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      Volume 89, Issue 6

      December 2017

    • Quantum eraser for three-slit interference

      NAVEED AHMAD SHAH TABISH QURESHI

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      It is well known that in a two-slit interference experiment, if the information, on which of the two paths the particle followed, is stored in a quantum path detector, the interference is destroyed. However, in a set-up where this path information is ‘erased’, the interference can reappear. Such a set-up is known as a quantum eraser. A generalization of quantum eraser to a ‘three-slit’ interference is theoretically analysed. It is shown that three complementary interference patterns can arise out of the quantum erasing process.

    • Three-dimensional coupled double-distribution-function lattice Boltzmann models for compressible Navier–Stokes equations

      RUO-FAN QIU YAN-CHENG YOU CHENG-XIANG ZHU RONG-QIAN CHEN JIAN-FENG ZHU

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      Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, aredeveloped in this paper. The main differences between the two models are discrete equilibrium density and total energy distribution function. One is the D3Q25 model obtained from spherical function, and the other is theD3Q27 standard lattice model obtained from Hermite expansions of the corresponding continuous equilibrium distribution functions. The two models are tested by numerical simulations of some typical compressible flows, and their numerical stability and precision are also analysed. The results indicate that the two models are capable for supersonic flows, while the one from Hermite expansions is not suitable for compressible flows with shock waves.

    • Zakharov equations for viscous flow and their use in the blood clot formation

      AI-PING ZHOU XIAO-QING LI

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      For theoretical study, blood can be regarded as a viscous electrically conducting fluid of negative ions and protons. Zakharov equations including viscosity are relevant for describing the behaviour of blood plasma. The dispersion formula is derived from the perturbation method and is solved numerically. It turns out that the imaginary part of one root of the perturbation frequency is greater than zero, and modulation instability occurs. This would lead to the formation of blood clot. The viscous force can suppress the occurrence of instability and prevent thrombosis. One can find that the chaotic state of blood signals human health.

    • Inducement and enhancement of multiple coherence resonances in unidirectionally coupled neural systems: Random and time-periodic coupling strength

      JIANCHENG SHI MIN LUO CHUSHENG HUANG

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      The effect of cooperative coupling strength (CCS), i.e., random coupling strength and time-periodic coupling strength, on multiple coherence resonances in unidirectionally coupled neural system has been investigated. Results show that noise, frequency and amplitude play efficient roles for the enhancement of various coherent behaviours. There exist an optimal frequency and an optimal amplitude which make the system to display the best coherent behaviours. Furthermore, the novel coherence biresonance (CBR) induced by frequency of CCS and coherence multiresonances (CMR) induced by amplitude of CCS, are found.

    • Complex dynamics of a new 3D Lorenz-type autonomous chaotic system

      FUCHEN ZHANG XIAOFENG LIAO GUANGYUN ZHANG CHUNLAI MU

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      This paper investigates a new three-dimensional continuous quadratic autonomous chaotic system which is not topologically equivalent to the Lorenz system. The dynamical behaviours of this system are furtherinvestigated in detail, including the ultimate boundedness, the invariant sets and the global attraction domain according to Lyapunov stability theory of dynamical systems. The innovation of the paper lies in the fact that this paper not only proves this chaotic system is globally bounded for the parameters of this system but also gives a familyof mathematical expressions of global exponential attractive sets with respect to the parameters of this system. To validate the ultimate bound estimation, numerical simulations are also investigated. Numerical simulations verify the effectiveness and feasibility of the theoretical scheme.

    • On adaptive modified projective synchronization of a supply chain management system

      HAMED TIRANDAZ

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      In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.

    • Transition properties of the Be-like K$\alpha$ X-ray from Mg IX

      FENG HU SHUFANG ZHANG YAN SUN MAOFEI MEI CUICUI SANG JIAMIN YANG

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      Energy levels among the lowest 40 fine-structure levels in Be-like Mg IX are calculated using grasp2K code. The wavelengths, oscillator strengths, radiative rates and lifetimes for all possible K$\alpha$ transitions have been calculated using the multiconfiguration Dirac–Fock method. The accuracy of the results is determined through extensive comparisons with the existing laboratory measurements and theoretical results. The present data can be used reliably for many purposes, such as the line identification of the observed spectra, and modelling and diagnostics of magnesium plasma.

    • Dynamic evolution of double $\Lambda$ five-level atom interacting with one-mode electromagnetic cavity field

      N H ABDEL-WAHAB AHMED SALAH

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      In this paper, the model describing a double $\Lambda$ five-level atom interacting with a single mode electromagnetic cavity field in the (off) non-resonate case is studied. We obtained the constants of motion for the considered model. Also, the state vector of the wave function is given by using the Schrödinger equation when the atom is initially prepared in its excited state. The dynamical evolutions for the collapse revivals, the antibunching of photons and the field squeezing phenomena are investigated when the field is considered in a coherent state. The influence of detuning parameters on these phenomena is investigated. We noticed that the atom–field properties are influenced by changing the detuning parameters. The investigation of these aspects by numerical simulations is carried out using the Quantum Toolbox in Python (QuTip).

    • Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

      MITESH CHAKRABORTY VINEET KUMAR RAI

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      The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM)with themicroscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. $g$-tensor and $D$ tensor, has been determined by using the ORCA program package developed by F Neese $\it{et al}$. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor ($D^{SO}$) of the axial ZFS parameter $D$. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of $\rm{Mn}^{2+}$ ion in the host matrix.

    • First-principle calculations of structural, electronic, optical, elastic and thermal properties of $\rm{MgXAs_{2} (X = Si, Ge)}$ compounds

      S CHEDDADI K BOUBENDIRA H MERADJI S GHEMID F EL HAJ HASSAN S LAKEL R KHENATA

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      First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite $\rm{MgXAs_{2} (X = Si, Ge)}$ have been performed within the density functional theory (DFT) using the full potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson(mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, $C_{11}, C_{12}, C_{13}, C_{33}, C_{44}$ and $C_{66}$ are evaluated. The effects of temperature and pressure on some macroscopic properties of $\rm{MgSiAs_{2}}$ and $\rm{MgGeAs_{2}}$ are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.

    • Multiswitching compound antisynchronization of four chaotic systems

      AYUB KHAN DINESH KHATTAR NITISH PRAJAPATI

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      Based on three drive–one response system, in this article, the authors investigate a novel synchronization scheme for a class of chaotic systems. The new scheme, multiswitching compound antisynchronization (MSCoAS), is a notable extension of the earlier multiswitching schemes concerning only one drive–one response system model. The concept of multiswitching synchronization is extended to compound synchronization scheme such that the statevariables of three drive systems antisynchronize with different state variables of the response system, simultaneously. The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, sufficient condition is obtained to achieve MSCoAS between four chaotic systems and the corresponding theoretical proof is given.Numerical simulations are performed using Lorenz system in MATLAB to demonstrate the validity of the presented method.

    • $K^{0}_{S}$ Production from beryllium target using 120 GeV/c protons beam interactions at the MIPP experiment

      A SINGH A KUMAR R RAJA V BHATNAGAR V SINGH

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      We have measured the cross-section for the $K^{0}_{S}$ production from beryllium target using 120 GeV/c protons beam interactions at the main injector particle production (MIPP) experiment at Fermilab. The data were collected with target having a thickness of 0.94% of the nuclear interaction length. The $K^{0}_{S}$ inclusive differential cross-section in bins of momenta is presented covering momentum range from 0.4GeV/c to 30GeV/c. The measured inclusive $K^{0}_{S}$ production cross-section amounts to $39.54 \pm 1.46\delta_{stat} \pm 6.97\delta_{syst}$ mb and the value is compared with the prediction of FLUKA hadron production model.

    • Time-delayed chameleon: Analysis, synchronization and FPGA implementation

      KARTHIKEYAN RAJAGOPAL SAJAD JAFARI GUESSAS LAAREM

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      In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware–software co-simulation and the results are presented.

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