Single-beam analysis of damaged beams: Comparison using Euler–Bernoulli and Timoshenko beam theory

A new general formulation that is applicable to the damaged, linear elastic structures ‘unified framework’ is used to obtain analytical expressions for natural frequencies and mode shapes. The term mode shapes is used to mean the displacement modes, the section rotation modes, the sectional bending strain modes and sectional shear strain modes. The formulation is applicable to damaged elastic self-adjoint systems. The formulation has two unique aspects: First, the theory is mathematically rigorous since no assumptions are made regarding the physical behavior at a damage location, therefore there is no need to substitute the damage with a hypothetical elastic element such as a spring. Since the beam is not divided at the damage location, rather than an 8 by 8, only a 4 by 4 matrix is solved to obtain the natural frequencies and mode shapes. Second, the inertia effects due to damage which have till now been neglected by researchers are accounted for. The formulation uses a geometric damage model, perturbation of mode shapes and natural frequencies, and a modal superposition technique to obtain and solve the governing differential equation. Timoshenko beam theory is then taken as an example, and its results are compared with results using Euler–Bernoulli beam theory and finite element models. The range of applicability of the two theories is ascertained for damage characteristics such as depth and extent of damage and beam characteristics such as slenderness ratio and Poisson?s ratio. The paper considers rectangular notch like non-propagating damage as an example of the damage.     

Superhalogen properties of ReOn (n = 1–5) species and their interactions with an alkali metal: an ab initio study

First principle density functional approach is employed to investigate the ground-state geometries and stabilities of ReO_n species (n = 1–5) in neutral as well as anionic forms. It is revealed that Re can bind stably with five O atoms indicating the maximum oxidation state of Re as high as +10. The electron affinities of ReO_n suggest that these species behave as superhalogens for n ≥ 3 which become as large as 7.25 eV for n = 5. The interaction of ReO_n superhalogens with appropriate alkali metals is stronger than that of halogens leading to the synthesis of more stable complex compounds. This idea is illustrated by considering the interaction of ReO_n superhalogens with K atom, forming KReO_n complexes which are relatively more stable than KF molecule. In such complexes, ReO_n unit closely mimics the behaviour of F atom when compared with KF.     

Multiplet splittings and other properties from density functional theory: an assessment in iron–porphyrin systems

In transition metal compounds with spin states close in energy, the magnitude and sign of the energy splitting calculated with density functional theory depends strongly on the functional used. Therefore we must turn to additional criteria to assess the level of accuracy and reliability of predictions based on this level of theory. We report optimized geometries, total energies, and Mössbauer quadrupole splitting values for low-spin and high-spin, ferric and ferrous model hemes using a variety of gradient-corrected and hybrid functionals. In one model, the iron–porphyrin is axially ligated by two strong-field imidazole ligands [FeP(Im)₂] and has a low-spin ground state. In the other model complex the axial ligands are two weak-field, water molecules [FeP(H₂O)₂], and have a high-spin ground state. Among all the functionals used (UHF, B3LYP, B3LYP*, BLYP, half-and-half, LSDA), the B3LYP hybrid functional most consistently reproduced the experimental geometry, Mössbauer, and spin state data for the two model hemes. Simply gradient-corrected functionals exhibit strong biases towards low spin states, while Hartree–Fock favours strongly high spin states. These findings suggest that for systems with similar characteristics of several accessible electronic spin configurations, it is imperative to include properties other than just the energy in the assessment of the DFT predictions.     

57Fe hyperfine interactions in M1 and M2 sites of olivine from Omolon meteorite: study using Mössbauer spectroscopy

Study of olivine (Fe, Mg)₂SiO₄ from Omolon meteorite was performed using Mössbauer spectroscopy with a high velocity resolution at 295 and 90 K. Components related to ⁵⁷Fe in crystallographically non-equivalent M1 and M2 sites in olivine were determined and its Mössbauer hyperfine parameters were evaluated at both temperatures. A Fe^2?+?–Mg^2?+? distribution coefficient and a temperature of cation equilibrium distribution for olivine from Omolon were evaluated on the basis of Mössbauer parameters.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

An analysis of phonon emission as controlled by the combined interaction with the acoustic and piezoelectric phonons in a degenerate III–V compound semiconductor using an approximated Fermi–Dirac distribution at low lattice temperatures

Compound semiconductors being piezoelectric in nature, the intrinsic thermal vibration of the lattice atoms at any temperature gives rise to an additional potential field that perturbs the periodic potential field of the atoms. This is over and above the intrinsic deformation acoustic potential field which is always produced in every material. The scattering of the electrons through the piezoelectric perturbing potential is important in all compound semiconductors, particularly at the low lattice temperatures. Thus, the electrical transport in such materials is principally controlled by the combined interaction of the electrons with the deformation potential acoustic and piezoelectric phonons at low lattice temperatures. The study here, deals with the problem of phonon growth characteristics, considering the combined scattering of the non-equilibrium electrons in compound semiconductors, at low lattice temperatures. Beside degeneracy, other low temperature features, like the inelasticity of the electron–phonon collisions, and the full form of the phonon distribution have been duly considered. The distribution function of the degenerate ensemble of carriers, as given by the heated Fermi–Dirac function, has been approximated by a simplified, well-tested model. The model which has been proposed earlier, makes it much easier to carry out analytically the integrations without usual oversimplified approximations.     

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions VII: tin nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ _int thick stationary tin target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20^○<θ<125^○. Cross-sections on tin nuclei are compared with cross-sections on beryllium, carbon, copper, tantalum and lead nuclei.     

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions VI: carbon nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ _int thick stationary carbon target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20°<θ<125°. Cross-sections on carbon nuclei are compared with cross-sections on beryllium, copper, tantalum and lead nuclei.     

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions IV: copper nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ _abs thick stationary copper target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20°<θ<125°. The inclusive pion production cross-sections are compared to those on beryllium and tantalum, published by us recently.     

Cross-sections of large-angle hadron production in proton–and pion–nucleus interactions V: lead nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ _int thick stationary lead target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20°<θ<125°. Cross-sections on lead nuclei are compared with cross-sections on beryllium, copper, and tantalum nuclei.     

Cross sections of large-angle hadron production in proton– and pion–nucleus interactions III: tantalum nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% λ _abs thick stationary tantalum target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20°<θ<125°. They are of particular relevance for the optimization of the design parameters of the proton driver of a neutrino factory.     

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions II: beryllium nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons and charged pions, in the interactions with a 5% λ _abs thick stationary beryllium target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20° <θ<125°.     

Comment on: “growth,spectroscopic studies,and third order non-linear optical analysis of an organic dicarboxylic acid based single crystal: urea oxalic acid” [Chin. J. Phys., 56 (2018) 1449–1466]

In a recent paper [Chin. J. Phys., 56 (2018) 1449–1466] Jeeva et al. have studied the physical properties of the Urea Oxalic acid (UOA) Crystals. The authors have used a wrong approach to calculate the reflectance spectra of the samples and obtained values of this parameter are incorrect. Consequently, other reported optical parameters in the commented paper that are calculated based on the reflectance such as refractive index, real and imaginary parts of the optical dielectric constant, optical and electrical conductivity and electrical susceptibility are incorrect.