Regularity of isoperimetric sets in ℝ² with density

We consider the isoperimetric problem in R2with density. We show that, if the density is C0,α, then the boundary of any isoperimetric set is of class C1,α3-2α. This improves the previously known regularity

A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas

A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential "softened" at short distances. Using exact numerical techniques, we study the low temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighbouring droplets.Comment: 4 pages, 4 figure

Quantum Bubbles in Microgravity

The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.Comment: 7 pages, 7 figures; published versio

Electrochemical biosensors for tracing cyanotoxins in food and environmental matrices

The adoption of electrochemical principles to realize on-field analytical tools for detecting pollutants represents a great possibility for food safety and environmental applications. With respect to the existing transduction mechanisms, i.e., colorimetric, fluorescence, piezoelectric etc., electrochemical mechanisms offer the tremendous advantage of being easily miniaturized, connected with low cost (commercially available) readers and unaffected by the color/turbidity of real matrices. In particular, their versatility represents a powerful approach for detecting traces of emerging pollutants such as cyanotoxins. The combination of electrochemical platforms with nanomaterials, synthetic receptors and microfabrication makes electroanalysis a strong starting point towards decentralized monitoring of toxins in diverse matrices. This review gives an overview of the electrochemical biosensors that have been developed to detect four common cyanotoxins, namely microcystin-LR, anatoxin-a, saxitoxin and cylindrospermopsin. The manuscript provides the readers a quick guide to understand the main electrochemical platforms that have been realized so far, and the presence of a comprehensive table provides a perspective at a glance

A Hybrid Screen-Printed Strip for Enhanced Electroanalysis towards Lead and Cadmium in Multi-Matrices

Although heavy metals represent a major treat for ecosystem and human health, reference methods for their monitoring are characterized by time-consuming procedures, skilled personel and sophisticated equipment (e.g. ICP-MS, AAS). The development of portable solutions is required, particularly improving interventions and reducing complexity. To this regards, an electrochemical strip for the determination of lead and cadmium in clinical, environmental and food matrices have been developed. The Bismuth film-based flexible device has been optimized and it has been able to detect cadmium and lead, respectively, down to the detection limit of 1.3 and 2 ppb. The use of Whatman No.1 chromatographic paper has allowed to improve the sensitivity towards the detection of heavy metals, because of the porosity that allowed to pre-concentrate species. This led to an improvement in the sensitivity, with a detection limit of 0.3 and 0.5 ppb, respectively, to cadmium and lead, and offers the possibility to tune the sensitivity according to needs, e.g., improving the number of pre-concentration steps. Subsequently, the application of the electrochemical sensor in drinking water, mussel and blood serum was evaluated, demonstrating how these hybrid polyester-paper electrochemical strips can significantly lower the time and costs for on-site measurements, through analytical methods of simple use. The accuracy has been evaluated by comparison with ICP-MS measurements, giving satisfactory results

Electrochemical Impedance Spectroscopy study on ammonia-fed Solid Oxide Fuel Cells

The use of ammonia as a fuel is one of the promising pathways to decarbonize the energy sector. When ammonia is converted into power in the so-called "Ammonia-to-Power", the most interesting technology is the Solid Oxide Fuel Cell (SOFC) that can operate directly with ammonia and reach high performance in terms of efficiency. SOFCs are a high-efficiency and, potentially, low-cost technology, but still suffer from degradation issues related to internal losses. An innovative experimental technique to evaluate losses evolution caused by degradation is electrical impedance spectroscopy (EIS), followed by measurement data post-processing through the Distribution of Relaxation Times (DRT) analysis. In this study, a single SOFC is studied with a combined EIS and DRT methodology, when operating with a gas mixture of hydrogen, nitrogen and ammonia. The results identify the contribution to DRT of fuel dilution and the internal ammonia decomposition reaction

Structure, Bose-Einstein condensation and superfluidity of two-dimensional confined dipolar assemblies

Low temperature properties of harmonically confined two-dimensional assemblies of dipolar bosons are systematically investigated by Monte Carlo simulations. Calculations carried out for different numbers of particles and strengths of the confining potential yield evidence of a quantum phase transition from a superfluid to a crystal-like phase, consistently with what is observed in the ho- mogeneous system. It is found that the crystal phase nucleates in the center of the trap, as the density increases. Bose-Einstein condensation vanishes at T = 0 upon entering the crystalline phase, concurrently with the disappearance of the superfluid response.Comment: 10 pages, 9 figure