Sur un formalisme explicitant la loi des distances des planetes

The well-known Titius-Bode law (T-B) giving distances of planets from the Sun was improved by Basano and Hughes (1979) who found: $$a_n = 0.285 \times 1.523^n ;$$ a _n being the semi-major axis expressed in astronomical units, of then-th planet. The integern is equal to 1 for Mercury, 2 for Venus etc. The new law (B-H) is more natural than the (T-B) one, because the valuen=?∞ for Mercury is avoided. Furthermore, it accounts for distances of all planets, including Neptune and Pluto. It is striking to note that this law:

1. does not depend on physical parameters of planets (mass, density, temperature, spin, number of satellites and their nature etc.).
2. shows integers suggesting an unknown, obscure wave process in the formation of the solar system.

In this paper, we try to find a formalism accounting for the B-H law. It is based on the turbulence, assumed to be responsible of accretion of matter within the primeval nebula. We consider the function $$\psi ^2 (r,t) = |u^2 (r,t) - u_0^2 |$$ , whereu ²(r, t) stands for the turbulence, i.e., the mean-square deviation velocities of particles at the pointr and the timet; andu ₀ ² is the value of turbulence for which the accretion process of matter is optimum. It is obvious that Ψ²(r _n,t₀) = 0 forr _n=0.285×1.523 ⁿ at the birth timet ₀ of proto-planets. Under these conditions, it is easily found that $$\psi ^2 (r,t_0 ) = \frac{{A^2 }}{r}\sin ^2 [\alpha log r - \Phi (t_0 )]$$ With α=7.47 and Φ(t ₀)=217.24 in the CGS system, the above function accounts for the B-H law. Another approach of the problem is made by considering fluctuations of the potentialU(r, t) and of the density of matter ρ(r, t). For very small fluctuations, it may be written down the Poisson equation $$\Delta \tilde U(r,t_0 ) + 4\pi G\tilde \rho (r,t_0 ) = 0$$ , withU(r, t)=U ₀(r)+?(r, t ₀ ) and \(\tilde \rho (r,t_0 )\) . It suffices to postulate \(\tilde \rho (r,t_0 ) = k[\tilde U(r,t_0 )/r^2 ](k = cte)\) for finding the solution $$\tilde U(r,t_0 ) = \frac{{cte}}{{r^{1/2} }}\cos [a\log r - \zeta (t_0 )]$$ . Fora=14.94 and ζ(t ₀)=434.48 in CGS system, the successive maxima of ?(r,t ₀) account again for the B-H law. In the last approach we try to write Ψ(r, t) under a wave function form $$\Psi ^2 (r,t) = \frac{{A^2 }}{r}\sin ^2 \left[ {\omega \log \left( {\frac{r}{v} - t} \right)} \right].$$ It is emphasized that all calculations are made under mathematical considerations.     

Damage formation associated with bending under a constant moment

Deformation within the Earth's lithosphere is largely controlled by the rheology of the rock. Fracture and faulting are characterized by elastic rheologies with brittle mechanisms, while folding and flow are characterized by plastic and/or viscous rheologies due to ductile mechanisms. However, it has been recognized that deformation that resembles ductile behavior can be produced within the confines of the brittle lithosphere. Specific examples are folds that form in the shallow crust, steep hinges at subduction zones that are accompanied by seismicity, and large-scale deformation at plate boundaries. In these cases, the brittle lithosphere behaves elastically with fracture and faulting yet produces ductile behavior. In this paper, we attempt to simulate such ductile behavior in elastic materials using continuum damage mechanics. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. We utilize a modified form of damage mechanics that represents a reduction in frictional strength of preexisting fractures and faults. We use this empirical approach to simulate the bending of the lithosphere under the application of a constant moment.We use numerical simulations to obtain elastostatic solutions for plate bending and where the longitudinal stress at a particular node exceeds a yield stress, we apply damage to reduce Young's modulus at the node. Damage is calculated at each time step by a power-law relationship of the ratio of the yield stress to the longitudinal stress and the yield strain to the longitudinal strain. This results in the relaxation of the material due to increasing damage. To test our method, we apply our damage rheology to an infinite plate deforming under a constant bending moment. We simulate a wide range of behaviors from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Using this method, stress relaxation produces elastic-perfectly plastic behavior in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage leading to failure, analogous to the acceleration of microcrack formation and acoustic emissions prior to failure. The changes in the rate of damage accumulation in failure cases are similar to the changes in b-values of acoustic emissions observed in triaxial compression tests of fractured rock and b-value changes prior to some large earthquakes. Thus continuum damage mechanics can simulate the phenomenon of ductile behavior due to brittle mechanisms as well as observations of laboratory experiments and seismicity.     

Comparison of Fiberglass and Other Polymeric Well Casings Part II. Sorption and Leaching of Trace-Level Organics

This paper contains the results of a laboratory study that was designed to compare sorption of low (mg/L) concentrations of 11 organic solutes by six polymeric materials (acrylonitrile butadiene styrene [ABS], fluorinated ethylene propylene [FEP], fiberglass-reinforced epoxy [FRE] and fiberglass-reinforced plastic [FRP], polyvinyl chloride [PVC], and poly-tetrafluoroethylene [PTFE]).
During this six-week study, ABS sorbed analytes much more rapidly and to a greater extent than did the other materials, and PVC and FRE sorbed analytes more slowly and to a lesser extent than the other materials tested.
As the study progressed, an increasing number of spurious peaks were found in the high performance liquid chromatography (HPLC) chromatograms of some of our samples, indicating that leaching of some consituents had occurred. By the end of the study, there were 11 additional peaks in the ABS samples, five in the FRP samples, and one in the FRE samples. Analysis by purge and trap gas chromatography/mass spectrometry (GC/MS) of those samples and of well water samples that were exposed to the casings for 500 hours revealed the identity of some of the leached constituents; acrylonitrile and styrene (components of ABS), chloroform and ethylbenzene (an intermediate in the production of styrene) from the ABS pipe, and toluene, 1,1,1-trichloroethane, and ethylbenzene from the FRP casing.     

Rb-Sr provenance ages from weathered and stream transported quartz grains from the Harney Peak Granite,Black Hills,South Dakota

Weathered quartz grus and stream transported quartz of the Harney Peak Granite, Black Hills, South Dakota, contain low concentrations of Rb (generally 0.3–6.8 ppm) and Sr (0.2–2.0 ppm) and variable Sr isotopic ratios (0.759–1.070).Six of seven single grains of large composite quartz grus which recently entered the weathering environment define an apparent isochron age (about 1800 Myr) and initial ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio (0.7066) that approximate the whole-rock isochron age (1707 Myr) and initial ratio (0.7143) of the Harney Peak Granite. Apparently the Rb-Sr systematics of these grains were not significantly altered during initial weathering. Leached fluid inclusion material from a ca. 2 g aggregate of composite quartz grains contains very little Rb or Sr (0.019 and 0.17 μg, respectively) and has a very low ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio (0.739). The Rb and Sr content of the quartz grains appears to be concentrated in minute, heterogeneously-distributed mineral inclusions.Five aggregates of more completely weathered, small non-composite quartz grains produce a widely scattered pattern on an isochron diagram with all samples plotting below the 1707 Myr isochron. Examination by SEM of these grains shows solution and precipitation features on their relatively large effective surface areas. The differential precipitation of Rb is believed to have been the major perturbating chemical process during weathering.Three aggregates of stream quartz grains define an apparent isochron age of 1777 Myr and an initial ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio of 0.720 that suggest the initial ‘igneous’ Rb-Sr characteristics of the stream quartz were re-attained during their transportation, probably as a result of removal of the outer weathered surface by abrasion. The apparent resistance to chemical weathering of stream quartz and quartz which has just entered the weathering environment suggests that this mineral may be extremely useful in studies of provenance and the geochronology of strongly weathered terranes.     

Coexisting K-rich alkaline and shoshonitic magmatism of arc affinities in the Proterozoic: a reassessment of syenitic stocks in the southwestern Grenville Province

Biotite-rich syenitic stocks in the Mont-Laurier area of the southwestern Grenville Province are shown to belong to the first recorded Proterozoic example of an ultrapotassic, K-rich alkaline and shoshonitic rock association with clear arc affinities. The plutons investigated were previously considered mostly syenitic, typical of nepheline syenite alkaline suites, slightly metamorphosed and late-tectonic with respect to the Grenville orogeny. We find that they postdate the regional metamorphism and comprise a felsic to ultramafic range of rock types belonging to two series: (1) a potassic-to-ultrapotassic, silica-undersaturated series of biotite-rich nepheline-bearing syenite, syenite, monzonite, diorite and pyroxenite, and (2) a shoshonitic, critically silicasaturated series of quartz syenite and amphibole-bearing syenite, with rare monzonite and diorite. The ubiquitous biotite, previously regarded as metamorphic, is reinterpreted as igneous and diagnostic of the potassic character. The shoshonitic and potassic series display the strong enrichment in Al, Ca, K and large-ion-lithophile elements relative to the high-field-strength elements (e.g. Ba/Nb722, La/YB45) and the low contents in Mg that are characteristic of arc-related magmas. The syenitic rocks consistently share the distinctive arc-related geochemical signature of their mafic counterparts. Syenites may thus represent a potential source of paleotectonic information for high grade terranes. Geochemical discriminants (Nb_N/Ta_N and Hf_N/Ti_N ratios) indicate that the shoshonitic and potassic series are unrelated by closedsystem fractionation processes. Rather, the chemical differences between the two series probably reflect differences in source characteristics and conditions of melting. Similar plutons occur throughout the Central Metasedimentary Belt of the southwestern Grenville Province. They define a 1089 to 1076 Ma, 450-km-long grenvillian potassic alkaline plutonic (PAP) province. The presence of this K-rich alkaline province indicates that the scarcity of K-rich rocks in the Precambrian could be only apparent and a consequence of misidentification of K-rich plutons in metamorphosed Precambrian terranes. These 1.1 Ga ultrapotassic to shoshonitic plutonic rocks are geochemically similar to shoshonites and leucitites of the Sunda arc. This similarity suggests that subduction-type enrichment processes were operating in the Proterozoic in ways similar to those of modern settings.     

Mixed messages in iron oxide–copper–gold systems of the Cloncurry district,Australia: insights from PIXE analysis of halogens and copper in fluid inclusions

Proterozoic rocks of the Cloncurry district in NW Queensland, Australia, are host to giant (tens to hundreds of square kilometers) hydrothermal systems that include (1) barren regional sodic–calcic alteration, (2) granite-hosted hydrothermal complexes with magmatic–hydrothermal transition features, and (3) iron oxide–copper–gold (IOCG) deposits. Fluid inclusion microthermometry and proton-induced X-ray emission (PIXE) show that IOCG deposits and the granite-hosted hydrothermal complexes contain abundant high temperature, ultrasaline, complex multisolid (type 1) inclusions that are less common in the regional sodic–calcic alteration. The latter is characterized by lower salinity three-phase halite-bearing (type 2) and two-phase (type 3) aqueous inclusions. Copper contents of the type 1 inclusions (>300 ppm) is higher than in type 2 and 3 inclusions (<300 ppm), and the highest copper concentrations (>1,000 ppm) are found both in the granite-hosted systems and in inclusions with Br/Cl ratios that are consistent with a magmatic source. The Br/Cl ratios of the inclusions with lower Cu contents are consistent with an evaporite-related origin. Wide ranges in salinity and homogenization temperatures for fluid inclusions in IOCG deposits and evidence for multiple fluid sources, as suggested by halogen ratios, indicate fluid mixing as an important process in IOCG genesis. The data support both leaching of Cu by voluminous nonmagmatic fluids from crustal rocks, as well as the direct exsolution of Cu-rich fluids from magmas. However, larger IOCG deposits may form from magmatic-derived fluids based on their higher Cu content.     

The concept of hydrological connectivity and its contribution to understanding runoff‐dominated geomorphic systems

The term ‘connectivity’ is increasingly being applied in hydrological and geomorphological studies. Relevant research encompasses aspects of landscape connectivity, hydrological connectivity and sedimentological connectivity. Unlike other disciplines, notably ecology, published studies show no consensus on a standard definition. This paper provides an overview of how existing research relates to the concept of connectivity in both ecology and hydrology by proposing and evaluating a conceptual model of hydrological connectivity that includes five major components: climate; hillslope runoff potential; landscape position; delivery pathway and lateral connectivity. We also evaluate a proposed measure of connectivity called the volume to breakthrough to quantify changing connectivity between different environments and catchments. Copyright © 2007 John Wiley & Sons, Ltd.     

Introduction to special issue on connectivity in water and sediment dynamics

Connectivity has emerged in recent years as a significant conceptual framework within which to address the spatial and temporal variability in runoff and sediment transport. This special issue draws together several of the papers that were presented in the session “Connectivity in water and sediment dynamics: how do we move forwards?” at the 2012 General Assembly of the European Geosciences Union in Vienna, Austria. The papers submitted for this special issue fall into three groups: empirical studies, modelling studies, and conceptual development. Although it may be evident that the concept of connectivity helps us to express the complexity (in terms of water and sediment yields) of landscape responses to rainfall inputs, does it improve our ability to understand or predict those responses? There would still seem to be some way to go in connectivity research before this nagging concern can be assuaged. That it can be will undoubtedly be an important task for a number of ongoing research initiatives. Copyright © 2015 John Wiley & Sons, Ltd.     

Ground-air temperature tracking and multi-year cycles in the subsurface temperature time series at geothermal climate-change observatory

Long-term observations of air, near-surface (soil) and ground temperatures, collected between 1994 and 2011, monitored in the Geothermal Climate Change Observatory at Spo?ilov, Prague (GCCO) are analyzed to better understand the relationship between these quantities and to describe the mechanism of heat transport at the land-atmosphere boundary layer. The 17 years long monitoring series provided a surprisingly small mean ground-air temperature offset of only 0.31 K with no clear annual course and with the offset value changing irregularly even on a daily scale. Such value is substantially lower than similar values (1–2 K and more) found elsewhere, but it may be well characteristic for a mild temperate zones, when all so far available information referred rather to more southern locations. As many other observed geophysical data, temperature time series consist of a systematic pattern (usually a set of identifiable components) contaminated by random noise, which makes the identification of the proper pattern difficult. To identify the existing systematic patterns (cycles) of the temperature-time series at several depth levels in the investigated depth interval 0–40 m, the observed data were processed with the help of the Fast Fourier Transform (FFT) and Recurrence Quantification Interval (RQI) analysis. The latter represents recently developed powerful technique to uncover hidden periodicities in a noisy time environment. At low frequency band the RQI may provide far finer resolution than the conventional FFT technique. The results proved considerable similarity for all investigated depth levels. In addition to the annual wave all measured series proved to have a more complex pattern including predominantly 8-year and 11 years long periodicities. The results were compared with similar analysis of the meteorological air temperature series as well as with the results of other similar studies. The potential dynamics explaining the occurrence of the 8-year wave is briefly discussed.     

433 Eros lineaments: Global mapping and analysis

Using images and laser ranging data from the NEAR-Shoemaker mission, we map lineaments on the surface of Eros in order to investigate the relationship between surface morphology and interior structure. Several sets of lineations are clearly related to visible impact craters, while others suggest that different parts of the asteroid may have undergone different stress histories. Some of these sets infer internal structure, at least on a local level. This structure may derive from Eros' parent body and suggest, although largely coherent, Eros' interior may have portions that have not undergone a common history.