Solutions to the Painlev\'e V equation through supersymmetric quantum mechanics

In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlev\'e V (PV) equation, a second-order non-linear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator, while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.Comment: 39 pages, 18 figures, 4 tables, 70 reference

Relationships between diatoms and the environment in Spanish reservoirs

Diatoms are very useful environmental indicators in limnological and paleolimnological studies. Spanish reservoirs offer a valuable opportunity for the study of relationships between diatoms and environmental conditions, since these ecosystems are abundant in this country and the patterns of their regional limnology are well established. We report the results from a study carried out on diatom communities in 40 reservoirs from several Spanish water basins. More than 200 diatom taxa were found. A canonical correspondence analysis was applied to the abundance data of the most common taxa and the main physical and chemical variables. This analysis showed that mineralisation (conductivity and alkalinity) was the most important environmental factor explaining diatom distribution, while trophic state was the second most important. These results are similar to those in previous studies on phytoplankton in Spanish reservoirs. Conductivity and alkalinity optima of the selected taxa allow us to consider these taxa as good indicators of water mineral content in similar ecosystems.Las diatomeas son indicadores ambientales muy útiles en estudios limnológicos y paleolimnológicos. En España los embalses ofrecen una gran oportunidad para el estudio de las relaciones entre las diatomeas y las condiciones ambientales, ya que son ecosistemas muy abundantes y las principales características de su limnología regional están bien estudiadas. Se presentan aquí los resultados de un estudio sobre las comunidades de diatomeas efectuado en 40 embalses de diversas cuencas hidrográficas españolas. En ellos se encontraron más de 200 taxones de diatomeas. Se efectuó un análisis de correspondencias canónicas con los datos de abundancia de los taxones más frecuentes y las principales variables físico-químicas. Este análisis muestra que el factor con mayor influencia sobre las comunidades de diatomeas es la mineralización (conductividad y alcalinidad), y en segundo lugar el grado trófico. Estos resultados son similares a estudios previos sobre el fitoplancton de embalses españoles. Los valores de los óptimos respecto a la conductividad y alcalinidad de los principales taxones, permiten considerar dichos taxones como buenos indicadores del contenido mineral del agua en ecosistemas similares

The lava flow invasion hazard map at Mount Etna and methods for its dynamic update

This special issue of Annals of Geophysics contains seventeen peer-reviewed papers that cover a wide variety of topics related to the V3-LAVA Project funded by the Italian Dipartimento della Protezione Civile in the framework of the 2007– 2009 Agreement with the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The frequent eruptions of Mount Etna can produce lava flows that can cover distances long enough to invade vulnerable areas on the flanks of the volcano. These require improvements to our forecasting tools for the effective assessment of lava-flow hazards, to help the local authorities to make the necessary decisions during a volcanic eruption. The LAVA Project aims to develop, validate and unify methods for mapping the areas around Etna that are threatened by lava invasion within the next 50 years, and also within the immediate days after an eruption has begun. Both timescales of lava-hazard mapping call for estimations of the probabilities of vent openings – using geological evidence over the long-term, and monitoring data over the short-term

Lava flow susceptibility map of mt etna based on numerical simulations

We constructed maps of probability of lava inundation using computer simulations considering the past eruptive behaviour of the Mt. Etna volcano and data deriving from monitoring networks. The basic a priori assumption is that new volcanoes will not form far from existing ones and that such a distribution can be performed using a Cauchy kernel. Geophysical data are useful to update or fine tune the initial Cauchy kernel to better reflect the distribution of future volcanism. In order to obtain a final susceptibility map, a statistical analysis permits a classification of Etna’s flank eruptions into twelve types. The simulation method consists of creating a probability surface of the location of future eruption vents and segmenting the region according to the most likely historical eruption on which to base the simulation. The paths of lava flows were calculated using the MAGFLOW Cellular Automata (CA) model, allowing us to simulate the discharge rate dependent spread of lava as a function of time

Modelling lava flows by Cellular Nonlinear Networks (CNN): preliminary results

International audienceThe forecasting of lava flow paths is a complex problem in which temperature, rheology and flux-rate all vary with space and time. The problem is more difficult to solve when lava runs down a real topography, considering that the relations between characteristic parameters of flow are typically nonlinear. An alternative approach to this problem that does not use standard differential equation methods is Cellular Nonlinear Networks (CNNs). The CNN paradigm is a natural and flexible framework for describing locally interconnected, simple, dynamic systems that have a lattice-like structure. They consist of arrays of essentially simple, nonlinearly coupled dynamic circuits containing linear and non-linear elements able to process large amounts of information in real time. Two different approaches have been implemented in simulating some lava flows. Firstly, a typical technique of the CNNs to analyze spatio-temporal phenomena (as Autowaves) in 2-D and in 3-D has been utilized. Secondly, the CNNs have been used as solvers of partial differential equations of the Navier-Stokes treatment of Newtonian flow

CO2\mathrm{CO_2} exploding clusters dynamics probed by XUV fluorescence

Clusters excited by intense laser pulses are a unique source of warm dense matter, that has been the subject of intensive experimental studies. The majority of those investigations concerns atomic clusters, whereas the evolution of molecular clusters excited by intense laser pulses is less explored. In this work we trace the dynamics of $\mathrm{CO_2}$ clusters triggered by a few-cycle 1.45-$\mu$m driving pulse through the detection of XUV fluorescence induced by a delayed 800-nm ignition pulse. Striking differences among fluorescence dynamics from different ionic species are observed

A new device hypothesis for water extraction from air and basic air condition system in developing countries

This work proposes a new device for air treatment with dehumidification and water recovery/storage, with possible mitigation of indoor environmental conditions. The system is based on Peltier cells coupled with a horizontal earth‐to‐air heat exchanger, it is proposed as an easy‐to-implement alternative to the heat pumps and air handling units currently used on the market, in terms of cost, ease of installation, and maintenance. The process provides the water collection from the cooling of warm‐humid air through a process that leads to condensation and water vapor separation. The airflow generated by a fan splits into two dual flows that lap the two surfaces of the Peltier cells, one flow laps the cold surfaces undergoing sensible, latent cooling with dehumidification; the other flow laps the hot surfaces and heats up. The airflow undergoes thermal pre‐treatment through the underground horizontal geothermal pipe that precedes the Peltier cells. In the water storage tank, which also works as a mixing chamber, the two air streams are mixed to regulate the outlet temperature. The system can be stand‐alone if equipped with a photovoltaic panel and a micro wind turbine, able to be used in places where electricity is absent. The system, with different configurations, is modeled in the African city Kigali, in Rwanda

Assessment and modeling of lava flow hazard on Mt. Etna volcano

A methodology for constructing a probability map of lava inundation by considering the past eruptive behavior of the Mt. Etna volcano is described. The basic a priori assumption is that new vents will not form far from existing ones and that such a distribution can be performed using a Gaussian kernel. The methodology follows several steps: computation of a susceptibility map that provides the spatial probability of vent opening; evaluation of the temporal probability for the occurrence of the hazard during the considered time interval; characterization of the expected eruptions; numerical simulations of lava flow paths and elaboration of the hazard map. The application of MAGFLOW code, a physical-mathematical model, for simulating the lava flow paths represents the central part of this methodology for the hazard assessment at Mt. Etna. The simulation approach, to assess lava flow hazard, provides a more robust and locally accurate analysis than a simple probabilistic approach and accounts for the influence of the actual topography on the path of future lava flows