Canonical dual finite element method for solving post-buckling problems of a large deformation elastic beam

This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar beams with large elastic deformations. The mathematical beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions.     

Refinements of the Weyl Pure Geometrical Thick Branes From Information‐Entropic Measure

This work aims to analyse the so‐called configurational entropy in the Weyl pure geometrical thick brane model. The Weyl structure plays a prominent role in the brane thickness of this model. We find a set of parameters associated to the brane width where the configurational entropy exhibits critical points. The information‐theoretical measure sets bounds into parameter of Weyl pure geometrical brane model. In addition, we also argue that a similar approach can be useful to analyze the corrections to Newtonian and Coulombian potentials in Weyl scenarios.     

Comparison of standard‐based and standardless methods of quantification used in X‐ray fluorescence analysis: Application to the exoskeleton of clams

In this work, we aim at achieving the most accurate quantitative determination of the composition of exoskeletons of bivalves from Tagus estuary with Energy Dispersive X‐ray Fluorescence. Samples from the shells of clams ranging from the Bronze Ages to the 16th century A.D . belonging to the Museu Arqueológico de Almada, and also from the shells of clams collected recently in the same region, were analyzed for comparison of the trace element composition and detection of heavy metals. The analysis was performed with 2 Energy Dispersive X‐ray Fluorescence setups, one with triaxial geometry and another with a conventional geometry and vacuum capabilities. Samples were pressed as pellets, and the spectra collected with both setups were evaluated using standardless fundamental parameter based software's implemented in each setup, and by comparing with standard reference materials of similar matrix. The comparison of the results obtained with different methods lead to the conclusion that the most realistic results were obtained with calibration curves obtained with external standards and correction the fluorescent intensities with the Compton scattering peak. When comparing the obtained concentrations for all the analyzed periods, results showed a decrease of Fe in the 12th Century. Regarding the environmental current state of the Tagus estuary, there were no heavy metals detected above the safety regulations.     

An image processing study of a reentrant discotic cholesteric – biaxial cholesteric phase transition

In this work, we study and characterize the cholesteric sequence of phases (Ch_Dr ? Ch_B ? Ch_D), where the first Ch_Dr is the reentrant cholesteric discotic phase, Ch_B is the cholesteric biaxial phase and the second Ch_D is the cholesteric discotic phase. This sequence of phases is studied through polarized light microscopy and image processing technique, where, for the first time, the domains and borders of these transitions are established and characterized. They are also investigated and optically characterized throughout their textures.     

Scalar bosons under the influence of noninertial effects in the cosmic string spacetime

In this paper we present two different classes of solutions for the Klein–Gordon equation in the presence of a scalar potential under the influence of noninertial effects in the cosmic string spacetime. We show that noninertial effects restrict the physical region of the spacetime where the particle can be placed, and furthermore that the energy levels are shifted by these effects. In addition, we show that the presence of a Coulomb-like scalar potential allows the formation of bound states when the Klein–Gordon equation is considered in this kind of spacetime.     

Likelihood analysis of the minimal AMSB model

We perform a likelihood analysis of the minimal anomaly-mediated supersymmetry-breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that either a wino-like or a Higgsino-like neutralino LSP, \(\tilde{\chi }^0_{1}\), may provide the cold dark matter (DM), both with similar likelihoods. The upper limit on the DM density from Planck and other experiments enforces \(m_{\tilde{\chi }^0_{1}} \lesssim 3 \,\, \mathrm {TeV}\) after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the \(\tilde{\chi }^0_{1}\), the measured value of the Higgs mass favours a limited range of \(\tan \beta \sim 5\) (and also for \(\tan \beta \sim 45\) if \(\mu > 0\)) but the scalar mass \(m_0\) is poorly constrained. In the wino-LSP case, \(m_{3/2}\) is constrained to about \(900\,\, \mathrm {TeV}\) and \(m_{\tilde{\chi }^0_{1}}\) to \(2.9\pm 0.1\,\, \mathrm {TeV}\), whereas in the Higgsino-LSP case \(m_{3/2}\) has just a lower limit \(\gtrsim 650\,\, \mathrm {TeV}\) (\(\gtrsim 480\,\, \mathrm {TeV}\)) and \(m_{\tilde{\chi }^0_{1}}\) is constrained to \(1.12 ~(1.13) \pm 0.02\,\, \mathrm {TeV}\) in the \(\mu >0\) (\(\mu <0\)) scenario. In neither case can the anomalous magnetic moment of the muon, \((g-2)_\mu \), be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, though there are some prospects for direct DM detection. On the other hand, if the \(\tilde{\chi }^0_{1}\) contributes only a fraction of the cold DM density, future LHC Open image in new window -based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant, and interference effects enable \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) to agree with the data better than in the SM in the case of wino-like DM with \(\mu > 0\).     

Observable acceleration of jets by a Kerr black hole

In the framework of a model based on the gravitational field of the Kerr black hole, we turn to investigate the kinematic behavior of extragalactic jets. We analytically calculate the observable velocities and accelerations along any geodesic. Then, by numerical calculations, we apply our results to a geodesic, typical of the M87 jet, and probe our results by confrontation to recent observations. A transition from non-relativistic to ultrarelativistic speeds at subparsec scale is highlighted. This transition comes sooner and more abruptly than in models based on magnetic paradigm, which indicates that we need a weaker magnetic field to explain observed synchrotron radiation. We attribute the ejection phenomenon to the repulsive effect of the gravitomagnetic Kerr field.     

Energy Propagation in Classical Harmonic Lattices with Diluted Disorder

We consider the problem of a harmonic lattice in which masses’ distribution is a superposition of a random and a periodic distribution. Classical equations for the mass displacement and velocities are solved using a second-order Euler formalism. Energy flow was investigated on two distinct experiments: (i) We injected an initial wave-packet with energy E ₀ and analyzed the dynamics of the resulting energy pulse; (ii) we pumped one of the sides of the lattice with a external signal and then we observed the propagation of the pulse until the other side of chain. Our calculations suggest that the diluted disordered mass distribution promotes energy dynamics at high frequency limit.     

Fatigue Crack Growth Behaviour in Friction Stir Welded Aluminium–Lithium Alloy Subjected to Biaxial Loads

Experimental Techniques - In this article, biaxial load fatigue crack growth tests are reported. Specimens were made of an advanced aluminium–lithium alloy AA2198-T8 joined by the friction...     

Simultaneous analysis of esters and acylglycerols in biodiesel by high-performance liquid chromatography with refractive index detection

Currently, gas chromatography (GC) is the most widely used analytical technique to verify the quality of biodiesel in relation to its glyceride and fatty acid methyl ester (FAME) contents, even though its use has some disadvantages, such as damage to the injector and column caused by the presence of trace levels of triacylglycerols in biodiesel, which means the column has to be replaced every 3 months; the need for the sample to be derivatized, which, while improving chromatographic separation, also increases analysis time; and the use of several imported standard solutions. The main aim of this work was to use high-performance liquid chromatography with refractive index detection (HPLC-RI) to simultaneously quantify the glyceride (mono, di, and triacylglycerol) and FAME contents of biodiesel. The proposed method showed satisfactory results when compared with those obtained by the reference method (GC), particularly when these results were within the working ranges of the reference method. The proposed method using HPLC-RI is therefore promising and could potentially be used instead of the reference method, since the results it yielded were statistically equivalent, with 95% confidence, to the results obtained by the reference method (GC) for the nine samples of commercial biodiesel analyzed in this study.