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.     

Spatiotemporal changes in cadmium contamination in the Seine estuary (France)

Cadmium (Cd) is among the major contaminants in the Seine estuary. In the biota, the RNO (Réseau National d’Observation, the French Mussel-Watch) has shown that Cd concentrations in mussels living at the mouth of the estuary are related to changes in inputs to this area of phosphogypsum, a calcium sulphate that is a by-product of the phosphoric acid naturally enriched with Cd. In the water column, Cd concentrations at several key estuary sites show a very marked trend toward decreased contamination in the particles as well as in the dissolved phase. The behavior of Cd in the estuary has been studied between 1991 and 1998 in the framework of the scientific program Seine-Aval. This program has highlighted punctual Cd inputs in the estuarine water column. The partition of Cd between the dissolved and the particulate phase, previously described in various estuaries, is characterized by an intense phenomenon of solubilization in the mixing zone freshwater-seawater, but the colloidal Cd fraction remains low along the whole salinity gradient, about 5% to 10% of the apparent dissolved fraction. Although the decrease of inputs induced a fall of Cd concentrations in the water column, laboratory experiments show that the estuarine particles are far from being exhausted in Cd. Despite continuous efforts to reduce the urban and industrial inputs into the estuarine and coastal waters, the Seine estuary still remains very contaminated by Cd.     

Splash detachment of sand particles under varying contact stress field of wind-driven raindrop impact

The effects of wind-driven rain (WDR) on sand detachment were studied under various raindrop obliquities. Results suggested a significant reduction in compressive stress on sand surfaces for a two-dimensional experimental set-up in a wind tunnel. During experiments, sand particles in splash cups were exposed to both wind-free rain (WFR) and WDR driven by horizontal winds of 6.4, 8.9 and 12.8 m s⁻¹ and rainfall intensities of 50, 60, 75 and 90-mm h⁻¹ to assess the sand detachment rate (D, in g m⁻² s⁻¹). The effects of sand moisture state (dry and wet) on the detachment of different-sized particles (0.20–0.50 and 0.50–2.00 mm, respectively) were also tested. Factorial analysis of variance showed that shear and compressive stress components evaluated by horizontal and vertical kinetic energy flux terms (KE_x and KE_y, respectively, in J m⁻² s⁻¹) along with their vector sum (KE_r, in J m⁻² s⁻¹) explained the variation in D. Neither sand size nor sand moisture was statistically significant alone although binary interactions of KE_r, KE_x and KE_y with the sand size and three-way interaction of KE_x, sand size and moisture were statistically significant. These results can be explained by size-dependent variation in sand compressibility and surface friction related to the total stress field developed by a given partition of shear and compressive stresses of wind-driven oblique raindrops (KE_x/KE_y). Further analysis of the variation of the unit sand detachment rate (D_u = D/KE_r = g J⁻¹) with rain inclination (α, in degrees) better revealed the effect of WDR obliquity on D_u that further changed with sand size class and moisture state. Finally, the difference in the resulting stress field differentiable by the oblique raindrop trajectories of the experiment over sand surface significantly affected the non-cohesive particle detachment rates, to some extent interacted with size-dependent compressibility and interface shear strength of sand grains.     

Tectonometamorphic evolution of the Atbashi high‐P units (Kyrgyz CAOB,Tien Shan): Implications for the closure of the Turkestan Ocean and continental subduction–exhumation of the South Kazakh continental margin

The South Tien Shan (STS) belt results from the last collision event in the western Central Asian Orogenic Belt (CAOB). Understanding its formation is of prime importance in the general framework of the CAOB. The Atbashi Range preserves high‐P (HP) rocks along the STS suture, but still, its global metamorphic evolution remains poorly constrained. Several HP units have been identified: (a) a HP tectonic mélange including boudins of mafic eclogites in a sedimentary matrix, (b) a large (>100 km long) high‐P metasedimentary unit (HPMU) and (c) a lower blueschist facies accretionary prism. Raman Spectroscopy on carbonaceous material combined with phengite and chlorite multiequilibria and isochemical phase diagram modelling indicates that the HPMU recorded homogeneous P–T conditions of 23–25 kbar and 560–570°C along the whole unit. ⁴⁰Ar/³⁹Ar dating on phengite from the HPMU ranges between 328 and 319 Ma at regional scale. These ages are interpreted as (re‐) crystallization ages of phengite during T_max conditions at a pressure range of 20–25 kbar. Thermobarometry on samples from the HP tectonic mélange provides similar metamorphic peak conditions. Thermobarometry on the blueschist to lower greenschist facies accretionary prism indicates that it underwent P–T conditions of 5–6 kbar and 290–340°C, highlighting a 17–20 kbar pressure gap between the HPMU‐tectonic mélange units and the accretionary prism. Comparison with available geochronological data suggests a very short time span between the prograde path (340 Ma), HP metamorphic peak (330 Ma), the T_max (328–319 Ma) and the final exhumation of the HPMU (303–295 Ma). Extrusion of the HPMU, accommodated by a basal thrust and an upper detachment, was driven by buoyant forces from 70–75 km up to 60 km depth, which directly followed continental subduction and detachment of the HPMU. At crustal depths, extrusion was controlled by collisional tectonics up to shallow levels. Lithological homogeneity of the HPMU and its continental‐derived character from the North Tien Shan suggest this unit corresponds to the hyper‐extended continental margin of the Kazakh continent, subducted southward below the north continental active margin of the Tarim craton. Integration of the available geological data allows us to propose a general geodynamic scenario for Tien Shan during the Carboniferous with a combination of (a) N‐dipping subduction below the Kazakh margin of Middle Tien Shan until 390–340 Ma and (b) S‐dipping subduction of remaining Turkestan marginal basins between 340 and 320 Ma.