Nekhoroshev estimate for isochronous non resonant symplectic maps

We prove that non resonant isochronous symplectic maps in a neighborhood of an elliptic fixed point are stable for exponentially long times with the inverse of the distance from the fixed point. In the proof we make use of the majorant series method together with an idea for optimizing remainder estimates first applied to Hamiltonian problems by Nekhoroshev.     

An Innovative Approach to Meteorite Analysis by Laser‐Induced Breakdown Spectroscopy

An innovative approach of double pulse laser‐induced breakdown spectroscopy (DP‐LIBS) coupled with optical microscopy was applied to the characterisation and quantitative analysis of the Agoudal iron meteorite in bulk sample and in petrographic thin section. Qualitative analysis identified the elements Ca, Co, Fe, Ga, Li and Ni in the thin section and the whole meteorite. Two different methods, calibration‐free LIBS and one‐point calibration LIBS, were used as complementary methodologies for quantitative LIBS analysis. The elemental composition data obtained by LIBS were in good agreement with the compositional analyses obtained by traditional methods generally applied for the analysis of meteorites, such as ICP‐MS and EDS‐SEM. Besides the recognised advantages of LIBS over traditional techniques, including versatility, minimal destructivity, lack of waste production, low operating costs, rapidity of analysis, availability of transportable or portable systems, etc., additional advantages of this technique in the analysis of meteorites are precision and accuracy, sensitivity to low atomic number elements such as Li and the capacity to detect and quantify Co contents that cannot be obtained by EDS‐SEM.     

Constraints from geochemistry and Sr–Nd isotopes for the origin of albitite deposits from Central Sardinia (Italy)

Major- and trace-element contents and Sr–Nd isotope ratios were determined in albitite, albitized and unaltered late-Variscan granitoid samples from the world-class Na-feldspar deposits of central Sardinia, Italy. The albite deposit of high economic grade has geological, textural, and chemical features typical of metasomatic alteration affecting the host granitoids. Albitization, locally accompanied by chloritization and epidotization, was characterized by strong leaching of Mg, Fe, K, and geochemically similar trace elements, and by a significant increase of Na. Ca, and P were moderately leached in the most metasomatized rocks. Other major (Si, Ti, Ca) and trace elements (U, Th, Y, and Zr), along with light (LREE) and middle (MREE) rare-earth elements, behaved essentially immobile at the deposit scale. The Nd-isotope ratios (0.512098 to 0.512248) do not provide information on the emplacement age of the unaltered late-Variscan granitoids. On the other hand, their Sr-isotope ratios fit an errorchron of 274±29 Ma (1σ error), in fair agreement with all published ages of Sardinian Variscan granitoids. The very low Rb content of albitized rocks precludes application of the Rb–Sr radiometric system to determine the age of albitization. The Sm–Nd system is not applicable either, because the ¹⁴³Nd/¹⁴⁴Nd ratios of albitized rocks and unaltered granitoids overlap. The overlap confirms that Sm and Nd were substantially immobile during albitization. On the other hand, the measured ⁸⁷Sr/⁸⁶Sr ratios of the albitized rocks are appreciably lower than those of the unaltered host granitoids, whereas, their initial Sr-isotope ratios are higher. This seems to suggest that a) albitization was induced by non-magmatic fluids rich in radiogenic Sr, and b) albitization occurred shortly after the granitoid emplacement. This conclusion is supported by Nd isotopes, because unaltered granitoids and albitites fit the same reference isochron at 274 Ma. The fluids acquired radiogenic Sr by circulation through the Lower Paleozoic metasedimentary basement. Specifically, it is estimated that Sr supplied by the non-carbonatic basement represents about 22 wt% of total Sr in albitite.     

Temperature,fluid content and rheology of localized ductile shear zones in subsolidus cooling plutons

Temperature and fluid content are critical parameters that control rock rheology and strain localization in the continental crust. Here, we determine by thermodynamic modelling the of localized ductile shearing during cooling of three different granitoid plutons: the Rieserferner and the Adamello plutons in the Italian Alps, and the Lake Edison pluton in the Sierra Nevada—USA. Shear zones exploited precursor joints, associated veins and alteration zones. and P−T phase diagram sections were computed with Perple_X in the system MnO−Na₂O−CaO −K₂O−FeO−MgO−Al₂O₃−SiO₂−H₂O−Fe₂O₃. The phase diagram sections show that the nucleation of the brittle precursors (joints, veins) occurred at T» 450°C at fluid-saturated conditions. Localized ductile shearing likely occurred at temperature ranging between 420 and 460°C evolving from initially fluid-saturated to fluid-undersaturated conditions in a closed system. In this temperature range, granitoid rocks are potentially subject to a series of retrograde metamorphic reactions replacing the load-bearing feldspars with weaker phyllosilicates. Metamorphic reactions occurred in spatial association with the precursory structures, leading to localized shearing. Decreasing temperature and fluid-undersaturated conditions likely hampered progressive strain accommodation in shear zones by slowing down metamorphic reactions, thermally activated dislocation creep processes, fluid-mediated deformation mechanisms and weakening mechanisms. Polyphase granitoid ultramylonite and mylonitic quartz veins have been affected differently by the fluid-undersaturated conditions of the system, as consequence of different dominant deformation mechanisms and syn-kinematic paragenesis during localized shearing. Localized ductile shearing in cooling plutons effectively occurs in a limited temperature range (420–460°C) in which the strain accommodation capacity of the shear zone is controlled by the negative feedback between the cooling rate, the kinetics of metamorphic reactions and deformation mechanisms, and the consumption of the limited amount of available fluids.     

Mantle rheology: radial and lateral viscosity variations inferred from microphysical creep laws

Inferences on the rheology of the mantle based on theoretical and experimental rate equations for steady state creep are discussed and compared with results from geophysical models. The radial increase of viscosity by one to three orders of magnitude across the mantle, required by inversion of postglacial rebound and geodynamic data, is confirmed by microphysical models based on the estimation of continuous and discontinuous changes of creep parameters with depth. The upper mantle (viscosity 10²⁰–10²¹ Pa s) is likely to show non-Newtonian rheology (power-law creep) for average grain sizes larger than 0.1 mm as an order of magnitude. Given the variability of both grain size and stress conditions, local regions of linear rheology can be present. The rheology of transition zone and lower mantle (viscosity 10²²–10²⁴ Pa s) cannot be definitely resolved at present. Estimation of creep parameters leads to possible nonlinear or mixed rheology, if grain sizes are not lower than 0.1 mm and flow conditions can be approximated by a constant strain rate of about 10⁻¹⁵ s⁻¹. This conclusion can be modified by different flow conditions (e.g. a decrease in strain rate or constant viscous dissipation). Furthermore, experiments on fine-grained garnetites and perovskite analogues have shown that diffusion creep is predominant at laboratory conditions. However, the pressure dependence of creep in these phases is unknown, and therefore direct extrapolation to lower mantle conditions is necessarily speculative. Lateral variations of viscosity, largest in the upper and lowermost mantle (up to 2–4 orders of magnitude) are predicted by models based on lateral temperature anomalies derived from seismic tomographic models.     

Experimental models of extension of continental lithosphere weakened by percolation of asthenospheric melts

Analogue models are used to investigate extension of a continental lithosphere weakened by asthenospheric melts percolating through the upper mantle, a process that has been hypothesised to control the opening of the Ligurian Tethys. Models were performed in a centrifuge apparatus and reproduced, by using materials such as sand and viscous mixtures, extension of 60-km thick, three-layer continental lithosphere floating above the asthenosphere. The percolated lithospheric mantle was assumed to be characterised by a rheological behaviour similar to that of the asthenosphere. Two sets of experiments investigated the influence on deformation of (1) the thickness of the percolated mantle and the associated strength contrast between the normal and weakened lithosphere, and (2) the lateral width of the weakened zone. Model results suggest that mantle percolation by asthenospheric melts is able to promote strong localised thinning of the continental lithosphere, provided that a significant thickness of the lithospheric mantle is weakened by migrating melts within a narrow region. Strain localisation is maximised for percolation of the whole lithospheric mantle and strong strength contrast between the normal and weakened lithosphere. Under these conditions, the thickness of the lithosphere may be reduced to less than 12 km in 3 Ma of extension. Conversely, localised thinning is strongly reduced if the thickness of the percolated zone is ≤1/3 of the thickness of the whole lithospheric mantle and/or the lithosphere is weakened over wide regions. Overall, model results support the working hypothesis that mantle percolation by asthenospheric melts is a controlling factor in the transition from distributed continental deformation to localised oceanic spreading.     

Stresses and velocities in orogenic wedges with power-law rheology and linearly varying longitudinal strain rate

A two-dimensional analytical solution for stress, strain rate, and velocity is obtained for parallel-sided and wedge-shaped blocks with generalized viscous rheology (linearly viscous and power-law) deforming in plane strain. The main assumptions used in the derivation of the solution are that the material is incompressible, the longitudinal gradient in shear stress is much less than the vertical gradient of vertical normal stress, and the longitudinal strain rate varies linearly in the horizontal direction. Velocity boundary conditions are specified at the top of the block, and shear stress boundary conditions at the base of the block. In the one-dimensional case (where stress and strain rate do not vary in the longitudinal direction), the solution reduces to a well-known solution for the deformation of parallel-sided ice sheets [Nye, J. F. (1957) The distribution of stress and velocity in glaciers and ice sheets. Proceedings of the Royal Society of London A-239, 113–133]. The stress equilibrium for tapered wedges [Platt, J. P. (1986) Dynamics of orogenic wedges and the uplift of high-pressure metamorphic rocks. Geological Society of America Bulletin 97, 1037–1053] is a special case of the present stress solution. Implementation of the solution requires the subdivision of the wedge into vertical segments, and yields the tectonic normal and shear stresses that must be applied to the rear of a block with specified rheology in order to maintain a given longitudinal strain rate. The solution makes it possible to model deformation patterns analytically with longitudinally varying strain rate (including coeval compression and extension) and with vertical components of velocity reflecting the effects of underplating.     

Effects of clogging on stream macroinvertebrates: An experimental approach

The influence of streambed sediment clogging on macroinvertebrate communities was investigated in the Lemme creek (NW Italy). To assess how fine sediment accumulation can influence the colonisation process and community composition of macroinvertebrates, we placed 48 traps in the riverbed. The traps consisted of boxes built with metal net (mesh 1 cm, height 15 cm, sides 5 cm) covered with nylon net except for the apex, allowing access exclusively from the top. We created four trap types filled with 100% gravel, 30% sand and 70% gravel, 70% sand and 30% gravel and 100% sand. After 20 and 40 days, we removed 6 traps/type. Macroinvertebrates rapidly colonised the traps, as we found no significant community differences between the two removal dates. Among the four trap types, we found significant differences in taxa number and abundance, which both decreased with increasing clogging. Thus, our study supports the hypothesis that clogging and the accumulation of fine substratum elements strongly affects benthic stream communities.