Element sets for high-order Poincaré mapping of perturbed Keplerian motion

The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in Celestial Mechanics and Astrodynamics, e.g., to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits using the high-order Taylor expansion of a Poincaré or stroboscopic map. The HOTM is only accurate close to the expansion point and therefore the number of revolutions for which the map is accurate tends to be limited. The proper selection of coordinates is of key importance for improving the performance of the HOTM method. In this paper, we investigate the use of different element sets for expressing the high-order map in order to find the coordinates that perform best in terms of accuracy. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and center manifolds of Poincaré maps.     

Why chromatic imaging matters

During the last two decades, the first generation of beam combiners at the Very Large Telescope Interferometer has proved the importance of optical interferometry for high-angular resolution astrophysical studies in the near- and mid-infrared. With the advent of 4-beam combiners at the VLTI, the u ? v coverage per pointing increases significantly, providing an opportunity to use reconstructed images as powerful scientific tools. Therefore, interferometric imaging is already a key feature of the new generation of VLTI instruments, as well as for other interferometric facilities like CHARA and JWST. It is thus imperative to account for the current image reconstruction capabilities and their expected evolutions in the coming years. Here, we present a general overview of the current situation of optical interferometric image reconstruction with a focus on new wavelength-dependent information, highlighting its main advantages and limitations. As an Appendix we include several cookbooks describing the usage and installation of several state-of-the art image reconstruction packages. To illustrate the current capabilities of the software available to the community, we recovered chromatic images, from simulated MATISSE data, using the MCMC software SQUEEZE. With these images, we aim at showing the importance of selecting good regularization functions and their impact on the reconstruction.     

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions

The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to \(J_{15}\). A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.     

Efficient design of direct low-energy transfers in multi-moon systems

In this contribution, an efficient technique to design direct (i.e., without intermediate flybys) low-energy trajectories in multi-moon systems is presented. The method relies on analytical two-body approximations of trajectories originating from the stable and unstable invariant manifolds of two coupled circular restricted three-body problems. We provide a means to perform very fast and accurate computations of the minimum-cost trajectories between two moons. Eventually, we validate the methodology by comparison with numerical integrations in the three-body problem. Motivated by the growing interest in the robotic exploration of the Jovian system, which has given rise to numerous studies and mission proposals, we apply the method to the design of minimum-cost low-energy direct trajectories between Galilean moons, and the case study is that of Ganymede and Europa.     

Dynamics of arrays of floating point-absorber wave energy converters with inter-body and bottom slack-mooring connections

If point absorbers are employed in the extensive exploitation of the offshore wave energy resource, they should be deployed in arrays, the distance between the elements in the array being possibly tens of meters. In such cases, it may be more convenient that the array is spread moored to the sea bottom through only some of its elements, located in the periphery, while the other array elements are prevented from drifting and colliding with each other by connections to adjacent elements. An array of identical floating point absorbers located at the grid points of an equilateral triangular grid is considered in the paper. A spread set of slack-mooring lines connect the peripheric floaters to the bottom. A weight is located at the centre of each triangle whose function is to pull the three floaters towards each other and keep the inter-body mooring lines under tension. The power take-off system (PTO) is a linear damper activated by the buoy heaving motion. The whole system–buoys, moorings and power take-off systems–is assumed linear, so that a frequency domain analysis may be employed. Hydrodynamic interference between the oscillating buoys in array is accounted for. Equations are presented for a set of three identical point absorbers. This is then extended to more complex equilateral triangular grid arrays. Results from numerical simulations, with regular and irregular waves, are presented for the motions and power absorption of hemispherical converters in arrays of three and seven elements and for different mooring parameters and wave incidence angles. Comparisons are given with the unmoored and independently-moored buoy situations.     

Distribution patterns of interstitial polychaetes in sandy beaches of southern Brazil

This study describes the distribution patterns of interstitial polychaetes along morphodynamic gradients on six exposed sandy beaches in Santa Catarina and Paraná (South Brazil). Three random transects were sampled at two points on each beach, one at the swash and another at the surf zone, in winter and summer conditions. Six sediment replicates were collected at each sampling point using a corer of 4.6 cm internal diameter that removed 10 cm into the sediment. Abundance and composition of interstitial polychaete were correlated to wave height, slope, grain size, CaCO₃, chlorophyll a , omega indexes, temperature and relative tide range using a canonical correspondence analysis (CCA). A factorial ANOVA showed that taxa richness, mean density and Shannon's diversity were significantly higher at the reflective beaches, but average values differ significantly between transects and these differences change according to the beach zones on both sampling dates. PERMANOVA showed that polychaete associations differ among transects according to the beach zones. The composition of interstitial polychaete associations was significantly correlated to beach morphodynamics and features (P < 0.01). Polychaete associations of reflective beaches were more diverse than in other morphodynamic states. Intermediate beaches may also sustain diverse associations due to temporal variability of the morphodynamic patterns. Beaches presenting extreme dissipative morphodynamics and compacted sediments appear to be unfavourable for the occurrence of interstitial polychaetes.     

Response of BITS (a benthic index based on taxonomic sufficiency) to water and sedimentary variables and comparison with other indices in three Adriatic lagoons

The European Water Framework Directive (WFD, 2000/60/EC) recommends the development of biotic indices for assessing the ecological quality status of water bodies. The Benthic Index based on Taxonomic Sufficiency (BITS) was specifically developed for lagoonal systems, according to the tolerant/opportunistic approach. Macrobenthic data, variables indicative of eutrophication and variables indicative of sedimentary organic matter quality were collected during 18 surveys carried out between 2004 and 2005 in three Adriatic coastal lagoons (Venice Lagoon, Sacca di Goro, Lesina Lagoon). The relationship between environmental variables and biotic indices (AMBI, BENTIX, BITS, BOPA and FINE) was tested using multivariate analyses. Indices based on species classification level appeared to relate better with the variables describing organic matter quality, whereas BITS, which is based on family classification level, seemed related to eutrophication indicative variables, such as sulphide, ammonium, dissolved oxygen and orthophosphate concentrations. The BITS approach reduces the costs associated with sorting and identification of organisms. Providing a rapid assessment of ecological quality, and producing an ecologically relevant classification, BITS seems a promising tool for monitoring programs of Adriatic lagoonal ecosystems. Its sensitivity in reflecting the field conditions elsewhere, however, remains to be assessed.     

A control-volume finite-element method for three-dimensional multiphase basin modeling

In this paper we describe a 3D control-volume finite-element method to solve numerically the coupled partial differential equations (PDEs) governing geological processes involved in the evolution of sedimentary basins. These processes include sediment deposition and deformation, hydrocarbon generation, multiphase fluid flow, and heat transfer in deforming porous media.     

The Holocene tephrostratigraphic record of Lake Shkodra (Albania and Montenegro)

Two cores were recovered in the southeastern part of Lake Shkodra (Montenegro and Albania) and sampled for identification of tephra layers. The first core (SK13, 7.8 m long) was recovered from a water depth of 7 m, while the second core (SK19, 5.8 m long) was recovered close to the present‐day shoreline (water depth of 2 m). Magnetic susceptibility investigations show generally low values with some peaks that in some cases are related to tephra layers. Naked‐eye inspection of the cores allowed the identification of four tephra layers in core SK13 and five tephra layers in core SK19. Major element analyses on glass shards and mineral phases allowed correlation of the tephra layers between the two cores, and their attribution to six different Holocene explosive eruptions of southern Italy volcanoes. Two tephra layers have under‐saturated composition of glass shards (foiditic and phonolitic) and were correlated to the AD 472 and the Avellino (ca. 3.9 cal. ka BP) eruptions of Somma‐Vesuvius. One tephra layer has benmoreitic composition and was correlated to the FL eruption of Mount Etna (ca. 3.4 cal. ka BP). The other three tephra layers have trachytic composition and were correlated to Astroni (ca. 4.2 cal. ka BP), Agnano Monte Spina (ca. 4.5 cal. ka BP) and Agnano Pomici Principali (ca. 12.3 cal. ka BP) eruptions of Campi Flegrei. The ages of tephra layers are in broad agreement with eight ¹⁴C accelerator mass spectrometric measurements carried out on plant remains and charcoal from the lake sediments at different depths along the two cores. The recognition of distal tephra layers from Italian volcanoes allowed the physical link of the Holocene archive of Lake Shkodra to other archives located in the central Mediterranean area and the Balkans (i.e. Lake Ohrid). Five of the recognised tephra layers were recognised for the first time in the Balkans area, and this has relevance for volcanic hazard assessment and for ash dispersal forecasting in case of renewed explosive activity from some of the southern Italy volcanoes. Copyright © 2009 John Wiley & Sons, Ltd.