Fourier analysis of the light curves of eclipsing variables,II

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.     

On the structure of Saturn's rings and the ‘real’ rotational period for the planet

An analysis of the Lowell Observatory photographic plates of Saturn gave the following results: (1) ring A and B show peculiar brightness distributions around the planet, from which we conclude that both are composed of particles in synchronous rotation. (2) The leading side of the particles in ring A is brighter than the trailing side by about 4%, which may indicate an interaction between such particles and the interplanetary medium. (3) Scans of the rings across the major axis show a small (～0.3″) region of enhanced brightness, from which we derive a value ofT _s =10^h13 _. ^m 8±5 _. ^m 4 for the actual planetary rotational period of Saturn. (4) In order to explain the synchronous rotation, the particles in ring A have to be at least 42 m in diameter.     

Modeling nonlinear seagrass clonal growth: Assessing the efficiency of space occupation across the seagrass flora

The clonal growth of 9 seagrass species was modeled using a simulation model based on observed clonal growth rules (i.e., spacer length, rhizome elongation rates, branching rates, branching angle) and shoot mortality rates for seagrass species. The results of the model confirmed the occurrence of complex, nonlinear growth of seagrass clones derived from internal dynamics of space occupation. The modeled clones progressed from a diffuse-limited aggregation (DLA), dendritic growth, identified with a guerrilla strategy of space occupation, to a compact (Eden) growth, comparable to the phalanx strategy of space occupation, once internal recolonization of gaps, left by dead shoots within the clone, begins. The time at which seagrass clones shifted from diffuse limited to compact growth was predictable from the branching angle and frequency of the species and varied from 1 yr to several decades among species. As a consequence the growth behavior and the apparent growth strategy of the species changes with the development of the clones. The results of the model demonstrate that the emergent complexity of seagrass clonal growth is contained within the simple set of growth rules that can be used to represent clonal growth.     

Alpine reworking of Ordovician protoliths in the Western Carpathians: Geochronological and geochemical data on the Muráñ Gneiss Complex, Slovakia

Magmatic protoliths of Ordovician age have been identified in the metamorphic rocks of the Muráñ Gneiss Complex, Veporic Unit (Central Western Carpathians). Vapor digestion single zircon U–Pb dating yields an intrusion age of 464 ± 35 Ma (upper intercept) for the granite protolith. A lower intercept age of 88 ± 40 Ma records amphibolite-facies metamorphic overprint in the Cretaceous, during the Alpine orogeny. Geochemical and isotopic data suggest crustal origin of the orthogneiss. Nd_initial are between − 2.6 and − 5.0 and T_DM^Nd between 1.3 and 1.5 Ga (two-step approach). ⁸⁷Sr / ⁸⁶Sr_initial ratios vary between 0.7247 and 0.7120, and a steep REE pattern further constrains the crustal affinity of these rocks. Associated amphibolite bodies have Nd_initial values of 6.5, ⁸⁷Sr / ⁸⁶Sr_initial ratio of 0.7017, and a flat REE pattern. They are interpreted as MORB derived metabasites. Whole-rock Pb isotope analyses define a linear array in a ²⁰⁶Pb / ²⁰⁴Pb vs. ²⁰⁷Pb / ²⁰⁴Pb diagram with an age of ca. 134 Ma, consistent with intense Alpine metamorphism and deformation.

These basement rocks of the Central Western Carpathians are interpreted as Ordovician magmatic rocks intruded at an active margin of Gondwana. They represent the eastern prolongation of Cambro–Ordovician units of the European Variscides, which were part of the peri-Gondwana superterrane and accreted to Laurussia during the Variscan orogeny. Variscan metamorphic overprint is not recorded by the isotopic data of the Muráñ Gneiss Complex. Alpine metamorphism is the most dominant overprint.     

Study of geothermal water intrusion due to groundwater exploitation in the Puebla Valley aquifer system, Mexico

Significant intrusion of geothermal water into fresh groundwater takes place in the Puebla Valley aquifer system, Mexico. The decline in the potentiometric surface due to the overexploitation of the groundwater induces this intrusion. This hydrological system comprises three aquifers located in Plio-Quaternary volcanic sediments and Mesozoic calcareous rocks. The hydraulic balance of the aquifer shows that the annual output exceeds the natural inputs by 12 million m³. Between 1973 and 2002, a drop in the potentiometric surface, with an 80 m cone of depression, was identified in a 5-km-wide area located southwest of the city of Puebla. Chemical analyses performed on water samples since 1990 have shown an increase in total dissolved solids (TDS) of more than 500 mg/L, coinciding with the region showing a cone of depression in the potentiometric surface. A three-dimensional flow and transport model, based on the hydrogeological and geophysical studies, was computed by using the MODFLOW and MT3D software. This model reproduces the evolution of the aquifer system during the last 30 years and predicts for 2010 an additional drawdown in the potentiometric surface of 15 m, and an increase in the geothermal water intrusion.     

A Practical Procedure for the Measurement of Fragmentation by Blasting by Image Analysis

Summary. The operation of a digital image analysis system in a limestone quarry is described. The calibration of the system, required in order to obtain moderately reliable fragmentation values, is done from muckpile sieving data by tuning the image analysis software settings so that the fragmentation curve obtained matches as close as possible the sieving. The sieving data have also been used to extend the fragment size distribution curves measured to sizes below the system’s optical resolution and to process the results in terms of fragmented rock, discounting the material coming from a loose overburden (natural fines) that is cast together with the fragmented rock. Automatic and manual operation modes of the image analysis are compared. The total fragmentation of a blast is obtained from the analysis of twenty photographs; a criterion for the elimination of outlier photographs has been adopted using a robust statistic. The limitations of the measurement system due to sampling, image processing and fines corrections are discussed and the errors estimated whenever possible. An analysis of consistency of the results based on the known amount of natural fines is made. Blasts with large differences in the amount of fines require a differentiated treatment, as the fine sizes tend to be the more underestimated in the image analysis as they become more abundant; this has been accomplished by means of a variable fines adjustment factor. Despite of the unavoidable errors and the large dispersion always associated with large-scale rock blasting data, the system is sensitive to relative changes in fragmentation.     

Catastrophic debris flows near Machu Picchu village (Aguas Calientes), Peru

Slope movements together with intensive river erosion and the following accumulation are the leading processes in the landscape evolution in the area of Machu Picchu village (former Aguas Calientes), which is located close to the Machu Picchu Sanctuary. Debris flows affect not only the bottoms of valleys or canyons, but also debris fans at the termini of the drainage basins, which are heavily inhabited at some places. The most recent event in the Machu Picchu village occurred in April 2004, but several others were documented in a broader area in the last 50 years. The field inspections at Machu Picchu (May and September 2004; June and September 2005) together with oral testimony revealed the nature and behavior of the debris flow. Machu Picchu village can be assessed as a zone with high landslide risk in relation to its urban development. Despite that, the village recorded a rapid growth (threefold population increase) without urban control within the past two decades. Precipitation, which is the main triggering factor of the debris flows, and natural hazard management of the Machu Picchu village are discussed in this paper.     

Will the river Irtysh survive the year 2030? Impact of long-term unsuitable land use and water management of the upper stretch of the river catchment (North Kazakhstan)

The Irtysh river basin all the way from river spring in China across Kazakhstan as far as the Russian part of Siberia is among the most ecologically endangered and affected regions on our planet. The study provides a summary of the historical reasons for anthropological interventions in this area, which began with the construction of plants of the military—industrial complexes in the forties of the last century during World War II. These plants have a major share in extreme high concentrations of heavy metals in surface as well in groundwaters locally. The Semipalatinsk nuclear polygon plays a specific role as a source of contamination of local waters. The release of top secret data enabled us to gain knowledge about serious problems related to high radioactivity of groundwaters, which should spread uncontrollably through a system of secondary fissures activated by nuclear blasts. Another serious problem in this region is the quantitative aspect of contamination. Model simulations of water balance indicate that large industrial development in the spring area in China and continuously increasing water consumption in Kazakhstan may lead to desiccation of the lower stretch of this large river in Siberia during the summer months of 2030.     

The Spačice eclogite: constraints on the P–T–t history of the Gföhl granulite terrane, Moldanubian Zone, Bohemian Massif

Summary In the Kutná Hora Complex, the Běstvina Formation, which is similar to Gf?hl granulite, contains eclogite that has escaped widespread retrograde recrystallization. The eclogite assemblage, garnet + omphacite + quartz + rutile ± plagioclase, yields an estimate for peak metamorphic conditions of 18–20 kbar and 835–935 °C, which is comparable to that determined from felsic granulite, 14–20 kbar and 900–1000 °C. Garnet in eclogite exhibits both prograde and retrograde compositional zoning, from which constraints on thermal history of the Gf?hl terrane can be derived by diffusion modelling. At 900 °C, a garnet grain of 800–1000 μm radius would homogenize in 7.5–11.7 million years, but the existence of compositional gradients on a length scale of 100–200 μm suggests that the duration of peak metamorphism may have been limited to ∼500,000 years. Diffusion modelling of retrograde zoning in garnet yields a cooling rate of 150–100 °C/m.y. for a radius of 800–1000 μm and initial temperature of 900 °C. The relatively brief duration of high-pressure/high-temperature metamorphism and rapid cooling and exhumation of the Gf?hl terrane may be a consequence of lithospheric delamination during Early Carboniferous collision of Bohemia (Teplá-Barrandia) and Moldanubia (Franke, 2000).     

Alteration, evaluation and use of extremaduran granite residues

The necessity of eliminating debris from a granite quarry has awakened an interest in applications of by-products, called “marginal arids”, in different fields, like construction and foundations for roadways, restoration, material for the manufacture of artificial rocks, and artesian products etc. Conclusions obtained from the results of tests carried out by X-ray diffraction of granite quarry by-products in Extremadura, Spain, submitted to different treatments, are established. Test pieces from two quarries are analyzed and compared generally and specifically, for commercial use. Finally, conclusions relating to essays in test pieces and mineral dynamics of marginal arid granite are exposed.