A Geometric Interpretation of Integrable Motions

Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where Newtonian motions are seen as geodesics of suitable -mechanical- manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N = 2 Toda model, and for a modified Hénon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.     

Detrital geochronology of unroofing magmatic complexes and the slow erosion of Oligocene volcanoes in the Alps

Tectonic reconstructions and quantitative models of landscape evolution are increasingly based on detailed analysis of detrital systems. Since the definition of closure temperature in the 1960s, mineral ages of low-temperature geochronometers are traditionally interpreted as the result of cooling induced by erosion, whose rate is a simple, unique function of age patterns. Such an approach can lead to infer paradoxically high erosion rates that conflict with compelling geological evidence from sediment thickness in basins. This indicates that tectonic and landscape models that solely interpret mineral ages as due to cooling during exhumation may not be valid.Here we propose a new approach that takes into account the effects of both crystallization and exhumational cooling on geochronometers, from U–Pb on zircon to fission tracks on apatite. We first model the mechanical erosion of an unroofing magmatic complex and the resulting accumulation and burial of the eroded units in reverse order in the basin. Detrital mineral ages follow a regular pattern downsection. Some mineral ages, such as e.g. U–Pb ages of zircons, cluster around the “magmatic age”, i.e. the crystallization of the magma. Its value is constant along the stratigraphic column in the sedimentary basin; we refer to this behavior as “stationary age peak”. Some other mineral ages, such as e.g. apatite fission-track ages, are often younger than the magmatic age. When they vary smoothly with depth, they define a “moving age peak”, which is the only possible effect of undisturbed cooling during overburden removal, and can therefore be used to calculate an erosion rate.The predictions of our model were tested in detail on the extremely well-studied Bregaglia (Bergell) orogenic pluton in the Alps, and on the sedimentary succession derived from its erosion, the Gonfolite Group. The consistency between predicted and observed age patterns validates the model. Our results resolve a long-standing paradox in quantitative modelling of erosion–sedimentation, namely the scarcity of sediment during apparently fast erosion. Starved basins are the observational baseline, and modelling must be tuned to include a correct analysis of detrital mineral geochronology in order to reconcile perceived discrepancies between stratigraphical and geochronological information. In addition, our data demonstrate that volcanoes were active on top of the growing Oligocene Alps.This study illustrates rigorous criteria for detrital mineral geochronology that are applicable to any geological setting, including magmatic arcs and collision orogens, and provides fundamental interpretive keys to solve complex puzzles and apparent paradoxes in geological reconstructions.     

Distinction between amorphous and healed planar deformation features in shocked quartz using composite color scanning electron microscope cathodoluminescence (SEM‐CL) imaging

Planar deformation features (PDFs) in quartz are one of the most reliable and most widely used forms of evidence for hypervelocity impact. PDFs can be identified in scanning electron microscope cathodoluminescence (SEM‐CL) images, but not all PDFs show the same CL behavior: there are nonluminescent and red luminescent PDFs. This study aims to explain the origin of the different CL emissions in PDFs. Focused ion beam (FIB) thin foils were prepared of specific sample locations selected in composite color SEM‐CL images and were analyzed in a transmission electron microscope (TEM). The FIB preparation technique allowed a direct, often one‐to‐one correlation between the CL images and the defect structure observed in TEM. This correlation shows that composite color SEM‐CL imaging allows distinction between amorphous PDFs on one hand and healed PDFs and basal Brazil twins on the other: nonluminescent PDFs are amorphous, while healed PDFs and basal Brazil twins are red luminescent, with a dominant emission peak at 650 nm. We suggest that the red luminescence is the result of preferential beam damage along dislocations, fluid inclusions, and twin boundaries. Furthermore, a high‐pressure phase (possibly stishovite) in PDFs can be detected in color SEM‐CL images by its blue luminescence.     

Thermal inertia of main belt asteroids smaller than 100 km from IRAS data

Recent works have shown that the thermal inertia of km-sized near-Earth asteroids (NEAs) is more than 2 orders of magnitude higher than that of main belt asteroids (MBAs) with sizes (diameters) between 200 and 1000 km. This confirms the idea that large MBAs, over hundreds millions of years, have developed a fine and thick thermally insulating regolith layer, responsible for the low values of their thermal inertia, whereas km-sized asteroids, having collisional lifetimes of only some millions years, have less regolith, and consequently a larger surface thermal inertia.Because it is believed that regolith on asteroids forms as a result of impact processes, a better knowledge of asteroid thermal inertia and its correlation with size, taxonomic type, and density can be used as an important constraint for modeling of impact processes on asteroids. However, our knowledge of asteroids’ thermal inertia values is still based on few data points with NEAs covering the size range 0.1-20 km and MBAs that .Here, we use IRAS infrared measurements to estimate the thermal inertia values of MBAs with diameters and known shapes and spin vector, filling an important size gap between the largest MBAs and the km-sized NEAs. An update to the inverse correlation between thermal inertia and diameter is presented. For some asteroids thermophysical modeling allowed us to discriminate between the two still possible spin vector solutions derived from optical lightcurve inversion. This is important for (720) Bohlinia: our preferred solution was predicted to be the correct one by Vokrouhlický et al. [2003. The vector alignments of asteroid spins by thermal torques. Nature 425, 147-151] just on theoretical grounds.     

Comparison of the fish assemblages associated with Posidonia oceanica after the partial loss and consequent fragmentation of the meadow

An extensive Posidonia oceanica meadow was partially destroyed by excavation, resulting in areas of seagrass habitat of equal complexity (shoot density) but different heterogeneity (degree of fragmentation). The fish assemblages associated with differently fragmented beds were compared from a landscape perspective. Differences in the fish assemblages were detected, with several species showing different patterns: (1) species that increased their abundance along with the degree of bed fragmentation, (2) species that were more abundant in fragmented beds, but did not show differences between more or less fragmented beds, and (3) species that were mostly abundant in large seagrass patches or in the continuous meadow. The fish assemblages were also affected by depth, but further research is needed to determine properly this effect. Some ecological mechanisms are suggested to operate in the interaction between P. oceanica and the held fish assemblage.     

A physical analogue model to analyse interactions between tensile stresses and dissolution in carbonate slopes

A physical analogue model was developed to analyse the relationship between tensional states in rock masses, seepage and karst processes. Use was made of an experimental apparatus consisting of two hydraulic circuits realized by drilling two holes into each of two blocks of sampled limestone from the central Apennines (Italy). A static load (208.85 kg) was applied to one of the blocks in order to elicit tensile stresses within it. Physical and chemical monitoring data showed that the main process involved was temperature-dependent CaCO₃ dissolution. This process was more marked in the loaded block circuit, as Ca⁺⁺ concentration in circulated water reached 54 mg/L, whereas only 28 mg/L was reached in the unloaded one. The interaction between load and dissolution caused the observed opening of microcracks, as confirmed by further increase of water loss and by dilution in the loaded block circuit, resulting in a decrease of Ca⁺⁺ concentration. These findings were confirmed by recording additional water losses after increasing the load up to 445.05 kg. A finite difference numerical model showed that tensile stresses (max 20 kPa) within the loaded block were clustered at the intersection of the main joints with the flowpaths, thus representing points of preferential and accelerated dissolution.This study is part of a research project on analogical and numerical modelling for geological risk mitigation being conducted at CERI, Research Centre for Geological Risks of the University of Rome “La Sapienza” (Valmontone, Roma, Italy; http://www.ceri@uniroma1.it).     

Indentation of a continent with a built-in thickness change: experiment and nature

Orogens oblique to the direction of plate convergence are currently attributed to obliquity between the margins of one or both of the sutured continents to their direction convergence. We use a single analogue experiment and natural examples to illustrate a potential additional factor: variations in strength of the indented continent at a high angle to the convergence direction. The wavelengths of structures in laterally shortened lithosphere depend on the strength of the most competent layers. Lateral variations in crustal thickness must therefore lead to structures oblique to any applied lateral compression.

An analogue experiment was performed to explore this phenomenon. A two-layer ‘indented continent’ was modelled by a brittle upper crust of sand above a lower crust of high-viscosity polymer floating on a single layer of low-viscosity syrup representing the mantle. The well-known strike-slip structures allowing lateral escape to distant weak boundaries were hindered by lateral boundaries in front of the indenter. This allowed us to focus on the effects of a thickness change built into the ‘indented continent’ along a zone parallel to the direction in which a vertical rigid wall advancing at a steady rate represented the indenter. Vertical escape led to an ‘orogenic belt’ oblique to the advancing wall; this obliquity influences subsequent lateral escape. Model scaling and interpretations are based on Extended Thin Sheet Approximation (ETSA) and standard theories of faulting.

Four sectors of the Alpine–Himalayan orogen (Iran, Tunisia, the Eastern Alps and the Himalaya) are oblique to the continental convergence direction, and we point to thickness changes at high angles to the suture that may account for this geometry. As crustal thicknesses north of oblique sectors of the Himalayas are not yet known, we speculate on them.

We infer from the main difference between our experiment and all our examples chosen from nature that vertical orogenic escape was oblique to our model suture but can be parallel to natural sutures.