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      Volume 90, Issue 5

      May 2018

    • XUV pulse effect on signal modulations of harmonic spectra from $\rm{H}^{+}_{2}$ and $\rm{T}^{+}_{2}$


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      The effects of signal modulations on the molecular high-order harmonic generations in $\rm{H}^{+}_{2}$ and $\rm{T}^{+}_{2}$ have been theoretically investigated. It is found that with the introduction of the XUV pulse, due to the absorption of the extra XUV photons in the recombination process, multiplateaus on the harmonic spectra, separated by the XUV photon energy can be found. Moreover, this multiplateau structure is insensitive to the wavelength of the XUV pulse. In shorter pulse duration, the intensities of the multiplateaus from $\rm{H}^{+}_{2}$ are higher than those from $\rm{T}^{+}_{2}$; while in longer pulse duration, the opposite results can be found. Finally, by changing the delay time of the XUV pulse, the signal modulations (including the amplitude and the frequency modulations) of the multiplateaus can be controlled.

    • Exciton binding energy in a pyramidal quantum dot


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      The effects of spatially dependent effective mass, non-parabolicity of the conduction band and dielectric screening function on exciton binding energy in a pyramid-shaped quantum dot of GaAs have been investigatedby variational method as a function of base width of the pyramid. We have assumed that the pyramid has a square base with area $a \times a$ and height of the pyramid $H = a/2$. The trial wave function of the exciton has been chosen according to the even mirror boundary condition, i.e. the wave function of the exciton at the boundary could be non-zero. The results show that (i) the non-parabolicity of the conduction band affects the light hole (lh) and heavy hole (hh) excitons to be more bound than that with parabolicity of the conduction band, (ii) the dielectric screening function (DSF) affects the lh and hh excitons to be more bound than that without the DSF and (iii) the spatially dependent effective mass (SDEM) affects the lh and hh excitons to be less bound than that without the SDEM. The combined effects of DSF and SDEM on exciton binding energy have also been calculated. The results are compared with those available in the literature.

    • Envisaging quantum transport phenomenon in a muddled base pair of DNA


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      The effect of muddled base pair on electron transfer through a deoxyribonucleic acid (DNA) molecule connected to the gold electrodes has been elucidated using tight binding model. The effect of hydrogen and nitrogen bonds on the resistance of the base pair has been minutely observed. Using the semiempirical extended Huckel approach within NEGF regime, we have determined the current and conductance vs. bias voltage for disordered base pairs of DNA made of thymine (T) and adenine (A). The asymmetrical behaviour amid five times depreciation in the current characteristics has been observed for deviated Au–AT base pair–Au devices. An interesting revelation is thatthe conductance of the intrinsic AT base pair configuration attains dramatically high values with the symmetrical zig-zag pattern of current, which clearly indicates the transformation of the bond length within the strands of base pair when compared with other samples. A thorough investigation of the transmission coefficients $T(E)$ and HOMO–LUMO gap reveals the misalignment of the strands in base pairs of DNA. The observed results present an insight to extend this work to build biosensing devices to predict the abnormality with the DNA.

    • New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel $(G^{'} / G)$-expansion method


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      In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrödinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrödinger equation to nonlinear complex fractional nonlinear Schrödinger equation. We apply new auxiliary equation method and novel $(G^{'} / G)$-expansion method on nonlinear complex fractional Schrödinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.

    • Analytical static structure factor for a two-component system interacting via van der Waals potential


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      In this work, we derive analytical solutions for static structure factor for homogeneous and isotropic solution composed of two components interacting with each other via simple van der Waals potential which isinversely proportional to the sixth power of the distance between the two components. We assume that the first component is the solvent and the second component is the dissolved material which has low concentration or density in comparison to the concentration of the solvent, i.e. dilute solution, which is common for macromolecular fluids. The presented solution is obtained using direct and inverse Fourier transforms in solving Ornstein–Zernike equations(OZE) for multicomponent systems. We calculated isothermal compressibilities as a function of concentration and comparison with other simulation and theoretical results are presented. We believe that the presented solution can be useful in studying biomolecular fluids and other soft matter fluids.

    • Optimum parameters controlling distortion and noise of semiconductor laser under analog multichannel modulation


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      This paper presents a comprehensive modelling and simulation study on the optimum parameters that control the distortion and noise of semiconductor lasers (SLs) subject to multichannel modulation for use in analog cable television (CATV) fibre links. The study is based on numerical integration of the rate equation model of the semiconductor laser. The parameters comprise the modulation index per channel $(m/ch)$, number of loaded channels $(N)$ and fibre length $(L_{F})$. The signal distortions include the composite second-order (CSO) and composite triple beat (CTB) distortions. The noise is assessed in terms of the relative intensity noise (RIN) and carrier-to-noise ratio(CNR). In order to achieve acceptable CNR values for SL, $m/ch$ should be less than 7.5 and 2% when loading 12 and 80 channels, respectively. For the CATV fibre link with $L_{F}$ = 10 km, the increase in the number of channels from 12 to 80 corresponds to lowering the optimum value of $m/ch$ from 7 to 1%. The increase of $L_F$ to 50 km limits the optimum value of $m/ch$ between 1.4 and 1%, which corresponds to loading between 12 and 17 channels only.

    • Parametrisation of the experimental fusion–fission cross-sections


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      We have presented non-linear analytical formula for fusion–fission cross-sections. This is achieved by analysing many fusion–fission experiments of the compound nuclei of atomic number range $23 \leq Z \leq 146$ available in literature. Our parametrised formula can reproduce the fusion–fission cross-sections which agree well with the experiments. Our parametrisations depend on the charges and masses of the compound nuclei and fission fragments only. These results can be used as a guideline for estimating the fusion–fission cross-sections in those cases where measurements do not exist and also for studying new nuclei which are not yet explored.

    • A novel grid multiwing chaotic system with only non-hyperbolic equilibria


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      The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil’nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify thefeasibility of this new grid multiwing chaotic system.

    • Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy


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      This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.

    • Investigation of graphene-integrated tunable metamaterials in THz regime


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      A metallic fishnet metamaterial structure in sub-THz region is presented. The proposed structure is based on hexagonal resonators. Simulations have been performed by a 3D full-wave electromagnetic simulator and a negative refractive index has been observed at the frequency range between 0.55 and 0.70 THz with the help of the graphene layer. In order to observe the effect of the graphene layer, the metamaterial structure has been simulatedand examined before and after graphene integration. Significant modification in the propagation properties has been observed after the graphene integration. Change in S-parameters with the size variation of hexagonal resonators and alteration in graphene thickness are also presented as a parametric study to show the tunability of the structure. Suitability of the metamaterial for sensor applications has been investigated. The proposed metamaterial structure is promising to be effectively used for tunability and sensor applications.

    • $^{16}\rm C$-elastic scattering examined using several models at different energies


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      In the present paper, the first results concerning the theoretical analysis of the $^{16} \rm{C}$ + p reaction by investigating two elastic scattering angular distributions measured at high energy compared to low energy for this system are reported. Several models for the real part of the nuclear potential are tested within the optical model formalism. The imaginary potential has a Woods–Saxon shape with three free parameters. Two types of density distribution and three different cluster structures for $^{16}\rm{C}$ are assumed in the analysis. The results are compared with each other as well as with the experimental data to give evidence of the importance of these studied items.

    • Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems


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      In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

    • A family of solutions to the Einstein–Maxwell system of equations describing relativistic charged fluid spheres


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      In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

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