Equilibrium Points and Central Configurations for the Lennard-Jones 2- and 3-Body Problems

In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard-Jones potential. A central configuration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard-Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central configurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we find the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria. This revised version was published online in July 2006 with corrections to the Cover Date.     

Esterases activities and lipid peroxidation levels in muscle tissue of the shanny Lipophrys pholis along several sites from the Portuguese Coast

This study is part of a project aiming to validate the use of the intertidal shanny Lipophorys pholis as a sentinel species in pollution monitoring in NW European marine ecosystems. To this end, a characterisation of acethylcholin (AChE), butyrylcholin (BChE) and propionylcholin (PrChE) esterases in L. pholis muscle was performed and the results indicated that AChE was predominant. Furthermore, the use of eserine sulphate and BW284c51 (0.64–800 μM), and iso-OMPA (0.08–16 mM), confirmed the measurement of true cholinesterases (ChEs) as well as the presence of pseudocholinesterases. The field application of these markers to L. pholis, sampled in seven locations along the Portuguese coast, revealed that fish were likely to be affected by neurotoxic compounds. This was indicated by the significant depletion of AChE (p < 0.05) in animals collected at urban and industrialised sites, compared with those from reference locations. The inclusion of a marker of effect, measured as lipid peroxidation levels in muscle tissue, also revealed the existence of site differences. Overall, the study further validates the utility of L. pholis in pollution monitoring studies.     

Size and composition of inorganic colloids in a peri-alpine, glacial flour-rich lake

From June 2004 to October 2005, particle size distributions (PSD) and the mineralogy of inorganic colloids in Lake Brienz, a glacial flour-rich Swiss lake, and in its tributaries (the Aare and Lütschine rivers), were quantified by single particle counting based on light scattering (0.1-2 μm) combined with transmission electronic microscopy coupled with energy dispersive spectroscopy and selected area electron diffraction. The two lake tributaries differ in terms of the geology of their catchment area and in their hydrology: the River Lütschine’s glacial regime is unperturbed, while the River Aare has been significantly modified by hydroelectric installations. The dependence of the colloid concentration numbers on colloid diameters can be described by a power-law distribution in all cases. The power-law slopes in the River Aare were consistently smaller, and the total colloid number concentrations consistently higher, (mean values: −3.89 and 6.2 × 10⁸ mL⁻¹, respectively) than in the River Lütschine (−3.61 and 1.7 × 10⁸ mL⁻¹). The measured PSD in the lake were dependent on season and depth: homogenous in the whole epilimnion in winter and modified by river intrusions in summer. In this season, the presence of a river turbid plume above the thermocline is a significant source of colloids in the epilimnion, where their concentration was high (mean value: 5.1 × 10⁷ mL⁻¹). The same main mineral types were found in the different systems: 2:1 minerals, feldspars, chlorite and quartz; with a few particles of oxides. Differences in their relative concentrations in the rivers, essentially reflecting the geological differences of the respective catchment areas, made it possible to trace the origin of the mineral colloids present in lake surface waters throughout the year. The relationship between colloid size and mineralogy was assessed, showing that different minerals have distinct size distributions. In the rivers, where almost no aggregates were observed, PSD would essentially be the result of the nature (particle formation and mineralogy) of the colloids, whereas in the lake, aggregation and sedimentation processes would also play a role, particularly in summer.     

On the central configurations of the planar 1 + 3 body problem

We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and non-symmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.     

On the existence of central configurations of <Emphasis Type="Italic">p</Emphasis> nested regular polyhedra

In this paper we prove, for all p ≥ 2, the existence of central configurations of the pn-body problem where the masses are located at the vertices of p nested regular polyhedra having the same number of vertices n and a common center. In such configurations all the masses on the same polyhedron are equal, but masses on different polyhedra could be different.     

New radiometric and geomorphologic evidences of a last glacial maximum older than 18 ka in SW European mountains: the example of Redes Natural Park (Cantabrian Mountains,NW Spain)

Abstract

The first numerical age determinations from radiocarbon dating establish the chronology of glacial events in Redes Natural Park (Cantabrian Mountain, NW Spain). A core drilled in an ice-dammed deposit provided a minimum age of 28 990 ± 230 years BP for the maximum glacial expansion (phase I). Another core from a cirque bottom-fill provided organic sediment with 20 640 ± 300 years BP, a minimum age for the first glacial retreat (phase II). Radiometric dating of proglacial deposits interpreted as synchronous with the last glacial maximum phase in neighbouring Cornelia basin (Picos de Europa), yield ages of 40 480 ± 820 years BP. The chronological data presented in this work are consistent with the model of glacier evolution established in the Pyrénées, with a glacial maximum phase for the last glacial period older than 18 ka. © 2002 Éditions scientifiques et médicales Elsevier SAS. AU rights reserved.     

Dynamic hybrid terrain representation based on convexity limits identification

Hybrid digital terrain models combine terrain data with different topologies and resolutions. Cartographic digital terrain models are typically composed of regular grid data that can be locally refined by adding a Triangulated Irregular Network (TIN) that represents morphologically complex terrain parts. Direct rendering of both datasets to visualize the digital terrain model generates discontinuities, as the meshes are disconnected. The utilization of complete/partial precomputed tessellation solutions solves the problem of quality, but limits the applicability of the representation to models with a fixed relative position between datasets. In this paper, we present a new scheme for hybrid terrain representation that permits the dynamic generation of the adaptive tessellation required to join the grid and TIN models. Our proposal permits the dynamic modification of the relative position between datasets. This increases the representation capabilities for those applications where this property is interesting as, for example, urban and landscape planning applications. The algorithm we propose is based on the identification of convex areas on the TIN and the efficient generation of triangles to join the models based on this convex structure. As a result, high quality models without discontinuities are obtained, increasing the flexibility of previous solutions based on fixed precomputations.     

Long-term divergent tidal flat benthic community recovery following hypoxia-induced mortality

Macrobenthos recovery after hypoxia-induced mass mortality was assessed in an estuarine tidal mudflat during 3 years. During the first 2 years, a Pearson-Rosenberg type of community recovery took place along with the improving bottom water oxygen conditions. After 3 months, spionid polychaetes became superabundant (i.e. opportunistic peak), followed rapidly by a steep decline (i.e. ecotone point). Subsequently, a moderate increase in species richness and a steep increase in biomass, related to the growth of long-lived species occurred (i.e. transition region). Afterwards, however, the recovering community diverged again from the ambient, undisturbed, sediments due to enhanced recruitment success of long-lived species presumably resulting from the lowered interference from bioturbation during early recovery stages in the disturbed plots. Hence, despite early community recovery may be more or less deterministic, lagged divergent community reassembling may occur at the longer-term, thereby contributing to benthos patchiness in areas which are frequently subjected to disturbances.     

First evidence of fiberglass ingestion by a marine invertebrate (Mytilus galloprovincialis L.) in a N.W. Mediterranean estuary

Alfacs Bay is a N.W. Mediterranean estuary important for mussel (Mytilus galloprovincialis) aquaculture. During studies at the site, fiberglass particles were detected. The presence of fiberglass occurred naturally in the water throughout the study period (November 2006 to July 2007). An investigation was undertaken into its role in the feeding behavior of the local mussels. Fiberglass was present in all types of mussel samples. Rejection, which we would have expected for the whole study period, was only evident during the second season studied. To our knowledge, this is the first report of the ingestion of fiberglass by a marine organism. Our novel finding indicates the need to investigate fiberglass ingestion by marine organisms at different levels of the food web and the possible implications for human health and the health of the organisms themselves. In addition, we propose the use of mussels as sentinel organisms to monitor fiberglass contamination in marine ecosystems.