Discretization of asymptotic line parametrizations using hyperboloid patches

Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary quadrilaterals are skew. We classify the simply connected affine A-nets that can be extended to continuously differentiable surfaces by gluing hyperboloid surface patches into the skew quadrilaterals. The resulting surfaces are called "hyperbolic nets" and are a novel piecewise smooth discretization of surfaces parametrized along asymptotic lines. It turns out that a simply connected affine A-net has to satisfy one combinatorial and one geometric condition to be extendable - all vertices have to be of even degree and all quadrilateral strips have to be "equi-twisted". Furthermore, if an A-net can be extended to a hyperbolic net, then there exists a 1-parameter family of such C^1-surfaces. It is briefly explained how the generation of hyperbolic nets can be implemented on a computer. The article uses the projective model of Pluecker geometry to describe A-nets and hyperboloids.Comment: 27 pages, 17 figure

MONITORIZAÇÃO DE MICROALGAS PLANCTÔNICAS POTENCIALMENTE TÓXICAS NA ÁREA DE MARICULTURA DA ENSEADA DE ARMAÇÃO DE ITAPOCOROY - PENHA - SC

This paper is a descriptive synthesis of approximately 17 months of phytoplankton sampling in the shellfish culture area of Enseada de Armação do Itapocoroy (Penha - Santa Catarina - Brazil). The goal of this program was to know the local phytoplankton composition, specially the toxic and potentially toxic ones; to verify the characteristics of water masses associated to the different phytoplankton assemblies and to monitor the occurrence of blooms of toxic or potentially toxic species, in order to prevent human intoxication by ingestion of contaminated shellfish. The results have indicated the occurrence of seasonal patterns in species succession. Potential producers of diarrhetic toxins tend to occur in winter and spring. From late spring to late summer the occurrence of Trichodesmium spp. indicate the possible presence of cyanobacteria toxins. Alexandrium fraterculus - a potential producer of paralytic toxin - has ocurred only in low cell densities and mainly in winter.O presente trabalho trata-se de uma síntese de aproximadamente 17 meses de amostragens de fitoplâncton na área de maricultura da Enseada de Armação do Itapocoroy, município de Penha, Santa Catarina. Os objetivos foram conhecer as principais espécies de microalgas planctônicas ocorrentes no local, especialmente as espécies tóxicas ou potencialmente tóxicas; verificar as características das massas de água associadas às diferentes espécies ou assembléias de microalgas (salinidade, temperatura e transparência) e monitorar a ocorrência de densidades elevadas de espécies tóxicas ou potencialmente tóxicas para prevenir possíveis intoxicações pela ingestão de moluscos com acúmulo de ficotoxinas. Os resultados indicam a ocorrência de padrões sazonais de sucessão de espécies. Espécies potencialmente produtoras de toxinas diarréicas e amnésicas tendem a ocorrer nos meses de inverno e primavera. Entre o final da primavera e durante o verão a ocorrência de Trichodesmium spp. indica possibilidade de toxinas de cianobactérias. Alexandrium fraterculus - um potencial produtor de toxina paralisante - ocorreu em pequenas densidades e principalmente no inverno

Characterizing the multi-dimensional reaction dynamics of dihalomethanes using XUV-induced Coulomb explosion imaging

Site-selective probing of iodine 4d orbitals at 13.1 nm was used to characterize the photolysis of CH2I2 and CH2BrI initiated at 202.5 nm. Time-dependent fragment ion momenta were recorded using Coulomb explosion imaging mass spectrometry and used to determine the structural dynamics of the dissociating molecules. Correlations between these fragment momenta, as well as the onset times of electron transfer reactions between them, indicate that each molecule can undergo neutral three-body photolysis. For CH2I2, the structural evolution of the neutral molecule was simultaneously characterized along the C-I and I-C-I coordinates, demonstrating the sensitivity of these measurements to nuclear motion along multiple degrees of freedom

Marine Heatwaves, Sewage and Eutrophication Combine to Trigger Deoxygenation and Biodiversity Loss: A SW Atlantic Case Study

Marine heatwaves (MHWs) are a major concern worldwide due to their increasing impacts in recent years, and these extreme events may trigger deoxygenation of coastal waters affected by sewage and eutrophication. Here we investigate the combined effects of MHWs and nutrient enrichment on the water quality and biodiversity of the Bay of Santa Catarina Island (Brazil). We used historical (1994–2020) sea surface temperature data from satellites and in situ physical, chemical and biological parameters to assess temporal trends. Oxygen levels have been decreasing whilst phosphorus levels have been increasing in the bay. During the austral summer of 2020 a regional sea surface heatwave was detected by satellite, lasting for 9 days and coinciding with our research cruise. During this period, seawater temperatures reached 29.8°C and anoxia was detected for the first time in the bay. A decrease in macrobenthic and phytoplankton community richness correlated with decreases in oxygen both through time and towards more urbanized areas. Overall, poor wastewater treatment is a key stressor that combined with MHWs to degrade coastal waters. Mitigation strategies are needed to minimize the impact of MHWs, including improved sewage treatment, restoration and conservation of wetlands and the use of nature-based technologies to promote coastal ecosystem recovery.</jats:p