Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

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.     

Rainfall induced debris flows in pyroclastic deposits, Campania (southern Italy)

A combination of empirical and physically based hydrological models has been used to analyze historical data on rainfall and debris-flow occurrence in western Campania, to examine the correlation between rainfall and debris-flow events.

Rainfall data from major storms recorded in recent decades in western Campania were compiled, including daily series from several rain gauges located inside landslide areas, supplemented by hourly rainfall data from some of the principal storms.

A two-phase approach is proposed. During phase 1, soil moisture levels have been modelled as the hydrological balance between precipitation and evapotranspiration, on a daily scale, using the method of Thornthwaite [Geograph. Rev. 38 (1948) 55].

Phase 2 is related to the accumulation of surplus moisture from intense rainfall, leading to the development of positive pore pressures. These interactions take place on an hourly time scale by the “leaky barrel” (LB) model described by Wilson and Wiezoreck [Env. Eng. Geoscience, 1 (1995) 11]. In combination with hourly rainfall records, the LB model has been used to compare hydrological effects of different storms. The critical level of retained rain water has been fixed by the timing of debris-flow activity, related to recorded storm events.

New rainfall intensity–duration thresholds for debris-flow initiation in western Campania are proposed. These thresholds are related to individual rain gauge and assume a previously satisfied field capacity condition. The new thresholds are somewhat higher than those plotted by previous authors, but are thought to be more accurate and thus need less conservatism.     

Thermal decay of carbonate dimension stones: fabric,physical and mechanical changes

This paper deals with the effects of thermal stresses on selected carbonate rocks used as dimension stones. They are Mesozoic calcareous and dolomitic rocks cropping out in Apulia (southern Italy) that, for their physico-mechanical and aesthetic properties, have always been finding a large application both as ornamental stones and as simple construction materials; their use is attested not only in Italy, in works of archaeological, historical and artistic interest too. The cause–effect relationships of thermal degradation were studied by means of an artificial accelerated ageing test, in order to provide a perspective about the decay of carbonate stones due to diurnal and seasonal temperature fluctuations, as well as thermal shocks during events of fire development. The stone samples were subjected to thermal cycles in a muffle furnace, ranging from 100 to 700 °C; after each cycle, several non-destructive and semi-destructive tests were carried out: mass and volume measurements, mercury intrusion porosimetry, sclerometer tests, ultrasonic tests, thin-section observations and determination of chromatic alterations through image analysis and Munsell charts method. In this way, the qualitative and quantitative modifications induced in fabric, physical and mechanical properties were discussed. The results highlight the fundamental role of depositional and diagenetic fabric that, together with mineralogical composition, represents the most significant discriminating factor in the response of the stone to thermal stresses.     

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.     

Advances and Practices on the Research,Prevention and Control of Land Subsidence in Coastal Cities

Land subsidence severely threatens most of the coastal plains around the world where high productive industrial and agricultural activities and urban centers are concentrated. Coastal subsidence damages infrastructures and exacerbates the effect of the sea-level rise at regional scale. Although it is a well-known process, there is still much more to be improved on the monitoring, mapping and modeling of ground movements, as well as the understanding of controlling mechanisms. The International G...     

Exhumation patterns along shallow low‐angle normal faults: an example from the Altotiberina active fault system (Northern Apennines,Italy)

A multi‐method approach (palaeothermal and thermochronological analyses; thermal modelling) is applied to reconstruct the exhumation history of the Altotiberina Fault (ATF), a representative example of crustal‐scale active low‐angle normal faulting in the Northern Apennines (Italy). Thermal maturity and thermochronological data yield similar burial histories but different exhumation patterns for the sedimentary successions in the hangingwall and the footwall of the ATF. Since 3.8 Ma, the ATF footwall has exhumed at rates of 0.90 mm a^?1. Exhumation led to bending and deactivation of the ATF uppermost portion as a result of tectonic unloading and isostatic adjustment, followed by migration of extension and the development of a set of domino‐like, east‐dipping normal faults, rooting on the buried portion of the ATF. ATF activity and isostatic rebound exhumed Triassic rock units from depths of about 4 km. We suggest that isostatic instability is accommodated at shallow crustal levels, in a similar way to what is observed on larger structures at mid‐low crustal levels.     

Salinity and periodic inundation controls on the soil‐plant‐atmosphere continuum of gray mangroves

Salinity and periodic inundation are both known to have a major role in shaping the ecohydrology of mangroves through their controls on water uptake, photosynthesis, stomatal conductance, gas exchanges, and nutrient availability. Salinity, in particular, can be considered one of the main abiotic regulating factors for halophytes and salt‐tolerant species, due to its influence on water use patterns and growth rate. Ecohydrological literature has rarely focused on the effects of salinity on plant transpiration, based on the fact that the terrestrial plants mostly thrive in low‐saline, unsaturated soils where the role of osmotic potential can be considered negligible. However, the effect of salinity cannot be neglected in the case of tidal species like mangroves, which have to cope with hyperosmotic conditions and waterlogging. We introduce here a first‐order ecohydrological model of the soil/plant‐atmosphere continuum of Avicennia marina—also known as gray mangrove—a highly salt‐tolerant pioneer species able to adapt to hyperarid intertidal zones and characterized by unique morphological and ecophysiological traits. The A. marina's soil‐plant‐atmosphere continuum takes explicitly into account the role of water head, osmotic water potential, and water salinity in governing plant water fluxes. A. marina's transpiration is thus modeled as a function of salinity based on a simple parameterization of salt exclusion mechanisms at the root level and a modified Jarvis' expression accounting for the effects of salinity on stomatal conductance. Consistently with previous studies investigating the physiology of mangroves in response to different environmental drivers, our results highlight the major influence of salinity on mangrove transpiration when contrasted with other potential stressors such as waterlogging and water stress.     

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.