Two-dimensional approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.Comment: 11 pages, 5 figures. v2: a brief description of the principal bibliography has been adde

Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x¨=f(x,t)\ddot{x}=f(x,t)

In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\'e II, Sitnikov and Hill-Schr\"odinger equation. We emphasize in Painlev\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.Comment: 15 pages without figures (19 pages and 6 figures in the published version

Linking plant composition and arthropod abundance to establish little bustard breeding requirements in pastureland dominated landscapes

Most research on steppe bird habitat selection has been focused on the effects of management regimes or vegetation structure. However, much less is known on how plant composition is related with steppe bird occurrence. We investigated microhabitat of little bustard territorial males and females during the nesting and chick-rearing season in areas with dominance of pastureland focusing on plant composition. We searched for relationships between preferred vegetation and arthropod abundance in order to identify the contribution of different vegetation typologies in providing essential trophic resources for the species. Surveys of little bustards were made using car and foot transects. Plant composition was obtained within a 50 × 50 cm square at four sampling replicates and arthropod availability was sampled using a sweep net. Statistical procedures were conducted in three steps: (1) analysis of variance was used to identify at univariate level the plant composition and arthropod variables that were significantly related with both male and female occurrence sites; (2) principal components analysis was performed using the variables with significant results at univariate level; (3) model averaging on generalized linear and mixed models was applied to evaluate the selection probability of each principal component. The species occurs in sites with high floristic richness and high abundance of Fabaceae species, although plant composition differs from male to female sites. These variables were found to be crucial to provide higher abundances of arthropods, notably of Acrididea, Formicidae and some groups of Coleoptera which are decisive for the selection of displaying or female breeding sites

The importance of grazing regime in the provision of breeding habitat for grassland birds: The case of the endangered little bustard (Tetrax tetrax)

In Mediterranean dry grasslands, grazing by domestic animals is an important agricultural activity on dry grasslands. Several bird species occur in these grazed habitats and are now experiencing a near continuous decline. We investigated the impact of livestock grazing on the threatened little bustard (Tetrax tetrax L.). The study was conducted at the NATURA 2000 Site/Important Bird Area of Cabrela, Portugal. Our main goals were to investigate responses of little bustard territorial males and breeding females to different livestock management practices, namely pasture types, stocking rates and sward structure. Bird distribution was surveyed using car and foot surveys. Data on grazing was supplied by land managers every 10 days from February to June through field interviews. Generalised additive models and model averaging were used to compute predictive models. Results indicate that higher probabilities of occurrence were found in long-term pastures and under light-moderate grazing conditions (stocking rates around 0.4 LU/ha). Conversely, lower probabilities of occurrence were found in ungrazed or heavy grazed fields. Males occurred mostly in large fields, but this variable seemed to be less important for females. On the other hand, green plant cover and the vegetation height were good predictors for the occurrence of females but not for males. Females used mostly pastures with vegetation height around 20–25 cm. Our results suggest that grazing management plans that aim to conserve little bustard populations should consider (1) the maintenance of the larger long-term pastures and (2) the use of light-moderate stocking rates (0.2–0.6 LU/ha)