presence of large ion lithophile elements (LILE) and light rare earths (LREE)-bearing hydrous phases such as epidote and lawsonite, together with HFSE repositories as rutile and other Ti-rich minerals, controls the trace element budget of evolved fluids and fluid-mediated cycling of slab components into the overlying mantle.

Studies of fluid inclusions in eclogite–facies terrains suggest that subduction mainly evolves aqueous solutions, melts being produced only locally. Eclogite-facies rocks diffusely record processes of fluid–melt–rock interactions that exerted considerable control on the element and volatile budget of subduction fluids. Trace element fractionation during such interactions needs to be tested and quantified in more detail to achieve the ultimate compositions actually attained by fluids leaving off the slab. Variably saline inclusions with minor CO₂ and N₂ are trapped in rock-forming high pressure minerals; brines with up to 50% by weight dissolved solute are diffusely found in veins. The latter inclusions are residues after fluid–rock interactions and deposition of complex vein mineralogies: this evidence suggests increased mineral solubility into the fluid and formation, at a certain stage, of silicate-rich aqueous solutions whose geochemical behaviour and transport capacity can approach that of a melt phase. This is supported by experimental work showing high solubility of silicate components in fluids at high pressures. However, natural examples of inclusions trapping such a fluid and quantitative analyses of its major and trace element composition are not yet available.

Fluids in high and very high pressure rocks do not move over large scales and the channelways of fluid escape from the slab are not yet identified. This suggests that only part of the slab fluid is lost and returned to the surface via magmatism; the remaining trapped fraction being subducted into deeper levels of the upper mantle, to renew its budget of substances initially stored in the exosphere.     

沿岸地下水排放通量

海岸带地区,陆源物质由近岸向沿岸海洋输送的途径有很多,而在一些海岸或海湾,其中较普遍的一个过程就是海底地下水排放。它是发生在沿岸地区与毗邻海洋之间的又一个重要的陆海相互作用过程。目前,通过水文、直接测量和地球化学示踪法研究地下水排放的例子有很多,但对其进行定量估算仍面临着许多困难。本文主要介绍镭同位素地球化学示踪法的基本原理及应用,以海南东北部沿岸水域中镭同位素数据为例,计算得到相应的地下水排放通量为5.4×10-4dm3/(d.cm2)。     

Metasomatic zones in metamorphic rocks

Prediction of a unique sequence of metasomatic zones that would develop by intergranular diffusion with local equilibrium is possible only for relatively simple systems, unless extensive thermochemical and kinetic information is available. The complexity of the problem for a given example will depend on what portion of the set of chemical components required to describe the example are ‘diffusing components’, that is, components that move relative to ‘inert markers’. Diffusing components are commonly K-components (Thompson, 1970) for the various local equilibria of a sequence of metasomatic zones, since diffusion tends to impose a monotonie variation of the chemical potentials of these components across the zones. The number of diffusing components may vary from zone to zone in a particular example, as may the number of diffusing components that are K-components. Calculation of the rate of growth of a specific sequence of zones is relatively straightforward only for cases where the zones are primarily due to the variation of the chemical potential of one independent diffusing component. Calculation of the material transfer involved in the growth of a sequence of zones, assuming a single sharp initial contact is meaningful only if ‘inert markers’ or a discontinuity in the otherwise-constant ratio of two components indicate the present location of the initial contact. Examination of some natural calc-silicate diffusion zones suggests that a diffusion-imposed gradient in the chemical potential of calcium is largely responsible for the observed zonation. Metasomatic zones developed at the boundaries of ultramafic bodies, however, are produced by diffusion-imposed chemical potential gradients of several components, notably silica and magnesia, the number varying from zone to zone.