Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks

This paper deals with the computation of sectional curvature for the manifolds of $N$ landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the group action of diffeomorphisms. The inverse of the metric tensor for these manifolds (i.e. the cometric), when written in coordinates, is such that each of its elements depends on at most 2D of the ND coordinates. This makes the matrices of partial derivatives of the cometric very sparse in nature, thus suggesting solving the highly non-trivial problem of developing a formula that expresses sectional curvature in terms of the cometric and its first and second partial derivatives (we call this Mario's formula). We apply such formula to the manifolds of landmarks and in particular we fully explore the case of geodesics on which only two points have non-zero momenta and compute the sectional curvatures of 2-planes spanned by the tangents to such geodesics. The latter example gives insight to the geometry of the full manifolds of landmarks.Comment: 30 pages, revised version, typos correcte

CVD nano-coating of carbon composites for space materials atomic oxygen shielding

The present work analyzes the possibility to employ carbon nanostructures as a basic material to prevent the erosion effects of atomic oxygen suffered by the carbon fiber reinforced polymeric material used in low earth orbit space environment. The application of thin protecting coatings to base materials is a widely used method for preventing the atomic oxygen induced erosion, and thus degradation. The generic purpose is to integrate carbon nanostructures onto carbon composites surface in order to develop the basic substrate of advanced nanocomposite for atomic oxygen protection. The final goal is the characterization of carbon nanostructures-reinforced carbon composites by means of on-ground atomic oxygen simulation facility, with the future objective to assess and optimize the process of carbon-multiscale advanced composites production. With such an aim, a wide investigation on the methane chemical vapor deposition (CVD) over catalyzed carbon fiber-based substrates has been carried out. The as grown nanostructures have been analyzed in terms of morphology, as well as regarding the main features of the resulting growth (yield, purity, homogeneity, coating uniformity, etc.) and the influence of the deposition route operating parameters (catalyst typology, gas flowing rate, growth time/temperature, etc.). A high degree of reproducibility in terms of the relationship between the carbon deposit type/yield and the main process variables (catalyst and protocol) has been thus obtained. Finally, atomic oxygen ground tests have been conducted in order to evaluate the coating process effectiveness. The on-ground test in atomic oxygen environment, with respect to the performances of the reference carbon composites (in terms of total mass loss and atomic oxygen rate of erosion), showed a worsening for the disordered carbon deposit, while an intriguing improvement was achieved by the high-yield carbon nano-filaments deposition

A new advanced railgun system for debris impact study

The growing quantity of debris in Earth orbit poses a danger to users of the orbital environment, such as spacecraft. It also increases the risk that humans or manmade structures could be impacted when objects reenter Earth's atmosphere. During the design of a spacecraft, a requirement may be specified for the surviv-ability of the spacecraft against Meteoroid / Orbital Debris (M/OD) impacts throughout the mission; further-more, the structure of a spacecraft is designed to insure its integrity during the launch and, if it is reusable, during descent, re-entry and landing. In addition, the structure has to provide required stiffness in order to allow for exact positioning of experiments and antennas, and it has to protect the payload against the space environment. In order to decrease the probability of spacecraft failure caused by M/OD, space maneuver is needed to avoid M/OD if the M/OD has dimensions larger than 10cm, but for M/OD with dimensions less than 1cm M/OD shields are needed for spacecrafts. It is therefore necessary to determine the impact-related failure mechanisms and associated ballistic limit equations (BLEs) for typical spacecraft components and subsys-tems. The methods that are used to obtain the ballistic limit equations are numerical simulations and la-borato-ry experiments. In order to perform an high energy ballistic characterization of layered structures, a new ad-vanced electromagnetic accelerator, called railgun, has been assembled and tuned. A railgun is an electrically powered electromagnetic projectile launcher. Such device is made up of a pair of parallel conducting rails, which a sliding metallic armature is accelerated along by the electromagnetic effect (Lorentz force) of a cur-rent that flows down one rail, into the armature and then back along the other rail, thanks to a high power pulse given by a bank of capacitors. A tunable power supplier is used to set the capacitors charging voltage at the desired level: in this way the Rail Gun energy can be tuned as a function of the desired bullet velocity. This facility is able to analyze both low and high velocity impacts. A numerical simulation is also performed by using the Ansys Autodyn code in order to analyze the damage. The experimental results and numerical simulations show that the railgun-device is a good candidate to perform impact testing of materials in the space debris energy range

Fully Configurable Electromagnetic Wave Absorbers by Using Carbon Nanostructures

The configurable electromagnetic wave absorber (CEMA) defines a new method for the full design of layered carbon-based nanocomposites able to quasi-perfectly reproduce any kind of EM reflection coefficient (RC) profile. The method involves three main factors: (a) nanofillers-like carbon nanotube (CNT), carbon nanofiber (CNF), graphene nanoplatelet (GNP), and polyaniline (PANI) in different concentration versus the matrix; (b) the dielectric parameters of the nanoreinforced materials in the microwave range 2–18 GHz; (c) a numerical technique based on particle swarm optimization (PSO) algorithm within the MATLAB code of the EM propagation engine. Output is the layering of the wave absorber, that is, number of layers and material/thickness of each layer and the reflection/transmission simulated profiles. The frequency selective behavior is due to the multilayered composition, thanks to the direct/reflected wave combination tuning at interfaces. The dielectric characterization of the employed nanocomposites is presented in details: these materials constitute the database for the optimization code running toward the multilayer optimal solution. A FEM analysis is further proposed to highlight the EM propagation within the material’s bulk at different frequencies. The mathematical model of layered materials, the PSO objective function used for RC target fitting, and some results are reported in the text

Impact Response of Nanofluid-Reinforced Antiballistic Kevlar Fabrics

In this chapter the possibility to increase the resistance upon ballistic impact of typical Kevlar-based materials by means of silica nanofluids is investigated. Nanofluids are commonly known to have non-newtonian behavior, also indicated as shear thickening fluid (STF) property. STFs are very deformable materials in ordinary conditions (flowing like a liquid as long as no force is applied), but they turn into a very rigid solid-like material at high shear rates. The nanofluid optimization, mainly regarding its chemical and thermal stability, as well as the STF/fabric chemical coupling are crucial issues to tackle, in order to suitably exploit the STF property, i.e. to increase the fabric resistance upon impact. The present work summarizes some experimental results obtained on this subject. In particular, different kind of nanofluids realized by including several percentages of silica nanoparticles within polyethylene glycol are analyzed in terms of their morphological and rheological properties. Later on, the treatment with nanofluids of different typologies of Kevlar materials and the test panels manufacturing is described. Finally, the results of the ballistic characterization of the panels is presented and widely discussed. This latter is performed by means of an in-house built electromagnetic Coil Gun, able to explore a relatively large range of bullet velocity (up to 90m/s) with excellent precision and high degree of test reproducibility. The preliminary results obtained in such energy range show that STF impregnated fabrics have better penetration resistance compared to neat Kevlar, without affecting the fabric flexibility and, mainly, without overweighting the whole panel. That indicates that the addition of STFs to conventional ballistic fabrics enhance the material performances, thus suggesting further investigations in order to make such nanoreinforced materials effective for ballistic application

Different adaptation strategies of two citrus scion/rootstock combinations in response to drought stress

Scion/rootstock interaction is important for plant development and for breeding programs. In this context, polyploid rootstocks presented several advantages, mainly in relation to biotic and abiotic stresses. Here we analyzed the response to drought of two different scion/rootstock combinations presenting different polyploidy: the diploid (2x) and autotetraploid (4x) Rangpur lime (Citrus limonia, Osbeck) rootstocks grafted with 2x Valencia Delta sweet orange (Citrus sinensis) scions, named V/2xRL and V/4xRL, respectively. Based on previous gene expression data, we developed an interactomic approach to identify proteins involved in V/2xRL and V/4xRL response to drought. A main interactomic network containing 3,830 nodes and 97,652 edges was built from V/2xRL and V/4xRL data. Exclusive proteins of the V/2xRL and V/4xRL networks (2,056 and 1,001, respectively), as well as common to both networks (773) were identified. Functional clusters were obtained and two models of drought stress response for the V/2xRL and V/4xRL genotypes were designed. Even if the V/2xRL plant implement some tolerance mechanisms, the global plant response to drought was rapid and quickly exhaustive resulting in a general tendency to dehydration avoidance, which presented some advantage in short and strong drought stress conditions, but which, in long terms, does not allow the plant survival. At the contrary, the V/4xRL plants presented a response which strong impacts on development but that present some advantages in case of prolonged drought. Finally, some specific proteins, which presented high centrality on interactomic analysis were identified as good candidates for subsequent functional analysis of citrus genes related to drought response, as well as be good markers of one or another physiological mechanism implemented by the plants. (Résumé d'auteur