Using deuterated H3+ and other molecular species to understand the formation of stars and planets

The H3+ ion plays a key role in the chemistry of dense interstellar gas clouds where stars and planets are forming. The low temperatures and high extinctions of such clouds make direct observations of H3+ impossible, but lead to large abundances of H2D+ and D2H+ which are very useful probes of the early stages of star and planet formation. Maps of H2D+ and D2H+ pure rotational line emission toward star-forming regions show that the strong deuteration of H3+ is the result of near-complete molecular depletion of CNO-bearing molecules onto grain surfaces, which quickly disappears as cores warm up after stars have formed. In the warmer parts of interstellar gas clouds, H3+ transfers its proton to other neutrals such as CO and N2, leading to a rich ionic chemistry. The abundances of such species are useful tracers of physical conditions such as the radiation field and the electron fraction. Recent observations of HF line emission toward the Orion Bar imply a high electron fraction, and we suggest that observations of OH+ and H2O+ emission may be used to probe the electron density in the nuclei of external galaxies.Comment: Proceedings of the H3+ centennial symposium, to be published in RSPTA (editor: T. Oka

Universal Local symmetries and non-superposition in classical mechanics

In the Hilbert space formulation of classical mechanics (CM), pioneered by Koopman and von Neumann (KvN), there are potentially more observables that in the standard approach to CM. In this paper we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the KvN is extended to include the evolution of differential forms. Because of their non-invariance, those extra observables have to be removed. This removal makes the superposition of states in KvN, and as a consequence also in CM, impossible

The automation of next-to-leading order electroweak calculations

We present the key features relevant to the automated computation of all the leading- and next-to-leading order contributions to short-distance cross sections in a mixed-coupling expansion, with special emphasis on the first subleading NLO term in the QCD+EW scenario, commonly referred to as NLO EW corrections. We discuss, in particular, the FKS subtraction in the context of a mixed-coupling expansion; the extension of the FKS subtraction to processes that include final-state tagged particles, defined by means of fragmentation functions; and some properties of the complex mass scheme. We combine the present paper with the release of a new version of MadGraph5_aMC@NLO, capable of dealing with mixed-coupling expansions. We use the code to obtain illustrative inclusive and differential results for the 13-TeV LHC.Comment: 121 pages, 16 figure

Oxygen in dense interstellar gas - the oxygen abundance of the star forming core rho Oph A

Oxygen is the third most abundant element in the universe, but its chemistry in the interstellar medium is still not well understood. In order to critically examine the entire oxygen budget, we attempt here initially to estimate the abundance of atomic oxygen, O, in the only one region, where molecular oxygen, O2, has been detected to date. We analyse ISOCAM-CVF spectral image data toward rho Oph A to derive the temperatures and column densities of H2 at the locations of ISO-LWS observations of two [OI] 3P_J lines. The intensity ratios of the (J=1-2) 63um to (J=0-1) 145um lines largely exceed ten, attesting to the fact that these lines are optically thin. This is confirmed by radiative transfer calculations, making these lines suitable for abundance determinations. For that purpose, we calculate line strengths and compare them to the LWS observations. Excess [OI] emission is observed to be associated with the molecular outflow from VLA 1623. For this region, we determine the physical parameters, T and N(H2), from the CAM observations and the gas density, n(H2), is determined from the flux ratio of the [O I]63um and [O I]145um lines. For the oxygen abundance, our analysis leads to essentially three possibilities: (1) Extended low density gas with standard ISM O-abundance, (2) Compact high density gas with standard ISM O-abundance and (3) Extended high density gas with reduced oxygen abundance, [O/H] ~ 2E-5. As option (1) disregards valid [O I] 145um data, we do not find it very compelling; we favour option (3), as lower abundances are expected as a result of chemical cloud evolution, but we are not able to dismiss option (2) entirely. Observations at higher angular resolution than offered by the LWS are required to decide between these possibilities.Comment: Accepted for publication in A&

Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners

On the role of large cross-sectional deformations in the nonlinear analysis of composite thin-walled structures

The geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order theories are employed by using the Carrera unified formulation, which provides a tool to generate refined theories of structures in a systematic manner. In particular, beams and shell-like laminated composite structures are analyzed using a layerwise approach, according to which each layer has its own independent kinematics. Different stacking sequences are analyzed, to highlight the influence of the cross-ply angle on the static responses. The results show that the geometrical nonlinear effects play a crucial role, mainly when higher-order theories are utilized

Nonlinear Vibration Correlation and Buckling Analysis of Flat Plates and Shells

The employment of nondestructive techniques in aerospace industries is rising thanks to advances in technologies and analysis. This part of the aerospace testing industry is essential to design and validate the new structures’ methodology and safety. Therefore, robust and reliable nondestructive methods have been extensively studied for decades in order to reduce safety problems and maintenance cost. One of the most important and employed nondestructive methods to compute large-scale aerospace structures’ critical buckling load is the Vibration Correlation Technique (VCT). This methodology allows to obtain the buckling load and equivalent boundary conditions by interpolating the natural frequencies of the structures for progressively increasing loadings without considering instabilities. VCT has been successfully investigated and employed for many structures, but it is still under development for composite shell structures. The present work provides a numerical model for carrying out virtual VCT to predict the buckling load, to characterize the natural frequencies variation with progressive higher loadings, and to provide an efficient means for verifying the experimental VCT results. The proposed nonlinear methodology is based on the well-established Carrera Unified Formulation (CUF). CUF represents a hierarchical formulation in which the structural model’s order is considered the analysis’s input. According to CUF, any theory is degenerated into generalized kinematics and is compactly handled. By adopting this formulation, the nonlinear governing equations and the relative FE arrays of the two-dimensional (2D) theories are written in terms of Fundamental Nuclei (FNs). FNs represent the basic building blocks of the proposed formulation. In order to investigate far nonlinear regimes, the full Green-Lagrange strain tensor is considered. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. For an assessment of the robustness of the virtual VCT, several flat plate and shell structures are studied and compared with the solutions found in the available VCT literature. The results prove that the proposed approach provides results with an excellent correlation with the experimental ones, allowing to investigate the buckling load and the natural frequencies variation in the nonlinear regime with high reliability