• Issue front cover thumbnail

      Volume 88, Issue 3

      March 2017

    • Modified function projective combination synchronization of hyperchaotic systems


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      In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.

    • Estimation of the thermal diffusivity of solids based on instantaneous velocimetry using an interferometer


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      A conceptually new approach is proposed to estimate the thermal diffusivity of optically transparent solids at ambient temperature based on the ‘position-dependent instantaneous velocity’ of isothermal surfaces using a self-reference interferometer. A new analytical model is proposed using the exact solution to relate the instantaneous velocity of isothermal surfaces with the thermal diffusivity of solids. The experiment involves setting up a one-dimensional non-stationary heat flow inside the solid via step-temperature excitation to launch a spectrum of dissimilar ‘moving isothermal surfaces’ at the origin. Moving isothermal surfaces exhibit macroscale ‘rectilinear translatory motion’; the instantaneous velocity of any isothermal surface at any location in the heat affected region is unique and governed by the thermal diffusivity of the solids. The intensity pattern produced by the self-reference interferometer encodes the moving isothermal surfaces into the corresponding moving intensity points. The instantaneous velocities of the intensity points are measured. For a given thermo-optic coefficient, the corresponding values of the isothermal surfaces are predicted to estimate the thermal diffusivity of the solids using BK7 glass as an example. Another improved method is proposed in which thermal diffusivity is estimated without measuring thermo-optic coefficient and quartz glass is utilized as a specimen. The results obtained using the proposed approaches closely match with the literature value.

    • Hulth$\grave{e}$n potential models for $\alpha−\alpha$ and $\alpha−He^3$ elastic scattering


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      Simple Hulth$\grave{e}$n-type potential models are proposed to treat the $\alpha−\alpha$ and $\alpha−He^3$ elastic scattering. The merit of our approach is examined by computing elastic scattering phases through the judicious use of the phase function method. Reasonable agreements in scattering phase shifts are obtained with the standard data.

    • Alpha decay and cluster decay of some neutron-rich actinide nuclei


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      Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of $\alpha$-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model ($\bf{CYEM}$). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are $\alpha$-like nuclei.

    • Refinement of the community detection performance by weighted relationship coupling


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      The complexity of many community detection algorithms is usually an exponential function with the scale which hard to uncover community structure with high speed. Inspired by the ideas of the famous modularity optimization, in this paper, we proposed a proper weighting scheme utilizing a novel k-strength relationship whichnaturally represents the coupling distance between two nodes. Community structure detection using a generalized weighted modularity measure is refined based on the weighted k-strength matrix. We apply our algorithm on both the famous benchmark network and the real networks. Theoretical analysis and experiments show that the weighted algorithm can uncover communities fast and accurately and can be easily extended to large-scale real networks.

    • An effective Hamiltonian approach to quantum random walk


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      In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltoniansare generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, $\it{Sci. Rep}$. 3, 2829 (2013)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.

    • The effect of nonlinearity on unstable zones of Mathieu equation


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      Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of dynamic systems. In this paper, the stable and unstable regions of Mathieu equation are determined for three cases of linear and nonlinear equations using the homotopy perturbation method. The effect of nonlinearity is examined in the unstable zone. The results show that the transition curves of linear Mathieu equation depend on the frequency of the excitation term. However, for nonlinear equations, the curves depend also on initial conditions. In addition, increasing the amplitude of response leads to an increase in the unstable zone.

    • Multiswitching combination–combination synchronization of chaotic systems


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      In this paper, a novel synchronization scheme is investigated for a class of chaotic systems. Themultiswitching synchronization scheme is extended to the combination–combination synchronization scheme such that the combination of state variables of two drive systems synchronize with different combination of state variables of two response systems, simultaneously. The new scheme, multiswitching combination–combination synchronization (MSCCS), is a notable extension of the earlier multiswitching schemes concerning only the single drive–response system model. Various multiswitching modified projective synchronization schemes are obtained as special cases of MSCCS, for a suitable choice of scaling factors. Suitable controllers have been designed and using Lyapunov stability theory sufficient condition is obtained to achieve MSCCS between four hyperchaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed to validate the theoretical results.

    • A review on the solution of Grad–Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique


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      Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad–Shafranov equation (an axisymmetric,magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular crosssection of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

    • Monte Carlo simulation for the estimation of iron in human whole blood and comparison with experimental data


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      Monte Carlo N-particle (MCNP) code has been used to simulate the transport of gamma photon rays of different energies (22, 31, 59.5 and 81 keV) to estimate the iron content in solutions. In this study, MCNP simulation results are compared with experiment and XCOM theoretical data. The simulation shows that theobtained results are in good agreement with experimental data, and better than the theoretical XCOM values. The study indicates that MCNP simulation is an excellent tool to estimate the iron concentration in the blood samples. The MCNP code can also be utilized to estimate other trace elements in the blood samples.

    • Effects of electron–phonon interaction and impurity on optical properties of hexagonal-shaped quantum wires


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      We have investigated the influence of electron–phonon (e–p) interaction and hydrogenic donor impurity simultaneously on energy difference, binding energy, the linear, nonlinear and total refractive index changes and absorption coefficients of a hexagonal-shaped quantum wire. For this goal, we have used finite-elementmethod (FEM), a compact density matrix approach and an iterative procedure. It is deduced that energy difference and binding energy decrease by changing the impurity position with and without e–p interaction. The dipole matrix elements have complex behaviours in the presence of impurity with and without e–p interaction. The refractive index changes and absorption coefficients increase and shift towards lower energies by enhancing $a_1$ with central impurity. In the presence of central impurity, the absorption coefficients and refractive index changes enhance and shift toward higher energies when e–p interaction is considered.

    • Recent observational constraints on generalized Chaplygin gas in UDME scenario

      P THAKUR

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      Recent observational predictions suggest that our Universe is passing through an accelerating phase in the recent past. This acceleration may be realized with the negatively pressured dark energy. Generalized Chaplygin gas may be suitable to describe the evolution of the Universe as a candidate of unified dark matterenergy (UDME) model. Its EoS parameters are constrained using (i) dimensionless age parameter ($H_{0}t_{0}$) and (ii) the observed Hubble (H(z) − z) data (OHD) + baryon acoustic oscillation (BAO) data + cosmic microwavebackground (CMB) shift data + supernovae (Union2.1) data. Dimensionless age parameter puts loose bounds on the EoS parameters. Best-fit values of the EoS parameters $H_{0}, A_{s}$ and $\alpha$ ($A_{s}$ and $\alpha$ are defined in the energy density for generalized Chaplygin gas (GCG) and in EoS) are then determined from OHD+BAO+CMB+Union2.1 data and contours are drawn to obtain their allowed range of values. The present age of the Universe ($t_0$) and the present Hubble parameter ($H_0$) have been estimated with 1σ confidence level. Best-fit values of deceleration parameter (q), squared sound speed ($c^{2}_{s}$ ) and EoS parameter ($\omega$) of this model are then determined. It is seen that GCG satisfactorily accommodates an accelerating phase and structure formation phase.

    • Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube


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      The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re $\ll$ 1) is taken into account. The wavelength of metachronal wave is also considered to be very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of the slip parameter, the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micromachines in drug delivery.

    • A comparative analysis of the density distributions and the structure models of $^{9}$Li

      M AYGUN

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      In the present study, we have analysed the elastic scattering cross-section data of $^{9}$Li + $^{12}$C system at $E_{lab}$ = 540 MeV and $^{9}$Li + $^{208}$Pb system at $E_{c.m.}$ = 28.3 MeV for some cluster models and various density distributions of the $^{9}$Li nucleus. First, we have obtained five different density distributions of the $^{9}$Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the $^{9}$Li nucleus consisting of $^{6}$He + $^{3}$H and $^{8}$Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.

    • Phase-space treatment of the driven quantum harmonic oscillator


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      A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.

    • Inclusion of GENIE as neutrino event generator for INO ICAL


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      The iron calorimeter (ICAL) detector is the proposed underground neutrino-physics experiment in the INO cavern. Its main goal is the determination of sign of 2–3 mass-squared difference, $\Delta m^{2}_{32}$ $(=m^{2}_{3} − m^{2}_{2})$ in the presence of matter effects, apart from the precise measurement of other neutrino parameters. Like all other neutrino experiments, the INO Collaboration is going to interface its main software code with a neutrino event generator. The GENIE software is best suited for the ICAL experiment. But, it requires a fewmodifications before being incorporated in ICAL simulation to have better representation of the neutrino flux and to be more user friendly to the INO user. This paper reports all these modifications.

    • Isgur–Wise function in a QCD-inspired potential model with WKB approximation


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      We use Wentzel–Kramers–Brillouin (WKB) approximation for calculating the slope and curvature of Isgur–Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur–Wise function. Comparison is also made with those of Dalgarno method and variationallyimproved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation.

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