Extension of the solution of Kepler's equation to high eccentricities

The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ _n (ne). The expansion is convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically.     

Permanent Scatterers for landslide investigations: outcomes from the ESA-SLAM project

Within the SLAM project (Service for Landslide Monitoring), launched in 2003 by the European Space Agency (ESA) the Permanent Scatterers (PS) technique, a multi-image interferometric approach, coupled with the interpretation of aerial-photos and optical satellite images, was carried out for landslide investigations. The PS analysis was applied at a regional scale as support for landslide inventory mapping and at local scale for the monitoring of single well-known slope movements. For the integration of the PS measurements within a landslide inventory the Arno river basin (Italy) was chosen as test site for the presence of a high number of mass movements (to date about 300 areas at high landslide risk and more than 27,000 individual landslides mapped by the institutional authorities). About 350 SAR images have been interferometrically processed by means of the PS technique, with the detection of about 600,000 PS. The use of optical images contributed spatial meaning to the point-wise information provided by the PS, making it easier to identify terrain features related to slope instability and the landslide boundaries. Here we describe the employed methodology and its impact in the updating of a preexisting landslide inventory. 6.8% of the total number of landslides were characterized by ground displacement measurements from the PS: 6.1% of already mapped landslides and 0.8% of new unstable areas detected through the PS analysis. Moreover, most of the PS are located in urban areas, showing that the proposed methodology is suitable for landslide mapping in areas with a quite high density of urbanization, but that over vegetated areas it still suffers from the limitations induced by the current space-borne SAR missions (e.g. temporal de-correlation). On the other hand, the use of InSAR for the monitoring of single slow landslides threatening built-up areas has provided satisfactory results, allowing the measurement of superficial deformations with high accuracy on the landslide sectors characterized by a good radar reflectivity and coherence.     

Soluble organic compounds in fog and cloud droplets: what have we learned over the past few years?

We have recently set up a new procedure for characterising the water soluble organic compounds (WSOC) in fog water, for which information is still rather limited. Fog samples collected during the 1998–1999 fall–winter season in the Po Valley (Italy) were analysed following this procedure, which allows a quantitative determination of three main classes of organic compounds (neutral species, mono- and di-carboxylic acids, polycarboxylic acids), together accounting for ca. 85% of the total WSOC. This procedure also provides information on the main chemical characteristics of these three classes of compounds (functional groups, aliphatic vs. aromatic character, etc.). The enhanced chemical knowledge on fog/cloud chemical composition opens new scenarios as far as chemical and microphysical processes in clouds and fogs are concerned.     

Direct Current Plasma Emission Spectrometric Determination of Major, Minor and Trace Elements in Microwave Oven Acid Leachates of Powdered Whole Coal Samples

Major concentrations of Al₂O₃, Fe₂O₃, MgO, CaO, Na₂O and K₂O, minor levels of TiO₂, P₂O₅ and thirty petrologically, geochemically and environmentally significant trace elements have been determined in microwave oven acid leachates of whole powdered coal samples by direct current plasma‐atomic emission spectrometry (DCP‐AES). A single sample preparation procedure was suitable for all the determinations with no additional dilution step for major elements solution. Dried samples (0.5 g) were treated in low‐pressure PFA digestion vessels with HF/HCl/HNO₃/HClO₄ acids to quantitatively extract the analytes from the bulk material, while leaving the major part of organic matrix as a residue. The major constituents of geological samples, in particular the easily ionised elements (EIEs) such as alkali and alkaline earths, may complicate the instrumental determinations in DCP‐AES because of differential enhancements of elemental emission intensities and stray light interferences. Taking account of these factors, the coal matrix is considered to have very low major oxide totals as compared to many other common geo‐environmental and related materials (rocks, sediments, soil, ashes etc.). The sample size employed here, while yielding a relatively concentrated solution to cover a wide range of elemental determinations, provided a sample matrix that significantly diminished interferences for DCP measurements. The need for closely matching the unknowns and calibrators was eliminated except for overall acidity and an excess quantity of caesium for EIE buffering. Calibration of the spectrometer was accomplished by simple aqueous single element solutions as high concentration calibrators in addition to a reagent blank as a low concentration calibrator. Two point working curves were established to allow for the maximum concentrations of each element expected in the unknowns. The precision of determinations under routine conditions as well as the reproducibility of the leaching and precision of instrumental measurements have been evaluated. Relative standard deviations (RSD) were of 1–2% for those elements whose concentrations in solid samples were well above the limits of quantification. Method detection limits in the buffered solutions were also evaluated. To evaluate the accuracy of the microwave oven‐DCP method a suite of eight certified coal reference materials of differing rank, were analysed with good agreement with the certified and/or available published data. Results are presented for the uncertified major oxides in the AR series reference materials.     

Crystal-chemistry of clinopyroxenes from potassic and ultrapotassic rocks in central Italy: implications on their genesis

The clinopyroxenes mentioned have been investigated by single crystal X-ray diffraction combined with electron microprobe analysis. The aim of this study was to characterize the crystal-chemical variations of clinopyroxenes in order to delineate the intracrystalline constraints which are characteristic of specific magmatic environments. Clinopyroxenes (cpx) crystallized from peralkaline ultrapotassic melt with kamafugitic and lamproitic affinities are characterized by high Si contents, which are insensitive to variations in silica abundance and silica saturation of the melt. The high Si occupancy in clinopyroxenes from kamafugitic magma is coupled to large M1 (i.e. Mg and Fe²⁺) and M2 (high Ca occupancy) sites, whereas in clinopyroxenes from magmas with lamproitic affinity, high Si content is combined with large M1 but small M2 sites. Clinopyroxenes from Romantype alkaline potassic and ultrapostassic rocks are characterized by an expanded tetrahedron (high ^IVA1 content) and small M1 site which is combined with small M2 polyhedron in clinopyroxenes from the potassic rocks and large M2 site in those from the ultrapotassic rocks.     

Atomic structures and energies of grain boundaries in Mg2SiO4 forsterite from atomistic modeling

Grain boundaries influence many physical and chemical properties of crystalline materials. Here, we perform molecular dynamics simulations to study the structure of a series of [100] symmetric tilt grain boundaries in Mg₂SiO₄ forsterite. The present results show that grain boundary energies depend significantly on misorientation angle. For small misorientation angles (up to 22°), grain boundary structures consist of an array of partial edge dislocations with Burgers vector $\frac{1}{2}[001]$ associated with stacking faults and their energies can be readily fit with a model which adds the Peach-Koehler equation to the Read-Shockley dislocation model for grain boundaries. The core radius of partial dislocations and the spacing between the partials derived from grain boundary energies show that the transition from low- to high-angle grain boundaries occurs for a misorientation angle between 22° and 32°. For high misorientation angles (32.1° and 60.8°), the cores of dislocations overlap and form repeated structural units. Finally, we use a low energy atomic configuration obtained by molecular dynamics for the misorientation of 12.18° as input to simulate a high-resolution transmission electron microscopy (HRTEM) image. The simulated image is in good agreement with an observed HRTEM image, which indicates the power of the present approach to predict realistic atomic structures of grain boundaries in complex silicates.     

Chemical and isotopic assessment of surface water–shallow groundwater interaction in the arid Grande river basin,North-Central Chile

ABSTRACT

This paper analyses the composition of surface water and shallow groundwater in the Grande River basin, North-Central Chile, using this information to characterize water interactions. Chemical and isotopic data for surface water and groundwater (7 and 6 sampling locations, respectively) were obtained from three sampling campaigns performed in March–April (autumn), August–September (late winter) and December (early summer) 2012. Precipitation samples were also collected. Data was processed using spatial distribution charts, Piper and Stiff diagrams, and multivariate analysis. In general, the results for each method converge on a high degree of connectivity between surface water and shallow groundwater in the study area. Furthermore, approximately a 10% of groundwater contribution to the surface flow discharge was estimated for a particular reach. This multi-method approach was useful for the characterization of surface water–groundwater interactions in the Grande River basin, and may become a suitable and replicable scheme for studies in arid and semi-arid basins facing similar water management challenges.

Editor D. Koutsoyiannis; Associate editor B. Dewals     

Nonlinear seismic behaviour of wall-frame dual systems accounting for soil–structure interaction

The aim of this paper is to study the effects of soil–structure interaction on the seismic response of coupled wall-frame structures on pile foundations designed according to modern seismic provisions. The analysis methodology based on the substructure method is recalled focusing on the modelling of pile group foundations. The nonlinear inertial interaction analysis is performed in the time domain by using a finite element model of the superstructure. Suitable lumped parameter models are implemented to reproduce the frequency-dependent compliance of the soil-foundation systems. The effects of soil–structure interaction are evaluated by considering a realistic case study consisting of a 6-storey 4-bay wall-frame structure founded on piles. Different two-layered soil deposits are investigated by varying the layer thicknesses and properties. Artificial earthquakes are employed to simulate the earthquake input. Comparisons of the results obtained considering compliant base and fixed base models are presented by addressing the effects of soil–structure interaction on displacements, base shears, and ductility demand. The evolution of dissipative mechanisms and the relevant redistribution of shear between the wall and the frame are investigated by considering earthquakes with increasing intensity. Effects on the foundations are also shown by pointing out the importance of both kinematic and inertial interaction. Finally, the response of the structure to some real near-fault records is studied. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response of L��Aquila downtown from comparison between 2D synthetics spectral ratios of SH, P-SV and Rayleigh waves and observations of the 2009 earthquake sequence

This is the first part of a study on the seismic response of the L’Aquila city using 2D simulation and experimental data. We have studied two velocity-depth models with the aim of outlining the behavior of a velocity reversal in the top layer, which is associated with the stiff Brecce de L’Aquila unit (BrA). In this setting, the SMTH model is topped by a layer with about 2:1 impedance contrast with the underlying layer while the NORV model has no velocity reversal. We have simulated the propagation of SH and P-SV wavefields in the range 0–10 Hz for incidence 0°–90°. Earthquake spectral ratios of the horizontal and vertical components at six sites in L’Aquila downtown are compared to corresponding synthetics spectral ratios. The vertical component of P-SV synthetics enables us to investigate a remarkable amplification effect seen in the vertical component of the recorded strong motion. Sites AQ04 and AQ05 are best matched by synthetics from the NORV model while FAQ5 and AQ06 have a better match with synthetics spectral ratios from the SMTH model. All simulations show this behavior systematically, with horizontal and near-horizontal incident waves predicting the overall pattern of matches more clearly than vertical and near-vertical incidence. The model inferences are in agreement with new geological data reporting lateral passages in the top layer from the stiff BrA to softer sediments. Matches are good in terms of frequency of the first amplification peak and of spectral amplitude: the horizontal components have spectral ratio peaks predominantly at 0.5 Hz in the simulations and at 0.7 Hz in the data, both with amplitudes of 4, while the vertical component spectral ratios reach values of 6 at frequencies of about 1 Hz in both data and simulations. The vertical component spectral ratios are very well matched using Rayleigh waves with incidence at 90°. The NORV model without the velocity reversal predicts spectral ratio peaks for the horizontal components at frequencies up to 6 Hz. The reversal of velocity acts as a low-pass frequency filter on the horizontal components reducing the amplification effect of the sediment filled valley.     

Notes on Hori Method for Canonical Systems

In this paper a slightly different approach is proposed for the process of determining the functions S _m and H _m ^* of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t ^* as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach.