On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Comment on the “Analysis of the State of Stress During the 1997 Earthquake Swarm in Western Bohemia” by A. Slancová and J. Horálek (Studia geoph. et geod. 44(2000), 272–291)

Studia Geophysica et Geodaetica -     

Hydroextrusion as a possible mechanism for the ascent of diapirs,domes, and mantle plumes

A possible mechanism of the ascent of material within the Earth’s crust and mantle is the mechanism of hydroextrusion, i.e., the effect of squeezing of material under excess pressure. The major factors that predetermine the high plasticity of the material and its ability to produce hydroextrusions are high lithostatic pressures and temperatures. The phenomenon of hydroextrusion can be most clearly illustrated by the example of the origin of salt diapirs. The driving force of hydroextrusions of material in the crust and mantle is excess pressure, which can result from lateral differences between the densities of rocks (as is the case during the development of salt diapirs) and phase transitions associated with a volume increase. When the material of the upper mantle undergoes partial melting with the derivation of basaltic melts at depths of 60–100 km, excess pressures reach 80 MPa, whereas the plasticity limit of 20% melted rocks is no higher than 5 MPa. As a result, the partially molten material is forced from the melting region toward zones with lower lithostatic pressures. A local temperature increase in the transitional zones in the Earth’s mantle at positive dP/dT values of the phase transitions also gives rise to excess pressures, whose values can range from 100 to 800 MPa at a 0.5–3.0% volume change and which can be the driving force during the origin of mantle plumes. Original Russian Text ? V.N. Anfilogov, Yu.V. Khachai, 2006, published in Geokhimiya, 2006, No. 8, pp. 873–878.     

Use of Factor Analysis to Study the Distribution of Metalliferous Bauxitic Tailings in the Seabed of the Gulf of Corinth,Greece

In 1994, a detailed marine environmental survey was carried out in surface sediments of the northern flank (Antikyra Bay) and the basin floor of the Gulf of Corinth. Metalliferous tailings (red-mud slurry) of a bauxite processing plant are discharged through a pipeline at a water depth of 100 m, in the Antikyra Bay, covering an area of 16 km². The bauxitic tailings are detached from the main deposit at the outfalls, flow as turbidity currents downslope, and are redeposited on the basin floor of the Gulf of Corinth, where they cover an area of about 277 km². One hundred sediment samples, that were collected from red-mud deposits and the surrounding natural sediments, were analyzed for Ag, Al, Cd, Co, Cr, Cu, Fe, Hg, Mg, Mn, Ni, Pb, Si, Ti, V, and Zn concentrations. Statistical analysis of the heavy metals concentrations using factor analysis allowed (i) an examination of the interrelations among metals and (ii) distinguishing possible sample groups on the basis of metal concentrations in order to study the mechanisms of transport of the red mud and the degree of mixing with natural sediments. Factor 1 (Al, Cr, Ti, Fe, Co, Ni, Pb, Ag, Hg, V, Cd, and Cu) and the positive pole of Factor 2 (Cu, Ag, Cd, and Hg) are red-mud factors, reflecting different metal behaviors, which are related to processes that take place during the transport and redeposition of the red mud. The negative poles of Factors 2 and 3 and the positive pole of Factor 4 are related to natural sediment supply processes. Q-mode factor analysis identifies three distinct sediment groups located in different areas, on the base of the degree of mixing of red mud with natural sediments.     

REVIEWS

Book reviewed in this article:
GEOGRAPHY, ITS SCOPE AND SPIRIT. By J. O. M. Broek
GEOGRAPHY AS HUMAN ECOLOGY: METHODOLOGY BY EXAMPLE. Edited by S. R. Eyre and G. R. J. Jones
A PREFACE TO ECONOMIC GEOGRAPHY. By H. H. McCarty and J. B. Lindberg
A PROLOGUE TO POPULATION GEOGRAPHY. By W. Zelinsky     

Biogeochemical records of paleoenvironmental changes in Nainital Lake,Kumaun Himalayas,India

Rapid urbanization and increased tourism around Nainital Lake in the Kumaun Himalayan region in north India has raised concerns about sediment and water pollution. Lead-210 dated sediment cores from the lake represent ~95 years of accumulation and yield a mean sedimentation rate of ~4.7 mm year⁻¹. Total organic carbon (TOC), percent N and S and their atomic C/N and C/S ratios, stable isotopes (δ¹³C, δ¹⁵N, and δ³⁴S), and specific biomarkers (n-alkanes and pigments) were measured in the core. Organic matter is primarily derived from in-lake algal production and TOC flux varies from 1.0 to 3.5 g m⁻² year⁻¹. Sediments are anoxic (Eh −328 to −187 mV) and have low (0.10–0.30 g m⁻² year⁻¹) N, but high (0.37–1.0 g m⁻² year⁻¹) S flux. Shifts in δ¹³C, δ¹⁵N, and δ³⁴S suggest in-lake microbial processes dominated by denitrification and sulfate reduction. The sediments are dominated by short-chain hydrocarbons with low Carbon Preference Index values. The pigments indicate a gradual shift to cyanobacterial domination of the phytoplankton community in recent years. Despite an increase in external input of nutrients, the trophic state of the lake has remained largely unchanged, and the perceived human-induced impacts are limited.     

Natural aggregates in the performance and durability of concrete: chemical characteristics

This article continues from the earlier feature in Geology Today (2011, v.27, n.4) and looks at the influence of chemical reactivity within concrete due to the presence of unsound aggregates or deleterious material incorporated in the aggregate used in the concrete mix. Some of the more disruptive problems from chemical unsoundness come from the presence of chlorides, which cause rusting in reinforced concrete or, sulphate attack from ground waters. Both of these reactions are relatively common in Britain. Alkali–silica reactions with aggregates and cement is not too prevalent in Britain but can be very prevalent and disruptive elsewhere in the world.     

The neotectonics and geodynamics of the Lower Oka Region (East European Craton)

The neotectonic structures of the Lower Oka (Nizhneokskii) Region formed under different geodynamic conditions. This is attested by the morphology, orientation, internal structure, and jointing of the structures. The Oka-Tsna arc formed under the effect of tension from an inner source on the one hand and stress from the Alpian belt on the other hand. The latitudinally-oriented structures of the northwestern slope of the Tokmovo arc emerged as a result of uplift and widening. Both types of structure are combined within the limits of the Oka-Murom trough, which is a geodynamically active zone.