Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity

We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized equations on which we apply a pressure splitting and a Suliciu relaxation. On the resulting model, we apply a splitting of the flux into a linear implicit and an non-linear explicit part that leads to a scale independent time-step. The explicit step consists of a Godunov type method based on an approximative Riemann solver where the source term is included in the flux formulation. We develop the method for a first order scheme and give an extension to second order. Both schemes are designed to be well-balanced, preserve the positivity of density and internal energy and have a scale independent diffusion. We give the low Mach limit equations for well-prepared data and show that the scheme is asymptotic preserving. These properties are numerically validated by various test cases

Calibration of a solid state nuclear track detector (SSNTD) with high detection threshold to search for rare events in cosmic rays

We have investigated a commercially available polymer for its suitability as a solid state nuclear track detector (SSNTD). We identified that polymer to be polyethylene terephthalate (PET) and found that it has a higher detection threshold compared to many other widely used SSNTDs which makes this detector particularly suitable for rare event search in cosmic rays as it eliminates the dominant low Z background. Systematic studies were carried out to determine its charge response which is essential before any new material can be used as an SSNTD. In this paper we describe the charge response of PET to 129Xe, 78Kr and 49Ti ions from the REX-ISOLDE facility at CERN, present the calibration curve for PET and characterize it as a nuclear track detector

Exploring the ontogenetic scaling hypothesis during the diversification of pollination syndromes in <i>Caiophora</i> (Loasaceae, subfam. Loasoideae)

Phenotypic diversification of flowers is frequently attributed to selection by different functional groups of pollinators. During optimization of floral phenotype, developmental robustness to genetic and non-genetic perturbations is expected to limit the phenotypic space available for future evolutionary changes. Although adaptive divergence can occur without altering the basic developmental programme of the flower (ontogenetic scaling hypothesis), the rarity of reversion to ancestral states following adaptive radiations of pollination syndromes suggests that changes in the ancestral developmental programme of the flower are common during such evolutionary transitions. Evidence suggests that flower diversification into different pollination syndromes in the Loasoideae genus Caiophora took place during a recent adaptive radiation in the central Andes. This involved transitions from bee to hummingbird and small rodent pollination. The aim of this work was to examine if the adaptive radiation of pollination syndromes in Caiophora occurred through ontogenetic scaling or involved a departure from the ontogenetic pattern basal to this genus.Fil: Strelin, Marina Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Benitez-Vieyra, Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Fornoni, Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; Argentina. Universidad Nacional Autónoma de México; MéxicoFil: Klingenberg, Christian Peter. University of Manchester; Reino UnidoFil: Cocucci, Andrea Aristides. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; Argentin

Gaming with eutrophication: Contribution to integrating water quantity and quality management at catchment level

The Metropolitan Region of Sao Paulo (MRSP) hosts 18 million inhabitants. A complex system of 23 interconnected reservoirs was built to ensure its water supply. Half of the potable water produced for MRSP's population (35 m3/s) is imported from a neighbour catchment, the other half is produced within the Alto Tietê catchment, where 99% of the population lives. Perimeters of land use restriction were defined to contain uncontrolled urbanization, as domestic effluents were causing increasing eutrophication of some of these reservoirs. In the 90's catchment committees and sub committees were created to promote discussion between stakeholders and develop catchment plans. The committees are very well structured "on paper". However, they are not very well organised and face a lack of experience. The objective of this work was to design tools that would strengthen their discussion capacities. The specific objective of the AguAloca process was to integrate the quality issue and its relation to catchment management as a whole in these discussions. The work was developed in the Alto Tietê Cabeceiras sub-catchment, one of the 5 sub catchments of the Alto-Tietê. It contains 5 interconnected dams, and presents competitive uses such as water supply, industry, effluent dilution and irrigated agriculture. A RPG was designed following a companion modelling approach (Etienne et al., 2003). It contains a friendly game-board, a set of individual and collective rules and a computerized biophysical model. The biophysical model is used to simulate water allocation and quality processes at catchment level. It articulates 3 modules. A simplified nutrient discharge model permits the estimation of land use nutrient exportation. An arc-node model simulates water flows and associated nutrient charges from one point of the hydrographical network to another. The Vollenweider model is used for simulating specific reservoir dynamics. The RPG allows players to make individual and collective decisions related to water allocation and the management of its quality. Impacts of these decisions are then simulated using the biophysical model. Specific indicators of the game are then updated and may influence player's behaviour (actions) in following rounds. To introduce discussions on the management of water quality at a catchment level, an issue that is rarely explicitly dealt with, four game sessions were implemented involving representatives of basin committees and water and sanitation engineers. During the game session, the participants took advantage of the water quality output of the biophysical model to test management alternatives such as rural sewage collection or effluent dilution. The biophysical model accelerated calculations of flows and eutrophication rates that were then returned to the game board with explicit indicators of quantity and quality. Players could easily test decisions impacting on qualitative water processes and visualize the simulation results directly on the game board that was representing a friendly, virtual and simplified catchment. The Agualoca game proved its ability to turn complex water processes understandable for a non totally initiated public. This experience contributed to a better understanding of multiple-use water management and also of joint management of water quality and quantity. (Résumé d'auteur