A nonlinear elliptic problem with terms concentrating in the boundary

In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neighborhood of a portion $\Gamma$ of the boundary. We assume that this $\epsilon$-neighborhood shrinks to $\Gamma$ as the small parameter $\epsilon$ goes to zero. Also, we suppose the upper boundary of this $\epsilon$-strip presents a highly oscillatory behavior. Our main goal here is to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on $\Gamma$, which depends on the oscillating neighborhood

Accuracy of a DTM derived from full-waveform laser scanning data under unstructured eucalypt forest: a case study

A Digital Terrain Model (DTM) is fundamental for extracting several forest canopy structure metrics from data acquired with small-footprint airborne laser scanning (ALS). This modern remote sensing technology is based on laser measurements from a laser system mounted on an aircraft and integrated with a geodetic GNSS receiver and an inertial measurement unit (IMU) or inertia navigation system (INS). In the context of a research project for deriving forest inventory parameters and fuel variables under eucalypt stands in Mediterranean climates, the vertical precision of the DTM obtained by automatic filtering of full-waveform ALS data had to be evaluated. The DTM accuracy estimation on a study area with peculiar characteristics, which are often avoided in related studies, will also allow verifying the performance of full- waveform ALS systems. The accuracy estimation is carried out in a novel way. By novel way, it is meant an exhaustive, well-planned collection of reliable control data in forest environment. The collection of the control data involves the production of DTM on 43 circular plots (radius = 11.28m) using total stations and geodetic GNSS receivers. These DTM, with a total of 3356 points, allowed one to evaluate consistently and reliably the vertical accuracy of the terrain surface produced with ALS under a eucalypt forest. This global accuracy, expressed by the Root Mean Square Error (RMSE) of the vertical differences between the field surveyed surface and the ALS derived DTM surface is 0.15m (mean=0.08m and std=0.09m). This impressive value indicates that, for an ALS point cloud density of 10pts/m2 and footprint of 20 cm, the methodology used to extract the DTM from full- waveform ALS data under an unstructured eucalypt forest is very accurate. In this article it is addressed both the strategy adopted to collect the control data and the quality assessment of the DTM produced by means of the ALS data

Importance of DTM accuracy, precision and acquisition technique for estimating contributing areas of post-fire erosion at the slope and catchment scale

Wildfires are a frequent phenomenon in Portugal, affecting over 300.000 ha in dry years like 2003 and 2005. Directly and/or indirectly, wildfires can strongly enhance the hydrological response and associated sediment losses and, thereby, negatively affect land-use sustainability as well as ecosystem functioning of downstream aquatic habitats. Therefore, the EROSFIRE projects aim at developing a GIS-tool for predicting soil erosion hazard following wildfire and post-fire land management practices. Assessment and modeling of runoff and soil erosion rates critically depends on accurate estimates of the contributing areas. In the case of catchments as well as unbounded erosion plots (arguably, the only practical solution for slope-scale measurements), delineation of contributing area requires a Digital Terrain Model (DTM) with an adequate resolution and accuracy. The DTM that was available for the Colmeal study area (Goís municipality, central Portugal) was that of the 1:25.000 topographic map produced by the Military Geographic Institute. Since this study area involves a rather small experimental catchment of roughly 10 ha and relatively short study slopes of less than 100 m long, two different data acquisition techniques were used to produce high-resolution and high-accuracy DTM. One is aerial photogrammetry, whilst the other is terrestrial laser scanning. To produce a DTM by photogrammetric means, a dedicated digital aerial photography mission was carried out. The images had a pixel size of 10 cm. Manual measurements permitted to measure breaklines and were complemented by automatic measurements. In this way, a DTM in a TIN format was produced. This was further converted to grid format using the ArcGIS software system. Signalized control points allowed obtaining the DTM in the same global reference system as that employed for terrestrial laser scanning. The terrestrial laser scanning was done using a Riegl LMS Z360I, stationed in 8 points within the area to provide a complete coverage. The resulting dense cloud of points was filtered – by the company carrying out the scanning mission - to remove the non-terrain points (in particular vegetation). Several grids of different sizes were produced (0.10 x 0.10, 0.20 x 0.20, 0.50 x 0.50, 1 x 1 and 2 x 2 m2). The proposed work will compare and analyze estimates of contribution areas that were obtained with the two above-mentioned data acquisition techniques and for different spatial resolutions. This will be done for selected slope-scale sediment fences as well as for the outlet of the experimental catchment. In addition, different algorithms available in ArcGIS for TIN-to-grid conversion will be compared, since preliminary results have suggested that these procedures produce markedly different results

Testing gaussianity, homogeneity and isotropy with the cosmic microwave background

We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity and isotropy from each other. We focus both on isotropic estimators of non-gaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced "cosmic variances" that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMB data when searching for large scale "anomalies"Comment: 52 pages, 22 pdf figures. Revised version of the invited review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronomy

Addressing food and nutrition security in South Africa: A review of policy responses since 2002

Since 2002, a range of South African policies have attempted to address the disproportionate burden of food and nutrition insecurity on the population. Yet malnutrition among the poor has worsened. This study reviewed policies to examine their implications for food security and the treatment of malnutrition. Policies enacted between 2002 and 2017 were retrieved from government departments and the data were thematically analysed. A preliminary analysis shows that policy has aided production through input provision and capacity building. Taxation, school nutrition programmes and social grants are some of the food access initiatives, whilst micronutrient supplementation, breastfeeding campaigns and food fortification are policies specifically focused on nutrition. However, despite these interventions, food insecurity has remained due to gaps in and contradictions among policies and the lack of coordination in policy development and implementation, especially across sectors. To improve food and nutrition security, government must better engage with ideas about how to address food and nutrition security systemically, and develop the appropriate coordination mechanisms for a more holistic approach to this challenge