Non-minimality of corners in subriemannian geometry

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.Comment: 11 pages, final versio

Sets with constant normal in Carnot groups: properties and examples

We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite subRiemannian perimeter. The purpose of this paper is threefold. First, we prove some mild regularity and structural results in arbitrary Carnot groups. Namely, we show that for every constant-normal set in a Carnot group its subRiemannian-Lebesgue representative is regularly open, contractible, and its topological boundary coincides with the reduced boundary and with the measure-theoretic boundary. We infer these properties from a metric cone property. Such a cone will be a semisubgroup with nonempty interior that is canonically associated with the normal direction. We characterize the constant-normal sets exactly as those that are arbitrary unions of translations of such semisubgroups. Second, making use of such a characterization, we provide some pathological examples in the specific case of the free-Carnot group of step 3 and rank 2. Namely, we construct a constant normal set that, with respect to any Riemannian metric, is not of locally finite perimeter; we also construct an example with non-unique intrinsic blowup at some point, showing that it has different upper and lower subRiemannian density at the origin. Third, we show that in Carnot groups of step 4 or less, every constant-normal set is intrinsically rectifiable, in the sense of Franchi, Serapioni, and Serra Cassano

Ash-plume dynamics and eruption source parameters by infrasound and thermal imagery: The 2010 Eyjafjallajökull eruption

During operational ash-cloud forecasting, prediction of ash concentration and total erupted mass directly depends on the determination of mass eruption rate (MER), which is typically inferred from plume height. Uncertainties for plume heights are large, especially for bent-over plumes in which the ascent dynamics are strongly affected by the surrounding wind field. Here we show how uncertainties can be reduced if MER is derived directly from geophysical observations of source dynamics. The combination of infrasound measurements and thermal camera imagery allows for the infrasonic type of source to be constrained (a dipole in this case) and for the plume exit velocity to be calculated (54–142 m/s) based on the acoustic signal recorded during the 2010 Eyjafjallajökull eruption from 4 to 21 May. Exit velocities are converted into MER using additional information on vent diameter (50±10 m) and mixture density (5.4±1.1 kg/m3), resulting in an average ∼9×105 kg/s MER during the considered period of the eruption. We validate our acoustic-derived MER by using independent measurements of plume heights (Icelandic Meteorological Office radar observations). Acoustically derived MER are converted into plume heights using field-based relationships and a 1D radially averaged buoyant plume theory model using a reconstructed total grain size distribution. We conclude that the use of infrasonic monitoring may lead to important understanding of the plume dynamics and allows for real-time determination of eruption source parameters. This could improve substantially the forecasting of volcano-related hazards, with important implications for civil aviation safety

Could Dietary Goals and Climate Change Mitigation Be Achieved Through Optimized Diet? The Experience of Modeling the National Food Consumption Data in Italy

Objective: The aim of this study is to define a healthy and sustainable diet model with low GHGE, fulfilling dietary requirements, and considering current Italian food consumption patterns. Design: A duly designed database was developed, linking food nutritional composition and GHGE based on 921 food items consumed in Italy according to the last national food consumption survey (INRAN-SCAI 2005–2006). Linear programming was used to develop new diet plans separately for males and females, aged 18–60 years (n = 2,098 subjects), in order to minimize GHGE. The program is based on dietary goals and acceptability constraints as well as on 13 nutrient requirement constraints aiming to reach a healthy and acceptable diet for the Italian population. Results: Diet optimization resulted in a nutritionally adequate pattern minimizing GHGE values (4.0 vs. 1.9 kg CO2e/day for males and 3.2 vs. 1.6 kg CO2e/day for females). In both sexes, the nutrient intake of the optimized diet was at the established lower bound for cholesterol and calcium and at the established upper bound for free sugar and fiber. In males, intake of zinc was at the established lower bound whereas iron was at the established upper bound. Consumption of red meat and fruit and vegetables was at the established lower and upper bound, respectively, in both males and females. Despite the decrease in meat consumption, especially red meat, in the optimized diet with respect to the observed diet, levels of iron intake in females increased by 10% (10.3 vs. 11.3 mg/day) but remained below the adequate intake established in Italian national DRIs. Conclusions: An attainable healthy dietary pattern was developed that would lead to the reduction of GHGE by 48% for males and by 50% for females with respect to current food consumption in the Italian adult population. Health-promoting dietary patterns can substantially contribute to achieve related Sustainable Development Goals

Analysis of the P branch of the [nu]6 fundamental of carbon suboxide

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23682/1/0000651.pd