Determination of the potential in a synodic system

Determination of the potential field in a fixed (inertial) system may be accomplished by the solution of a homogeneous linear partial differential equation when a family of orbits of a body moving in the field is given. This partial differential equation was presented and thoroughly analyzed earlier. The present paper discusses the same problem in a rotating system where the centrifugal and Coriolis effects render the pertinent partial differential equation in general non-homogeneous and non-linear. A linear, though non-homogeneous, partial differential equation for the determination of the synodic potential is obtained only in the special case of iso-energetic families of orbits.     

Surfaces of zero velocity in the restricted problem of three bodies

Recent uses of computer graphics allow the representation of the three-dimensional surfaces of zero velocity, also known as Hill's or the Jacobian surfaces. The purpose of this paper is to show the actual surfaces rather than their projections which are available in the standard literature. The analytical properties of the surfaces are also available; therefore, this paper offers the pertinent references rather than the derivations.     

Limits of predictability of gravitational systems

The concept of finite predictability of gravitational many-body systems is related to the non-deterministic nature of celestial mechanics and of dynamics, in general. The basic, fundamental reasons for the uncertainty of predictions are as follows: (1) the initial conditions are known only approximately since they are obtained either from observations or from approximate computations; (2) the equations of motion given by a selected model describe the actual system only approximately; (3) the physical constants of the dynamical system have error limits; (4) the differential equations of motion are non-integrable and numerical integration methods must be used for solution, generating errors in the final result at every integration step.In addition to these reasons, mostly depending on our techniques, there are some more fundamental reasons depending on the nature of the dynamical system investigated. These are the appearance of regions of instability, non-integrability and chaotic motion.Details, effects and controls of these regions for finite predictability are discussed for various dynamical systems of importance in celestial mechanics with special emphasis on planetary systems.     

Carlin-type Gold Prospects in Surigao del Norte, Mindanao Island, Philippines: Their Geology and Mineralization Potential

Abstract. Three calcareous sedimentary rock-hosted Carlin type-like gold prospects were mapped in a mineral production sharing agreement area of Philex Gold Philippines Inc. in Taganaan municipality, Surigao del Norte province in Mindanao island in the Philippines. They occur along a 20–25 km long trend of known epigenetic gold and porphyry copper deposits that lie close to several splays of the Philippine Fault Zone. The gold district forms part of the Late Cretaceous Eastern Mindanao Range that hosts early Paleogene and late Pliocene to Quaternary intrusive rocks.
Gold is invisible in the jasperoid outcrops in Lascogon, Napo, and Danao prospects. The jasperoids occur in lenses of marls belonging to the Taganaan Marl Member that is associated to a turbiditic member of the Middle Miocene Mabuhay Formation. The marl lenses include gently dipping interbedded silty limestones and calcareous shales. The "invisible gold" mineralization in silicified calcareous rocks resembles Carlin-type deposits. Based on the mapped igneous and sedimentary rocks, a possible heat source for the gold mineralization is either or both of the two main phases of intrusion, Mabuhay An-desite or Alipao Andesite Porphyry. Forty-eight rock samples, fifteen stream sediment samples, and one soil sample were critical in delineating the general features of the potential Carlin-type prospects. The gold grades of jasperoids in the three prospects range from trace amounts to 20 g/t Au. Regional studies of gold and porphyry copper mineralization in the Surigao del Norte mineral district are important in delineating ore targets for drilling in the three prospects.     

Multiple causes of Earth's earliest global glaciation

In the context of Earth System evolution, the causal factors driving the Palaeoproterozoic Huronian global glaciations occupy a central position. The rise of O₂ at 2320 Ma, which eliminated most of the methane, was not apparently a single cause triggering the glaciation. At c. 2450 Ma mantle‐plume‐driven continental uplifts led to the emplacement of voluminous continental flood‐basalts in low latitudes that were subsequently dissected by rifting. Major topographical features and continental drainage patterns were most likely similar to those in younger continental flood‐basalt provinces and would have enabled deep weathering and erosion of extensive basalt‐covered continental areas. Intense consumption of atmospheric CO₂ by silicate weathering of fresh basaltic surfaces would have been further amplified by a constant organic carbon burial rate. These factors, similar to those of younger glacial periods, in combination with the diminished CH₄ greenhouse led to an onset of global cooling at the million‐year timescale.     

Unravelling the widening of the earliest Andean northern orogen: Maastrichtian to early Eocene intra‐basinal deformation in the northern Eastern Cordillera of Colombia

The onset of deformation in the northern Andes is overprinted by subsequent stages of basin deformation, complicating the examination of competing models illustrating potential location of earliest synorogenic basins and uplifts. To establish the width of the earliest northern Andean orogen, we carried out field mapping, palynological dating, sedimentary, stratigraphic and provenance analyses in Campanian to lower Eocene units exposed in the northern Eastern Cordillera of Colombia (Cocuy region) and compare the results with coeval succession in adjacent basins. The onset of deformation is recorded in earliest Maastrichtian time, as terrigenous detritus arrived into the basin marking the end of chemical precipitation and the onset of clastic deposition produced by the uplift of a western source area dominated by shaly Cretaceous rocks. Disconformable contacts within the upper Maastrichtian to middle Palaeocene succession document increasing supply of quartzose sandy detritus from Cretaceous quartzose rocks exposed in eastern source areas. The continued unroofing of both source areas produced a rapid shift in depositional environments from shallow marine in Maastrichtian to fluvial‐lacustrine systems during the Palaeocene‐early Eocene. Supply of immature Jurassic sandstones from nearby western uplifts, together with localized plutonic and volcanic Cretaceous rocks, caused a shift in Palaeocene sandstones composition from quartzarenites to litharenites. Supply of detrital sandy fragments, unstable heavy minerals and Cretaceous to Ordovician detrital zircons, were derived from nearby uplifted blocks and from SW fluvial systems within the synorogenic basin, instead of distal basement rocks. The presence of volcanic rock fragments and 51–59 Ma volcanic zircons constrain magmatism within the basin. The Maastrichtian–Palaeocene sequence studied here documents crustal deformation that correlates with coeval deformation farther south in Ecuador and Peru. Slab flattening of the subducting Caribbean plate produced a wider orogen (>400 km) with a continental magmatic arc and intra‐basinal deformation and magmatism.     

Shrinking Sphere Kinetics for Batch Dissolution of Mixed Particles of a Single Substance at High Under-Saturation: Validation with Sodium Chloride, but with Biogenic Silica in Mind

The cubic equation recently derived for the increase in concentration of a solute with time, as the solid dissolves in batch according to the shrinking sphere model at high under-saturation, is extended to dissolutions of mixtures of differently sized particles. This problem needs to be solved if batch dissolutions are to play their part in the proposed amelioration of global warming and associated climate change by accelerated ‘re-burial’ of excess CO₂ in ocean sediment. The upgraded model was tested using sodium chloride dissolved in 50% aqueous propanone, whence the model fitted two separate runs with 500 and 212 μm, and 212 and 38 μm, diameter crystals, respectively. The key to simulating dissolution in this way lies in the dissolutions being independent of each other. It is further shown that although this condition was implicit in the recent derivation of the cubic equation, it was not recognised at the time. The work should be applicable to any batch dissolution of mixed particles at high under-saturation, and hence, may find use in many industrial and laboratory dissolutions. Simulations show how agglomerated mixtures can yield a straight line on the plot of ln(1 − C/C _T) versus time, as was reported to occur recently with sodium chloride taken ‘straight from the bottle’. It is shown that this probably explains why exponential dissolutions may have seemed appropriate to the dissolution of biogenic silica in earlier literature. This study suggests that a new round of biogenic silica dissolutions, but with sieved samples, would be worthwhile, with the likelihood that shrinking sphere behaviour might well be found to characterise the kinetics. The opportunity is taken to investigate a number of aspects of the shrinking sphere model not generally discussed before, e.g. the graph for the change in surface area with time. The limitations of using cubic salt crystals with the shrinking sphere model are discussed.     

The Madinah eruption,Saudi Arabia: Magma mixing and simultaneous extrusion of three basaltic chemical types

During a 52-day eruption in 1256 A.D., 0.5 km³ of alkali-olivine basalt was extruded from a 2.25-km-long fissure at the north end of the Harrat Rahat lava field, Saudi Arabia. The eruption produced 6 scoria cones and a lava flow 23 km long that approached the ancient and holy city of Madinah to within 8 km. Three chemical types of basalt are defined by data point clusters on variation diagrams, i.e. the low-K, high-K, and hybrid types. All three erupted simultaneously. Their distribution is delineated in both scoria cones and lava flow units from detailed mapping and a petrochemical study of 135 samples. Six flow units, defined by distinct flow fronts, represent extrusive pulses. The high-K type erupted during all six pulses, the low-K type during the first three, and the hybrid type during the first two.Three mineral assemblages occur out of equilibrium in all three chemical types.Assemblage 1 contains resorbed olivine and clinopyroxene megacrysts and ultramafic microxenoliths (Fo₉₀ + Cr spinel + Cr endiopside) which fractionated within the spinel zone of the mantle.Assemblage 2 contains resorbed plagioclase megacrysts (An₆₀) with olivine inclusions (Fo₇₈) which fractionated in the crust.Assemblage 3 contains microphenocrysts of plagioclase and olivine in a groundmass of the same minerals with late-crystallizing titansalite and titanomagnetite; assemblage 3 crystallized at the surface and/or in the upper crust. Each assemblage represents a distinct range in PTX environment, suggesting that their coexistence in each chemical type may be a function of magma mixing. Such a process is confirmed by variable ratios of incompatible element pairs in a range of analyses.All three chemical types are products of mixing. Some of the hybrid types may have developed from surface mixing of the low-K and high-K lavas; however, the occurrence of all three types at the vent system suggests that subsurface mixing was the dominant process. We suggest that the Madinah flow was extruded from a heterogeneous magma chamber containing vertically stacked sections equivalent to the six eruptive pulses. This chamber may have developed contemporaneously with magma mixing when a crustal reservoir containing a magma in equilibrium with assemblage 2 was invaded by a more primitive magma containing cognate microxenoliths and megacrysts of assemblage 1.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts, and aqueous solutions—IV. Aluminum coordination in glasses and aqueous solutions and comments on the aluminum avoidance principle

The coordination of aluminum with oxygen in crystalline and amorphous alumina, aluminates, and aluminosilicates has been determined with magic angle spinning ²⁷Al nuclear magnetic resonance. The ²⁷Al NMR spectra of crystalline materials show that ^VIAl and ^IVAl can readily be distinguished. The same is not the case for amorphous aluminosilicates due to the superposition of a narrow peak, characteristic of ^IVAl, on a broad band. Our spectroscopic results indicate that Al coordination is not the determining factor in explaining differences in devitrification behavior of albite and anorthite glasses. The coordination of Al in aqueous solutions seems to prevent precipitation of the three common Al(OH)₃ polymorphs (^VIAl) at pH above 10. There is clear evidence to suggest that, in solutions containing Si as well as Al, aluminum coordination is related to the type of precipitate formed in acid (clays, ^VIAl, ^IVAl), and basic (zeolites, ^IVAl) environments. Zeolites can be precipitated in near neutral pH environments at higher temperatures, reflecting an increase in ^IVAl under these conditions. The Al avoidance principle for aluminosilicates does not seem to be a hard principle. It is likely that the validity of this principle depends on the type of modifying cation present in the aluminosilicate framework.