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      Volume 90, Issue 2

      February 2018

    • Dipole and Spin-Dipole Strength Distributions in $^{124,126,128,130}\rm{Te}$ Isotopes


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      We try to present the structure of $1^{−}$ excitations in open-shell $^{124,126,128,130}\rm{Te}$ isotopes. Electric dipole states are investigated within a translational and Galilean invariant model. Also, a theoretical description of charge conserving spin-dipole $1^{−}$ excitations is presented for the same isotopes. The energy spectra for both kinds of excitations are analysed in detail. Furthermore, a comparison of the calculated cross-sections and energies with the available experimental data is given.

    • Half-metallic ferromagnetism in $\rm{Ti_{2}IrZ (Z = B, Al, Ga, and In)}$ Heusler alloys: A density functional study


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      The first-principle density functional theory (DFT) calculations were employed to investigate the electronic structures, magnetic properties and half-metallicity of $\rm{Ti_{2}IrZ (Z = B, Al, Ga, and In)}$ Heusler alloys with $\rm{AlCu_{2}Mn-}$ and $\rm{CuHg_{2}Ti-}$type structures within local density approximation and generalised gradient approximation for the exchange correlation potential. It was found that $\rm{CuHg_{2}Ti-}$type structure in ferromagnetic state was energetically more favourable than $\rm{AlCu_{2}Mn-}$type structure in all compounds except $\rm{Ti_{2}IrB}$ which was stable in $\rm{AlCu_{2}Mn-}$type structure in non-magnetic state. $\rm{Ti_{2}IrZ (Z = B, Al, Ga, and In)}$ alloys in $\rm{CuHg_{2}Ti-}$type structure were half-metallic ferromagnets at their equilibrium lattice constants. Half-metallic band gaps were respectively equal to 0.87, 0.79, 0.75, and 0.73 eV for $\rm{Ti_{2}IrB}$, $\rm{Ti_{2}IrAl}$, $\rm{Ti_{2}IrGa}$, and $\rm{Ti_{2}IrIn}$. The origin of half-metallicity was discussed for $\rm{Ti_{2}IrGa}$ using the energy band structure. The total magnetic moments of $\rm{Ti_{2}IrZ (Z = B, Al, Ga, and In)}$ compounds in $\rm{CuHg_{2}Ti}$-type structure were obtained as $2\mu_{B}$ per formula unit, which were in agreement with Slater–Pauling rule $(M_{tot} = Z_{tot}−18)$. All the four compounds were half-metals in a wide range of lattice constants indicating that they may be suitable and promising materials for future spintronic applications.

    • Relativistic effects in the study of weakly bound $^{17}\rm{F}$ and $^{11}\rm{Be}$ nuclei


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      Relativistic effects are employed to describe the weakly bound nuclei of $^{17}\rm{F}$ and $^{11}\rm{Be}$. In order to calculate the energy levels of the ground state and the excited states of these nuclei, we solved the Dirac equation with pseudospin symmetry in the shell model by using the basic concept of supersymmetric shape invariance method. The results obtained from this approach are compared with a non-relativistic approach and experiment. It was then seen that the relativistic approach matches more with the experimental results.

    • Fermi integral and density-of-states functions in a parabolic band semiconductor degenerately doped with impurities forming a band tail


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      We provide the energy spectrum of an electron in a degenerately doped semiconductor of parabolic band. Knowing the energy spectrum, the density-of-states (DOS) functions are obtained, considering the Gaussian distribution of the potential energy of the impurity states, showing a band tail in them e.g., energy spectrum and density-of-states. Therefore, Fermi integrals (FIs) of DOS functions, having band tail, are developed by the exact theoretical calculations of the same. It is noticed that with heavy dopings in semiconductors, the total FI demonstrates complex functions, containing both real and imaginary terms of different FI functions. Their moduli possess an oscillatory function of $\eta$ (reduced Fermi energy = $E_{f}/k_{B}T, k_{B}$ is the Boltzmann constant and $T$ is the absolute temperature) and $\eta e$ (impurity screening potential), having a series solutions of confluent hypergeometric functions, $\Phi(a, b; z)$, superimposed with natural cosine functions of angle $\theta$. The variation of $\theta$ with respect to $\eta$ indicated resonance at $\eta$ = 1.5. The oscillatory behaviour of FIs show the existence of ‘band-gaps’, both in the real as well as in the forbidden bands as new band gaps in the semiconductor.

    • Perfect fluid cosmological Universes: One equation of state and the most general solution


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      Considering a homogeneous and isotropic Universe characterised by the Friedmann–Lemaître– Robertson–Walker line element, in this work, we have prescribed a general formalism for the cosmological solutions when the equation of state of the cosmic substance follows the general structure $\phi(p, \rho) = 0$, where $p$, $\rho$ are respectively the pressure and the energy density of the cosmic substance. Using the general formalism we recover some well-known solutions, namely, when the cosmic substance obeys the linear equation of state, a Chaplygin-type equation of state, or a nonlinear equation of state. Thus, the current work offers a new technique to solve the cosmological solutions without any prior relation between $p$ and $/rho$.

    • Classical system underlying a diffracting quantum billiard


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      For a point scatterer placed slightly off the centre of a circular enclosure, rays are found which vividly exhibit the effect of diffraction. The Schrödinger equation was mapped in the complex plane by employing a fractional linear transformation which brings the point scatterer to the centre. But the mass of the particle becomes a function of space coordinates, bearing anisotropy. For the transformed problem, the corresponding classical Hamiltonian is written and solved with Snell’s laws on the boundary. The solutions of the Hamilton’s equations thus found constitute, in fact, the ray-manifold underlying the diffraction at the level of the wave description.

    • Stokes shift and fine-structure splitting in CdSe/CdTe invert type-II and CdTe/CdSe type-II core/shell nanocrystals: Atomistic tight-binding theory


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      Using the atomistic tight-binding (TB) theory and configuration interaction (CI) description, it is showed that the Stokes shift and fine-structure splitting (FSS) in semiconductor core/shell nanocrystals are predominantly affected by the shell thickness and band profiles. CdSe/CdTe invert type-II and CdTe/CdSe type-II core/shell nanocrystals are used as the simulated candidates in order to obtain the different locations of the charge separation. This insight is important for the theoretical understanding and practical control by the type of the band alignments and sizes in growth shell for the entanglement of polarised photon pairs based on a biexciton cascade process. The manipulation of the Stokes shift and FSS by changing the band alignments and the thickness of the growth shell is studied here. The observations emphasise that there is a reduction of Stokes shift and FSS in CdSe/CdTe core/shell nanocrystals. In addition, it is found that the Stokes shift and FSS decrease with the increase in growth shell thickness in both CdSe/CdTe and CdTe/CdSe core/shell nanocrystals.

    • Thermodynamics properties of diatomic molecules with general molecular potential


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      In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy $U$, vibrational mean free energy $F$, vibrational entropy $S$ and vibrational specific heat capacity $C$. These thermodynamic functions are studied for the electronic state $\rm{X}^{1} \Sigma^{+}_{g}$ of $K_2$ diatomic molecules.

    • Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system


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      By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel’nikov equation and the multicomponent Schrödinger–Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel’nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constantbackground with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line roguewaves.Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger–Boussinesq system are generated.

    • Complex bifurcation patterns in a discrete predator–prey model with periodic environmental modulation


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      We consider the simplest model in the family of discrete predator–prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rateof the predator.We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based onthe correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.

    • Cluster-modified function projective synchronisation of complex networks with asymmetric coupling


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      This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novelsynchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method.

    • The synchronisation of fractional-order hyperchaos compound system


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      This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptivetechnique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.

    • Optical characteristics of a RF DBD plasma jet in various $\rm{Ar/O_{2}}$ mixtures


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      In this paper, using the optical emission spectroscopy (OES) technique, the optical characteristics of a radiofrequency (RF) plasma jet are examined. The $\rm{Ar/O_2}$ mixture is taken as the operational gas and, the Ar percentage in the $\rm{Ar/O_2}$ mixture is varied from 70% to 95%. Using the optical emission spectrum analysis of the RF plasma jet, the excitation temperature is determined based on the Boltzmann plot method. The electron density in the plasma medium of the RF plasma jet is obtained by the Stark broadening of the hydrogen Balmer $H_\beta$. It is mostly seen that, the radiation intensity of Ar $\rm{4p\rightarrow 4s}$ transitions at higher argon contributions in $\rm{Ar/O_2}$ mixture is higher. It is found that, at higher Ar percentages, the emission intensities from atomic oxygen (O) are higher and, the line intensities from the argon atoms and ions including O atoms linearly increase. It is observed that the quenching of $\rm{Ar}^\ast$ with $\rm{O}_2$ results in higher O species with respect to $\rm{O}_2$ molecules. In addition, at higher percentages of Ar in the $\rm{Ar/O_2}$ mixture, while the excitation temperature is decreased, the electron density is increased.

    • The galactic luminous supersoft X-ray source RXJ0925.7-4758/MR Vel


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      A steady-state model has been considered to explain the observed properties of the LSSS RXJ0925.7-4748/MR Vel. The steady-state models consist of a C–O core surrounded by a hydrogen-rich envelope of the solar abundances. At the bottom of the envelope, hydrogen is burned at the same rate as the star accreted it. Using the most recent proton capturing reaction rates and $\beta$-decay rates, the cyclic reactions have been studied. In the present work, effort has been made to explain the observed characteristics of the source RXJ0925.7-4758/MR Vel considering the above mentioned model. The calculated values of luminosity $(8.56 \times 10^{37} \rm{erg s^{−1}})$ and effective temperature (94.19 eV) tally well with the observed one. Photoionisation code CLOUDY has been used to explain the observed absorption edges in the spectrum of RXJ0925.7-4758/MR Vel.

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