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      Volume 90, Issue 1

      January 2018

    • Entanglement of a nonlinear two two-level atoms interacting with deformed fields in Kerr medium


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      In this paper we investigate the entanglement dynamics between two two-level atoms interacting with two coherent fields in two spatially separated cavities which are filled with a Kerr-like medium. We examine the effect of nonlinear medium on the dynamical properties of entanglement and atomic occupation probabilities in the case of even and odd deformed coherent states. The results show that the deformed fields play important roles in the evolution of entanglement. Also, the results demonstrate that entanglement sudden death, sudden birth and long-distance can be controlled by the deformation and nonlinear parameters.

    • Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures


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      In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the early epochs. It provides persistent fluctuations in the number count vs. apparent magnitude relation, as expected from the observation of a fractal distribution of the galaxies. We also present a stochastic evolution of density perturbations in the early Universe.

    • Quasi-gedanken experiment challenging the no-signalling theorem


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      Kennedy ($\it{Philos. Sci.} \bf{62}$, 4 (1995)) has argued that the various quantum mechanical no-signalling proofs formulated thus far share a common mathematical framework, are circular in nature, and do not preclude the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis,we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.

    • $N_2$ adsorption on the inside and outside the single-walled carbon nanotubes by density functional theory study


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      The adsorption energies, bond order, atomic charge, optical properties, and electrostatic potential of nitrogen molecules of armchair single-walled carbon nanotubes (SWCNTs) and nitrogen-doped single-walled carbon nanotubes (N-SWCNTs) were investigated using density functional theory (DFT). Our results show that adsorption of the $N_2$ molecules on the external wall of a nanotube is more effective than on the internal wall in SWCNTs. The results show that $N_2$ molecule(s) are weakly bonded to SWCNTs and N-SWCNTs through van der Waals-type interactions. The interaction of $N_2$ molecules with SWCNTs and N-SWCNTs is physisorption as the adsorption energy and charge transfer are small, and adsorption distance is large. The electronic transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) (H → L) have the maximum wavelength and the lowest oscillator strength. The potential sensor on the surface of pristine SWCNTs and N-SWCNTs for the adsorption of $N_2$ molecule(s) is investigated. The N-loaded single-walled carbon nanotube is introduced as a better $N_2$ molecule(s) detector when compared with SWCNTs.

    • Anisotropic stars obeying Chaplygin equation of state


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      In this work we provide a framework for modelling compact stars in which the interior matter distribution obeys a generalised Chaplygin equation of state. The interior geometry of the stellar object is described by a spherically symmetric line element which is simultaneously co-moving and isotropic with the exterior space–time being vacuum. We are able to integrate the Einstein field equations and present closed form solutions which adequately describe compact strange star candidates such as 4U 1538-52, PSR J1614-2230, Vela X-1 and Cen X-3 (Gangopadhyay $\it{et al, Mon. Not. R. Astron. Soc.} \bf{431}$, 3216 (2013)).

    • Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system


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      This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

    • Perturbation method for calculating impurity binding energy in an inhomogeneous cylindrical quantum dot with dielectric mismatch


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      In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of $\rm{GaAs-Al_{x}Ga_{1−x}As}$. Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement. The result shows that the ground-state binding energy decreases with the increase in dot size. The result is compared with infinite dielectric mismatch as a limiting case. The binding energy of the hydrogenic impurity is maximum for an on-axis donor impurity.

    • Design of optimised backstepping controller for the synchronisation of chaotic Colpitts oscillator using shark smell algorithm


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      In this paper, an adaptive backstepping controller has been tuned to synchronise two chaotic Colpitts oscillators in a master–slave configuration. The parameters of the controller are determined using shark smell optimisation (SSO) algorithm. Numerical results are presented and compared with those of particle swarm optimisation (PSO) algorithm. Simulation results show better performance in terms of accuracy and convergencefor the proposed optimised method compared to PSO optimised controller or any non-optimised backstepping controller.

    • A light weight multichannel analyser and $\gamma$-ray spectroscopy system: Application to estimate $^{40}K$ content in some potassium salts and building materials


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      A $\gamma$ -ray spectroscopy system based on a $1" \times 1"$ NaI(Tl) detector and $1.5"$ photomultiplier tube has been developed at IUAC for teaching laboratory applications involving radioactive sources. Following along the lines of the Phoenix and Expeyes hardware developed in the laboratory earlier, a low-cost, light weight multichannel analyser also has been developed. Here the details about the same are presented. The detector–analyser system has been used as a part of the postgraduate curriculum for measuring $^{40}\rm{K}$ content in some potassium salts and common building materials like brick, cement, concrete and sand.

    • Minority heating scenarios in $^{4}\rm{He(H)}$ and $^{3}\rm{He(H)}$ SST-1 plasmas


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      Anumerical analysis of ion cyclotron resonance heating scenarios in two species of low ion temperatureplasma has been done to elucidate the physics and possibility to achieve H-mode in tokamak plasma. The analysis is done in the steady-state superconducting tokamak, SST-1, using phase-I plasma parameters which is basically L-mode plasma parameters having low ion temperature and magnetic field with the help of the ion cyclotron heating code TORIC combined with ‘steady state Fokker–Planck quasilinear’ (SSFPQL) solver. As a minority species hydrogen has been used in $^{3}\rm{He}$ and $^{4}\rm{He}$ plasmas to make two species $^{3}\rm{He(H)}$ and $^{4}\rm{He(H)}$ plasmas to study the ion cyclotron wave absorption scenarios. The minority heating is predominant in $^{3}\rm{He(H)}$ and $^{4}\rm{He(H)}$ plasmas as minority resonance layers are not shielded by ion–ion resonance and cut-off layers in both cases, and it is better in $^{4}\rm{He(H)}$ plasma due to the smooth penetration of wave through plasma–vacuum surface. In minority concentration up to 15%, it has been observed that minority ion heating is the principal heating mechanism compared to electron heating and heating due to mode conversion phenomena. Numerical analysis with the help of SSFPQL solver shows that the tail of the distribution function of the minority ion is more energetic than that of the majority ion and therefore, more anisotropic. Due to good coupling of the wave and predominance of the minority heating regime, producing energetic ions in the tail region of the distribution function, the $^{4}\rm{He(H)}$ and $^{3}\rm{He(H)}$ plasmas could be studied in-depth to achieve $\rm{H}$-mode in two species of low-temperature plasma.

    • Effects of the particle spin polarisation on the unstable modes in the anisotropic dense system


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      Polarisation of the particle spin can be an important problem for different plasmas. In this article, the contribution of the electron spin on the growth rate of the temperature anisotropy of electromagnetic instabilities has been investigated. Results show that polarisation of the electron spin will restrict the instability growth rate while instability can survive due to the spin-depolarised electrons even when the requested temperature anisotropy is vanished. Instability can reach the damping state exponentially due to the spin-polarised electrons while it can grow linearly due to the spin-depolarised (the semi-classical) electrons.

    • Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors


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      Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in $R^{3}$, the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic,quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for $a > 0$, and a chaotic attractor coexisting with a quasiperiodic attractor for $a = 0$. Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.

    • Study of chaos in chaotic satellite systems


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      In this paper,we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan–Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

    • FPGA implementation of fractional-order discrete memristor chaotic system and its commensurate and incommensurate synchronisations


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      A new fourth-order memristor chaotic oscillator is taken to investigate its fractional-order discrete synchronisation. The fractional-order differential model memristor system is transformed to its discrete model and the dynamic properties of the fractional-order discrete system are investigated. A new method for synchronising commensurate and incommensurate fractional discrete chaotic maps are proposed and validated. Numerical results are established to support the proposed methodologies. This method of synchronisation can be applied for any fractional discrete maps. Finally the fractional-order memristor system is implemented in FPGA to show that thechaotic system is hardware realisable.

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