Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Deformation styles as a key for interpreting glacial depositional environments

Lithostratigraphical and lithofacies approaches used to interpret glacial sediments often ignore deformation structures that can provide the key to environment of formation. We propose a classification of deformation styles based on the geometry of structures rather than inferred environment of formation. Five styles are recognised: pure shear (P), simple shear (S), compressional (C), vertical (V) and undeformed (U). These dictate the first letter of the codes; the remaining letters conveying the evidence. This information can be used to reconstruct palaeostress fields and to infer physical properties of sediments when they deformed. Individual structures are not diagnostic of particular environments but the suite of structures, their relative scale, stratigraphical relationships, and orientation relative to palaeoslopes and to palaeoice‐flow directions can be used to infer the environment in which they formed. This scheme is applied at five sites in west Wales. The typical succession is interpreted as subglacial sediments overlain by meltout tills, flow tills and sediment flows. Paraglacial redistribution of glacial sediments is widespread. Large‐scale compressional deformation is restricted to sites where glaciers readvanced. Large‐scale vertical deformation occurs where water was locally ponded near the ice margin. There is no evidence for glaciomarine conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

Structural Evolution of the Eastern Margin of Eurasia in Late Mesozoic and Cenozoic

This paper features the structural evolution of the eastern margin of Eurasia in Late Mesozoic and Cenozoic.It is characterized by three stages of development: the riftogenic stage (Jurassic-Early Cretaceous), the platform stage (Late Cretaceous) and the neotectonic one (Paleogene-Quarternary). The boundaries between these stages are distinctly fixed by the geological time limits of planetary range. It is demonstrated that the riftogenic and neotectonic stages were characterized by a high degree of geodynamic activity, and the platform one by a decrease in contrast of tectonic movements. The main river net was formed in the Early Cretaceous and in the Neogene. It experienced a serious reconstruction accompanied by the formation of the Amur River valley being similar to the modem one.     

Contribution of storms to groundwater recharge in the semi‐arid region of Karnataka,India

This paper describes the application of environmental isotopes and injected tracer techniques in estimating the contribution of storms as well as annual precipitation to groundwater recharge and its circulation, in the semi‐arid region of Bagepalli, Kolar district, Karnataka. Environmental isotopes ²H, ¹⁸O and ³H were used to study the effect of storms on the hydrological system, and an isotope balance was used to compute the contribution of a storm component to the groundwater. Some of the groundwater samples collected during the post‐storm periods were highly depleted in stable isotope content with higher deuterium excess relative to groundwater from the pre‐storm periods. Significant variation in deuterium excess in groundwater from the same area, collected in two different periods, indicates the different origin of air masses. The estimated recharge component of a storm event of 600 mm to the groundwater was found to be in the range of 117–165 mm. There was no significant variation in environmental tritium content of post‐storm and pre‐storm groundwater, indicating the fast circulation of groundwater in the system. After completion of the environmental isotope work, an injected radiotracer ³H technique was applied to estimate the direct recharge of total precipitation to the groundwater. The estimated recharge to the groundwater is 33 mm of the 550 mm annual precipitation during 1992. Copyright © 2003 John Wiley & Sons, Ltd.     

Using bright ellipticals as dark energy cosmic clocks

The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w _Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.