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.     

Application of the global modal approach to the spiral galaxies

We have tested the applicability of the global modal approach in the density wave theory of spiral structure for a sample of spiral galaxies with measured axisymmetric background properties. We report here the results of the simulations for four galaxies: NGC 488, NGC 628, NGC 1566, and NGC 3938. Using the observed radial distributions for the stellar velocity dispersions and the rotation velocities we have constructed the equilibrium models for the galactic disks in each galaxy and implemented two kinds of stability analyses - the linear global analysis and 2D-nonlinear simulations. In general, the global modal approach is able to reproduce the observed properties of the spiral arms in the galactic disks. The growth of spirals in the galactic disks can be physically understood in terms of amplification by over-reflection at the corotation resonance. Our results support the global modal approach as a theoretical explanation of spiral structure in galaxies. This revised version was published online in August 2006 with corrections to the Cover Date.     

The hydrological influence of black locust plantations in the loess area of northwest China

Black locust (Robina pseudoacacia) has become one of the most important shelter species in the loess area of northwest China. This paper summarizes recent research concerning its hydrological influence, including canopy interception, litter absorption capacity, its effect on rainfall kinetic energy, infiltration rates, surface runoff, soil moisture, and evapotranspiration, and its role in soil conservation. Several predictive models are listed. on the basis of existing results, optimum characteristics for an effective plantation are defined, and problems requiring further research are identified.     

Nutrient (P, N) dynamics in the southwestern Kattegat, Scandinavia: sedimentation and resuspension effects

 The yearly nutrient supply from land and atmosphere to the study area in SW Kattegat is 10 900 tons of N and 365 tons of P. This is only few percent of the supply from adjacent marine areas, as the yearly transport through the study area is 218 000 tons of N and 18 250 tons of P. Yearly net deposition makes up 1340 tons of N (on average 2.5 g m^–2 yr^–1) and 477 ton of P (on average 0.9 g m^–2 yr^–1). Shallow-water parts of the study area have no net deposition because of frequent (>35% of the year) resuspension. Resuspension frequency in deep water is <1% of the year. Resuspension rates, as averages for the study area, are 10–17 times higher than net deposition rates. Because of resuspension, shallow-water sediments are coarse lag deposits with small amounts of organic matter (1.1%) and nutrients (0.04% N and 0.02% P). Deep-water sediments, in contrast, are fine grained with high levels of organic matter (11.7%) and nutrients (0.43% N and 0.15% P). Laboratory studies showed that resuspension changes the diffusive sediment water fluxes of nutrients, oxygen consumption, and penetration into the sediment. Fluxes of dissolved reactive phosphate from sediment to water after resuspension were negative in organic-rich sediments (13.2% organic matter) with low porosity (56) and close to zero in coarse sediments with a low organic matter content (2.3%) and high porosity (73). Fluxes of inorganic N after resuspension were reduced to 70% and 0–20% in relation to the rates before resuspension, respectively. Received: 10 July 1995 · Accepted: 19 January 1996     

Latitudinal transport by barotropic waves in Titan's stratosphere.: II. Results from a coupled dynamics-microphysics-photochemistry GCM

We present a 2D general circulation model of Titan's atmosphere, coupling axisymmetric dynamics with haze microphysics, a simplified photochemistry and eddy mixing. We develop a parameterization of latitudinal eddy mixing by barotropic waves based on a shallow-water, longitude-latitude model. The parameterization acts locally and in real time both on passive tracers and momentum. The mixing coefficient varies exponentially with a measure of the barotropic instability of the mean zonal flow. The coupled GCM approximately reproduces the Voyager temperature measurements and the latitudinal contrasts in the distributions of HCN and C₂H₂, as well as the main features of the zonal wind retrieved from the 1989 stellar occultation. Wind velocities are consistent with the observed reversal time of the North-South albedo asymmetry of 5 terrestrial years. Model results support the hypothesis of a non-uniform distribution of infrared opacity as the cause of the Voyager temperature asymmetry. Transport by the mean meridional circulation, combined with polar vortex isolation may be at the origin of the latitudinal contrasts of trace species, with eddy mixing remaining restricted to low latitudes most of the Titan year. We interpret the contrasts as a signature of non-axisymmetric motions.