Kinematic Expansion Research Articles

Vibration analysis of thermally loaded isotropic and composite beam and plate structures

This work proposed the use of the Carrera Unified Formulation (CUF) for the vibration and buckling analysis of structures subjected to thermal loads. In detail, the variation of natural frequencies for progressively large thermal loads is investigated. Here, particular attention is focused on the study of buckling thermal loads as degenerate cases of the vibration analysis and on the mode aberration caused by thermal stresses. From this standpoint, the use of CUF for the development of high-order beam and plate models is fundamental. Indeed, Lagrange-like (LE) polynomials are considered for developing the kinematic expansion and Layerwise (LW) theories are employed to characterize the complex phenomena that may appear in composite structures. A linearized formulation to study the natural frequencies variation as a function of the progressive increasing thermal loadings is adopted. Different isotropic and laminated composite structures have been analyzed and compared with the Abaqus solution to validate the presented methodology and provide some benchmark solutions. In addition, a parametric study was conducted to evaluate the stacking sequence and thickness effect in the vibration modes and thermal buckling loads. The results document the excellent accuracy and reliability of the presented methodology and show the potentialities of this numerical tool able to analyze cases that are difficult to study experimentally.

Generalized higher order layerwise theory for the dynamic study of anisotropic doubly -curved shells with a mapped geometry

An innovative generalized Layer-Wise (LW) approach is proposed for the modal analysis of anisotropic doubly-curved shells with an arbitrary shape by employing the Generalized Differential Quadrature (GDQ) method. The geometrical description of shell structures can be traced from both the differential geometry and mapping technique based on a proper definition of the blending functions.The kinematic field is described in each lamina by employing several interpolating polynomials in a generalized setting, while developing a LW theory that involves different orders of kinematic expansion. The Equivalent Single Layer (ESL) generalized formulation is, thus, derived as particular case of the LW theory. Angle-ply generally anisotropic laminated shells are here investigated, as well as layups with a thick foam softcore. Several numerical examples are illustrated, including different boundary conditions of the mapped geometry, different geometric curvatures for both unmapped and mapped paths, along with a variety of interpolating polynomials and expansion orders of the kinematic field. The accuracy of the proposed model is well-established by a comparative evaluation between our solutions in terms of frequencies and mode shapes and predictions based on classical 3D finite elements.

Revisiting the Cygnus OB associations

ABSTRACT OB associations play an important role in Galactic evolution, though their origins and dynamics remain poorly studied, with only a small number of systems analysed in detail. In this paper, we revisit the existence and membership of the Cygnus OB associations. We find that of the historical OB associations only Cyg OB2 and OB3 stand out as real groups. We search for new OB stars using a combination of photometry, astrometry, evolutionary models, and an SED-fitting process, identifying 4680 probable OB stars with a reliability of >90 per cent. From this sample, we search for OB associations using a new and flexible clustering technique, identifying six new OB associations. Two of these are similar to the associations Cyg OB2 and OB3, though the others bear no relationship to any existing systems. We characterize the properties of the new associations, including their velocity dispersions and total stellar masses, all of which are consistent with typical values for OB associations. We search for evidence of expansion and find that all are expanding, albeit anisotropically, with stronger and more significant expansion in the direction of Galactic longitude. We also identify two large-scale (160 pc and 25 km s−1) kinematic expansion patterns across the Cygnus region, each including three of our new associations, and attribute this to the effects of feedback from a previous generation of stars. This work highlights the need to revisit the existence and membership of the historical OB associations, if they are to be used to study their properties and dynamics.

Six-Gluon amplitudes in planar mathcal{N} = 4 super-Yang-Mills theory at six and seven loops

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

Interplay of the CGC and TMD frameworks to all orders in kinematic twist

A framework for an improved TMD (iTMD) factorization scheme at small x, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD kt ≪ Q regime and the BFKL kt ∼ Q regime. In this article, we study the relation between CGC and iTMD amplitudes. We first show how the dipole-size expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Finally we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low x framework. This allows to reinterpret the dilute expansion as a Wandzura-Wilczek approximation in the large kt regime.

Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis

A higher-order mathematical formulation with applications is presented in this paper for the free vibration analysis of arches and beams made of composite materials. Higher-order shear deformation theories are required to capture accurately the three-dimensional behavior of these structures through a one-dimensional scheme. Several orders of kinematic expansion are investigated and compared. In addition, the so-called zig–zag theories obtained through the use of the well-known Murakami's function are employed. Their effectiveness is extremely clear when laminates with inner-soft cores are analyzed. A set of numerical applications is presented to prove the accuracy of the current methodology. In particular, the comparison with exact solutions and results available in the literature or obtained through three-dimensional finite element commercial codes justifies the use of higher-order models, in which the displacement field is defined through the arbitrary choice of the maximum order of kinematic expansion. The in-plane vibrational modes of arches and beams, as well as annular ring structures, are computed and presented, discussing also the Poisson effect on the solutions.

Linear Static Behavior of Damaged Laminated Composite Plates and Shells.

A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software.

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.

Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method

The main purpose of this work is to perform the free vibration analysis of several laminated composite doubly-curved shells, singly-curved shells and plates, characterized by a continuous thickness variation. Variable thickness could affect the design of shell structures since it allows to tailor the stiffness features in the most stressed areas within the domain, keeping the weight constant. As a consequence, an improved dynamic behavior may be exhibited. The governing equations are solved numerically by the Generalized Differential Quadrature (GDQ) method, which has proven to be an accurate, stable and reliable numerical tool. Its accuracy is tested by means of several comparisons with analytical and semi-analytical results available in the literature, and with the solutions obtained by a three-dimensional finite element (FE) model. The theoretical approach considered in the current paper is general and allows consideration of many higher-order structural theories in a unified manner, in which the order of the kinematic expansion can be chosen arbitrarily.

An analysis of composite beams by means of hierarchical finite elements and a variables separation method

Laminated composite three-dimensional beams are investigated by means of hierarchical one-dimensional finite elements and a space decomposition approach. The global three-dimensional problem is separated by a Proper Generalised Decomposition into two coupled ones over the cross-section approximation space and on the beam axis approximation space. The size of the resulting problem is smaller than that of a classical equivalent finite element solution. The approximation of the displacements versus the cross-section and along the axis are general regardless the kinematic expansion order and the number of nodes per element thanks to a Unified Formulation. Accurate yet computationally affordable solutions are obtained.

Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories

The present work illustrates a general formulation for higher-order layer-wise (LW) theories. It aims to analyze doubly-curved laminated shells and panels when soft-core properties are selected. The present approach has its own roots in the Carrera Unified Formulation (CUF) for which the stretching effect of each layer is not neglected. CUF allows to take the kinematic expansion order as a free parameter for the representation of any higher order formulation. This paper shows the explicit fundamental operators for the LW approach when static analysis is investigated. The mathematical problem is solved using a strong formulation approach, termed Generalized Differential Quadrature (GDQ) method. Moreover, the so-called Generalized Integral Quadrature (GIQ) method is used for evaluating the through-the-thickness quantities of the theory such as the stiffness constants, computed layer by layer. Numerical applications are related to the recovery of the inter-laminar stresses and strains that have been compared to reference solutions obtained by a commercial three-dimensional (3D) FEM code.

Kinematic properties of superbubbles in the Antennae, M83 and Arp 270

AbstractSuperbubbles and large scale expansion in galaxies are important indicators of activity in galaxies: they are formed in starbursts and around active nuclei. Superbubbles can be used to give information about the star-forming region which produced them. We present in-depth results of our study of kinematically detected superbubbles using a method based on Fabry-Perot spectroscopy, which allows us to map regions of expansion across the entire disk of a galaxy. Three objects have been selected for this poster based on the interest of the results they show: two interacting galaxies, the Antennae and Arp270, at different stages of galaxy interaction, and the more isolated galaxy M83. We present the kinematic expansion maps, as well as a census of detected superbubbles and a dynamical study of their properties.

The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: The free vibration analysis

This paper presents a general two-dimensional approach for solving doubly-curved laminated composite shells using different kinematic expansions along the three orthogonal directions of the curvilinear shell model. The Carrera Unified Formulation (CUF) with different thickness functions along the three orthogonal curvilinear directions is applied to completely doubly-curved shells and panels, different from spherical and cylindrical shells and plates. Furthermore, the fundamental nuclei for doubly-curved structures are presented in their explicit form for the first time by the authors. These fundamental nuclei also allow to consider doubly-curved structures with variable thickness. In addition, the theoretical model includes the Murakami’s function (also known as zig-zag effect). For some problems it is useful to have an in-plane kinematic expansion which is different from the normal one. The 2D free vibration problem is numerically solved through the Local Generalized Differential Quadrature (LGDQ) method, which is an advanced version of the well-known Generalized Differential Quadrature (GDQ) method. The main advantage of the LGDQ method compared to the GDQ method is that the former can consider a large number of grid points without losing accuracy and keeping the very good stability features of GDQ method as already demonstrated in literature by the authors.

Hydrogen lines as a diagnostic tool for studying multicomponent emitting regions in hot young stars: magnetosphere, X-wind, and disk wind

Infrared interferometric observations with high spatial and spectral resolution and their quantitative modeling provide us with a unique opportunity to improve our understanding of the circumstellar environment of young stars and the accretion-ejection process. The goal of this paper is to investigate various models of the emitting regions in young Herbig Ae/Be stars that consist of (i) a compact rotating magnetosphere; (ii) an X-wind; and (iii) a disk wind. These models can be used, for example, to quantitatively interpret line profile measurements and infrared interferometric observations with the AMBER instrument of the Very Large Telescope Interferometer (VLTI) in the high spectral resolution mode (R = 12 000). VLTI/AMBER observations allow us to resolve the disk wind region and study the flux contribution of the unresolved magnetosphere and X-wind region to the total line flux. Analyzing the results of our nonLTE calculations, we conclude that the mechanisms of the different broadening of emission lines of different series include (1) the kinematic expansion due to the motion of the outflowing, accelerating gas in the magneto-centrifugal disk wind; (2) the Stark effect; and (3) the rotation of the magnetosphere. We also investigated extinction effects that can influence the shape of the line profiles. We considered the obscuration of the outer disk wind by an opaque dust and gas disk, the obscuration of the disk wind by a flared disk or by dust in the disk wind itself, and absorption of the star and disk continuum radiation in the disk wind along the line of sight. We show that due to extinction effects, the line profiles can change from double-peaked to single-peaked and P Cygni profiles. We studied the contribution of the different components of the stellar environment to different hydrogen emission lines and investigated how this contribution is dependent on the model parameters. The results of this study can be used for the detailed modeling of the emitting regions of individual young stars.

Scalar field power-law cosmology with spatial curvature and dark energy-dark matter interaction

We consider a late closed universe of which scale factor is a power function of time using observational data from combined WMAP5+BAO+SNIa dataset and WMAP5 dataset. The WMAP5 data give power-law exponent, $\alpha = 1.01$ agreeing with the previous study of $H(z)$ data while combined data gives $\alpha=0.985$. Considering a scalar field dark energy and dust fluid evolving in the power-law universe, we find field potential, field solution and equation of state parameters. Decaying from dark matter into dark energy is allowed in addition to the non-interaction case. Time scale characterizing domination of the kinematic expansion terms over the dust and curvature terms in the scalar field potential are found to be approximately 5.3 to 5.5 Gyr. The interaction affects in slightly lowering the height of scalar potential and slightly shifting potential curves rightwards to later time. Mass potential function of the interacting Lagrangian term is found to be exponentially decay function.

Cosmography beyond standard candles and rulers

We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different data sets: Supernovae type Ia and Gamma Ray Bursts, the Baryonic Acoustic Oscillations, the cosmic microwave background power spectrum and the Hubble parameter as measured from surveys of galaxies. This data set allows to put constraints on the cosmographic expansion with unprecedented precision. We also present forecasts for the coefficients of the kinematic expansion using future but realistic data sets: constraints on the coefficients of the expansions are likely to improve by a factor ten with the upcoming large scale structure probes. Finally, we derive the set of the cosmographic parameters for several cosmological models (including $\Lambda$CDM) and compare them with our best fit set. While distance measurements are unable to discriminate among these models, we show that the inclusion of the Hubble data set leads to strong constraints on the lowest order coefficients and in particular it is incompatible with $\Lambda$CDM at 3-$\sigma$ confidence level. We discuss the reliability of this determination and suggest further observations which might be of crucial importance for the viability of cosmographic tests in the next future.

A REVISED AGE FOR UPPER SCORPIUS AND THE STAR FORMATION HISTORY AMONG THE F-TYPE MEMBERS OF THE SCORPIUS-CENTAURUS OB ASSOCIATION

We present an analysis of the ages and star-formation history of the F-type stars in the Upper Scorpius (US), Upper Centaurus-Lupus (UCL) and Lower Centaurus-Crux (LCC) subgroups of Scorpius-Centaurus. We find that 1) our empirical isochrones are consistent with the previously published age-rank of the Sco-Cen subgroups, 2) LCC and UCL appear to reach the main sequence turn-on at spectral types ~F4 and ~F2, respectively. An analysis of the A-type stars shows US reaching the main sequence at about spectral type ~A3. 3) The median ages for the pre-main sequence members of UCL and LCC are 16 Myr and 17 Myr, respectively, in agreement with previous studies, however we find that 4) Upper Sco is much older than previously thought. The luminosities of the F-type stars in US are typically a factor of ~2.5 less luminous than predicted for a 5 Myr old population for four sets of evolutionary tracks. We reexamine the evolutionary state and isochronal ages for the B-, A-, and G-type Upper Sco members, and the evolved M supergiant Antares, and estimate a revised mean age for Upper Sco of 11+/-1+/-2 Myr (statistical, systematic). Using radial velocities and Hipparcos parallaxes we calculate a lower limit on the kinematic expansion age for Upper Sco of >10.5 Myr (99% confidence). However, the data are statistically consistent with no expansion. We reevaluate the inferred masses for the known substellar companions in Upper Sco using the revised age. Specifically, we estimate the mass of 1RXS J1609-2105b to be 14^{+2}_{-3} Mjup, suggesting that it is a brown dwarf rather than a planet. Finally, we find the fraction of F-type stars exhibiting Ha emission and/or a K-band excess consistent with accretion to be 0/17 (<19%; 95% C.L.) in US at ~11 Myr, while UCL has 1/41 (2^{+5}_{-1}%; 68% C.L.) accretors and LCC has 1/50 (2^{+4}_{-1}%; 68% C.L.) accretors at ~16 Myr and ~17 Myr, respectively. [Abridged]

A Cat's Eye view of the Eskimo from Saturn

AbstractThe 3-D and kinematic structure of the Eskimo nebula, NGC 2392, has been notoriously difficult to interpret given its complex morphology, multiple kinematic components and its nearly pole-on orientation along the line of sight. Here we present the most comprehensive high resolution spectroscopic mapping of the Eskimo planetary nebula to date. The data consist of 21 spatially resolved, long-slit echelle spectra tightly spaced over the Eskimo and along its bipolar jets. This data set allowed us to construct a velocity-resolved [NII] channel map of the nebula with a resolution of 10 km/s that disentagles the differente kinematic components of the nebula and reveals clearly for the first time the kinematic expansion pattern for each of the components. The spectroscopic information is combined with a HST image to construct the first detailed three dimensional model of the Eskimo with the code SHAPE. With this model we demostrate that the Eskimo is nearly a twin to the Saturn nebula, but rotated 90° to the line sight. Furthermore, we show that the main characteristics of our model apply to the general properties of the group of elliptical planetary nebulae with ansae, once the orientation is considered.

Bayesian analysis and constraints on kinematic models from union SNIa

The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter (constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter (constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with theflat ΛCDM model.Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q0 and j0) and for the transition redshift (zt) between a past phase of cosmic deceleration to a current phase of acceleration are given.All models characterize an accelerated expansion for theuniverse today and largely indicate that it was decelerating inthe past, having a transition redshift around 0.5.The cosmic jerk is not strongly constrained by the present supernovae data.For the most realistic kinematic models the 1σ confidence limitsimply the following ranges of values: q0 ∊ [−0.96, −0.46], j0 ∊ [−3.2, −0.3] and zt ∊ [0.36, 0.84],which are compatible with the ΛCDM predictions, q0 = −0.57 ± 0.04, j0 = −1 and zt = 0.71 ± 0.08.We find that even very simple kinematic models are equally good to describe the data compared to the concordance ΛCDM model, and that the current observations are not powerful enough to discriminate among all of them.

The Hamiltonian approach to Yang–Mills [formula omitted]: Expansion scheme and corrections to string tension

We carry out further analysis of the Hamiltonian approach to Yang–Mills theory in 2 + 1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schrödinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range −0.3% to −2.8%, moving our prediction closer to the recent lattice estimates.