The theory of asynchronous relative motion II: universal and regular solutions

Two fully regular and universal solutions to the problem of spacecraft relative motion are derived from the Sperling–Burdet (SB) and the Kustaanheimo–Stiefel (KS) regularizations. There are no singularities in the resulting solutions, and their form is not affected by the type of reference orbit (circular, elliptic, parabolic, or hyperbolic). In addition, the solutions to the problem are given in compact tensorial expressions and directly referred to the initial state vector of the leader spacecraft. The SB and KS formulations introduce a fictitious time by means of the Sundman transformation. Because of using an alternative independent variable, the solutions are built based on the theory of asynchronous relative motion. This technique simplifies the required derivations. Closed-form expressions of the partial derivatives of orbital motion with respect to the initial state are provided explicitly. Numerical experiments show that the performance of a given representation of the dynamics depends strongly on the time transformation, whereas it is virtually independent from the choice of variables to parameterize orbital motion. In the circular and elliptic cases, the linear solutions coincide exactly with the results obtained with the Clohessy–Wiltshire and Yamanaka–Ankersen state-transition matrices. Examples of relative orbits about parabolic and hyperbolic reference orbits are also presented. Finally, the theory of asynchronous relative motion provides a simple mechanism to introduce nonlinearities in the solution, improving its accuracy.     

Decomposition of functions for elliptic orbits

In the algebraA of functions periodic in the mean anomaly we relate the problem of integrating over the mean anomaly with that of decomposing an element ofA as the direct sum of two functions, one in the kernel of the Lie derivative in the Keplerian flow and one in the image of this Lie derivative. We propose recursive rules amenable to general purpose symbolic processors for accomplishing such decomposition in a wide subclass ofA. We introduce the dilogarithmic function to express in exact terms quadratures involving the equation of the center.     

A deformed Pliocene-Quaternary alluvial and red paleosol succession in the Eastern Betics: Paleomagnetic,rock-magnetic and sedimentological pilot study

Summary An integrated pilot paleomagnetic and sedimentological study has been conducted in the Neogene-Quaternary infilling materials of the Bajo Segura Basin (Eastern Betics, SE Spain). The studied sediments belong to the youngest (late Pliocene-Quaternary) lithostratigraphic unit of the basin (P-Q unit). The statistical analysis of tectonic striations and stylolitic dissolutions on the conglomerate limestone clasts indicates a NNW-SSE maximum compression direction. This is in accordance with the principal susceptibility axes, determined from the anisotropy of magnetic susceptibility measurements (AMS) of the interbedded siltstones where the Kmax axis group in a subhorizontal N 080° E direction.A total of 45 core samples have been collected from 16 stratigraphic siltstone levels encompassing the described section at Crevillente with the aim to establish a magnetochronology. Upwards in the section the NRM intensity and bulk susceptibility vary from 10^–2 to 10^–3 A/m and from 1550 to 100 × 10^–6 SI, respectively. The mean characteristic remanent magnetization (ChRM) after bedding correction (Dec/Inc = 10°/60°, ₉₅ = 8.7°, k = 15.9) is deviated slightly towards the E from the reference N direction, and could reflect a deflection related to the observed magnetic fabric although no clear correlation exists with AMS parameters. The derived magnetostratigraphy reveals only one reversal boundary within the upper third of the section, delimiting an upper reversal magnetozone which has been tentatively correlated with the Olduwai subchron close to the Plio-Pleistocene boundary.Pilot and preliminary rock-magnetic experiments and standard X-ray difraction (XRD) analysis have been performed on typical samples in order to establish the carriers of magnetization and characterize the sedimentological and magnetic-acquisition processes in these sediments. Magnetic carriers seem to be dominated by magnetite with a relative grain size within the PSD state (pseudo single-domain) threshold, but closer to the MD (multi domain) threshold, which favours the detrital origin for the magnetite.     

Calpionellid biostratigraphy of the Upper Tithonian–Upper Valanginian interval in Western Sicily (Italy)

A revision of the calpionellid bio-chronostratigraphy in Western Sicily (Italy) was carried out, in order to update the taxonomy of this group, through the identification of some genera (Borziella, Longicollaria, Chitinoidella, Dobeniella, Sturiella, Borzaiella and Praecalpionellites) and species (Remaniella catalanoi Pop, Remaniella duranddelgai Pop, Remaniella colomi Pop, Remaniella borzai Pop, Remaniella filipescui Pop) recorded for the first time in the area. The studied sections, belonging to the Trapanese and Saccense Domains (Western Sicily), include at the base the upper portion of the Rosso Ammonitico Unit (Upper Tithonian), followed by the Lattimusa Formation (Lower Cretaceous). The quantitative and biostratigraphic analysis of the calpionellid assemblages allowed us to identify 13 assemblages and to define some important bioevents for the Upper Tithonian–Valangianian interval. The recorded calpionellid bioevents allowed us to recognize Zone/Subzone schema, which have been correlated with the bio-chronostratigraphy previously proposed for the Western Tethys. Editorial handling: M. Chiari (Guest) & J.-P. Billon-Bruyat     

Joints,faults and palaeostress evolution in the Campo de Dalias (Betic Cordilleras,southeastern Spain)

The Campo de Dal??as, located between the central and eastern Betic Cordilleras, shows an evolution determined by the overprinting of two main stress fields since Pliocene times. The first of these develops hybrid and tensional joint sets up to Pleistocene (100 000 yr) and is characterized by NNW–SSE horizontal trend of compression and an ENE–WSW horizontal extension. The second stress field has prolate to triaxial extensional ellipsoids, also with ENE–WSW horizontal extension, and continues to be active today. The most recent stresses produce the reactivation of previous joints as faults whose trends are comprised mainly from N120°E to N170°E and have a normal and transtensional regime, with dextral or sinistral components. The palaeostress evolution of this region is similar to that undergone by other basins of the Eastern Betic Cordilleras, although the Pliocene–Pleistocene transcurrent deformations in the Campo de Dal??as only develop joints and not strike-slip faults.     

On matrix diffusion: formulations, solution methods and qualitative effects

 Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ _m ² R _m D _m  / L _m ², whereas late-time behavior (long tracer tests) depends only on φ _m R _m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. Received, October 1997 · Revised, November 1997 · Accepted, December 1997     

Integrating in situ measurements of an index of connectivity to assess soil erosion processes in vineyards

ABSTRACT

In this research, we survey soil erosion processes using an index of connectivity and a non-invasive and long-term assessment in situ technique: the improved stock unearthing method (ISUM), for which the vineyard of Castilla La Mancha under tillage management was selected. Our results show, that in 10 years, the total average soil surface level decreased by – 1.6 cm and the total soil mobilization was up to 17.7 Mg ha^?1 year^?1. The surrounding lands of the survey plot showed meagre connectivity; however, smaller linear features with higher values were found as possible locations for potential rill generation. The survey plot is traversed by one of these linear features. In this inter-row survey, we found relatively low connectivity values. As a conclusion, we confirm that both methods can be useful to assess soil erosion processes in vineyards and detect areas that could increase the desertification as a consequence of non-sustainable soil erosion rates.     

Shaking table tests of a reinforced concrete waffle–flat plate structure designed following modern codes: seismic performance and damage evaluation

Shaking table tests were conducted on a scaled reinforced concrete waffle–flat plate structure. It represented a conventional construction design under current building codes in the Mediterranean area. The test structure was subjected to a sequence of four seismic simulations of increasing magnitude. Each simulation was associated with a seismic hazard level characterized by the mean return period P_R. The test structure performed well for the simulations associated with P_R = 95, 475 and 975 years but collapsed under the maximum considered earthquake of P_R = 2475 years. Damage concentrated at column bases, where the maximum chord rotation reached 93% of the ultimate capacity, and at the transverse beams of the exterior plate‐to‐column connection that failed in torsion. It is shown that most (from 85% to 90%) of the energy input by the earthquake that contributes to damage is dissipated by the plate. The capacity curve of the tested structure estimated from the experimental base shear vs. top displacement relationship allowed us to compute the overstrength (1.4). It is close to the maximum established by European code EN 1998‐1 (1.5). Based on a detailed study of the test results, potential updates to current codes and design recommendations are suggested. Copyright © 2015 John Wiley & Sons, Ltd.