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      Volume 92, Issue 6

      June 2019

    • A novel approach via mixed Crank–Nicolson scheme and differential quadrature method for numerical solutions of solitons of mKdV equation


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      The purpose of the present study is to obtain numerical solutions of the modified Korteweg–de Vries equation (mKdV) by using mixed Crank–Nicolson scheme and differential quadrature method based on quintic B-spline basis functions. In order to control the effectiveness and accuracy of the present approximation, five well-known test problems, namely, single soliton, interaction of double solitons, interaction of triple solitons, Maxwellian initial condition and tanh initial condition, are used. Furthermore, the error norms $L_{2}$ and $L_{\infty}$ are calculated for single soliton solutions to measure the efficiency and the accuracy of the present method. At the same time, the three lowest conservation quantities are calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants are calculated and presented. After all these processes, the newly obtained numerical results are compared with results of some of the published articles.

    • Laser-induced modulation of optical band-gap parameters in the III–V-type semiconductors from the density-of-state (DOS) calculations


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      Optical band gap ($E_{g0}$) is a parameter of paramount importance in describing various transport and opto-electronic properties of the III–V-type low band-gap semiconductors. In the present communication, an attempt has been made to develop an energy–momentum ($E−\bar{k}$) dispersion relation for studying the density-of-state (DOS) and band-gap-related parameters. The external laser excitation has been treated as a perturbation. It has been shown theoretically that due to such excitation with different intensity ($I$) and wavelength ($\lambda$), the band edge of the conduction band (CB) of the III–V compound semiconductors moves vertically upward, indicating laser modulation (increase) of $E_{g0}$ and related parameters compared to those of the normal ones (unperturbed). Therefore, in the presence of light, the original CB edge forms a pseudo-CB edge above the unperturbed CB edge in the forbidden band (FB) zone. This new development of the ($E−\bar{k}$) relationship has also been extended for the estimation of exact optical effective mass (OPEM) of an electron in some III–V compound semiconductors. The OPEM variation with carrier concentration showed a continuous decreasing nature, while the corresponding variation of electron effective mass (EEM) (without laser excitation) exhibited an increasing trend. The present theoretical results would be important for the deeper understanding of the variation of OPEM with $I$ and $\lambda$. The observed new results will also be beneficial for studying laser-induced effects in semiconductor heterostructures with different applications in optoelectronic devices.

    • Nonlinear ion flux caused by dust ion-acoustic nonlinear periodic waves in non-thermal plasmas


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      The propagation of dust ion-acoustic nonlinear periodic (cnoidal) waves is investigated in an unmagnetised dusty plasma characterised by a non-thermal electron population. The equations describing the dynamics of the wave potential in the first and second orders of perturbation theory are derived, and their nonsecularperiodic solutions are found. The average nonlinear ion flux caused by the propagation of a cnoidal waveis determined. The nonlinear ion flux is found to depend significantly on dust concentration and non-thermalityparameter.

    • Nanocatalytic physicochemical adsorption and degradation of organic dyes


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      Physicochemical adsorption and degradation of the azo dye, methylene blue (MB), when irradiated by visible and UV light in aqueous ZnO suspension have been investigated. The novelty of this work is to investigate the effect of dye concentration up to 200 mg/l, keeping the nanocatalysts’ concentration invariant as 1 g/l. The nanocatalysts before and after degradation process have been analysed to understand the mechanism of dye removal using X-ray diffractometer (XRD), Fourier-transform infrared spectroscopy (FTIR) and thermal gravimetric analyser(TGA). The results show that UV light degrades the dye to its intermediates through chemi-adsorption, whereas the visible light induces physisorption of dye molecules on ZnO nanocatalysts. The XRD pattern of the ZnO nanocatalysts revealed no changes in the internal structure of ZnO after the degradation process, confirming thereuse of catalysts.

    • Structure of system solutions of ion sound and Langmuir dynamical models and their applications


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      The present study deals with the system of equations for the ion sound and Langmuir waves (SEISLWs) by employing the extended simple equation, modified F-expansion and exp($−\Psi(\xi)$) expansion methods for constructing novel exact travelling wave solutions. Graphical simulations of some solutions are helpful to study the behaviour of SEISLWs. Hence, this approach is practically effective and productive to better understand the nonlinear problems in mathematics, physics and engineering.

    • Vibrational resonance in a harmonically trapped potential system with time delay


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      This paper is focussed on investigating the effect of linear time delay on vibrational resonance of a harmonically trapped potential system driven by a biharmonic external force with two wildly different frequencies$\omega$ and $\Omega$ with $\omega \ll \Omega$. Firstly, the approximate analytical expression of the response amplitude $\mathcal{Q}$ at the low frequency $\omega$ is obtained by means of the direct separation of the slow and fast motions, and then we verified the numerical simulation by using the fourth-order Runge–Kutta method and found that it is in good agreement with the theoretical analysis. Next, the influence of the time-delay parameters on the vibrational resonance are discussed. There are some meaningful conclusions. If $\tau$ is a controllable parameter, the response amplitude $\mathcal{Q}$ not only exhibits periodicity but also can be amplified via the cooperation of $F$ and $\tau$ . If the time-delay intensity parameter $r$ is a controllable parameter, the response amplitude $\mathcal{Q}$ is found to be much larger than that in the absence of time delay. Moreover, adjusting $r$ can result in a better response than adjusting $\tau$ . This undoubtedly gives us a superior way to amplify the weak low-frequency signal.

    • Electro-osmotic flow and heat transfer of a non-Newtonian nanofluid under the influence of peristalsis


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      This paper investigates the electro-osmotic flow of non-Newtonian nanofluid through a peristaltic microchannel by considering the influence of electro-osmotic phenomenon. The effects of the Brownian and thermophoresis parameters are taken into account. The problem is modulated and its governing equations are solved analytically by assuming long wavelength and low Reynolds number. The distributions of the axial velocity, temperature, nanoparticles volume fraction and volumetric flow rate are achieved and plotted under the influence of various parameters. In addition, the expressions for the skin friction, Nusselt number and Sherwood number are obtained and illustrated through a set of graphs. Furthermore, the trapping phenomenon is examined with the Rayleigh, Brownian and thermophoresis parameters. The present results are useful in medical and biological applications, especially in cancer therapy, which involves suspended nanoparticles of gold in blood (nanofluid)passing through a peristaltic tube (artery).

    • Dynamical analysis of a new three-dimensional fractional chaotic system


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      In the present paper, a new fractional chaotic system proposed by the authors is discussed. Moreover, based on the stability theory of fractional-order systems, conditions for the stability of nonlinear fractional-order systems are presented, and the existence and uniqueness of the solutions of the resulting new fractional chaotic attractor are also studied. Next, the necessary conditions for the existence of chaotic attractors in new fractionalchaotic system are reported, and at the end the stability analysis of the corresponding equilibria is given. Last but not the least, the presented numerical simulations confirm the validity of our analysis.

    • Design of polarisation-dependent multiband terahertz frequency-selective surface using two resonators


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      The aim of this paper is to present the frequency-selective surface (FSS) filter operating in the terahertz regime, emphasising on its polarisation-dependent nature. The FSS filter consists of two-concentric hexagonal-shaped metal strips embossed on a gold layer over the teflon substrate, created in the form of a split ring resonator (SRR). The emphasised polarisation-dependent nature of the FSS structure has been proved by analysing the frequency response. Numerical simulation has been done using the CST microwave studio software. Resonance occurs at five frequencies in the transverse electric (TE) mode and at four frequencies in the transverse magnetic (TM) mode, describing the polarisation-dependent nature of the proposed FSS filter structure.

    • Effects of slip on Cu–water or $\rm{Fe_{3}O_{4}}$–water nanofluid flow over an exponentially stretched sheet

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      This study aims to report the boundary layer flow of nanofluid over an exponentially stretched sheet in the presence of velocity slip as well as thermal slip. Utilising similarity transformations, the governing momentum and temperature equations are converted into ordinary differential equations and then solved numerically by shooting technique. An interesting behaviour of the solution for the converted self-similar equations is noted: dual solutions are obtained for some particular range of values of the governing parameters for the flow past an extended sheet. A comparison is made between the boundary layer flow of Cu–water and $\rm{Fe_{3}O_{4}}$–water nanofluids. Both fluid velocity and temperature increase due to the enhancement in the velocity slip parameter. With the rising values of solid volume fraction, velocity diminishes but temperature increases.

    • Solitary wave and modulational instability in a strongly coupled semiclassical relativistic dusty pair plasma with density gradient


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      Using a set of fluid equations to describe the inertial dust grain component in a dense collisionless unmagnetised plasma under the influence of weakly relativistic semiclassical electrons and positrons, the propagation of dust-acoustic wave is studied in the strong coupling regime when the dust density is non-uniform.Our main aim is to analyse the role of semiclassical and relativistic environment (frequently encountered in astrophysical context) on various features of strongly coupled dusty plasma. The semiclassical environment of the electrons and positrons is assumed to be described by the Chandrasekhar equation of state. Our second aim is to see the effect of spatial variation of the dust equilibrium density, which is known to occur due to the deformation of the Debye sheath which in turn leads to polarisation force.Anew type of nonlinear Schrödinger equation with spatially varying coefficient is deduced and its modulational stability is studied in detail. In the last section, we have taken recourse to Madelung picture to deduce a variable coefficient Korteweg–de Vries equation from this new nonlinear Schrödinger equation.

    • Model of tunnelling through quantum dot and spin–orbit interaction


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      Solvable mathematical model is suggested for tunnelling through quantum dot. The model is based on the theory of self-adjoint extensions of symmetric operators. The spin–orbit interaction is taken into account. The transmission coefficient is obtained. The result is compared with the case where spin–orbit interaction is absent.

    • Solitons and other solutions for coupled nonlinear Schrödinger equations using three different techniques


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      In this paper, we apply three different techniques, namely, the sine–cosine method, the new extended auxiliary equation method and the modified simple equation method for constructing many new exact solutions with parameters as well as bright–dark, singular and other soliton solutions of the coupled nonlinear Schrödinger equations. The solutions of these coupled nonlinear equations are compared with the well-known results.

    • Parameter estimation of chaotic systems based on extreme value points


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      Parameter estimation and synchronisation of chaotic systems are one of the hottest topics in the field of nonlinear science. In this paper, we addressed how to utilise the obtained experimental time series to estimate multiple parameters in chaotic systems. On the basis of relations of critical points and extreme value points, as wellas the least squares estimation, we deduced a novel statistical parameter estimation corollary method to evaluate the unknown parameters in chaotic systems. In order to illustrate the feasibility and effectiveness of the proposed method, three numerical simulation results are presented, where the validity of the proposed method is verified in detail. Furthermore, we also investigated the effects of time-series noise and system disturbances for the proposed method, and the results showed that the proposed method is robust to uncertainties.

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