One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.

Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Assessment of environment, land management, and spatial variables on recent changes in montado land cover in southern Portugal

Montado decline has been reported since the end of the nineteenth century in southern Portugal and increased markedly during the 1980s. Consensual reports in the literature suggest that this decline is due to a number of factors, such as environmental constraints, forest diseases, inappropriate management, and socioeconomic issues. An assessment on the pattern of montado distribution was conducted to reveal how the extent of land management, environmental variables, and spatial factors contributed to montado area loss in southern Portugal from 1990 to 2006. A total of 14 independent variables, presumably related to montado loss, were grouped into three sets: environmental variables, land management variables, and spatial variables. From 1990 to 2006, approximately 90,054 ha disappeared in the montado area, with an estimated annual regression rate of 0.14 % year-1. Variation partitioning showed that the land management model accounted for the highest percentage of explained variance (51.8 %), followed by spatial factors (44.6 %) and environmental factors (35.5 %). These results indicate that most variance in the large-scale distribution of recent montado loss is due to land management, either alone or in combination with environmental and spatial factors. The full GAM model showed that different livestock grazing is one of the most important variables affecting montado loss. This suggests that optimum carrying capacity should decrease to 0.18–0.60 LU ha-1 for livestock grazing in montado under current ecological conditions in southern Portugal.

How well can models predict changes in species distributions? A 13-year-old otter model revisited

Species distribution and ecological niche models are increasingly used in biodiversity management and conservation. However, one thing that is important but rarely done is to follow up on the predictive performance of these models over time, to check if their predictions are fulfilled and maintain accuracy, or if they apply only to the set in which they were produced. In 2003, a distribution model of the Eurasian otter (Lutra lutra) in Spain was published, based on the results of a country-wide otter survey published in 1998. This model was built with logistic regression of otter presence-absence in UTM 10 km2 cells on a diverse set of environmental, human and spatial variables, selected according to statistical criteria. Here we evaluate this model against the results of the most recent otter survey, carried out a decade later and after a significant expansion of the otter distribution area in this country. Despite the time elapsed and the evident changes in this species’ distribution, the model maintained a good predictive capacity, considering both discrimination and calibration measures. Otter distribution did not expand randomly or simply towards vicinity areas,m but specifically towards the areas predicted as most favourable by the model based on data from 10 years before. This corroborates the utility of predictive distribution models, at least in the medium term and when they are made with robust methods and relevant predictor variables.