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.     

Elucidation of different forms of organic carbon in marine sediments from the Atlantic coast of Spain using thermal analysis coupled to isotope ratio and quadrupole mass spectrometry

Analysis of river, estuary and marine sediments from the Atlantic coast of Spain using thermogravimetry–differential scanning calorimetry–quadrupole mass spectrometry–isotope ratio mass spectrometry (TG–DSC–QMS–IRMS) was used to (a) distinguish bulk chemical hosts for C within a sediment and humic acid fraction, (b) track C pools with differing natural C isotope ratios and (c) observe variation with distance from the coast. This is the first application of such a novel method to the characterisation of organic matter from marine sediments and their corresponding humic acid fractions. Using thermal analysis, a labile, a recalcitrant and a refractory carbon pool can be distinguished. Extracted humic fractions are mainly of recalcitrant nature. The proportion of refractory carbon is greatest in marine sediments and humic acid fractions. Quadrupole mass spectrometry confirmed that the greatest proportion of m/z 44 (CO₂) and m/z 18 (H₂O) were detected at temperatures associated with recalcitrant carbon (510–540 °C). Isotope analysis detected progressive enrichment in δ¹³C for the sediment samples with an increase in marine influence. Isotopic heterogeneity in the refractory organic matter in marine sediments could be due to products of anthropogenic origin or natural combustion products. Isotope homogeneity of humic acids confirms the presence of terrigenous C in marine sediments, allowing the terrestrial input to be characterised.     

HP–LT Variscan metamorphism in the Cubito-Moura schists (Ossa-Morena Zone, southern Iberia)

Multi-equilibrium thermobarometry shows that low-grade metapelites (Cubito-Moura schists) from the Ossa–Morena Zone underwent HP–LT metamorphism from 340–370 °C at 1.0–0.9 GPa to 400–450 °C at 0.8–0.7 GPa. These HP–LT equilibriums were reached by parageneses including white K mica, chlorite and chloritoid, which define the earliest schistosity (S₁) in these rocks. The main foliation in the schists is a crenulation cleavage (S₂), which developed during decompression from 0.8–0.7 to 0.4–0.3 GPa at increasing temperatures from 400–450 °C to 440–465 °C. Fe³⁺ in chlorite decreased greatly during prograde metamorphism from molar fractions of 0.4 determined in syn-S₁ chlorites down to 0.1 in syn-S₂ chlorites. These new data add to previous findings of eclogites in the Moura schists indicating that a pile of allochtonous rocks situated next to the Beja-Acebuches oceanic amphibolites underwent HP–LT metamorphism during the Variscan orogeny. To cite this article: G. Booth-Rea et al., C. R. Geoscience 338 (2006).     

Late Pleistocene highstand and recession of a small, high-altitude pluvial lake, Jakes Valley, central Great Basin, USA

Models of factors controlling late Pleistocene pluvial lake-level fluctuations in the Great Basin are evaluated by dating lake levels in Jakes Valley. “Jakes Lake” rose to a highstand at 13,870 ± 50 ¹⁴C Yr B.P., receded to a stillstand at 12,440 ± 50 ¹⁴C yr B.P., and receded steadily to desiccation thereafter. The Jakes Lake highstand is roughly coincident with highstands of lakes Bonneville, Lahontan and Russell. The rise to highstand and recession of Jakes Lake were most likely controlled by a storm track steered by the polar jet stream. The final stillstand of Jakes Lake helps constrain timing of northward retreat of the polar jet stream during the Pleistocene-Holocene transition.     

Rodent paleofaunas as indicators of climatic change in Europe during the last 125,000 years

This paper presents a quantitative reconstruction of the European late Pleistocene paleoclimate based on 72 rodent assemblages of five sequences from France, Germany and Bulgaria, covering the last interglacial-glacial cycle. They show a pattern of severe changes in temperature, with reduced precipitation during the coldest periods. A tentative correlation between the isotopic and palynological records and the paleotemperature changes is shown. These changes are consistent with variations in atmospheric circulation patterns in response to an expanding-retracting Fennoscandian ice-sheet. They can be attributed to the enhancement-weakening of the Scandinavian-Polar anticyclone and its associated dry winds, the south-north shifting of the North Atlantic Polar Front, and the varying supply of moist air from the Atlantic. Qualitative paleoenvironmental analysis shows broadleaved-deciduous forests in France and Bulgaria during most of the studied period. Taiga and tundra appeared in eastern France during the lower Würm. The German sequence indicates the presence of coniferous forests. These results are broadly consistent with other paleobiological records (mammalian, avian and insect faunas, isotopic record in dental tissue, palynology). The main discrepancies with the paleoclimate inferred from the palynological record are found during the coldest periods and are probably due to the interaction between vegetation, climate, and atmospheric CO₂ levels.     

U–Pb evidence for a polyorogenic evolution of the HP–HT units of the NW Iberian Massif

. A isotope dilution thermal ionisation mass spectrometry U-Pb geochronological study was carried out on the high-pressure and high-temperature units (HP-HT units) overlying the oceanic suture in the Allochthonous Complexes of the NW Iberian Variscan Belt. The rocks investigated are seven granulite- to eclogite-facies paragneisses and one leucosome within mafic high-pressure granulites in the Ordenes and Cabo Ortegal Complexes of NW Spain. U-Pb dating of zircon, monazite, titanite and rutile reveal the presence of a pervasive Early Ordovician metamorphic event at ca. 500-480 Ma and a later Early Devonian event at ca. 400-380 Ma. The U-Pb ages, in conjunction with petrological and structural data, indicate that the high-pressure event recorded by these rocks is Early Ordovician in age. Monazite ages in the paragneisses suggest that peak metamorphic conditions were reached at ca. 500-485 Ma. Subsequently, the rock ensemble underwent exhumation accompanied by partial melting and zircon growth at ca. 485-470 Ma. Melting of mafic granulites was coeval with this latter episode as indicated by zircon crystallisation age in the leucosomes dated at ca. 486 Ma. Based on these data and on the general features of magmatism and metamorphic evolution, it is proposed that this process took place at a convergent plate boundary within a peri-Gondwanan oceanic domain. Monazite, titanite and rutile data in some of the samples studied show evidence of a second metamorphic episode that took place between ca. 400 and 380 Ma (with a peak at ca. 390-385 Ma). This Early Devonian event, at variance with the previous one, was not pervasive, but, rather, was localised in areas of intense Variscan tectonothermal reworking. It is claimed that this later metamorphic event was recorded by the U-Pb system in areas where monazite and titanite growth was enhanced by fluid circulation in highly strained rocks (Variscan shear zones). According to previous structural studies and Ar-Ar dating of fabrics, this Early Devonian episode took place as the HP-HT units were deformed and thrusted upon the ophiolitic units in the early stages of the Variscan collision.     

Crystallization conditions of Los Angeles, a basaltic Martian meteorite

The texture of Los Angeles (stone 1) is dominated by relatively large (0.5−2.0 mm) anhedral to subhedral grains of pyroxene, and generally subhedral to euhedral shocked plagioclase feldspar (maskelynite). Minor phases include subhedral titanomagnetite and ilmenite, Fe-rich olivine, olivine+augite-dominated symplectites [some of which include a Si-rich phase and some which do not], pyrrhotite, phosphate(s), and an impact shock-related alkali- and silica-rich glass closely associated with anhedral to euhedral silica grains. Observations and model calculations indicate that the initial crystallization of Mg-rich pigeonitic pyroxenes at ≤1150 °C, probably concomitantly with plagioclase, was followed by pigeonitic and augitic compositions between 1100 and 1050 °C whereas between 1050 and 920 to 905 °C pyroxene of single composition crystallized. Below 920 to 905 °C, single composition Fe-rich clinopyroxene exsolved to augite and pigeonite. Initial appearance of titanomagnetite probably occurred near 990 °C and FMQ-1.5 whereas at and below 990 °C and ≥FMQ-1.5 titanomagnetite and single composition Fe-rich clinopyroxene may have started to react, producing ilmenite and olivine. However, judging from the most common titanomagnetite compositions, we infer that most of this reaction likely occurred between 950 and 900 °C at FMQ-1.0±0.2 and nearly simultaneously with pyroxene exsolution, thus producing assemblages of pigeonite, titanomagnetite, olivine, ilmenite, and augite. We deem this reaction as the most plausible explanation for the formation of the olivine+augite-dominated symplectites in Los Angeles. But we cannot preclude possible contributions to the symplectites from the shock-related alkali- and silica-rich glass or shocked plagioclase, and the breakdown of Fe-rich pigeonite compositions to olivine+augite+silica below 900 °C. Reactions between Fe-Ti oxides and silicate minerals in Los Angeles and other similar basaltic Martian meteorites can control the T-fO₂ equilibration path during cooling, which may better explain the relative differences in fO₂ among the basaltic Martian meteorites.     

Spatial and temporal variation of the nekton and hyperbenthos from a temperate European estuary with regulated freshwater inflow

The aquatic macrofauna of the Guadalquivir estuary were sampled (1 mm mesh persiana net) at 5 sampling sites located along the entire (except the tidal freshwater region) estuarine gradient of salinity (outer 50 km). A total of 134 fish and macroinvertebrate species was collected but only 62 were considered common or regularly present in the estuary. Univariate measures of the community structure showed statistically significant differences among sampling sites: species richness, abundance, and biomass decreased in the upstream direction, being positively correlated with the salinity. Temporal differences of these three variables were also statistically significant. While a clear seasonal pattern (minimum densities in winter and maximum in spring-summer) was observed for abundance and biomass, no such pattern existed for the number of species. Mysids was the most dominant group throughout the estuary (96% to 99% of abundance; 49% to 85% of biomass), although fish biomass was also important at the outer estuary (36% to 38%). Multivariate analyses indicated highly significant spatial variation in the macrofaunal communities observed along the salinity gradient. These analyses suggest that the underlying structure was a continuum with more or less overlapping distributions of the species dependent on their ability to tolerate different physicochemical conditions. There were also significant temporal (intermonthly + interannual) variation of the estuarine community; the relative multivariate dispersion indicated that monthly variation was more considerable (relative multivariate dispersion >1) at the outer part of the estuary during the wet year (last 20 km) and was higher in the inner stations during the dry year (32 to 50 km from the river mouth). Since a clear negative exponential relationship was observed between the freshwater input (from a dam located 110 km upstream) and water salinity at all sampling stations, it is concluded that the human freshwater management is probably affecting the studied estuarine communities. While the higher seasonal (long-term) stability of the salinity gradient, due to the human control of the freshwater input, may facilitate the recruitment of marine species juveniles during the meteorologically unstable early-spring, the additional (short-term) salinity fluctuations during the warm period may negatively affect species that complete their lifecycle within the estuary.     

Sub-wavebase cross-bedded grainstones on a distally steepened carbonate ramp, Upper Miocene, Menorca, Spain

Cross‐bedded grainstones on carbonate ramps and shelves are commonly related to the locus of major wave energy absorption such as shorelines, shoals or shelf breaks. In contrast, on the Early Tortonian carbonate platform of Menorca (Balearic Islands), coarse‐grained, cross‐bedded grainstones are found at a distance from the palaeoshoreline where they were deposited below the wavebase. Excellent exposures along continuous outcrops on the sea cliffs of Menorca reveal the depositional profile and three‐dimensional distribution of the different facies belts of the Tortonian ramp depositional system. Basinward from the palaeoshoreline, fan deltas and beach deposits pass into 5‐km‐wide gently dipping bioturbated dolopackstone (inner and middle ramp), then into 12–20°‐dipping dolograinstone/rudstone clinobeds (ramp slope) and, finally, into subhorizontal fine‐grained basinal dolowackestone to dolopackstone (outer ramp). In this Miocene example, coarse‐grained grainstones exist in five different settings other than beach deposits: (1) on the middle ramp, where cross‐bedded grainstones were deposited by currents roughly parallel to the shoreline at 40–70 m estimated water depth and are interbedded with gently dipping bioturbated dolomitized packstones; (2) on the upper slope, where clinobeds are composed mostly of in situ rhodoliths and red‐algae fragments; (3) on the lower slope, as small‐scale bedforms (small three‐dimensional subaqueous dunes) migrating parallel to the slope; (4) at the transition between the lower slope and the outer ramp, where mollusc‐rich and rhodolithic rudstones and grainstones, interbedded in dolomitized laminated wackestones containing abundant planktonic foraminifera, infill slide/slump scars as upslope‐backstepping bodies (backsets); (5) at the toe of the slope, where coarse skeletal grainstones indicate bedform migration parallel to the platform margin, induced by currents at more than 150 m estimated water depth. This Late Miocene example also illustrates how changes in intrabasinal environmental conditions (nutrients and/or temperature) may produce changes in stratal patterns and facies architecture if they affect the biological system. Two depositional sequences compose the Miocene platform on Menorca, where a reef‐rimmed platform prograded onto an earlier distally steepened ramp. The transition from the ramp to the reef‐rimmed platform was effected by an increase in accommodation space caused by ecological changes, promoting a shift from a grain‐ to a framework‐producing biota.