CHANGES IN MELTING BEHAVIOR AND MORPHOLOGY ON ANNEALING OF LINEAR AND BRANCHED POLYETHYLENE

Changes in morphology and melting behavior of various types of commercial polyethylenes as a result of annealing were studied using differential scanning calorimetry, transmission electron microscopy, and density measurements. The range of polyethylenes whose densities varied between 0.96 and 0.90 g/cm³ included linear polyethylene (LPE), high-density polyethylene, a 1-octene copolymer traditional linear low density polyethylene, low density polyethylene, and a 1-octene copolymer prepared by Dow's INSITE constrained geometry catalysts technology. Two sets of samples were initially prepared by fast cooling and slow cooling from the melt. Despite an initial lower crystalline content and crystal thickness for the fast cooled (FC) branched polyethylene samples, a higher melting temperature than for the slow cooled (SC) samples was found using a 10°C/min heating rate. In concordance with a recent work, melting–recrystallization processes are held responsible for the anomalous behavior. The annealing treatment consisted of heating the two sets of samples at 1°C/min from room temperature to a temperature located at the start of the endotherm. The thermal treatment stabilizes the crystals through an increase in their thickness, which prevents melting–recrystallization processes from taking place on subsequent heating. A lower melting temperature after annealing was observed for the FC branched polyethylene samples. No such behavior was found for the SC samples and even for the FC LPE sample.     

Generalized Klein–Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca–Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein–Gordon potential (KGP) and Klein–Gordon field (KGF) equations for massive dyons from the generalized Proca–Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein–Gordon equations.     

On the ergodic sum rate for multiuser satellite–aerial–terrestrial networks

In this paper, we investigate the ergodic sum rate (ESR) for the downlink of a multi-user satellite–aerial–terrestrial network (SATN) with decode-and-forward (DF) protocol, where a multi-antenna unmanned aerial vehicle (UAV) acts as an aerial relay to assist the signal convey from satellite to multiple terrestrial users, which is also corrupted by co-channel interference. To maximize the ESR of the considered system, a beamforming (BF) scheme based on statistical channel state information is proposed to conduct space division multiple access (SDMA) in the UAV–terrestrial links. Then, by assuming that the satellite–UAV link and the UAV–terrestrial links undergo correlated Shadowed-Rician fading and correlated Rayleigh fading, respectively, we derive the analytical expression of ESR for our considered system with proposed BF scheme. Finally, numerical results are provided to verify the correctness of the theoretical analysis and demonstrate the superiority of our proposed BF scheme.     

Optical parameters and work function of Zn–In–Sn–O films

The work function behavior of Zn–In–Sn–O (ZITO) films with various Zn and Sn contents were studied. The work function increased with addition of Zn content. With further increase of Zn contents, the work function gradually decreased. The work function behavior can be investigated by (1) Fermi level position relative the carrier concentration, (2) ionization potential by the surface dipole change. The Fermi level position related the carrier concentration was calculated by Drude parameters, and ionization potential measured by UPS. As results, we confirmed that the work function of ZITO may be linked to changes in ionization potential, not carrier concentration.     

BI-HAMILTONIAN REPRESENTATION,SYMMETRIES AND INTEGRALS OF MIXED HEAVENLY AND HUSAIN SYSTEMS

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain equation, formulated in a two-component form, we present recursion operators, Lax pairs of Olver–Ibragimov–Shabat type and discover their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point and second-order symmetries, integrals and bi-Hamiltonian representations of these systems and their symmetry flows together with infinite hierarchies of nonlocal higher symmetries.     

Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.     

Finite temperature aspect ratio in ultra-cold Bose gas for large N

We present a detailed study of the temperature dependence of the condensate fraction, collective excitation and aspect ratio profiles of a Bose-condensed gas in a harmonic trap for large numbers of condensate atoms up to 85000. These quantities are calculated self-consistently using the generalized Hartree–Fock–Bogoliubov (GHFB) equations. We determine the evolution of the aspect ratio at zero and finite temperature via the condensed fraction. We compare our results with experimental data and we find a good agreement.     

Hyperkähler metric and GMN ansatz on focus–focus fibrations

In this paper, we study the hyperkähler metric and practise GMN’s construction of hyperkähler metric on focus–focus fibrations. We explicitly compute the action–angle coordinates on the local model of focus–focus fibrations, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then we study the canonical semi-flat metric on it. After the instanton correction, finally we are able to get a reconstruction of the generalized Ooguri–Vafa metric.     

Sonochemically synthesized mono and bimetallic Au–Ag reduced graphene oxide based nanocomposites with enhanced catalytic activity

Graphene oxide (GO) supported Ag and Au mono-metallic and Au–Ag bimetallic catalysts were synthesized using a sonochemical method. Bimetallic catalysts containing different weight ratios of Au and Ag were loaded onto GO utilizing a low frequency horn-type ultrasonicator. High frequency ultrasonication was used to efficiently reduce Ag(I) and Au(III) ions in the presence of polyethylene glycol and 2-propanol. Transmission electron microscopy (TEM–EDX) and X-ray photoelectron spectroscopy were used to analyze the morphology, size, shape and chemical oxidation states of the prepared metallic catalysts on GO. The catalytic efficiency of the prepared catalysts were compared using 4-nitrophenol (4-NP) reduction reaction and the subsequent formation of 4-aminophenol (4-AP) that was also monitored using UV–vis spectrophotometry. The results revealed that Au–Ag–GO bimetallic catalysts showed high activity for the conversion of 4-NP to 4-AP than their monometallic counterparts. Amongst different weight ratios (1:1, 1:2 and 2:1) between Au and Ag, the 1:2 (Au:Ag) catalyst exhibited very good catalytic performance for the conversion of 4-NP to 4-AP. A total reduction of 4-NP took place within a short period of time if Au–GO was reduced first followed by Ag reduction, whereas a lower reduction rate was observed if Ag–GO was reduced first. The same trend was observed for all the ratios of bimetallic catalysts prepared by this method. The initial unfavorable reduction potential of Ag(I) is likely to be responsible for the above order. It was found that applying dual frequency ultrasonication was a highly effective way of preparing bimetallic catalysts requiring relatively low levels of added chemicals and producing bimetallic catalysts with GO with improved catalytic efficiency.     

Analytic continuation,the Chern–Gauss–Bonnet theorem,and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics

We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature $(p,q)$ directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern–Gauss–Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern–Gauss–Bonnet theorem in this setting for certain complex metrics.     

TODA–HEISENBERG CHAIN: INTERACTING σ-FIELDS IN TWO DIMENSIONS

We study a (2 + 1)-dimensional system that can be viewed as an infinite number of O(3) σ-fields coupled by a nearest-neighbour Heisenberg-like interaction. We reduce the field equations of this model to an integrable system that is closely related to the two-dimensional relativistic Toda chain and the Ablowitz–Ladik equations. Using this reduction we obtain the dark-soliton solutions of our model.     

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

DARBOUX INTEGRABILITY OF A SIMPLIFIED FRIEDMAN–ROBERTSON–WALKER HAMILTONIAN SYSTEM

We characterize the Darboux first integrals of a simplified Friedman–Robertson–Walker Hamiltonian system depending on one parameter.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.     

FUNCTIONAL REPRESENTATION OF THE NEGATIVE AKNS HIERARCHY

This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local systems of higher order, derive the generating function of the conservation laws and the N-dark-soliton solutions for the extended AKNS hierarchy. As an additional result we obtain the functional representation of the Landau–Lifshitz hierarchy.     

Magnetosonic shock waves in dense astrophysical electron–positron–ion plasmas

Multifluid quantum magnetohydrodynamic model (QMHD) is used to investigate small but finite amplitude magnetosonic shock waves in dense) electron–positron–ion (e–p–i) plasmas. The Korteweg–de Vries–Burgers (KdVB) equation is derived by using reductive perturbation method. It is noticed that variations in the positron density modify the profile of magnetosonic shocks in dense e–p–i plasmas significantly. The numerical results are also presented by taking into account the dense plasma parameters from published literature of astrophysical conditions, in compact stars.     

Faddeev–Jackiw quantization of the higher derivative Chern–Simons gauge theory in the first-order formalism

We analyse the physical constraints of the higher derivative Chern–Simons gauge model by means of Faddeev–Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev–Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac–Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations.     

The rotation–vibration spectrum of diatomic molecules with the Tietz–Hua rotating oscillator and approximation scheme to the centrifugal term

The Tietz–Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov–Uvarov method and Pekeris approximation to the centrifugal term, we have obtained the solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed form. Some remarks and numerical results are also presented for some diatomic molecules.     

Optical solitons with Chen–Lee–Liu equation by Lie symmetry

This paper avails of classical Lie symmetry analysis to exhibit optical solitons to Chen–Lee–Liu model. By the aid of the proposed method, we secure symmetries that transform the model to a system of ordinary differential equations which are subsequently investigated by a number of methods to recover bright, dark and singular solitons.     

Soft X-ray photoelectron spectroscopic investigation of Au-deposited amorphous In–Ga–Zn–O thin-film surface

Thin Au layers (0.04 nm, 0.06 nm, 0.08 nm, 0.21 nm) were deposited on an amorphous In–Ga–Zn–O (a-IGZO) thin-film surface by thermal evaporation in an ultrahigh vacuum. The chemical-state changes of the Au layer and the a-IGZO surface were investigated by measuring the Au 4f, O 1s, In 3d, Ga 3d and Zn 3d peaks as well as the valence bands by soft X-ray photoelectron spectroscopy. Upon initial deposition, an oxidized Au component formed, whereas a metallic Au component was dominant. At the later deposition stages, the metallic Au component dominated the spectral features. When the Au thickness was thicker than 0.08 nm, a split Au 5d feature was apparent. And as the Au thickness continued to increase, In 3d showed a strong lower-binding-energy (lower-BE) component; the Ga 3d and Zn 3d also showed lower-BE components, but of much reduced intensities relative to In 3d. These results seem to imply that compared with other elements, Au atoms prefer to occupy oxygen vacancies and strongly interact with In atoms.