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      Volume 89, Issue 3

      September 2017

    • A new perspective of ground band energy formulae

      J B GUPTA

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      A host of alternative energy formulae for the ground bands of even $Z$ even $N$ nuclei are available in the literature. The usual approach is to compare the relative numerical accuracy of the predictions of the level energies by these formulae, for varying deformations of the nuclear core and for high spins. The soft rotor formula and variable moment of inertia model, the $ab$ and $pq$ formulae, the rotation vibration interaction and power index formulae are illustrated. Here, a new perspective is presented, with emphasis on the limitation of the region of their physical validity and on deriving useful meaning of their parameters.

    • Raising and lowering operators for quantum billiards


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      For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m$, $n$, the index which represents a class is $c = m$ mod $kn$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by the application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.

    • Electrical characteristics for capacitively coupled radio frequency discharges of helium and neon


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      In this study, a symmetric radio frequency (RF) (13.56 MHz) electrode discharge system of simple geometry has been designed and made. The electrical properties of capacitive RF discharge of pure neon and pure helium have been obtained from current and voltage waveforms using different reactor designs. Calculations are done, in detail, according to the homogeneous discharge model of capacitively coupled RF. Electrical properties of bulk plasma and sheath capacitance are also investigated at low pressure using this model.

    • Graphene-based tunable terahertz filter with rectangular ring resonator containing double narrow gaps


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      A plasmonic band-pass filter based on graphene rectangular ring resonator with double narrow gaps is proposed and numerically investigated by finite-difference time-domain (FDTD) simulations. For the filter with or without gaps, the resonant frequencies can be effectively adjusted by changing the width of the graphene nanoribbon, the coupling distance and chemical potential of graphene. In addition, by introducing narrow gaps in the rectangular ring resonators, it shows the single frequency filtering effect. Moreover, the structure also shows high sensitivity fordifferent surrounding mediums. This work provides a novel method for designing all-optical integrated components in optical communication.

    • Model-free adaptive sliding mode controller design for generalized projective synchronization of the fractional-order chaotic system via radial basis function neural networks

      L M WANG

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      A novel model-free adaptive sliding mode strategy is proposed for a generalized projective synchronization (GPS) between two entirely unknown fractional-order chaotic systems subject to the external disturbances. To solve the difficulties from the little knowledge about the master–slave system and to overcome the bad effects of the external disturbances on the generalized projective synchronization, the radial basis function neural networks are used to approach the packaged unknown master system and the packaged unknown slave system (including the external disturbances). Consequently, based on the slide mode technology and the neural network theory, a model-free adaptive sliding mode controller is designed to guarantee asymptotic stability of the generalized projective synchronization error. The main contribution of this paper is that a control strategy is provided for the generalized projective synchronization between two entirely unknown fractional-order chaotic systems subject to the unknown external disturbances, and the proposed control strategy only requires that the master system has the same fractional orders as the slave system. Moreover, the proposed method allows us to achieve all kinds of generalized projective chaos synchronizations by turning the user-defined parameters onto the desired values. Simulation results show the effectiveness of the proposed method and the robustness of the controlled system.

    • Sensitivity of reactor multiplication factor to positions of cross-section resonances


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      Neutron–nuclear interaction cross-section is sensitive to neutron kinetic energy and most nuclei exhibit resonance behaviour at specific energies within the resonance energy range, spanning from a fraction of an electron volt to several tens or hundreds of kilo electron volts. The energy positions of these resonances correspond to the excitation energy levels of the compound nucleus that are formed as intermediate states during the interaction. Though these positions, thanks to sophistication in science and technology, are known reasonably precisely for the materials of reactor interest, deviations or spread in this data among different evaluations cannot be ruled out. In this work, the effect of such a spread in the resonance positions of the reactor materials on the multiplication factor of an infinite reactor, is obtained. The study shows that the effect on a thermal reactor is more pronounced than on a fast reactor.

    • Spatiotemporal soliton clusters in the $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity


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      From a generic transformation, a $(3+1)$-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $m = 0$, Gaussian solitons are constructed. For the modulation depth $q = 1$ and the azimuthal parameter $m \neq 0$, vortex solitons are obtained. In the limit $q = 0$ and $m \neq 0$, and for some specific values of the parameters $(m, l)$, multipole solitons are presented.

    • A scheme for designing extreme multistable discrete dynamical systems


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      In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence of infinitely many attractors in the system is obtained via partial synchronization between two systems for a given set of parameters. We give a conjecture that extreme multistable systems can be designed by coupling two m-dimensional dynamical systems in such a way that $i (1 \leq i \leq m − 1)$ number of state variables of the two systems synchronize completely and $(m − i )$ number of state variables keep constant difference. We demonstrate the applicability of our scheme in two-dimensional (2D) as well as threedimensional (3D) discrete dynamical systems. In particular, we discuss our scheme taking coupled 2D Hénon maps, coupled 2D Duffing maps and coupled 3D Hénon maps. We have analytically shown the existence of fixed points and period-2 orbits in the coupled system with the variation of initial conditions. These analytically derived conditions matched very well with the numerical simulation results. Variation of the largest Lyapunov exponent with the initial conditions is shown to confirm the existence of extreme multistability in the model. Our scheme may be useful for designing physically, chemically and biologically useful multistable discrete dynamical systems.

    • Gamma dosimetric parameters in some skeletal muscle relaxants


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      We have studied the attenuation of gamma radiation of energy ranging from 84 keV to 1330 keV $(^{170}Tm, ^{22}Na, ^{137}Cs, and ^{60}Co)$ in some commonly used skeletal muscle relaxants such as tubocurarine chloride, gallamine triethiodide, pancuronium bromide, suxamethonium bromide and mephenesin. The mass attenuation coefficient is measured from the attenuation experiment. In the present work, we have also proposed the direct relation between mass attenuation coefficient $(\mu/\rho)$ and mass energy absorption coefficient $(\mu_{en}/\rho)$ based on the nonlinear fitting procedure. The gamma dosimetric parameters such as mass energy absorption coefficient $(\mu_{en}/\rho)$, effective atomic number $\rm{(Z_eff )}$, effective electron density $(N_\rm{el})$, specific $\gamma$-ray constant, air kerma strength and dose rate are evaluated from the measured mass attentuation coefficient. These measured gamma dosimetric parameters are compared with the theoretical values. The measured values agree with the theoretical values. The studied gamma dosimetric values for the relaxants are useful in medical physics and radiation medicine.

    • Matter density distributions and elastic form factors of some two-neutron halo nuclei


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      The Skyrme–Hartree–Fock (SHF) method with MSK7 Skyrme parameter has been used to investigate the ground-state properties for two-neutron halo nuclei 6He, 11Li, 12Be and 14Be. These ground-state properties include the proton, neutron and matter density distributions, the corresponding rms radii, the binding energy per nucleon and the charge form factors. These calculations clearly reveal the long tail characterizing the halo nuclei as a distinctive featur

    • New exact models for anisotropic matter with electric field


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      We generate two newexact models for the Einstein–Maxwell field equations. In our models, we consider the stellar object that is anisotropic and charged with linear equation of state consistent with quark stars. We have a new choice of measure of anisotropy that is physically reasonable. It is interesting that in our models we regain previous isotropic results as special cases. Isotropic exact solutions regained include models by Komathiraj and Maharaj; Mak and Harko; and Misner and Zapolsky. We can also obtain particular anisotropic models obtained by Maharaj, Sunzu, and Ray. The exact solutions corresponding to our models are found explicitly in terms of elementary functions. The graphical plots generated for the matter variables and the electric field are well behaved. We also generate relativistic stellar masses consistent with observations.

    • An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations


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      Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the exp$(−\varphi(\zeta))$-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld–Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.

    • A novel fractional sliding mode control configuration for synchronizing disturbed fractional-order chaotic systems


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      In this paper, a new design of fractional-order sliding mode control scheme is proposed for the synchronization of a class of nonlinear fractional-order systems with chaotic behaviour. The considered design approach provides a set of fractional-order laws that guarantee asymptotic stability of fractional-order chaotic systems in the sense of the Lyapunov stability theorem. Two illustrative simulation examples on the fractional-order Genesio–Tesi chaotic systems and the fractional-order modified Jerk systems are provided. These examples show the effectiveness and robustness of this control solution.

    • Impact of optical gain broadening on characteristics of response function in the presence and absence of tunnelling injection for quantum dot semiconductor lasers


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      In this paper, the dynamics of QD semiconductor lasers is investigated numerically. Large and small signal modulations for various inhomogeneous broadenings have been studied. Computationally, we have solved the rate equation for two-state InAs QD semiconductor lasers and the effect of inhomogeneous broadening on response function and output power due to variation of QD parameters have been investigated in the presence and absence of tunnelling. Also, we have studied these effects on optical gain and output power. We have shown that tunnelling injection enhances the efficiency of the semiconductor laser.

    • Heat transfer with thermal radiation on MHD particle–fluid suspension induced by metachronal wave


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      In this article, effects of heat transfer on particle–fluid suspension induced by metachronal wave have been examined. The influence of magnetohydrodynamics (MHD) and thermal radiation are also taken into account with the help of Ohm’s law and Roseland’s approximation. The governing flow problem for Casson fluid model is based on continuity, momentum and thermal energy equation for fluid phase and particle phase. Taking the approximation of long wavelength and zero Reynolds number, the governing equations are simplified. Exact solutions are obtained for the coupled partial differential equations. The impact of all the embedding parameters is discussed with the help of graphs. In particular, velocity profile, pressure rise, temperature profile and trapping phenomena are discussed for all the emerging parameters. It is observed that while fluid parameter enhances the velocity profile, Hartmann number and particle volume fraction oppose the flow.

    • Solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili dynamic equation in dust-acoustic plasmas


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      Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

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