A multiple scales approach to maximal superintegrability

In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique called multiple scales method. If the outcome is positive, this test can be used to suggest maximal superintegrability, whereas when the outcome is negative it can be used to disprove it. This method can be regarded as a finite dimensional analog of the multiple scales method as a way to produce soliton equations. We use this technique to show that the real counterpart of a mechanical system found by Jules Drach in 1935 is, in general, not maximally superintegrable. We give some hints on how this approach could be applied to classify maximally superintegrable systems by presenting a direct proof of the well-known Bertrand's theorem.Comment: 30 pages, 4 figur

Rediscovering the scientific and didactic value of minor herbarium collections: the seeds and fruits collection by Gustavo Bonaventura

Seeds and fruits collections are very important from a systematic point of view and represent useful references in several disciplines and research fields. The Herbarium of Sapienza University of Rome (RO) hosts a Spermoteque/Carpoteque, which was organized by Gustavo Bonaventura (1902-1976). The purpose of this paper is to describe the heritage of Bonaventura's collection. It consists of 42 wooden boxes, globally hosting 3411 glass tubes containing seeds, fruits, and other materials. The collection was first of all catalogued; then, analysis were conducted regarding taxonomic composition, temporal and geographic coverage, institutions of provenience, collectors, content, and preservation status. The specimens refer to 2740 taxa, belonging to 890 genera and 135 families. Many genera of agricultural interest are present, each one with different cultivars. The collection spans across 130 years (1843-1975) and hosts specimens coming from all over the world. Materials were provided by several herbaria, botanical gardens and agrarian institutes, and by 50 collectors. The Bonaventura's collection is still a useful reference collection, testifying biodiversity over times and thus being useful for diachronic studies; moreover, it documents the interests of collectors and the past network activity between institutions

Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast

Real-time Green's function simulations of molecular junctions (open quantum systems) are typically performed by solving the Kadanoff-Baym equations (KBE). The KBE, however, impose a serious limitation on the maximum propagation time due to the large memory storage needed. In this work we propose a simplified Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA) to overcome the KBE limitation on time, significantly speed up the calculations, and yet stay close to the KBE results. This is achieved through a twofold advance: first we show how to make the GKBA work in open systems and then construct a suitable quasi-particle propagator that includes correlation effects in a diagrammatic fashion. We also provide evidence that our GKBA scheme, although already in good agreement with the KBE approach, can be further improved without increasing the computational cost.Comment: 13 pages, 13 figure

Analysis of enhanced diffusion in Taylor dispersion via a model problem

We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in an infinite channel. Taylor observed in the 1950's that, in such a setting, the tracer diffuses at a rate proportional to $1/\nu$, rather than the expected rate proportional to $\nu$. We provide a mathematical explanation for this enhanced diffusion using a combination of Fourier analysis and center manifold theory. More precisely, we show that, while the high modes of the concentration decay exponentially, the low modes decay algebraically, but at an enhanced rate. Moreover, the behavior of the low modes is governed by finite-dimensional dynamics on an appropriate center manifold, which corresponds exactly to diffusion by a fluid with viscosity proportional to $1/\nu$

Perspectives on alternatives to phthalate plasticized poly(vinyl chloride) in medical devices applications

Poly(vinyl chloride) (PVC) is one of the most important polymeric materials available today and is used to manufacture many items, ranging from packaging and toys to healthcare devices. PVC is per se a rigid material but it is made softer by compounding with plasticizers, particularly phthalate esters such as di-(2-ethylhexyl) phthalate (DEHP). In flexible plasticizer PVC (P-PVC), phthalates are not chemically bound to PVC and they are released into the external environment. In particular, prolonged contact of P-PVC based medical devices with body fluids or tissues has been shown to be associated with severe health risks. Major concerns regarding the safety of P-PVC in medical plastic items have been raised, and several alternatives to phthalates and to P-PVC itself as well as chemical/physical treatments of P-PVC to reduce DEHP migration have been proposed. This review outlines recent scientific approaches for preventing DEHP contamination of humans by P-PVC medical devices, highlighting the impact of the proposed alternative materials on human health and strategies for implementing them

Sc substitution for Mg in MgB2: effects on Tc and Kohn anomaly

Here we report synthesis and characterization of Mg_{1-x}Sc_{x}B_{2} (0.12T_{c}>6 K. We find that the Sc doping moves the chemical potential through the 2D/3D electronic topological transition (ETT) in the sigma band where the ``shape resonance" of interband pairing occurs. In the 3D regime beyond the ETT we observe a hardening of the E_{2g} Raman mode with a significant line-width narrowing due to suppression of the Kohn anomaly over the range 0<q<2k_{F}.Comment: 8 pages, 4 EPS figures, to be published in Phys. Rev.

High Temperature Stability of Onion-Like Carbon vs Highly Oriented Pyrolytic Graphite

Abstract The thermodynamic stability of onion-like carbon (OLC) nanostructures with respect to highly oriented pyrolytic graphite (HOPG) was determined in the interval 765–1030 K by the electromotive force (emf) measurements of solid electrolyte galvanic cell: (Low) Pt|Cr3C2,CrF2,OLC|CaF2s.c.|Cr3C2,CrF2,HOPG|Pt (High). The free energy change of transformation HOPG = OLC was found positive below 920.6 K crossing the zero value at this temperature. Its trend with temperature was well described by a 3rd degree polynomial. The unexpected too high values of LDrHT LT P ~DcPðTÞ jointly to the HR-TEM, STEM and EELS evidences that showed OLC completely embedded in rigid cages made of a Cr3C2/CrF2 matrix, suggested that carbon in the electrodes experienced different internal pressures. This was confirmed by the evaluation under constant volume of dP dT by the a k ratio for OLC (0.5 MPa K21) and HOPG (8 Pa K21) where a and k are the isobaric thermal expansion and isothermal compressibility coefficients, respectively. The temperature dependency of the pressure was derived and utilized to calculate the enthalpy and entropy changes as function of temperature and pressure. The highest value of the internal pressure experienced by OLC was calculated to be about 7 GPa at the highest temperature. At 920.6 K, DrH and DrS values are 95.8 kJ mol21 and 104.1 JK21 mol21, respectively. The surface contributions to the energetic of the system were evaluated and they were found negligible compared with the bulk terms. As a consequence of the high internal pressure, the values of the enthalpy and entropy changes were mainly attributed to the formation of carbon defects in OLC considered as multishell fullerenes. The change of the carbon defect fraction is reported as a function of temperature

Green roofs and green façades for improving sustainability of towns

Nowadays, buildings in Europe account for a consumption of 40% of total energy use and about 65% of total electricity consumption. According to the European Directive on the energy performance of buildings (EPBD Directive), solutions such as green roofs and green walls can help to reduce energy consumptions and the greenhouse gases emissions by buildings. The installation of plant systems covering some surfaces of the building allows to reach an improvement of the building's energy efficiency mainly by reducing the energy demand for cooling in warm periods. The green layers used for buildings contribute to improve thermal insulation, since they reduce the direct solar radiation while the evaporative cooling contributes to create a better local microclimate. This paper provides the first data collected by a green wall prototype in progress at ENEA Casaccia Centre to investigate the effects of this natural green solution on the energy efficiency of buildings. The project was funded by the Programme Research of Electrical System, and is being carried out in cooperation with the Universities of Pisa, Bari and Viterbo