On Szebehely's problem for holonomic systems involving generalized potential functions

We consider the problem of finding the generalized potential function V = U _i(q ¹, q ²,..., q ⁿ)q ⁱ + U(q ¹, q ²,...;q ⁿ) compatible with prescribed dynamical trajectories of a holonomic system. We obtain conditions necessary for the existence of solutions to the problem: these can be cast into a system of n – 1 first order nonlinear partial differential equations in the unknown functions U ₁, U ₂,...;, U _n, U. In particular we study dynamical systems with two degrees of freedom. Using adapted coordinates on the configuration manifold M ₂ we obtain, for potential function U(q ¹, q ²), a classic first kind of Abel ordinary differential equation. Moreover, we show that, in special cases of dynamical interest, such an equation can be solved by quadrature. In particular we establish, for ordinary potential functions, a classical formula obtained in different way by Joukowsky for a particle moving on a surface.Work performed with the support of the Gruppo Nazionale di Fisica Matematica (G.N.F.M.) of the Italian National Research Council.     

A hydraulic invariance‐based methodology for the implementation of storm‐water release restrictions in urban land use master plans

A hydraulic invariance (HI)‐based methodology was developed as a tool to support implementation of storm flow control measures into land use master plans (LUMPs) for urban catchments. The methodology is based on the use of simple hydrologic analysis to compare predevelopment and postdevelopment catchment flow release scenarios. Differently from previous literature examples, for which the parcel scale is usually considered for the analysis, HI was pursued assuming the LUMP areas of transformation as the basic units for assigning storm water control measures in the form of flow release restrictions. The methodology was applied to a case study catchment in the southern part of the City of Catania (Italy), for which the LUMP re‐design has been recently proposed. Simulations were run based on the use of the EPA‐Storm Water Management Model and allowed deriving flow release restrictions in order to achieve HI at the subcatchment level for design events of different return period.     

Exploiting historical rainfall and landslide data in a spatial database for the derivation of critical rainfall thresholds

Critical rainfall thresholds for landslides are powerful tools for preventing landslide hazard. The thresholds are commonly estimated empirically starting from rainfall events that triggered landslides in the past. The creation of the appropriate rainfall–landslide database is one of the main efforts in this approach. In fact, an accurate agreement between the landslide and rainfall information, in terms of location and timing, is essential in order to correctly estimate the rainfall–landslide relationships. A further issue is taking into account the average moisture conditions prior the triggering event, which reasonably may be crucial in determining the sufficient amount of precipitation. In this context, the aim of this paper is exploiting historical landslide and rainfall data in a spatial database for the derivation of critical rainfall thresholds for landslide occurrence in Sicily, southern Italy. The hourly rainfall events that caused landslides occurred in the twentieth century were specifically identified and reconstructed. A procedure was proposed to automatically convert rain guages charts recorded on paper tape into digital format and then to provide the cumulative rainfall hyetograph in digital format. This procedure is based on a segmentation followed by signal recognition techniques which allow to digitalize and to recognize the hyetograph automatically. The role of rainfall prior to the landslide events was taken into account by including in the analysis the rainfall occurred 5, 15 and 30 days before each landslide. Finally, cumulated rainfall duration thresholds for different exceedance probability levels were determined. The obtained thresholds resulted in agreement with the regional curves proposed by other authors for the same area; antecedent rainfall turned out to be particularly important in triggering landslides.     

Calcio-carbonatite melts and metasomatism in the mantle beneath Mt. Vulture (Southern Italy)

At Mt. Vulture volcano (Basilicata, Italy) calcite globules (5–150 μm) are hosted by silicate glass pools or veins cross-cutting amphibole-bearing, or more common spinel-bearing mantle xenoliths and xenocrysts. The carbonate globules are rounded or elongated and are composed of a mosaic of 2–20 μm crystals, with varying optical orientation. These features are consistent with formation from a quenched calciocarbonatite melt. Where in contact with carbonate amphibole has reacted to form fassaitic pyroxene. Some of these globules contain liquid/gaseous CO₂ bubbles and sulphide inclusions, and are pierced by quench microphenocrysts of silicate phases. The carbonate composition varies from calcite to Mg-calcite (3.8–5.0 wt.% MgO) both within the carbonate globules and from globule to globule. Trace element contents of the carbonate, determined by LAICPMS, are similar to those of carbonatites worldwide including ΣREE up to 123 ppm. The Sr–Nd isotope ratios of the xenolith carbonate are similar to the extrusive carbonatite and silicate rocks of Mt. Vulture testifying to derivation from the same mantle source. Formation of immiscibile silicate–carbonatite liquids within mantle xenoliths occurred via disequilibrium immiscibility during their exhumation.     

Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective

A comprehensive parametric approach to study the probability distribution of rainfall data at scales of hydrologic interest (e.g. from few minutes up to daily) requires the use of mixed distributions with a discrete part accounting for the occurrence of rain and a continuous one for the rainfall amount. In particular, when a bivariate vector (X, Y) is considered (e.g. simultaneous observations from two rainfall stations or from two instruments such as radar and rain gauge), it is necessary to resort to a bivariate mixed model. A quite flexible mixed distribution can be defined by using a 2-copula and four marginals, obtaining a bivariate copula-based mixed model. Such a distribution is able to correctly describe the intermittent nature of rainfall and the dependence structure of the variables. Furthermore, without loss of generality and with gain of parsimony this model can be simplified by some transformations of the marginals. The main goals of this work are: (1) to empirically explore the behaviour of the parameters of marginal transformations as a function of time scale and inter-gauge distance, by analysing data from a network of rain gauges; (2) to compare the properties of the regression curves associated to the copula-based mixed model with those derived from the model simplified by transformations of the marginals. The results from the investigation of transformations’ parameters are in agreement with the expected theoretical dependence on inter-gauge distance, and show dependence on time scale. The analysis on the regression curves points out that: (1) a copula-based mixed model involves regression curves quite close to some non-parametric models; (2) the performance of the parametric regression decreases in the same cases in which non-parametric regression shows some instability; (3) the copula-based mixed model and its simplified version show similar behaviour in term of regression for mid-low values of rainfall. An erratum to this article can be found at     

Isoseismals of the strongest Friuli aftershocks of September 1976

Summary Isoseismal maps of the three strongest Friuli aftershocks of September 1976 were compiled using the contributions from European countries within the shaken area. The characteristic features of the macroseismic fields are discussed.     

La nuova carta magnetica d'Italia (Isogone al 1° gennaio 1940) dell'Istituto Geografico Militare

Riassunto L'Autore, accennato alla carta del Palazzo del 1892 e dimostrata la necessità di una più precisa carta rispondente alle accresciute esigenze civili e militari, tratta del nuovo rilievo magnetico d'Italia basato su ben 1529 stazioni eseguite dall'Istituto Geografico Militare dal 1932 al 1937 e quindi della nuova carta magnetica con le isogone al 1° gennaio 1940 testé pubblicata dallo stesso Istituto.

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Zusammenfassung Der Verf., nach Erwähnung der erdmagnetischen Karte von Palazzo des Jahres 1892 hervorhebt die Notwendigkeit einer genaueren den vermehrten zivilen und militärischen Ansprüchen entsprechender Aufnahme; eine solche neue erdmagnetische Aufnahme Italiens ist vom Istituto Geografico Militare in den Jahren 1932–1937 durchgeführt worden und zwar mit zusammen 1529 Stationen. Diese Arbeit wird beschrieben und erörtet besonders in Zusammenhang mit der hier vorgestellten neuen Isogonen-Kart, bezogen auf dem 1. Januar 1940.

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Résumé L'Auteur, après avoir mentionné la carte magnétique du Prof. Palazzo (1892) et démontré la nécessité d'une carte plus précise et plus correspondante à l'accroissement des exigences civiles et militaires, s'entretient sur le nouveau levé magnétique d'Italie, qui se base sur les observations de 1529 stations, esecutées par l'Istituto Geografico Militare entre 1932 et 1937; ensuite il illustre la nouvelle carte magnétique des isogones, au l.er Janiver 1940, qui vient d'être publiée par le même Institut et qui est jointe au présent mémoire.

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Quest'articolo è in parte un riassunto di quanto io stesso ebbi a scrivere in alcune memorie precedenti edite dall'Istituto Geografico Militare e dalla Società Italiana per il Progresso delle Scienze.     

When do rock glacier fronts fail? Insights from two case studies in South Tyrol (Italian Alps)

The fronts of two rock glaciers located in South Tyrol (Italian Alps) failed on 13 August 2014, initiating debris flows in their downslope channels. A multimethod approach including climate, meteorological, and ground temperature data analysis, aerial image correlation, as well as geotechnical testing and modeling, led to the reconstruction of the two events. An integrated investigation of static predisposing factors, slowly changing preparatory factors, and potential triggering events shed light on the most likely reasons for such failures. Our results suggest that the occurrence of front destabilization at the two rock glaciers can only partly be explained by the occurrence of heavy rainfall events. Indeed, antecedent hydrological and thermal ground conditions were characterized by a saturated active layer favored by a snow-rich winter and extensive precipitation in late spring and summer. Also, the rising trend of air temperature during spring and summer months since 1950s might explain the concurrent marked displacement of the two rock glaciers. Indeed, geotechnical investigations have provided strong indications that one of the investigated rock glacier fronts was at a marginally stable state prior to 2014. As rainfall events more intense than the one that occurred in August 2014 were previously recorded in the same area without resulting failures at the studied rock glaciers, we propose that both predisposing and preparatory destabilizing factors have played a key role in the 2014 rock glacier front failures.