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      Volume 94, All articles

      Continuous Article Publishing mode

    • Dynamical behaviour of fractional-order finance system


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      In this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana–Baleanu–Caputo (ABC) and Caputo derivatives. Picard–Lindelof’s method shows the existence and uniqueness of the solution. Numerical techniques show that ABC derivative strategy can be used effectively to overcome the risk of investment. An active control strategy for controlling chaos is used in this system. The stabilisation of equilibrium is obtained by both theoretical analysis and simulation results.

    • A geometric look at the objective gravitational wave function reduction


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      There is a famous criterion for objective wave function reduction which is derived by using the Shrödinger–Newton equation [L Diosi, Phys. Lett. A 105(4–5), 199 (1984)]. In this regard, a critical mass for the transition from quantum world to the classical world is determined for a particle or an object. In this paper, we shall derive that criterion by using the concept of Bohmian trajectories. This study has two consequences. The first is, it provides a geometric framework for the problem of wave function reduction. The second is, it represents the role of quantum and gravitational forces in the reduction process.

    • Exact solutions of a quantum system placed in a Kratzer potential and under a uniform magnetic field


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      We propose Whittaker function approach as a theoretical method for finding exact solutions of a quantum mechanical system placed in the Kratzer potential. We then show that the effect of an external uniform magnetic field on this system can be satisfactorily determined using variational method. By following the one-step treatment suggested in this study, we increase the reliability and the accuracy of the solutions of Schrödinger equation for a quantum mechanical system placed in potential energy and perturbed by a uniform magnetic field that proves to be useful in modelling physical phenomena. We find that the achieved numerical and analytical results agree very well with those already published and those calculated using the Numerov method.

    • Predictions on structural, electronic, magnetic and thermal properties of new Heusler alloys Cr$_{2}$NbSi$_{1−x}$Ge$_x$ from first-principles calculations

      I ASFOUR

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      In this study, by using full-potential linearised augmented plane wave (FP-LAPW) method with the generalised gradient approximation (GGA) based on density functional theory (DFT), the structural, electronic, elastic and magnetic properties of the Heusler alloys Cr$_2$NbSi$_{1−x}$Ge$_x$ have been evaluated. The AlCu$_2$Mnl-type structure is more stable than the CuHg$_2$Ti-type structure at equilibrium volume for the compounds. The ground-state properties of our alloys including the lattice parameter and bulk modulus were calculated. In view of Poisson’s and Pugh’s ratio, the ductility and brittleness of Cr$_2$NbSi$_{1−x}$Ge$_x$ has been analysed. The mechanical stability is maintained throughout the pressure range with high value of Debye temperature. The electronic band structures and density of states of our compounds show a half metallic character with total magnetic moments, −3.00 $\mu$B per formula unit with indirect band gap, $E_{g} = 0.152$ eV and 0.262 eV for Cr$_2$NbSi and Cr$_2$NbGe respectively. Furthermore, we have analysed the thermal properties by the quasi-harmonic Debye model. Through the obtained results, we can say that these compounds can be strong candidates for future spintronic applications.

    • Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitude damping noise channels


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      In this work, we studied the relaxation dynamics of coherences of different orders present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single and double-quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double-quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping (CPD) channel acting simultaneously on both spins in conjunction with a generalised amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a CPD channel acting simultaneously on both the spins.

    • Two bursting patterns induced by system solutions approaching infinity in a modified Rayleigh–Duffing oscillator


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      In this paper, the mechanism of system solutions approaching infinity is explored based on a modified Rayleigh–Duffing oscillator with two slow-varying periodic excitations. System solutions approaching infinity is a new novel route to bursting oscillation, and are not reported yet. The system can be separated into a fast subsystem and a slow subsystem according to the slow–fast analysis method. We find that there is a critical value for the fast subsystem, which limits the original region of the stable equilibrium point and the stable limit cycle, the right of which is the divergent region. When the control parameter slowly varies closely to the critical value $\delta_{\mathrm{CR}}$, both the stable equilibrium point and the stable limit cycle quickly leave the original region and approach positive infinity. The mechanism of two different bursting forms called bursting oscillation of point/point and bursting oscillation of cycle/cycle induced by system solutions approaching infinity are explored. This paper provides a new possible route to bursting oscillation unrelated to bifurcations and deepens the comprehension of bursting dynamics behaviours. Lastly, the accuracy of our study is verified by overlapping the transformed phase portraits onto the bifurcation diagrams.

    • Fast transverse instability due to RF cavity impedance in the ILSF storage ring


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      In this paper, the single bunch fast transverse instabilities of the electron beam in the ILSF storage ring due to the RF cavity impedance are investigated. We consider Satoh’s formalism (that studied mode coupling instabilities based on the Vlasov equation) and Lindberg’s formalisms (that studied mode coupling instabilities based on the Fokker–Planck equation). The Lindberg formalisms are rewritten to broad-band RF cavity impedance. It is shown that the zero chromaticity limits of both approaches completely coincide. In addition, we discuss the current threshold at high chromaticity that includes higher-order azimuthal and radial modes.

    • An iteration algorithm for the time-independent fractional Schrödinger equation with Coulomb potential


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      A numerical formula is derived which gives solutions of the fractional Schrödinger equation in time-independent form in the case of Coulomb potential using Riemann–Liouville definition of the fractional derivative and the quadrature methods. The formula is applied for electron in the nucleus field for multiple values of fractional parameter of the space-dependent fractional Schrödinger equation and for each value of the space-dependent fractional parameter, multiple values of energies are applied. Distances are found at which the probability takes its maximum value. Values of energy obtained in this study corresponding to the maximum value of probability are compared with the energy values resulted from the fractional Bohr’s atom formula in the fractional quantum mechanics.

    • Effect of magnetic field on the mixed convection Fe$_{3}$O$_{4}$/water ferrofluid flow in a horizontal porous channel


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      The effect of an external magnetic field on the mixed convection Fe$_{3}$O$_{4}$/water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles 0 ≤ $\varphi$ ≤ 0.05, magnetic numbers 0 ≤ Mn ≤ 100, Reynolds numbers 100 ≤ Re ≤ 500, Darcy numbers 10$^{−3}$ ≤ Da ≤ 10$^{−1}$ and porosity parameters 0.7 ≤ $\epsilon$ ≤ 0.9 while fixing the Grashof number at 10$^{4}$. Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter.

    • Compact and strong window core steering magnets with homogeneous dipole field


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      A typical axially compact, square window core steering magnet has a very small 2D good field region (GFR) of 18% of the iron core aperture. It is weak with 85% of its dipole in the fringes. Increasing the currentfed area (coil) to increase the dipole strength lowers the good field zone. Some novel and simple coil shapes can expand their 2D/3D GFR to 94/40% of the iron aperture. They are axially compact, i.e., stronger with 60–65% of the dipole in fringes. The reduction in error sextupole field is more profound. A novel 2D coil shape with vanished 2D sextupole proves the concept. For axially short cores, a gap between the coil and the iron aperture can increase the 3D sextupole, missing in 2D simulations. A new asymmetric one-axis steering magnet core and coil shape with high dipole field and homogeneity is also given. The new, practical coil shapes significantly improve the dipole field homogeneity and strength of these magnets.

    • The neutron halo structure of $^{14}$B, $^{22}$N, $^{23}$O and $^{24}$F nuclei studied via the generalised Woods–Saxon potential


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      The radial wave functions of the generalised Woods–Saxon (GWS) potential within the two-body model of (Core $+ n$) have been used to study the ground-state density distributions of protons, neutrons and matter and the associated root mean square (rms) radii of neutron-rich $^{14}$B, $^{22}$N, $^{23}$O and $^{24}$F halo nuclei. The calculated results show that the radial wave functions of the generalised Woods–Saxon potential within the two-body model succeed in reproducing neutron halo in these exotic nuclei. Elastic electron scattering form factors for these nuclei are studied by combining the charge density distributions with the plane-wave Born approximation (PWBA).

    • Non-linear Rayleigh–Bénard magnetoconvection in temperature-sensitive Newtonian liquids with heat source

      ARUNA A S

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      The present paper aims at weak non-linear stability analysis followed by linear analysis of finite amplitude Rayleigh–Bénard magnetoconvection problem in an electrically conducting Newtonian liquid with heat source/sink. It is showed that the internal Rayleigh number, thermorheological parameter and Chandrasekhar number influence the onset of stationary convection and Nusselt number. The generalised Lorenz model derived for the problem is essentially the classical Lorenz model with its coefficients depending on the variable heat source (sink), viscosity and the applied magnetic field. The result of the parameters’ influence on the critical Rayleigh number explains their effect on the Nusselt number as well. The effect of increasing strength of the magnetic field in stabilising the system and diminishing heat transport is demonstrated. But the heat source and variable viscosity work together to make the system unstable, as their effect enhances heat transfer.

    • State feedback control and observer-based adaptive synchronisation of chaos in a memristive Murali–Lakshmanan–Chua circuit


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      In this paper we report the control and synchronisation of chaos in a memristive Murali–Lakshmanan–Chua (MLC) circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux-controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques, the concept of adaptive synchronisation and observer-based approaches have been used to effect synchronisation of chaos. Both these techniques are based on state space representation theory which is well known in the field of control engineering. As in our earlier works on this circuit, we have derived the Poincaré discontinuity mapping (PDM) and zero time discontinuity mapping (ZDM) corrections, both of which are essential for realising the true dynamics of non-smooth systems. Further, we have constructed the observer- and controller-based canonical forms of the state space representations, have set up the Luenberger observer, derived the controller gain vector to implement state feedback control and calculated the gain matrices for switch feed back and finally performed parameter estimation for effecting observer-based adaptive synchronisation. Our results obtained by numerical simulation include time plots, phase portraits, estimation of the parameters and convergence of error graphs and phase plots showing complete synchronisation.

    • Quasi-exact and asymptotic iterative solutions of Dirac equation in the presence of some scalar potentials


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      In this paper, the Dirac equation in the presence of some scalar potentials based on $sl$(2) Lie algebra is solved by quasi-exact solvability theory. The configuration of the classes III and VI potentials in the Turbiner’s classification is constructed. Then, the Bethe ansatz equations are calculated so that the energy eigenvalues and eigenfunctions are obtained. Also, we study the problem by using asymptotic iteration method. Finally, we compare the results obtained by these two methods.

    • Contributory effect of diffusive heat conduction and Brownian motion on thermal conductivity enhancement of nanofluids


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      The effect of diffusive heat conduction and Brownian motion on the enhancement of thermal conductivity in nanofluids is presented here. Al$_{2}$O$_{3}$ and TiO$_{2}$ nanofluids were prepared at four different wt. fractions of 1%, 0.5%, 0.1% and 0.05% and their thermal conductivity values were measured over temperatures ranging from 25 to 55°C for every 10°C interval. The thermal conductivity of nanofluids increased with the increase in concentration and temperature. Diffusive thermal conduction and Brownian motion contribute to thermal conductivity enhancement. However, diffusive heat conduction has major contribution to thermal conductivity enhancement in nanofluids. The thermal boundary resistance was found to be increasing with wt. fraction and decreasing with temperature elevation. Finally, a correlation is presented using group method of data handling (GMDH) neural network to predict the thermal conductivity of nanofluids.

    • Influence of excluded volume interactions on the dynamics of dendrimer and star polymers in layered random flow


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      The influence of excluded volume interactions (EVIs) governs the dynamics of branched polymeric structures. Therefore, we developed a theory with the inclusion of ubiquitous EVIs on average square displacement (ASD) of the centre of mass in layered random flow (LRF). The mean-field approach is used to account for effective EVIs between non-bonded monomers of generalised Gaussian structures. The effect of polymer topology is analysed under the influence of $\delta$- and power-law correlated LRF. Qualitatively, the theory predicts two anomalous powerlaw regimes: (i) the intermediate time subdiffusive behaviour with enhanced ASD, due to EVIs, shows the internal motion of the chain and (ii) the long-time superdiffusive behaviour with slightly suppressed ASD represents the overall diffusion of the polymer. The time dependence of ASD in the presence of EVIs reveals the anomalous long-time dynamics governed by a power-law, $t^{{2−α}/2}$. The model with EVIs predicts enhanced swelling of the polymeric structure and the stretching regime in the magnitude of the ASD. The influence of EVIs in star polymer causes enhanced delay in cross-over time which is further increased with increase in functionality. Dendrimer structure with EVI delays the cross-over time with spacer length. Finally, the increase in EVIs in all topologies causes the enhancement in ASD and delay in cross-over time from subdiffusive to superdiffusive regime.

    • Energy deposition of heavy-ion beams in neutronless fusion reaction


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      Recent advances in laser-plasma accelerators have made possible the production of high-power beams with very low divergence. In this paper, the carbon heavy-ion beam was used to provide optimal conditions for the ignition of P$–^{11}$B clean fuel pellets using the Deira-4 simulation code. The calculations showed that generating maximum ion heating of about 140 keV requires a laser with an intensity of 10$^{21}$ W/cm$^2$ and a radiation time of 20 ps, which provide medium heating conditions for ignition.

    • Some Bianchi I dark energy models in Brans–Dicke theory


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      The present article deals with the study of interacting and non-interacting dark energy (DE) and dark matter (DM) in the spatially homogeneous and anisotropic Bianchi I space–time within the framework of Brans–Dicke (BD) scalar–tensor theory of gravitation. As the set of field equations is not closed, exact solutions are obtained using power-law relation and assuming a linearly varying deceleration parameter. The physical acceptability and stability of the obtained model are scrutinised using energy conditions and squared speed of sound. The statefinder diagnostic method is adopted to discuss and measure the deviation of the considered model from the $\Lambda$ cold dark matter ($\Lambda$CDM) model.

    • Approximate technique for solving fractional variational problems


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      The purpose of this paper is to suggest a numerical technique to solve fractional variational problems (FVPs). These problems are based on Caputo fractional derivatives. Rayleigh–Ritz method is used in this technique. First we approximate the objective function by the trapezoidal rule. Then, the unknown function is expanded in terms of the Bernstein polynomials. By this method, a system of algebraic equations is driven. We provide examples to show the effectiveness of this technique, which is considered in the current study.

    • Effects of aberrations on the point spread function and the two-point resolution with versatile apodization pupils


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      In this work, efficient amplitude-apodization pupils have been presented for tailoring the point spread function (PSF), which results in a decreased full-width at half-maximum (FWHM) and suppressed sidelobes. Comparison of PSF intensity profiles for both the unapodized and apodized cases have been reported. By analysing the resulting PSFs, the well-known effects induced by monochromatic aberrations such as defocussing effect, and the primary spherical aberration have been controlled for various degrees of apodization parameter $\beta$. It is shown that the two-point resolution of the apodized optical system significantly increased in the presence of aberrations. The proposed pupil apodizer is very effective in enhancing the resolution of the optical systems applicable in imaging and focussing applications.

    • The Fredholm determinant for Hulthén-distorted non-local separable potential: Application to $\alpha-\alpha$ elastic scattering


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      Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthén-distorted non-local separable potential is constructed and expressed in the maximum reduced form. Using boundary conditions (regular and irregular), two approximate energy-dependent interactions corresponding to the parent non-local potential are also constructed. The phase shifts for the $\alpha–\alpha$ elastic scattering are computed by using (i) exact expression for the Fredholm determinant and (ii) energy-dependent local interactions by exploiting the phase function method. The merits of our constructed equivalent energy-dependent potentials are judged by comparing the $\alpha–\alpha$ elastic scattering phases with our exact calculation and standard data.

    • On the interaction between tripod-type four-level atom and one-mode field in the presence of a classical homogeneous gravitational field


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      In this paper, we investigate the effects of gravitational field on the dynamical behaviour of nonlinear atom–field interaction. We consider a moving tripod-type four-level atom interacting with a single mode field in the presence of a classical homogeneous gravitational field. The analytical solution of the model is calculated by using the Schr\"odinger equation for a coherent electromagnetic field and when the atom is in its excited state. The influence of the detuning parameter and the classical homogeneous gravitational field on the temporal behaviour of atomic inversion, Mandel Q-parameters, purity of the atomic system and concurrence is studied. Our proposal has many advantages over the previous optical schemes and can be realised in several multiple experiments, such as quantum gravity. The results show that the gravity parameter has an important effect on the properties of these phenomena. Finally, conclusions and some features and comments are given.

    • Effect of point/line heat source and Hall current on free convective flow between two vertical walls


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      The influence of a point heat source and Hall current on the laminar hydromagnetic free convective flow of an incompressible and electrically conducting viscous liquid between two vertical walls has been studied. A wavelet function is utilised to mathematically formulate the point or line heat source. The incidental equations on the flow have been processed subject to the Boussinesq approximation. A unified analytical solution of basic equations like thermal energy and momentum has been derived by employing Laplace transform technique. The impacts of the pertinent physical parameters, such as Hall parameter, magnetic field and point heat source, on the velocity field are explained graphically. The valuable result from the investigation is that an increase in the length of the point heat source leads to the enhancement of the velocity profiles. Moreover, it is noticeable that an enhancement of Hall current has a direct connection with the primary factor of the volumetric flow rate and skin friction.

    • On the analytic representation of Newtonian systems


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      We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation, when transformed to the self-adjoint form, allows one to find an appropriate Lagrangian representation (direct analytic representation) for it. On the other hand, the same Newtonian equation in conjunction with its adjoint provides a basis to construct a different Lagrangian representation (indirect analytic representation) for the system. We obtain the time-dependent Lagrangian of the damped harmonic oscillator from the self-adjoint form of the equation of motion and at the same time identify the adjoint of the equation with the so-called Bateman image equation with a view to construct a time-independent indirect Lagrangian representation. We provide a number of case studies to demonstrate the usefulness of the approach derived by us. We also present similar results for a number of nonlinear differential equations by using an integral representation of the Lagrangian function and make some useful comments.

    • Integrability and exact solutions of deformed fifth-order Korteweg–de Vries equation


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      We consider a deformed fifth-order Korteweg–de Vries (D5oKdV) equation and investigated its integrability and group theoretical aspects. By extending the well-known Lax pair technique, we show that the D5oKdV equation admits a Lax representation provided that the deformed function satisfies certain differential constraint. It is observed that the D5oKdV equation admits the same differential constraint (on the deforming function) as that of the deformed Korteweg–de Vries (DKdV) equation. Using the Lax representation, we show that the D5oKdV equation admits infinitely many conservation laws, which guarantee its integrability. Finally, we apply the Lie symmetry analysis to the D5oKdV equation and derive its Lie point symmetries, the associated similarity reductions and the exact solutions.

    • Optical solitons for complex Ginzburg–Landau model with Kerr, quadratic–cubic and parabolic law nonlinearities in nonlinear optics by the exp($-\Phi(\zeta))$ expansion method


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      The optical solitons for the complex Ginzburg–Landau model with Kerr law, quadratic–cubic law and parabolic law are obtained via the exp($-\Phi(\zeta))$ expansion method. Many abundant solutions such as complex dark singular, complex periodic-singular and plane-wave solutions are derived for this model. These complex solutions are useful for understanding the physical properties for this model. Figures are presented for these solutions to show the dynamics for these waves.

    • A generalised short pulse equation: Darboux transformation and exact solutions


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      We construct infinitely many conservation laws of the generalised short pulse equation with the help of its Lax pairs. By a reciprocal transformation, the generalised short pulse equation was transformed to the first negative flow of Sawada–Kotera hierarchy. On the basis of Darboux and reciprocal transformations, we obtain some exact solutions of the generalised short pulse equation.

    • Exact solutions of time-fractional generalised Burgers–Fisher equation using generalised Kudryashov method


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      This study deals with the generalised Kudryashov method (GKM) for the time-fractional generalised Burgers–Fisher equation (TF-GBF). Using the transformation of travelling wave, the TF-GBF is transformed into a non-linear ordinary differential equation (NLODE). Later, GKM has been applied in the resultant equation which is a novel technique to obtain exact solutions. These exact solutions are plotted and the power series solution is also derived.

    • Empirical formula for beta-particle-induced bremsstrahlung yields


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      We have measured the $\beta$-particle-induced bremsstrahlung energy yield and photon yield in the energy range 0.1668–2.274 MeV using beta sources such as $^{35}$S (0.1668), $^{99}$Tc (0.293), $^{147}$Pm (0.225), $^{90}$Sr(0.5462), $^{204}$Tl (0.76), $^{91}$Y (1.5), $^{32}$P (1.71) and $^{90}$Y (2.274 MeV) in thick targets of atomic number range $13< Z< 83$. We have used a NaI(Tl) detector to measure the bremsstrahlung radiations. Based on the experimental results, we have constructed a semiempirical formula for $\beta$-particle-induced bremsstrahlung energy yield and photon yield. This formula produces bremsstrahlung energy yield and photon yield in the energy range 0.1668 MeV$ < E_{\rm{max}} < 2.274$ MeV for thick targets within the atomic number range $13 < Z < 83$. The values produced by the present formula are compared with the experiments.

    • Bulk viscous accelerating Universe in $f (R, T)$ theory of gravity


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      In this paper, we propose that the late-time acceleration of the Universe is due to bulk viscous fluid and trace of energy–momentum tensor $T$ in $f (R, T )$ theory of gravity. We assume that $f (R, T ) = f (R)+2 f (T )$ with $f (R) = R$ and $f (T ) = \lambda T$ where $\lambda$ is a constant, $R$ and $T$ are the Ricci scalar and trace of energy–momentum tensor. First, we obtain an exact solution of the bulk viscous Universe in $f (R, T )$ gravity, then we use observational Hubble data (OHD), the baryon acoustic oscillation (BAO) distance ratio data as well as SN Ia data to constrain the parameters of the derived bulk viscous Universe. Our estimations show that in the model under consideration $H_{0} = 69.089$ km/Mpc/s which is in good agreement with recent astrophysical observations. We ascertain the present age of the derived Universe as well as the signature flipping behaviour of deceleration parameter. Some physical properties of the derived model are also discussed.

    • On the solitary wave solutions of modified Benjamin–Bona–Mahony equation for unidirectional propagation of long waves


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      In this article, generalised Kudryashov technique has been implemented to construct new soliton solutions of modified Benjamin–Bona–Mahony (mBBM) equation. Also, the optimal homotopy asymptotic method (OHAM) has been employed to estimate the numerical solution. The solutions thus acquired by the above methods are illustrated graphically. The techniques considered here are efficacious, plausible and can be employed in mathematical physics to compute new exact and numerical solutions of NPDEs.

    • Dark matter through the quark vector current portal


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      We consider models of light dark matter coupled to quarks through a vector current interaction. For low energies, these models must be treated through the effective couplings to mesons, which are implemented here through the chiral Lagrangian. We find the signals of dark matter annihilation and decay to the light mesons, and find the expected photon spectrum from the decay of the hadrons. We compare the current and future observations, and show that there is a significant discovery reach for these models.

    • A modified chaotic oscillator with megastability and variable boosting and its synchronisation using contraction theory-based control which is better than backstepping and nonlinear active control


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      This paper reports a modified 2D periodically forced oscillator. Numerical simulation results using the phase portrait and Lyapunov exponents’ spectrum say that the proposed oscillator depicts megastability. Offset boosting in the new system is shown using the variable boostable phenomenon. Very limited research is available on such type of oscillator. Further, in this paper, a controller based on contraction theory is designed for the synchronisation between the two identical modified chaotic oscillators. The performances of the designed controller are compared with two widely used and well-known controllers for the chaotic systems. These controllers are (i) nonlinear active controller (NAC) and (ii) backstepping controller (BSC). It is found that the contraction theory-based controller performs better in terms of the less synchronisation time, negligible steady-state error and low control energy. Further, synchronisation between two identical Rossler chaotic systems is also presented to validate the effectiveness of the contraction theory. The simulation results validate the objectives of this paper.

    • Power law memory of natural convection flow of hybrid nanofluids with constant proportional Caputo fractional derivative due to pressure gradient


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      In this work, influence of hybrid nanofluids on heat transfer flow of a viscous fluid due to pressure gradient is discussed with innovative constant proportional Caputo fractional derivative. For this purpose, we consider an infinite vertical wall which is exponentially moving in the $x$-direction with variable temperature. Nanosized particles of Cu and Al$_{2}$O$_{3}$ are suspended in water, the base fluid. The governing equations of the problem are converted into dimensionless form. Further, we develop the constant proportional Caputo fractional model with a new operator with power law kernel which can be used to study the fluid behaviour for different values of fractional parameter at the present time. We applied the Laplace transform method to obtain the solutions and to see the impact of hybrid nanofluids and fractional parameter $\alpha$ respectively. We compared the present results with the recently published work (Nehad et al, $Adv. Mech. Eng.$ 11(7): 1 (2019)) with Caputo fractional derivative. As a result, we have found that the present solutions are best to describe the memory concept of temperature and velocity. For small values of fractional parameter, temperature and velocity have maximum values and for larger values of fractional parameter, temperature and velocity have minimum values. Further, rate of heat transfer and skin friction are also computed in tabular forms and it is found that Nusselt number with CPC is much less than that is computed with Caputo fractional derivative for greater values of fractional parameter $\alpha$.

    • Terahertz broadband metamaterial absorber enabled by SiO$_{2}$, polyimide and PET dielectric substrates


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      A broadband polarisation-insensitive terahertz (THz) metamaterial absorber (MMA) is presented in this paper. The MMA consists of a simple planar structure as a unit cell and an optically transparent indium tin oxide (ITO) ground plane, both are separated by a 50 $\mu$m dielectric substrate. We designed three combinations of MMA here, which are ITO–polyimide–ITO, ITO–polyethylene terephthalate (PET)–ITO and ITO–silicon dioxide (SiO$_{2}$)–ITO for the same planar structure. By changing the substrate of the structure, the resonant frequency and bandwidth of the absorber structure can be varied. The numerical simulation of the absorber shows that the absorptivity is $>$ 96% for all three substrates. Polyimide, PET and SiO$_{2}$ based absorbers demonstrated the bandwidth of 0.558 THz,0.603 THz and 0.658 THz with covered broadband frequency range of 0.4254–0.9829 THz, 0.457–1.16 THz and 0.511–1.169 THz respectively. ITO–PET–ITO absorber structure produced optical transparency. These bandwidths are compatible and convenient for electronic sources in the terahertz region. This study also provides applications in THz sensing and imaging, communication and detection systems.

    • Viscous Ricci dark energy model with matter creation: Exact solution and observational tests


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      In this paper, the dissipative mechanism (bulk viscosity and matter creation) is introduced to describe the effects of cosmic non-perfect fluid on the Ricci dark energy (RDE) model. We consider matter creation and bulk viscosity as two independent irreversible processes. Assuming suitable forms of the bulk viscous coefficient and matter creation rate, we find the exact solution of the field equations. We carry out fitting analysis on the cosmological parameters in the model by using Type Ia supernovae data, observational Hubble data and baryon acoustic oscillation (BAO) data with cosmic microwave background. We plot the trajectory of cosmological parameters with the best-fit values of model parameters and discuss all possible (deceleration, acceleration and their transitions) evolutions of the model. The current values of deceleration parameter and equation of state parameter are found to be $q_0=-0.362$ and $\omega_{\mathrm{eff}} = -0.575$, respectively. The age of the Universe is found to be $t_0 \simeq 13.397$ Gyr, which is very close to the $\Lambda$CDM model. We further discuss the geometrical diagnostic parameters such as statefinder and $Om$ to distinguish the model with $\Lambda$CDM model. Finally, we discuss the behaviour of energy conditions for our model and find that the model satisfies the null energy condition (NEC), weak energy condition (WEC) and dominant energy condition (DEC) while it violates strong energy condition (SEC).

    • Observation of Fano resonance in silver nanocube–nanosphere dimer


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      In this paper, we perform a theoretical investigation of the plasmon coupling in silver (Ag) nanocube–nanosphere dimer using finite difference time domain (FDTD) technique. Due to plasmonic Fano resonance, we observe a pronounced dip in the absorption spectrum, which is induced by the destructive interference between the bright dipole mode from the Ag nanocube and the dark quadrupole mode from the Ag nanosphere. We study the effects on the Fano resonance by varying the dimensions of the nanocube and nanosphere, as well as the intersurface gap distance between them. In addition, we vary the local dielectric environment surrounding the dimer and find a wide tuning in the Fano resonance line-shape. We calculate the localised surface plasmon resonance (LSPR) sensitivity of the nanocube–nanosphere dimer to the surrounding environment and find a high figure of merit (FOM) of 32.23, which indicates its promising potential as a plasmonic biosensor.

    • Effect of suction/blowing on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate with conjugate heating and inclined magnetic field


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      This article studies the effect of suction/blowing, inclined magnetic field, and chemical reaction on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate in porous medium incorporating the oscillatory plate movement as a linear combination of ‘cosine’ and ‘sine’ functions in time. Further, the mass and heat transfer characteristics are examined under the influence of conjugate mass and heat transfer phenomena at the boundary. The governing equations of the model, viz. the energy, mass transfer, and momentum, are transformed into the non-dimensional form adopting suitable non-dimensional variables and parameters. The exact analytic solutions of the model for species concentration and fluid temperature are obtained using Laplace transform technique whilst, the solution for the fluid velocity has been obtained numerically with the help of the INVLAP routine of MATLAB. The expressions for fluid temperature, species concentration, and velocity are obtained and studied graphically for various physical parameters influencing the fluid flow model taking into account the case of both suction and blowing. Further, the solutions when the Casson fluid parameter $\alpha\rightarrow\infty$ are also obtained as special cases. Results for the skin friction coefficient, Sherwood number, and Nusselt number are numerically calculated and put in tabular form. An increment for the inclination angle of the magnetic field enhances the fluid velocity while it has a reverse effect on skin friction. Increasing the Schmidt number Sc leads to a reduction in fluid concentration and increasing the value of thermal radiation accelerates fluid temperature. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

    • Image processing of Ramses II statue using speckle photography modulated by a new Hamming linear aperture

      A M HAMED

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      In this paper, a new concentric Hamming linear aperture is suggested. The point spread function (PSF) is computed for concentric Hamming linear aperture and it is compared with the corresponding circular, conventional Hamming and obstructed Hamming apertures. In addition, the autocorrelation corresponding to the aperture under consideration is computed and plotted. Application of the Hamming linear aperture in the formation of modulated speckle images of Ramses II statues using definite random diffuser is given. A diffuser limited by a circular uniform aperture is the basic element in the formation of ordinary speckle images located in the Fourier plane. Meanwhile,the Fourier spectrum of images of Ramses II multiplied by the ordinary speckle give modulated speckle images. Discrimination between the modulated speckle images is justified by comparing the profiles corresponding to each speckle image. Finally, the speckle contours and correlation of the modulated speckle images compared to the ordinary speckle images are investigated. It is noted that all computation and formation of images and plots are based on fast Fourier transform (FFT) techniques using Matlab codes.

    • Bipartite entanglement in Auger ionisation of N${_2}$


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      Quantum entanglement and its paradoxical properties are of paramount importance in quantum information theory. In recent years, there has been an increasing interest in the studies of high-dimensional quantum states and their impact on quantum communication as it can encode and process more data. Photonic entanglement is usually an evanescent property as it is destroyed easily by its interaction with an external environment. Electronic qubits are stable and can store information for a long time. However, qudit systems are more efficient, stable and allow noise robustness than qubit system. In this article, we investigate bipartite entanglement between doubly ionised molecular qudit and electronic qubit in the Auger emission process for N${_2}$ molecule following the absorption of a single photon without observing spin-orbit interaction (SOI). In the absence of SOI, Russell–Saunders coupling (L-S coupling) is applicable. The entanglement properties are estimated on the basis of negativity of partial transpose of the density matrix for Auger ionisation. We find that the entanglement depends on the spins of the singly ionised excited states and doubly ionised states of the molecules as well as on the directions of spin quantisation and of ejection of Auger electrons. A significant effect on the variation of negativity due to the linear dichroism (LD) has also been observed.

    • An efficient algorithm for inferring functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch


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      In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the spectral energy of the response oscillator. The spectral energy of the response oscillator is estimated using a modified S-transform algorithm with a short sliding window. We apply the proposed approach to master–slave Rössler systems and coupled Van der Pol oscillators with a frequency ratio of ~1:4 and show that when the slave signal is contaminated with white Gaussian noise at different signal-to-noise ratios (SNR), the new algorithm is well suited to assess the presence of coupling with $a priori$ known direction in noisy, unidirectionally coupled chaotic oscillators, especially in the case of weak and moderate coupling.

    • A new combined soliton solution of the modified Korteweg–de Vries equation


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      In this paper, the Riemann–Hilbert problem of the modified Korteweg–de Vries (mKdV) equation is studied, from which a new combined soliton solution is obtained. In addition, to illustrate the dynamics of the new combined soliton solution, an algebra technique is developed to demonstrate the soliton interactions using $Mathematica$ symbolic computations. The proposed method is effective in deriving and investigating new soliton solutions of the mKdV equation. The results also expand the understanding of the soliton structure of the mKdV equation.

    • Dynamic frequency analysis of stress–strain-dependent reversibly deformable broadband RF antenna over unevenly made elastomeric substrate


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      This paper presents the design and development of stretchable and deformable broadband antenna using low-cost silicone rubber-based dielectric substrate. A slot is introduced in the substrate to improve the stretchable behaviour. The dielectric properties of the substrate are measured using suspended ring resonator method. The proposed antenna uses silver elastomeric Lycra fabric as the conductive medium. The resistivity of the conducting Ag fabric is 1 $\Omega$ per sq. mm. The conducting patch and ground plane are attached with the substrate using silicone-based adhesive. The fabricated antenna is tested for its resonant characteristics using the vector network analyser.

    • Equation of state of PNJL model under the influence of thermal mass and magnetic field


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      We present analytical results of the equation of state (EOS) described by a model of thermal quark mass and magnetic potential term introduced in Polyakov–Nambu–Jona–Lasinio (PNJL) model for two-flavour quarks. Under the influence of thermal quark mass and magnetic field term in the potential, the calculated results of EOS using the model are enhanced in a good pattern up to the temperature $T=2.2T_c$ MeV and can follow result similar to the unmagnetised field when the temperature is increased beyond $T=2.2T_c$ MeV. The result shows that the thermodynamic behaviour agrees well with the standard properties of quantum chromodynamics (QCD) thermodynamics and enhance the result up to 2.2$T_c$ from the earlier predicted results and show the same behaviour beyond 2.2$T_c$ MeV.

    • Density functional study on structural and optoelectronic properties of cubic Mg$_x$Zn$_{1−x}$S$_y$Se$_{1−y}$ semiconductor quaternary alloys

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      In the case of technologically important Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary alloys, structural and optoelectronic properties have been calculated with density functional theory (DFT)-based full-potential linearised augmented plane-wave (FP-LAPW) approach. The Perdew–Burke–Ernzerhof generalised gradient approximation (PBE-GGA) for structural properties and both the modified-Becke–Johnson (mBJ) and Engel and Vosko GGA (EV-GGA) for optoelectronic properties are employed to calculate the respective exchange-correlation potentials. Each specimen within the Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary system is a direct band-gap ($\Gamma$-$\Gamma$) semiconductor. The lattice constant decreases, while bulk modulus and band gap increase nonlinearly with increasing anionic (S) concentration $y$ at each cationic (Mg) concentration $x$. On the other hand, nonlinear increment in lattice constant and band gap, but decrement in bulk modulus is found with increase in cationic concentration $x$ at each anionic concentration $y$. Calculated contour maps for lattice constants and energy band gaps would be useful in fabricating new quaternary alloys with preferred optoelectronic features. Optical properties of the specimens within the Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary system show several interesting features. Chalcogen-p→Zn-5s, 4p and chalcogen-p→Mg-4s, 4p optical excitations contribute intense peaks in each $\varepsilon_2(\varepsilon)$ spectrum. The composition dependence of each calculated zero-frequency limit shows opposite trend, while each calculated critical point shows similar trend of composition dependence of band gap. Moreover, calculations suggest the possibility of growth of several cubic Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary specimens on GaAs and InP substrates.

    • Mechanical conversion of the gravitational Einstein’s constant $\kappa$


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      This study attempts to answer the question of what space is made of and explores in this objective the analogy between the Einstein’s gravitational geometrical theory in one- and two-dimensional linear deformations and a possible space material based on strain measures done on the Ligo or Virgo interferometers. It draws an analogy between the Einstein’s gravitational constant $\kappa$ and the Young’s modulus and Poisson’s ratio of an elastic material that can constitute the space fabric, in the context of propagation of weak gravitational waves. In this paper, the space is proposed to have an elastic microstructure of $1.566\times10^{-35}$ m grain size as proposed in string theory, with an associated characteristic frequency $f$. The gravitational constant $G$ is the macroscopic manifestation of the said frequency via the formula $G = \pi f^ 2/\rho$, where $\rho$ is the density of the space material.

    • Hadron energy estimation from atmospheric neutrino events


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      The iron calorimeter (ICAL) at India-based neutrino observatory (INO) is designed to mainly observe the muons produced in the charged current interactions of atmospheric muon neutrinos and antineutrinos. The track of the muon is reconstructed using the hits they produce in the detector. From this track, the charge, the energy and the direction of the muon are estimated, which are used to do oscillation physics analysis. In a large fraction of events, a number of hadrons are also produced in addition to the muons. The charged hadrons also leave hits in the detector which can be utilised to estimate the hadron energy. In this work, we generate atmospheric neutrino events using two different neutrino event generators: NUANCE and GENIE. The generated events are passed through the Geant4 simulator of ICAL. In each case, we study the relation between hadron hits, defined to be the difference between the total number of hits and the muon track hits, and the hadron energy. We find that a non-negligible number of baryons are produced in atmospheric neutrino interactions. For $E_{had}$ < 5 GeV almost all the hadron energy is carried by these baryons. Finally, we formulate a procedure by which the hadron energy can be estimated from the number of hadron hits.

    • Effect of impurities and defect in thermal conductivity of lead sulphide


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      The phenomenon of heat conduction is important in semiconductor devices. This property is investigated on the basis of modified Callway model. The formalism was carried out using Hamiltonian, phonon Green’s function and equation of motion techniques for various scattering events. It was found that every scattering mechanism is independent of each other and does not affect the others. The thermal conductivity of lead sulphide (PbS) semiconductor has been studied on the basis of this concept. The results of the present model are in good agreement with experimental results and the model shows good future scope with other semiconductors and superconductors.

    • Lie symmetry reductions and dynamics of soliton solutions of (2+1)-dimensional Pavlov equation


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      In the present article, Lie group of point transformations method is successfully applied to study the invariance properties of the (2 + 1)-dimensional Pavlov equation. Applying the Lie symmetry method, we strictly obtain the infinitesimals, vector fields, commutation relation and several interesting symmetry reductions of the equation. The explicit exact solutions are derived under some limiting conditions imposed on the infinitesimals $\xi$, $\phi$, $\tau$ and $\eta$. Then, the Pavlov equation is transformed into a number of nonlinear ODEs through several symmetry reductions. These new exact solutions are more general and entirely different from the work of Kumar $et al$ (Pramana - J. Phys. 94: 28 (2020)). The obtained invariant solutions are examined analytically as well as physically through numerical simulation by giving free alternative values of arbitrary functions and constants. Consequently, graphical representations of all these solutions are studied and demonstrated in 3D-graphics and the corresponding contour plots. Interestingly, the solution profiles show the annihilation of three-dimensional parabolic profile, doubly soliton and elastic multisolitons and nonlinear wave nature form.

    • Nonlinear stability analysis of coupled azimuthal interfaces between three rotating magnetic fluids


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      The current work deals with the nonlinear azimuthal stability analysis of coupled interfaces between three magnetic fluids. The considered system consists of three incompressible rotating magnetic fluids throughout the porous media. Additionally, the system is pervaded by a uniform azimuthal magnetic field. Therefore, for simplicity, the problem is considered in a planar configuration. The adopted nonlinear approach depends mainly on solving the linear governing equations of motion with the implication of the corresponding convenient nonlinear boundary conditions. The linear stability analysis resulted in a quadratic algebraic equation in the frequency of the surface waves. Consequently, the stability criteria are theoretically analysed. A set of diagrams is plotted to discuss the implication of various physical parameters on the stability profile. On the other hand, the nonlinear stability approach revealed two nonlinear partial differential equations of the Schrödinger type. With the aid of these equations, the stability of the interface deflections is achieved. Subsequently, the stability criteria are theoretically accomplished and numerically confirmed. Regions of stability/instability are addressed to illustrate the implication of various parameters on the stability profile.

    • Electrochemical detection of sotalol on a magnetographite-epoxy electrode using magnetite nanoparticles


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      Sotalol hydrochloride (STHCl) is a cardiovascular agent, specifically an antiarrhythmic and betablocker,that can be used regularly for an extended period. However, it may have side effects, such as weakness and slow heart rate (bradycardia). Currently, techniques such as capillary zone electrophoresis and high-performance liquid chromatography have been widely used for the determination of sotalol hydrochloride, which increases the cost of the analysis. Hence, the aim of this study is to develop an electrochemical sensor, employing magnetographite epoxycomposite (m-GEC) electrode modified with magnetite nanoparticles (MNPs) functionalised with carboxyl for the detection of sotalol as a faster, cheaper, precise and sensitive alternative method. The MNPs have an average size of 7.5 nm and were characterised by transmission electron microscopy. The electrochemical behaviour of STHCl on the m-GEC electrode modified with MNPs, was investigated by cyclic voltammetry and differential pulse voltammetry (DPV). The supporting electrolyte was 0.1 mol l$^{−1}$ of phosphate buffer solution (pH = 7.0). Two oxidation peaks were observed: at a potential of 720 mV and at 920 mV vs. Ag/AgCl (KCl sat). Differential pulse voltammetry revealed linear calibration curves from 0.5 to 500 × 10$^{−6}$ mol l$^{−1}$, with a limit of detection of 0.015 × 10$^{−6}$ mol · l$^{−1}$. Finally, the modified electrode showed good sensitivity, selectivity and stability for thedetermination of sotalol in real samples.

    • Thermal entanglement and teleportation via thermally atomic entangled state in cavity QED


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      In this article, we study thermal entanglement between two-coupled two-level atoms interacting with a single-mode cavity field. The cavity mode is assumed to be initially in the vacuum state and the detuning parameter is large. The thermal entanglement in this two-qubit system is quantified in terms of the concurrence, as a proper measure for two-qubit mixed states. We investigate how the thermal entanglement depends on temperature, dipole coupling between the atoms and detuning parameter. In addition, we shall use the generated thermally atomic entangled state as a quantum channel for teleportation and we mainly concentrate on the fidelity of teleportation. Finally, the relationship between the quantum coherence and entanglement will be discussed.

    • Studies on the characteristics of TiO$_2$ photoanode and flavanol pigment as a sensitiser for DSSC applications


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      In the present work, dye-sensitised solar cell (DSSC) is fabricated using natural dye (Tecoma Stans)-sensitised TiO$_2$ as the photoanode, platinum as the counter electrode and lithium iodide and iodine as the electrolyte. Initially, TiO$_2$ nanoparticles are synthesised by the sol–gel technique using glacial acetic acid as the hydrolysing agent. The photoanodes are prepared by the Doctor Blade technique using the synthesised nanoparticles coated onto the fluorine-doped tin oxide (FTO) substrate and annealed at 400, 500 and 600$^\circ \rm C$ for 30 min. Structural analysis shows the anatase phase of the TiO$_2$ thin film with a tetragonal crystal structure. The optical transmittance is found to be around 95% with an optical band gap close to 3.1 eV and increases with an increase in annealing temperature. From the PL emission spectra, the excitation of the titania band is observed. The pigment flavan-4-ol which acts as a sensitiser is extracted from Tecoma Stans flower. From the absorption study of the pigment, the active region of radiation and the band gap are found to be around 550 nm and 2 eV respectively. FTIR analysis of the pigment shows a stable structure similar to that of the prepared photoanodes. CV analysis of the sensitiser shows maximum oxidation within the active region. Field emission scanning electron microscope (FE-SEM) analysis shows that the prepared photoanode (600$^\circ \rm C$) has spherical shape. The overall photoconversion efficiency of Tecoma Stans-sensitised TiO$_2$photoanode is 0.4491%.

    • Numerical analysis of ultrathin Cu(In,Ga)Se$_2$ solar cells with Zn(O,S) buffer layer


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      We performed an investigation on the behaviour of the electrical parameters of ultrathin Cu(In,Ga)Se$_2$ (CIGS) solar cells buffered with Zn(O,S). Using one-dimensional simulations and by defining a new structure, we achieved a significant reduction of the absorber and the buffer layers to evaluate the changes in the cell’s performance. The simulation results revealed that a good optimisation of the thickness and sulphur content of the Zn(O,S) buffer layer could be an ingenious way to reduce the thickness of the absorber without compromising the performance of the solar cells. A high efficiency of 16.9% is obtained for 0.5 $\mu$m of the absorber layer when the thickness and sulphur content of the Zn(O,S) layer are 10 nm and 0.9 respectively. At this configuration, we introduced p$^+$-CIGS and SnS layers at the CIGS/Mo interface as back surface field (BSF) to reduce interface recombinations, which are very predominant in ultrathin absorber. An improvement of 2% and 5.96% on the efficiency is obtained with the p$^+$-CIGS and SnS layers respectively. The shape of the band diagram shows good alignment and low band bending at the CIGS/OVC/Zn(O,S) interfaces and the corresponding conduction band offset is +0.2 eV between the CIGS and the Zn(O,S) layers. Ultrathin CIGS and Zn(O,S) layers can be helpful in improving the stability of the cell with regard to the results obtained from the electrical parameters.

    • Amorphisation of boron carbide under gamma irradiation


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      Boron carbide (B$_4$C) has been widely used in nuclear reactors and nuclear applications. In this work, the high-purity (99.9%) B$_4$C samples were irradiated using a gamma source ($^{60}$Co) with a dose rate ($D$) of 0.27 Gy/s at different gamma irradiation doses at room temperature. Phase and microstructural characterisation of B$_4$C samples were carried out using X-ray diffraction (XRD) and scanning electron microscopy (SEM). XRD results displayed some degradation of the diffraction peaks. The calculations reveal that 62% of B$_4$C has changed into the amorphous phase when the irradiation dose is 194.4 kGy. Fourier transform infrared spectroscopy (FTIR) was used to explain chemical bonds and functional groups of B$_4$C samples before and after gamma irradiation. The results showed that C–C chemical bonds are weaker than B–C chemical bonds and tend to break under gamma irradiation. Element mapping analysis for each gamma irradiation dose of B$_4$C samples was performed using SEM patterns. The dynamics of the elements on the surface and chemical formula of all B$_4$C samples were also determined after gamma irradiation.

    • Importance of self-shielding in mass measurements using $\gamma$-ray spectroscopy


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      Due to the exponential attenuation of photons in materials, thick samples will attenuate a large portion of photons. This is a source of error in methods such as neutron activation analysis, which use gamma spectroscopy to characterise a radioactive source. A method is developed to quantify the magnitude of self-shielding with the help of MCNP6. Then the mass of an unknown sample is determined by comparing the known sample mass and the photopeak counts of the unknown and the known samples following activation. The inclusion of self-shielding effects is shown to make this comparative mass analysis measurement technique more accurate. Accounting for the self-shielding effects allows the true source, instead of the shielded source, to be resolved by correcting for the photons that are attenuated as they try to escape the sample and reach the detector. The $\gamma$-ray measurements were made using several samples of varying shapes.

    • Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate


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      In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number. For stronger magnetic field, velocity decreases, while the temperature and concentration increase. It was also found that for shear thinning fluid the drag coefficient exhibits an increasing character when Weissenberg number increases, but for shear thickening fluid the drag coefficient shows the contrary nature. For small values of Dufour number, heat transfer rate enhances with increasing Soret number, but for higher values of Dufour number it slightly dies down with Soret number and the mass transfer rate reacts oppositely. In addition, due to increasing chemical reaction rate, the concentration and velocity decrease.

    • Ab-initio study of ordered III–V antimony-based semiconductor alloys GaP$_{1−x}$Sb$_{x}$ and AlP$_{1−x}$Sb$_{x}$


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      In this work, we have investigated the structural, electronic and thermodynamic properties of GaP$_{1−x}$Sb$_{x}$ and AlP$_{1−x}$Sb$_x$ ternary alloys for a number of ordered structures and compositions in a series of first principles calculations within the density functional theory, using full potential-linearised augmented plane-wave (FP-LAPW) method, as implemented in the WIEN2k code. The exchange-correlation effect was treated within the generalised gradient approximation (GGA) in the form of GGA-PBEsol to optimise the structure and to compute the ground-state properties. In addition to the GGA, the modified Becke–Johnson (mBJ) potential coupled with the spin-orbit interaction (SOI) was also applied to obtain reliable results for the electronic properties. Our investigation on the effect of composition on lattice constant, bulk modulus and band gap showed almost nonlinear dependenceon the composition. The GaP$_{1−x}$Sb$_x$ and AlP$_{1−x}$Sb$_x$ alloys are found to be semiconductors with a positive energy gap for the whole concentration range. The spin-orbit splitting $\Delta_{\rm{SO}}$ was found to increase with Sb composition with a marginal bowing parameter. Besides, a regular-solution model was used to investigate the thermodynamic stability of the alloys which mainly indicates a phase miscibility gap. In addition, the quasiharmonic Debye model was applied to analyse the effect of temperature and pressure on the Debye temperature and heat capacity.

    • Even–odd effect of the homologous series of nCHBT liquid crystal molecules under the influence of an electric field: A theoretical approach


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      In this work, we present the effect of electric field on 4-(trans-4$^\prime$-n-alkyl-cyclohexyl) isothiocyanatebenzene(nCHBT) liquid crystal (LC) molecules. Under the influence of an electric field, the birefringence exhibits the even–odd effect while order parameter, HOMO–LUMO gap, magic angle, isotropic polarisability, range of director angle and the refractive index do not exhibit any even–odd effect. The extension of the alkyl chain length of the nCHBT liquid crystal molecule exhibits the even–odd effect for the dipole moment and temperature from nematic to isotropic phase transition while the HOMO–LUMO gap remains constant. Still, order parameters, isotropic polarisability and refractive index have continuously increased. The odd carbon atom numbers present higher values than the even carbon atom numbers of the alkyl chain for the phase transition temperature. The nCHBTLC molecule expresses the order parameter, and birefringence is reciprocal to each other. For the whole series, there is an increase in order parameter, and a decrease in birefringence. The influence of the external electric field is analternative to the temperature for the optical parameter of nCHBT LC.

    • M-lump and lump–kink solutions of (2 + 1)-dimensional Caudrey–Dodd-Gibbon–Kotera–Sawada equation


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      In this paper, M-lump and interaction between lumps and kink solitons of the (2 + 1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation are studied based on Hirota bilinear form. M-lump solutions are derived by taking a ‘long wave’ limit of the N-soliton solutions, and the lump–kink solutions are presented consequently. In addition, evolutions of solutions are shown by choosing certain parameters.

    • A comprehensive theoretical analysis of ${12}$^B + ${58}$^Ni elastic scattering measured for the first time by using different density distributions, different nuclear potentials and different cluster approaches

      AYGUN M

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      Recently, Zevallos et al [Phys. Rev. C $\bf{99}$, 064613 (2019)] measured, for the first time, the elastic scattering data of $^{12}\rm{B} + ^{58}\rm{Ni}$ reaction at $E_{Lab} = 30.0$ and 33.0 MeV. For the first time, we show a comprehensive theoretical analysis of the experimental data of $^{12}\rm{B}+^{58}\rm{Ni}$ reaction. First, we propose alternative density distributions for the $^{12}\rm{B}$ nucleus, and obtain the elastic scattering angular distributions of $^{12}\rm{B} + ^{58}\rm{Ni}$ reaction with the help of these densities. Secondly, we calculate the elastic scattering cross-sections of $^{12}\rm{B} + ^{58}\rm{Ni}$ reaction by using 13 different nuclear potentials to reveal alternative nuclear potentials. Finally, we examine cluster structures such as $α + ^8\rm{Li}$ and $n + ^{11}\rm{B}$ of the $^{12}\rm{B}$ nucleus by using a simple approach, and acquire elastic scattering cross-sections of $^{12}\rm{B} + ^{58}\rm{Ni}$ reaction over these cluster approaches. We compare all the theoretical results with the experimentaldata, and discuss their similarities and differences. Also, we propose new equations of both normalisation constant and imaginary potential parameters for all the systems analysed.

    • Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations


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      We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated using time-space (i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of fractional diffusion equation, (v) two-coupled system of fractional stationary transonic plane-parallel gas flow equation and (vi) three-coupled system of fractional Hirota–Satsuma KdV equation. Also, we explicitly showed how to derive more than one exact solution of the equations as mentioned above using the invariant subspace method.

    • Relativistic potentials with rational extensions


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      In this paper, we construct isospectral Hamiltonians without shape-invariant potentials for the relativistic quantum mechanical potentials such as the Dirac oscillator and hydrogen-like atom.

    • A novel meminductor-based chaotic oscillating circuit and its DSP realisation for generating PN sequences


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      Meminductor is a novel nonlinear inductor with memory. A meminductor-based chaotic oscillating circuit that has only two linear resistors, two linear capacitors and a meminductor, is designed based on a mathematical model of the flux-controlled meminductor to study its characteristics in nonlinear circuit. Through the analysis of bifurcations, dynamic map and Lyapunov exponents, it is found that the system can exhibit some complex characteristics, such as an infinite number of equilibrium points and burst chaos. Especially, bifurcation without parameters and coexisting attractors appear under a fixed set of parameter values but different initial conditions. Moreover, random characteristics of the PN sequences generated from the chaotic circuit are tested via the test suit of National Institute of Standards and Technology (NIST), and the tested randomness definitely reaches the standards of NIST. Finally, a scheme for digitally realising this oscillating circuit is provided using the digital signal processor (DSP).

    • The linear term in the isobaric-mass-multiplet equation for $fp$-shell nuclei in the framework of spectral distribution theory


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      The one- plus two-body isospin non-conserving nuclear interactions, namely the isovector and isotensor ones, are included in the prediction of the energies of the ground state and the low-lying states of the $fp$ shell nuclei using spectral distribution theory. This in turn is used to calculate the linear term in the isobaric mass-multiplet equation and the predictions are then compared with experimental values after the addition of the Coulomb contribution. The agreement is found to be good as observed for $sd$ shell nuclei earlier. One also sees that in this method the contribution to the linear term comes almost completely from the one-body isovector Hamiltonian, resulting in a huge simplification of the problem.

    • Correction to: Analytical approaches to space- and time-fractional coupled Burgers' equations


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    • Influence of the dispersion coefficient and dielectric constant ratio on the asymmetric Gaussian potential quantum dot qubit with electromagnetic field


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      Selecting the asymmetric Gaussian (AG) potential to describe the confinement of electron in a disk-shaped quantum dot (QD), the ground state and the first excited state energy and wave function of the system are derived by using the Lee–Low–Pines (LLP) Pekar transformation variational method, and the two-level structure required for a qubit is constructed. The influence of material parameters such as the dispersion coefficient, dielectric constant ratio and electron–phonon coupling constant on the qubit properties of AG potential QD with the electromagnetic field are investigated. The results show that the electric field and magnetic field have opposite adjustment functions for the formation of qubit. The electric field is advantageous for the qubit survival and information storage, while magnetic field and electron–phonon coupling are detrimental to the qubit survival and information storage, respectively. The decoherence time of the qubit increases with increasing magnetic field cyclotron frequency ‘from the turning point’. Applying an electric field, increasing the dielectric constant ratio, the dispersion coefficient and the electron–phonon coupling constant of the materials are all beneficial to improve the coherence of the qubit.

    • Evaluation of the gamma and neutron shielding properties of 64TeO$_{2}$ + 15ZnO + (20 - $x$)CdO + $x$ BaO + 1V$_{2}$O$_{5}$ glass system using Geant4 simulation and Phy-X database software

      A AŞKIN

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      In this study, fast neutron removal cross-section and $\gamma$-ray shielding capabilities in terms of mass attenuation coefficient ($\mu_{m}$), transmission fractions ($T$), effective atomic numbers ($Z_{{\rm eff}}$), half-value layer (HVL) and exposure build-up factors (EBF) of the 64TeO$_{2}$ + 15ZnO + (20 - $x$)CdO + $x$BaO + 1V$_{2}$O$_{5}$ ($x$ = 0, 5, 10, 15, 20 mol%) glass system have been evaluated using Monte Carlo simulations carried out with Geant4 model of the high-purity germanium (HPGe) detector and Phy-X database software. The results of this study revealed that $\gamma$-ray shielding capability of the studied glass system increases with the increase of BaO content and decrease of CdO content in the chemical structure due to the high atomic number (Z) of Ba compared to Cd. The results also showed that increase of BaO fraction in the glass structure weakens the neutron shielding ability and by the use of low Z elements in the composites better shielding performance against neutrons can be obtained.

    • Control-based verification of multiatoms in a cavity


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      In this paper, we study a model of two two-level atoms interacting with a quantum field. An analytical solution is obtained which is used to study the information entropy of the system. It is shown that the nonlinear term plays a significant role in the behaviour of the minimum uncertainty (MU) compared with the concurrence (C). Our extensive study of information entropy of atoms–field interaction demonstrates that using the coupling strength between the atoms and the field as a controller parameter, one can control the dynamics of the system by increasing the lower bound of the entropic uncertainty relation or decreasing the entanglement.

    • Bursting oscillations with boundary homoclinic bifurcations in a Filippov-type Chua’s circuit


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      A modified version of the typical Chua’s circuit, which possesses a periodic external excitation and a piecewise nonlinear resistor, is considered to investigate the possible bursting oscillations and the dynamical mechanism in the Filippov system. Two new symmetric periodic bursting oscillations are observed when the frequency of external excitation is far less than the natural one. Besides the conventional Hopf bifurcation, two non-smooth bifurcations, i.e., boundary homoclinic bifurcation and non-smooth fold limit cycle bifurcation, are discussed when the whole excitation term is regarded as a bifurcation parameter. The sliding solution of the Filippov system and pseudo-equilibrium bifurcation of the sliding vector field on the switching manifold are analysed theoretically. Based on the analysis of the bifurcations and the sliding solution, the dynamical mechanism of the bursting oscillations is revealed. The external excitation plays an important role in generating bursting oscillations. That is, bursting oscillations may be formed only if the excitation term passes through the boundary homoclinic bifurcation. Otherwise, they do not occur. In addition, the time intervals between two symmetric adjacent spikes of the bursting oscillations and the duration of the system staying at the stable pseudonode are dependent on the excitation frequency.

    • Exact solution of the nonlinear fin problem with exponentially temperature-dependent thermal conductivity and heat transfer coefficient


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      This article studies a class of fin problems with two nonlinear terms arising from thermal conductivity and convection heat transfer coefficient. A one-dimensional convective straight fin is analysed for exponentially temperature-dependent thermal conductivity and exponentially temperature-dependent heat transfer coefficient. The exact fin temperature excess, heat transfer rate and fin efficiency are obtained and presented graphically. The obtained results show the strong influences of exponent indexes of thermal conductivity and convection transfer coefficient as well as thermogeometric fin parameter on the fin efficiency and heat flow.

    • Novel fractional-order chaotic systems of different order and multiswitching synchronisation


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      This paper gives multiswitching synchronisation scheme for a class of fractional-order chaotic systems by combining active and adaptive control theories. Adaptive controllers have been designed by using different laws of switching and fractional-order Lyapunov stability theory. We have also constructed a new fractional-order Duffing system. The fractional-order Duffing system and fractional-order Rabinovich–Fabrikant system have been taken as the drive system and the response system respectively. Applications have been demonstrated. Theoretical analysis and numerical simulations are also given to verify the robustness of the proposed controllers.

    • Application of the Caputo–Fabrizio derivative without singular kernel to fractional Schrödinger equations


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      In this work, we solve time, space and time-space fractional Schrödinger equations based on the non-singular Caputo–Fabrizio derivative definition for 1D infinite-potential well problem. To achieve this, we first work out the fractional differential equations defined in terms of Caputo–Fabrizio derivative. Then, the eigenvalues and the eigenfunctions of the three kinds of fractional Schrödinger equations are deduced. In contrast to Laskin’s results which are based on Riesz derivative, both the obtained wave number and wave function are different from the standard ones. Moreover, the number of solutions is finite and dependent on the space derivative order. When the fractional orders of derivatives become integer numbers (one for time derivative or/and two for space), our findings collapse to the standard results.

    • Probabilistic solution of nonlinear ship rolling in random beam seas


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      In this paper, the probability density function (PDF) and the mean up-crossing rate of nonlinear ship rolling in random beam seas are investigated. The excitation of stationary random sea waves is approximated as a second-order linear filtered white noise. The Fokker–Planck–Kolmogorov (FPK) equation governing the probability density function of ship rolling is a four-dimensional linear partial differential equation with varying coefficients, and obtaining its exact solution is much more sophisticated. The exponential-polynomial closure (EPC) method is applied to solve the corresponding FPK equation of the system. In numerical examples, linear-plus-cubic damping model and linear-plus-quadratic damping model with three different sea states are further examined. Comparison with the equivalent linearisation (EQL) method and Monte Carlo simulated results show that the proposed procedure is effective to obtain a satisfactory probability density function solution, especially in the tail region.

    • Singularity-free non-exotic compact star in $f (R, T)$ gravity


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      In the present work, we have searched for the existence of anisotropic and non-singular compact star in the $f (R, T)$ gravity by taking into account the non-exotic equation of state (EoS). In order to obtain the solutions of the matter content of the compact object, we assume the well-known barotropic form of EoS that yields the linear relation between pressures and energy density. We propose the existence of non-exotic compact star which shows the validation of energy conditions and stability within the perspective of $f (R,T)$ extended theory of gravity. The linear material correction in the extended theory and matter content of compact star can remarkably satisfy energy condition. We discuss various physical features of the compact star and show that the proposed model of the stellar object satisfies all regularity conditions and is stable as well as singularity-free.

    • Analysis of solution trajectories of fractional-order systems


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      The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw light on the relation between two trajectories $X (t)$ and $Y (t)$ of such a system, where the initial point $Y$ (0) is at some point X (t1) of the trajectory $X (t)$. In contrast with classical systems, these trajectories $X$ and $Y$ do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect.

    • Doppler narrowing of EIT linewidth in closed-loop systems


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      We theoretically investigate a five-level closed-loop M-type atomic system and a three-level closed-loop $\Lambda$-system in hot atomic vapour. In contrast to closed-loop $\Lambda$-system, two unpopulated ground states of the M-system are coupled by a microwave field. We find that thermal averaging in the M-system causes many interesting modification of probe absorption lineshape including narrowing, splitting and absorption enhancement. In M-system, the linewidth of probe absorption after thermal averaging becomes remarkably narrow (100 times smaller) with respect to the linewidth of stationary atoms. On the contrary, the closed-loop $\Lambda$-system generates only 1.6 times smaller linewidth in thermal vapour. The absence of population transfer through the microwave field leads to this significant narrowing effect in the M-system which is unachievable in closed-loop $\Lambda$-systems. Hence, M-system has potential application in high-resolution spectroscopy, generation of ultra slow light, phase-dependent optical switching, and in microwave electro- and magnetometry.

    • Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model


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      The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic detailsof the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.

    • Structural, magnetic and electrical properties of Ni–Co–Cu–Mn ferrite + PZT composite thick films


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      $\rm{Ni–Co–Cu–Mn\,Ferrite+PZT (PbZr_{0.52}Ti_{0.48}O_{3})}$ ferroelectric: composite thick filmswere prepared by the screen-printing method. The normal XRD and the low glancing angle XRD confirm the presence of both phases in the composite thick films. Back-scattered SEM shows 0-3 and 3-3 types of connectivity. The magnetic ordering of the ferrite phase was confirmed from $M–H$ hysteresis loop whereas the electric ordering of the ferroelectric phase was confirmed from $P–E$ hysteresis curve. Various measurable parameters from the loop were studied as a function of the mole percent of constituent phases. PUND (positive up negative down) analysis was done to determine the resultant polarisation contributed by the participating phases in the composites. Dielectric and magnetoelectric (ME) measurements were analysed in the light of PUND measured data.

    • An investigation on the stability of the structural and electronic properties of $ErX_{3} (X = Ga, In\,and\,Sn)$ intermetallic compounds


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      First-principle computations on structural and electronic properties of cubic rare-earth $\rm{ErX_{3} (X = Ga, In\,and\,Sn)}$ intermetallic compounds have been accomplished using the full-potential linearised augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). For the exchange correlation, we used local spin density approximation (LSDA) plus Hubbard parameter $U (LSDA+U)$ approach because of the strong on-site Coulomb repulsion between the localised $\rm{RE}-4 f$ states. Calculated ground-state properties such as lattice constant ($a_{0}$) and other parameters with exchange correlation functional are found compatible with the experimental results. The electronic properties have been determined in terms of band structures, total and partial density of states (DOSs) and Fermi surfaces, which demonstrate the metallic behaviour of all the compounds. Also, the effect of Hubbard potential on this is discussed in detail. The bonding descriptions of these compounds have also been evaluated from charge density difference plots, which display the presence of metallic and mixed covalent–ionic bonding. The determined magnetic moments explain the ferromagnetic behaviour of these compounds.

    • Electric charge quantisation in 331 models with exotic charges


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      The extensions of the Standard Model based on the $SU(3)_{C} \otimes SU(3)_{L} \otimes U(1)_{X}$ gauge group are known as 331 models. Different properties such as the fermion assignment and the electric charges of the exotic spectrum, that define a particular 331 model, are fixed by a $\beta$ parameter. In this article, we study the electric charge quantisation in two versions of the 331 models, set by the conditions $\beta = 1/(3\sqrt{3})$ and $\beta = 0$. In these frameworks, arise exotic particles, for instance, new leptons and gauge bosons with a fractional electric charge. Additionally, depending on the version, quarks with non-standard fractional electric charges or even neutral appear. Considering the definition of electric charge operator as a linear combination of the group generators that annihilates the vacuum, classical constraints from the invariance of the Lagrangian, and gauge and mixed gauge-gravitational anomalies cancellation, the quantisation of the electric charge can be verified in both versions.

    • Spin-polarised DFT study of the structural stability and half-metallicity of RbN in the CsCl, rocksalt and zinc-blende structures


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      We present first-principles calculations on the structural, mechanical, electronic, thermodynamic, lattice dynamic and magnetic properties of RbN in the CsCl, rocksalt (Rs) and zinc-blende (ZB) structures centred on spin-polarised density functional theory (DFT). It was established that in all the three structures, ferromagnetic (FM) state is more stable than the non-magnetic (NM) state. The results show that RbN exhibits half-metallic characteristics at the equilibrium lattice parameters and have small energy gaps of 1.205, 1.092 and 1.364 eV for CsCl, Rs and ZB structures respectively. We find that only the CsCl and Rs structures are mechanically, lattice dynamically and thermodynamically stable. Furthermore, the structures exhibit equal integer magnetic moment of $2 \mu_\rm{B}$ approximately.

    • Pseudopotential study of wide band-gap GaN at high pressures


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      A pseudopotential approach is used to study the lattice and elastic properties of the wide band-gap GaN at zero and high pressures up to 120 kbar. When the pressure is 0 kbar, our findings are generally in agreement with the data reported in the literature. The pressure dependence of lattice constant, polarity, transverse effective charge, elastic constants and their related mechanical parameters, and microhardness has been examined and discussed. Our results show that all these features exhibit a monotonic behaviour against pressure. Upon compression up to 120 kbar, our results suggest that the material in question remains mechanically stable with higher stiffness, becomes more resistant to the deformations or deflections and its chemical bond and rigidity become stronger.

    • Coexisting bubbles, multiple attractors, and control of multistability in a simple jerk system under the influence of a constant excitation force


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      We investigate the impact of a constant force excitation on the dynamics of a simple jerk system with piecewise quadratic nonlinearity.We demonstrate that in the presence of the forcing term, the model is asymmetric yielding more complex and striking bifurcation patterns such as parallel bifurcation branches, coexisting multiple asymmetric attractors, hysteretic dynamics, crises, and coexisting asymmetric bubbles of bifurcation. Accordingly, the coexistence of two, three, four, or five asymmetric periodic and chaotic attractors are reported by changing the model parameters and initial conditions. The control of multistability is investigated by using the method of linear augmentation. We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter. A very good agreement is observed between PSpice simulation results and the theoretical study.

    • Ion-acoustic compressive and rarefactive solitary waves in unmagnetised plasmas with positrons and two-temperature superthermal electrons


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      Ion-acoustic solitary waves (IASWs) in plasma consisting of ions, positrons and superthermal electrons in two distinct temperatures have been studied. The reductive perturbation method (RPM) has been employed to derive the Korteweg–de Vries and modified KdV equation. Numerical and analytical studies show that compressive and rarefactive solitons exist for the selected parametric range depending on the spectral indexes, $κ (κ_{h},κ_{c})$ and their respective densities ($\nu,\mu$). It is found that spectral indexes ($κ_{h},κ_{c}$) and their relative densities have significant impact on the basic properties, i.e., amplitude and width as well as on the nature of IASWs. Variations of amplitude and width for the compressive and rarefactive solitary waves have been analysed graphically with different plasma parameters like spectral indexes of cold and hot electrons ($k_{c}, k_{h}$), their respective densities, ionic temperature ratio, positron temperature ratio as well as with the temperature ratio of the two-electron species. The amplitude of the compressive (rarefactive) solitary waves increases (decreases) on increasing $k_{h}$. However, the amplitude of the compressive (rarefactive) solitary waves decreases (increases) on increasing $k_{c}$. The investigations of such solitary waves may be helpful for the critical understanding of space where superthermal electrons with two different temperatures exist along with positrons and ions (e.g. Saturn’s magnetosphere, pulsar magnetosphere).

    • New wave patterns to the doubly dispersive equation in nonlinear dynamic elasticity


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      This study aims to obtain travelling wave solutions of the doubly dispersive equation in nonlinear dynamic elasticity by the sine-Gordon expansion method. We give physical explanation of the presented solutions under suitable parameters via the 3D, 2D and contour simulations.

    • Realisation of parallel logic elements and memory latch in a quasiperiodically-driven simple nonlinear circuit


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      We investigate the effect of two aperiodic square waves in a quasiperiodically-driven Murali–Lakshmanan–Chua circuit. It is found that the response of the circuit produces logical output in both strange nonchaotic and chaotic regions. Changing the biasing of the circuit changes the response of the circuit into another kind of logic operation and SR flip flop. Further, we show how this circuit produces two logical elements as its outputs which are complementary to each other. It is also shown that the logical nature of the circuit persists even when experimental noise is present. Thus, we confirm that both the dynamical behaviours, namely strange nonchaos and chaos, can be efficient tools to construct computer architecture.

    • The influence of radiation emission on the thermodynamic and structural dynamic properties of liquid biosystems


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      The influence of radiation on the thermodynamic properties of liquid systems that are governed by the radiation-induced change in the chemical potentials of the liquid and its components has been studied. The irradiation of coexisting phases in the stationary state is shown to result in a shift of the phase transition point parameters. The temperature shift of the first-order phase transition under the influence of radiation is evaluated with regard to both the entropy and interaction factors in the chemical potential of the system. The results obtained from the MD simulation of the radiation influence on 10% saline quantitatively confirm the predictions of the introduced theoretical model of the irradiation process. To verify our theoretical assumptions concerning modifications in the local structure of the examined saline (water solution of NaCl at 10% concentration), experiments under the influence of irradiation were done.

    • Effect of $\rm{Me^{2+} /OH^{−}}$ ratio in the formation of $\rm{Mn_{0.5}Zn_{0.5}Fe_{2}O_{4}}$ nanoparticles of different sizes and shapes in association with thermomagnetic property


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      The influence of metal ion to hydroxide ion ($\rm{Me^{2+} /OH^{−}}$) ratio on the synthesis of $\rm{Mn_{0.5}Zn_{0.5}Fe_{2}O_{4}}$ (MZ5) ferrite nanoparticles is reported. The aim of this low-temperature co-precipitation technique is to produce MZ5 nanoparticles with different sizes in single domain range. The variation in $\rm{Me^{2+} /OH^{−}}$ ratio affects the growth and shape of the particles. The mechanism of nucleation and growth of the particles is discussed. EDX and XPS measurements show the change in stoichiometry of the composition when $\rm{Me^{2+} /OH^{−}}$ ratio changes. When the ratio is 0.52, Zn ion was found to be absent and the structure resembles $\rm{Mn_{x}Fe_{3−x}O_{4}}$. The defect in the composition changes magnetic properties such as saturation magnetisation and Curie temperature of the samples. 119 nm crystalline size with highest magnetisation ($\rm{80 Am^{2}/kg}$) is obtained which shows quite good response to induction heating (specific absorption rate (SAR) = 78 W/g). Moreover, SAR and intrinsic loss power (ILP) are higher for MZ5 ferrite than that are reported earlier. This shows the potential of magnetic induction heating in the treatment of cancer.

    • Chaos in a cyclic three-species predator–prey system with a partial consumption of superpredator


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      This paper aims at the detailed numerical analysis of a cyclic three species predator–prey model where the prey consumes only a part of the super-predator population. Such a model exists only when the prey acts as an omnivore. Here, we have investigated the dynamical behaviour of the prey, middle predator and super-predator. All the possible equilibrium points of the model are computed and the existence and stability condition of the equilibrium states are determined. The phase portraits are generated for different sets of parameter values. The long term behaviour of the system is investigated by studying the bifurcation structure and nature of the attractors, thereby identifying the domain of chaos, as each of the control parameter is varied independently. Finally, we show that a transition from chaotic domain to escape or vice-versa of the predator in a small region of the parameter plane leads to a fractal structure.

    • Non-contact excitation of piezoelectric components through bidirectional energy transfer system


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      The non-contact excitation of multiple piezoelectric components (PZT) through bidirectional electric field transmission system has been explored. In the proposed technique, two parallel plate capacitor-like structures have been designed with a pair of ground copper electrodes along with a live copper electrode, and two PZT plates are equidistantly placed in between each live and ground electrode. Experimentally, it has been observed that piezoelectric plates are wirelessly energised as a result of both electric and piezoelectric resonances. Maximum vibrational displacement can be obtained over the piezoelectric plates at a point,when the operating frequency of the E-field generator matches with the frequency of the mechanical resonance of the PZT plate. The maximum output power (Pout) across the non-contact stimulated piezoelectric plates principally depends on resonance, resistive load, vibration mode, driving frequency, position of PZT component etc. The output power obtained across the excited piezoelectric device by bidirectional non-contact energy transfer has been appreciably higher than that of the single PZT component excited by simple parallel-plate capacitor structure. The maximum output power of 0.271mW and 0.298 mW are acquired across piezoelectric plates at a resonance frequency of 924 kHz and 350 $\Omega$ optimal loads with 50 V input, when the live and ground electrodes are separated by 4 mm. By enacting the proposed wireless excitation technique, multiple piezoelectric devices can be energised together.

    • Electron-impact cross-sections of atmospherically relevant amines from intermediate to 5000 eV energy range


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      The amines are major source of environment pollutants emitted in atmosphere from variousanthropogenic sources. The non-thermal plasma (NTP)-based technology has proved successful in controlling the emitted amines reaching the atmosphere. The efficient NTP reactors rely on accurate electron–molecule collision data. The electron impact cross-sections are thus obtained for a few amines from ionisation threshold to 5000 eV using the single centre expansion (SCE) formalism. Themolecular wave function of each target is obtained from themulticentre expansion of the Gaussian-type orbitals within a single determinant Hartree–Fock self-consistent field scheme. The expansion of wave function, density and potential is carried out at the centre of mass of the molecules. The interaction potential included to model the electron interaction in the target comprises static, correlation polarisation and exchange types of potentials. The elastic cross-sections are obtained after solving the coupled scattering equations using Volterra integral form. The inelastic effects contributing to electron–molecule scatteringare approximated by the ionisation cross-sections. The total cross-sections obtained after summing the elastic and ionisation cross-sections are in good agreement with the available data. We have also tried to explain the effect of polarisation potential on scattering cross-sections. A semiempirical formula based on the spatial extent of the molecule is proposed to estimate the cross-sections for the homologous series of amine molecules.

    • Numerical study of multidimensional fractional time and space coupled Burgers’ equations


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      This paper declares a new spectral collocation technique to provide accurate approximate solutions of the one- and two-dimensional time and space fractional coupled Burgers’ equations (TSFCBEs) in which the fractional derivatives are defined according to Caputo’s definition. The suggested method is based on the shifted Gegenbauer polynomials (SGPs) for approximating the solution of TSFCBEs. The suggested technique reduces the considered problems to the solution of nonlinear algebraic equations (NLAEs). Moreover, the accuracy and reliability of the proposed method are confirmed through numerical examples. Finally, the obtained numerical results are compared with those previously reported in the literature.

    • Execution of Fredkin gate by a set of free fermions


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      It is not a trivial task to answer whether a free fermion-based architecture for a quantum computer can efficiently execute basic gates such as the Fredking gate. We show that a set of free fermions can efficiently execute Fredkin gate.

    • Systematics of multinucleon transfer in heavy-ion reactions


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      One-neutron pickup reactions for 52 projectile–target combinations were analysed using a systematics between transfer cross-sections and ground-state $Q$-values. One-neutron pickup transfer shows a good correlation between reduced transfer cross-sections and ground-state $Q$-values ($Q_{gg}$) if one separate the systems into two groups based on their $\rm{Z_{p} Z_{t}}$ product. Also, similar kind of systematics is applied to 2n, 3n and 4n pickup transfer and a good correlation is obtained between reduced transfer cross-sections and $Q_{gg}$ values, where no $\rm{Z_{p} Z_{t}}$ dependenceis seen.

    • Free convective Poiseuille flow through porous medium between two infinite vertical plates in slip flow regime


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      The present study investigates the heat and mass transfer of magnetohydrodynamic (MHD) free convection through two infinite plates embedded with porous materials. In addition to that the combined effect of viscous dissipation, heat source/sink considered in energy equation and thermodiffusion effect is taken care of in the mass transfer equation. Using suitable non-dimensional variables, the expressions for the velocity, temperature, species concentration fields, as well as shear stress coefficient at the plate, rate of heat and mass transfer, i.e. Nusselt number (Nu) and Sherwood number (Sh) are expressed in the non-dimensional form. These coupled nonlinear differential equations are solved using perturbation technique and their behaviour is demonstrated via graphs for various values of pertinent physical parameters namely, Hartmann number (Ha), Reynolds number (Re), Schmidt number (Sc), Soret number (So), permeability parameter etc. In a particular case, the present result was compared with earlier established results and the results are found to be in good agreement. However, major findings are elaborated in the results and discussion section.

    • Multiple solutions for non-Newtonian nanofluid flow over a stretching sheet with nonlinear thermal radiation: Application in transdermal drug delivery


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      We have explored multiple solutions for non-Newtonian Casson nanofluid flowpast a moving extending sheet under the influence of variable thermal conductivity and nonlinear radiation through a permeable medium with convective boundary conditions. The governing equations are transformed to ODEs by similarity transformations and then solved numerically by the Chebyshev pseudospectral (CPS) method. Dual solutions are obtained for velocity, temperature and nanoparticle concentration distributions with different values of physical parameters. Inthe present analysis, it was found that, the nonlinearity formula for thermal radiation gives a realistic description of nanofluid mathematical model depending on the existence of nanoscale particles. Furthermore, the concentration of nanoparticles is highly influenced by nonlinear thermal radiation due to the sizes of nanofluid, where linear radiation has a weak effect on the concentration distributions of nanoparticles. These results are very important in medicine, and more specifically for reinforcing the delivery of drugs through the skin, as the nanoparticle entrapment of drugs enhances delivery to, or absorption by, target cells. The transdermal drug delivery system offers huge clinical advantages over other dosage forms. As transdermal drug delivery offers controlled as well as predetermined rate of release of the drug into the patient, it can keep up steady-state nanofluid concentration.

    • Numerical approach of variable thermophysical features of dissipated viscous nanofluid comprising gyrotactic micro-organisms


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      This article addresses the heat and mass transport phenomena by performing a theoretical analysis of three-dimensional viscous fluid flow containing gyrotactic micro-organisms over a nonlinear stretched surface. Variable magnetic field is considered normal to the stretched surface to control the fluid flow. Thermal transportation is discussed in view of variable thermal conductivity. Variable characteristics of mass diffusion along with chemicalreaction are incorporated in mass transportation. Darcy–Forchheimer expression is used to characterise the porous medium. Also, Brownian motion and thermophoresis are incorporated to enhance the diffusion. The governing partial differential equations (PDEs) are derived using boundary layer analysis by assuming small magnetic Reynolds number. Appropriate transformation is used to convert complex system of coupled PDEs into nonlinearordinary differential equations (ODEs). Transformed problem is then tackled analytically using optimal homotopic procedure. Reliability of the suggested scheme is presented through error reduction table and also by comparing the obtained solution with the published ones. Graphs and tables are prepared to observe the impact of parameters on physical variables. Dimensionless stresses and rate of heat transfer are computed numerically. It has been observed that larger values of Brownian diffusion and thermophoresis increase the fluid temperature. Moreover, dimensionless stresses and rate of heat transfer are computed to check the reliability of the proposed procedure. These values are clearly in an excellent agreement with the previous findings reported in literature.

    • Design and calibration of a passive detector for separating neutron, proton and α-particles in mixed radiation fields


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      In this study, a new detector is designed based on CR-39, and separately calibrated for protons, neutrons and $\alpha$-particles under the same etching condition. To that end, an americium–beryllium standard source ($^{241}$Am–Be) and a plexiglass phantom for neutron irradiation, brass collimators and an americium standard source ($^{241}\rm{Am}$) for alpha irradiation, as well as a Van de Graaff accelerator for proton irradiation were employed. Sodium hydroxide solution of 6.25 N at $85^{\circ}\rm{C}$ was also used for CR-39 chemical etching. Considering the detection principle of the device, different filters were designed to help distinguish between fast neutron particles, thermal neutrons, albedo neutrons, protons and $\alpha$-particles in mixed radiation fields. Moreover, both the contribution of each particle and the ability of the designed detector to discriminate energy of charged particles were quantified.

    • Long-lived quantum coherence in a two-level semiconductor quantum dot


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      In this paper, we present an analytical solution for the system of two-level semiconductor quantum dot. In addition, we discuss the rates of the photon radiative and phonon radiationless transitions fromthe excited state ($\alpha_{12}, \alpha_{21}$), the rate of processes of pure dephasing ($\gamma$ ), the detuning parameter ($\Delta$) and the Rabi frequency ($\Omega$), on the atomic occupation probabilities ($\rho_{11}(t)$ and $\rho_{22}(t)$), the atomic population inversion ($\rho_{z}(t)$), the purity ($P_{A}(t)$), the von Neumann entropy ($S(t)$) and the information entropies ($H(\sigma_{x}), H(\sigma_{y})$ and $H(\sigma_{z})$). We clearly observe the emergence of long-lived quantum coherence phenomenon in all the curves for some special cases of $\alpha_{12}, \alpha_{21}, \gamma, \Delta$ and $\Omega$. Besides, the decay phenomenon is quite evident in the purity curves, which can be simply controlled by changing the values of $\alpha_{12}, \alpha_{21}$ and $\gamma$.

    • Features of Jeffrey fluid flow with Hall current: A spectral simulation


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      The Hall current in MHD flow stimulates substantial interest of researchers because of its wide rolein many geophysical, astrophysical and fluid engineering situations (construction of turbines, Hall accelerator and centrifugal machines). Motivated by such wide applications, the present work reports the influence of Hall current and thermal radiation on the three-dimensional Jeffrey fluid flow over a stretching surface. In order to achieve similar solution of the governing equations, transformation technique is adopted. The mathematical model is numerically solved by using a spectral technique, namely successive linearisation method (SLM). To explore the feature of various factors, e.g. Hall current and thermal radiation, the variation of flow dominant parameters on the obtained profiles are carefully elucidated with graphs. It can be sensed from the obtained graphs that primary and secondary velocity increase, but, temperature reduces with the enhancement in Hall current. Radiation parameter has the tendency to increase the temperature of the fluid.

    • Patterns of propagation of high-order nonlinear dispersion wave modelled by the generalised KP equation


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      A wide range of two-dimensional nonlinear wave is described by Kadomtsev–Petviashvili (KP) equation. We obtained the classification of travelling wave patterns to the generalised KP equation with high-ordernonlinear dispersive and dissipative terms. Among these patterns, some new phenomena can be acquired for the first time. Representations of wave propagation patterns were achieved by taking specific values of parameters. This means that all these patterns can be realised under appropriate physical conditions.

    • Coexisting chaotic attractors in a memristive system and their amplitude control


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      A memristive chaotic system of rotational symmetry is constructed and analysed. The dynamical behaviour of the system is demonstrated by phase trajectories, Lyapunov exponents and bifurcation diagrams. Coexisting attractors are observed and a simple approach for amplitude control is proposed according to the specific structure. It shows that this symmetric memristive system has partial amplitude control when a control function is introduced. The corresponding circuit implementation is given by generating a symmetric pair of chaotic attractors. Circuit results agree well with the theoretical analysis and numerical simulation.

    • MHD mixed convection flow of a nanofluid past a stretching surface of variable thickness and vanishing nanoparticle flux


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      This article aims to present the flow and heat transfer characteristics of a nanofluid past an elastic sheet having variable thickness in the presence of a magnetic field. Vanishing nanoparticle flux at the boundary has been taken into account for the passive control of nanoparticles. Two-phase model for the nanofluid has been considered. With the help of similarity transformations, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations along with the appropriate boundary conditions. The reduced equations are then solved numerically. The effects of buoyancy parameter,magnetic parameter, Brownian motion, thermophoresis parameter etc. on velocity, temperature and nanoparticle volume fraction are presented graphically and analysed in detail. Velocity, temperature and nanoparticle volume fraction are decreasing functions of wall thickness parameter for decelerated flow. Due to increasing values of thermophoresis parameter, the rate of heat transfer at the surface reduces while with the increase in the Brownian motion parameter the mass transfer rate at the surface increases.

    • A generalised approach to calculate various transport observables for a linear array of series and parallel quantum dots


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      A systematic generalised approach to find transport observables for a linear array of different quantum dot (QD) systems has been discussed, using non-equilibrium Green function (NEGF) formalism, in the presence of on-dot Coulomb interaction and inter-dot tunnelling. The equation of motion (EOM) method has been used to derive expressions for Green functions (GFs) within the simplest mean-field approximation to tackle the Coulomb correlation term. Starting from the mathematical structures of GFs for single, double and triple quantum dot systems, the expressions for GFs and transport observables have been generalised for the quantum dot systems containing N number of quantum dots in series as well as parallel linear array of dots. Further, the formulae so obtained have been used for numerical calculations of transmission probability and the I –V characteristics of linear arrays of quantum dots in series as well as parallel configuration containing up to three dots. The results show that, with the increase in number of dots in the scattering region, transmission probability and electron current decrease in series case, while both quantities increase in parallel configuration of dots. The inter-dot tunnelling leads to the splitting of transmission peaks in double QD system in series case whereas, it induces Fano effect in triple QD system in parallel configuration.

    • The solution of the Schrödinger equation for Makarov potential and homogeneous manifold $SL(2,\mathbb{C})/GL(1,\mathbb{C})$


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      In this study, we are going to obtain the energy spectrum and the corresponding solution of the noncentral Makarov potential. In this case, we consider the arbitrary angular momentum with quantum number l. In order to calculate the energy spectrum and eigenfunction we use the factorisation method. The factorisation methodleads us to discuss the shape-invariance condition with respect to any index as $n$ and $m$. Here, we also achieve the shape invariance with respect to the main quantum number $n$. It leads to the quantum-solvable models on real forms of the homogeneous manifold $SL(2,\mathbb{C})/GL(1,\mathbb{C})$ with infinite-fold degeneracy for $\gamma\upsilon = 0$ and $\gamma\upsilon \neq 0$. These processes also help us to obtain raising and lowering operators of states on the above-mentioned homogeneous manifold.

    • Dust-acoustic rogue waves in non-thermal plasmas


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      The nonlinear propagation of dust-acoustic waves (DAWs) and associated dust-acoustic rogue waves (DARWs), which are governed by the nonlinear Schrödinger equation, is theoretically investigated in a four componentplasma medium containing inertial warm negatively charged dust grains and inertialess non-thermal distributed electrons as well as isothermal positrons and ions. The modulationally stable and unstable parametric regimes of DAWs are numerically studied for the plasma parameters. Furthermore, the effects of temperature ratios of ion-to-electron and ion-to-positron, and the number density of ion and dust grains on the DARWs are investigated. It is observed that physical parameters play very crucial roles in the formation of DARWs. These results may be useful in understanding the electrostatic excitations in dusty plasmas in space and laboratory situations.

    • Likelihood theory in a quantum world: Tests with quantum coins and computers


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      By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence.We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.

    • Modified multiple scale technique for the stability of the fractional delayed nonlinear oscillator


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      In the present proposal, the familiar method of the parameter expansion is combined with the multiple scales to study the stability behaviour of the Riemann–Liouville fractional derivative applied to the cubic delayed Duffing oscillator. The analysis of the modified multiple scale perturbation leads to a system of nonlinear differential-algebraic equations governing the solvability conditions. The nonlinear differential equation was reduced to the linear differential equation with the help of the algebraic one. The stability attitude of the periodic motion is determined by the steady-state analysis. Such a periodic motion is needed to better understand the dynamics of the fractional cubic delayed Duffing oscillator.

    • Analysis of the evolution equation of a hyperbolic curve flow via Lie symmetry method


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      In this paper, based on the classical symmetry method, the group-invariant solutions of the evolution equation of a hyperbolic curve flow are investigated. The optimal system of the obtained symmetries is found, and the reduced equations and exact solutions of the evolution equation are discussed. Then explicit solutions are obtained by the power series method. In addition, the convergence of the power series solutions is proved. Theobjective shapes of the solutions of the evolution equation are performed.

    • Analysis of ferrite nanoparticles in liquid


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      The foremost aim of the present paper is to explore the impact of heat transport phenomenon in a ferrofluid via magnetic dipole. Three distinct ferrite nanoparticles are discussed in the present study with water as the base fluid. Magnetic dipole existing in ferrite nanoparticles plays a significant role in controlling the momentum and thermal boundary layers. The partial differential equations (PDEs) are changed into nonlinear coupled ordinary differential equation (ODEs) by utilising similar transformations. Flow occurs due to linear stretching sheet. For the evaluation of heat flux, Fourier’s law of heat conduction is employed. Effects of rising parameters on the magneto-thermomechanical coupling are examined numerically. The results indicate that the property of magneto-thermomechanical cooperation slows the motion of liquid particles, and accordingly, strengthen the heat transfer rate at the surface and skin friction coefficient. Further, Nusselt number enhances with larger solid volume fraction. A magnificent comparison with accessible results for definite cases has been made.

    • Shell model description of the core excited level structure of $^{89}\rm{Sr}$ nucleus and systematic features of the $N = 51$ odd-$A$ isotones


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      Shell-model calculations are performed using NuShellX code in the model space $\pi( f_{5/2}, p_{3/2}, p_{1/2}, g_{9/2}) \otimes \nu(g_{9/2}, g_{7/2}, d_{5/2}, h_{11/2})$, which probe the proton core excitation from the interior of $Z = 38$ semiclosed shell and neutron core excitation from the interior of $N = 56$ semiclosed shell for the level structure of $^{89}Sr$. Our calculations show that the excitation of a single $d_{5/2}$ neutron across $N = 56$ semiclosed shell into the $h_{11/2}$ orbit should have great effects on the excited states of $^{89}Sr$. In addition, the systematic features of proton core excitation across $Z = 38$ semiclosed shell into the $g_{9/2}$ orbit and neutron core excitation across $N = 56$ semiclosed shell into the $g_{7/2}, s_{1/2}, d_{3/2}, h_{11/2}$ orbits in $N = 51$ isotones are discussed.

    • New closed form solutions of the new coupled Konno–Oono equation using the new extended direct algebraic method


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      In this paper, we apply the new extended direct algebraic method (NEDAM) to solve new exact solutions of the new coupled Konno–Oono (CKO) equation, and construct exact solution expressed in terms of hyperbolic functions and trigonometric functions with arbitrary parameters. A comparison between our established results and the results obtained by the existing ones is also presented. As a newly developed mathematical tool, the proposedmethod is an effective and straightforward technique to work out new solutions of various types of nonlinear partial differential equations (NLPDEs) in applied sciences and engineering.

    • Zakharov–Kuznetsov–Burgers equation in a magnetised non-extensive electron–positron–ion plasma


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      In this paper, we have studied the three-dimensional (3D) electron-acoustic waves (EAWs) in a three component complex plasma containing $q$-non-extensive distributed hot electrons and positrons. The propagation characteristics of the 3D electron-acoustic (EA) shock waves under the influence of magnetic field have been studied. Our present plasma model supports the negative potential shocks. Combined action of dissipation ($\eta$), nonextensivity ($q$), concentration of positrons ($\beta$), temperature ratio of cold electrons to positrons ($\sigma$) and magnetic field ($\omega_{c}$) on the EA shock waves has been studied in detail and the findings obtained here will be beneficial in future astrophysical investigations.

    • Linear analysis of the dispersion relation of surface waves of a magnetic fluid in a square container under an external oblique magnetic field


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      In this study, free surface evolution of a magnetic fluid in a finite size tank which is subjected to an external magnetic field was investigated. The physical problem and equations governing fluid motion and magnetic field were given with boundary conditions. Using proper selection of variables, dimensionless equation system governing magnetic fluid sloshing were written. Resolution method based on multiple scale variables was presented and solution of the linear problem was given. The dispersion relation obtained in the finite depth case was compared with that corresponding to an infinite depth calculated with the same assumptions. Direction and magnitude of the external magnetic field, magnetic permeability ratio and surface tension effects on magnetic fluid free surface stability were analysed and important results were discussed.

    • Optimised wave perturbation for the linear instability of magnetohydrodynamics in plane Poiseuille flow


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      In this work, linear stability of an electrically conductive fluid experiencing Poiseuille flow for minimum Reynolds value under a normal magnetic field is analysed using the Chebyshev collocation method. The neutral curves of linear instability are derived by utilising Qualitat and Zuverlassigkeit (QZ) method. Instability of the magnetohydrodynamics for plane Poiseuille flowis introduced by solving the generalised Orr–Sommerfeld equation to determine the growth rates, wave number and spatial shapes of the eigenmodes. To solve linear problems, we use numerical methods which help us at each time step of the simulation, uncoupled by physical processes, which can improve the computational performance. This article provides the stability and error analysis, presents a concise study of the Poiseuille flow, and produces computational tests to support the given theory.

    • Soret and Dufour effects in the flow of viscous fluid by a curved stretching surface


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      The main focus in this study is to study the flow of a viscous fluid through a curved stretched surface. Soret and Dufour effects along with Joule heating are incorporated. Appropriate transformations yield the nonlinear ordinary differential system. Convergent series solutions of velocity, temperature and concentration are constructed. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. Skin friction coefficient, Nusselt and Sherwood numbers are also obtained and discussed graphically. Current computations reveal that the radial velocity experience decline with the increase of Hartman number. Further, fluid temperature declines for higher Prandtl and Soret numbers.

    • Models for membrane curvature sensing of curvature generating proteins


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      The curvature-sensitive localisation of proteins on membranes is vital for many cell biological processes. Coarse-grained models are routinely employed to study the curvature-sensing phenomena and membrane morphology at the length scale of a few micrometres. Two prevalent phenomenological models exist for modelling the experimental observations of curvature sensing: (1) the spontaneous curvature (SC) model and (2) the curvature mismatch (CM) model, which differ in their treatment of the change in elastic energy due to the binding of proteins on the membrane. In this work, the prediction of sensing and generation behaviour by these two models are investigated using analytical calculations as well as dynamic triangulation Monte Carlo simulations of quasispherical vesicles. While the SC model yields a monotonically decreasing sensing curve as a function of the vesicle radius, the CM model results in a non-monotonic sensing curve. We highlight the main differences in the interpretation of the protein-related parameters in the two models. We further propose that the SC model is appropriate for modelling peripheral proteins employing the hydrophobic insertion mechanism, with minimal modification of membrane rigidity, while the CM model is appropriate for modelling curvature generation using scaffolding mechanism where there is significant stiffening of the membrane due to protein binding.

    • The detection of effective atomic numbers of some potassium compounds using direct and linear differential scattering methods


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      In this work, the direct method and the linear differential scattering method were used to detect the experimental effective atomic numbers of some potassium compounds ($\rm{KH_{2}PO_{4}, KNO_{3}, K_{2}S_{2}O_{8}, KOH, K_{2}HPO_{4}, K_{2}SO_{4}, KCl, KIO_{3}}$ and $\rm{KI}$). The experiment has been done by using $^{241}\rm{Am}$ radioactive source, a Si(Li) detector and an energy-dispersive X-ray fluorescence spectrometer (EDXRFS). The experimental effective atomic numbers were compared with the effective atomic numbers obtained using WinXCom, FFAST, non-relativistic theory (NRT)and relativistic theory (RT).

    • Possible effects of galactic cosmic ray flux and low-cloud amounts on global surface temperature


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      The solar variations, solar–climate interactions, and the mechanisms controlling the response of Earth’s climate system are important to understand the effect of solar variability on climate change. The solar magnetic field is directly/indirectly disturbing the interplanetary space, the ionosphere, the magnetosphere, and even the atmosphere. To investigate the contribution of varying galactic cosmic flux, the role of sunspot number (Rz), galactic cosmic ray (GCR) rates, cloud condensation nuclei (CCN), total solar irradiance (TSI), $\rm{CO}_{2}$ concentration and the global surface temperature (GST) is examined. The variations of TSI can partially explain the global increase in temperature, and it accounts for about $0.5^{0}\rm{C}$ warming experienced from 1950 to 2016. Therefore, the future predictions of global warming should take into account the effects due to long-term changes in the galactic CRs, the low-level cloud condensation (LLC), etc. The concentrations of $\rm{CO}_{2}$ increased in the upper atmosphere by 19% during the last 65 years. A strong correlation between LLC and GST suggests a linear relationship between these parameters. These observations are suggestive of the possible role of GCRs in global climate.

    • Numerical and perturbation solutions of third-grade fluid in a porous channel: Boundary and thermal slip effects


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      The steady flow of a third-grade fluid due to pressure gradient is considered between parallel plane walls which are kept at different temperatures. The space between the plane walls is assumed to be a porous medium of constant permeability. The viscosity of the fluid is taken as constant as well as a function of temperature. It is further assumed that the fluid may slip at the wall surfaces. The consequence of this assumption results in non-linear boundary conditions at the plane walls. The temperature field is also supposed to satisfy thermal slip condition at the walls. The governing equations are modelled under these assumptions and the approximate solution is obtained using the perturbation theory. The skin friction coefficient is a decreasing function of slip parameters in the case of temperature-dependent viscosity models while no variation is noted for the case of constant viscosity via boundary slip parameter. The heat transfer rate increases with the boundary slip parameter and decreases with the thermal slip parameter. The validity of the approximated solution is checked by calculating the numerical solution as well. The absolute error is calculated and listed in tabular form in the case of constant and temperature-dependent viscosity via boundary and thermal slip parameters. The influence of various emerging parameters on flow velocity and temperature profile is discussed through graphs.

    • Lump solutions with higher-order rational dispersion relations


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      This paper aims to explore a kind of lump solutions in nonlinear dispersive waves with higher-order rational dispersion relations.We show that the second member in the commuting Kadomtsev–Petviashvili hierarchy is such an example, and construct its lump solutions, based on a Hirota trilinear form. The presented lump solutions have one peak and two valleys, where the global maximum and minimum values are achieved. A few three dimensional plots and contour plots are made for a specific example of the lumps.

    • Structural, electronic, elastic and magnetic properties of heavier $\rm{REIr}_{3}$ ($\rm{RE = Gd, Tb}$ and $\rm{Ho}$) intermetallic compounds


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      We present results on the bonding nature, structural, electronic, magnetic and elastic properties of $\rm{REIr}_{3}$ ($\rm{RE = Gd, Tb}$ and $\rm{Ho}$) intermetallic compounds adopting simple cubic $\rm{AuCu_{3}}$-type structure obtained using the full-potential linearlised augmented plane wave (FP-LAPW) method based on density functional theory. The local spin density approximation (LSDA) with Hubbard parameter ($\rm{LSDA} +U$) has been used for exchange and correlation effects to get accurate results because of the presence of highly localised $4 f$ electrons of rare-earth $\rm{(RE) (RE = Gd, Tb}$ and $\rm{Ho}$) atoms. The calculated lattice parameter is found to be consistent with the experimental results. The calculated magnetic moments predict ferromagnetic behaviour of these compounds. The electronic and bonding properties have been solved in terms of band structure, density of states (DOS) and charge density plots. These results confirm the metallic nature of these compounds. The bonding appearances of these compounds have also been interpreted from charge density plots. The elastic constants, shear modulus and Cauchy’s pressure are computed and they reveal that $\rm{GdIr_{3}}$ and $\rm{TbIr_{3}}$ compounds are ductile while $\rm{HoIr_{3}}$ shows brittle character.

    • Joint remote state preparation of an arbitrary eight-qubit cluster-type state


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      In this paper, we put forward a scheme to realise joint remote state preparation (JRSP) of an arbitrary eight-qubit cluster-type state with two non-maximally entangled Greenberger–Horne–Zeilinger (GHZ) states in a recursive manner. The senders begin by helping the remote receiver to construct one intermediate state which is related to the target state closely. Then, the receiver introduces auxiliary qubits and applies appropriate local operations to obtain the target eight-qubit cluster-type state. It is shown that one new GHZ channel can be distributed among three participants with a certain probability if the initial attempt fails.Moreover, compared with the previous protocols, in our scheme both quantum resources and classical communications are considerably reduced.

    • The influence of two kinds of time delays on the vibrational resonance of a fractional Mathieu–Duffing oscillator


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      Vibrational resonance is studied in a fractional Mathieu–Duffing oscillator with two types of time delays: fixed and distributed delays. The theoretical expression of the response amplitude is obtained by utilising the methodof direct partition of slow and fast motions. Relative errors between the theoretical prediction and the numerical simulation are introduced to verify the validity of analytical approaches. The relative error of the displacement andthe relative error of the response amplitude are calculated. Small relative errors show that the theoretical analysis is statistically correct. Therefore, the effects of fractional order, linear stiffness coefficient, low-frequency signal, time delay intensity and damping coefficient on the Mathieu–Duffing oscillator with distributed delay are studied successively. In order to better illustrate the impact of distributed time delay on the model, the case of fixed time delay is analysed and compared, and it can be found that the distributed delay has more significant influence than fixed delay on the system. In addition, the influence of distributed delay on the system is more significant than that of the fixed delay.

    • Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity


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      This paper examines new travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) model with Kerr nonlinearity using Bäcklund transformation method based on Riccati equation, Kudryashov method and a new auxiliary ordinary differential equation (ODE). The three methods are adequately utilised, and some new rational-type hyperbolic and trigonometric function solutions are derived in different shapes for the aforementioned model. We confirm that our methods are more efficient than the other methods and it might be used in many other such types of nonlinear equations arising in the basic fabric of communications network technology and nonlinearoptics.

    • Galerkin finite-element numerical analysis of the effects of heat generation and thermal radiation on MHD SWCNT–water nanofluid flow with a stretchable plate


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      Fundamental goal of the present communication is to analyse the viscous electrically conducting nanofluid flow near a stagnation region past a stretching sheet. Investigation of single-wall carbon nanotubes (SWCNTs) are done and water is employed as the base fluid. Combinations of the effects of heat generation, thermal radiation, viscous dissipation and Joule heating are considered. Mathematical modelling and examinations are done in the presence of magnetic field. Similarity variables are introduced to convert nonlinear partial differential equations into nonlinear ordinary differential equations. Numerical solutions of the governing modelled equations are collected by applying Galerkin finite-element method. Impacts of distinct influential parameters such as velocity ratio parameter, solid volume fraction, magnetic parameter, radiation parameter, heat generation parameter and Brinkmann number on velocity, temperature, surface shear stress and surface heat flux are obtained and discussed. Furthermore, comparison of the results of the current analysis is made with the earlier published data.

    • On the exact solutions of nonlinear evolution equations by the improved tan($\varphi/2$)-expansion method


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      In this paper, the improved tan($\varphi/2$)-expansion method (ITEM) is proposed to obtain more general exact solutions of the nonlinear evolution equations (NLEEs). This method is applied to the generalised Hirota–Satsuma coupled KdV (HScKdV) equation and (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) system. We have obtained four types of solutions of these equations such as hyperbolic, trigonometric, exponential and rational functions as an advantage of this method. These solutions include solitons, rational, periodic and kink solutions. Moreover, modulation instability is used to establish stability of the obtained solutions.

    • Superposition behaviour between lump solutions and different forms of $N$-solitons ($N \rightarrow\infty$) for the fifth-order Korteweg–de Vries equation


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      A lump-type solution of the (2 + 1)-dimensional generalised fifth-order Korteweg–de Vries (KdV) equation is obtained from the two-soliton solution by applying the parametric limit method. Some theorems and corollaries about the superposition behaviour between lump solutions and different forms of $N$-soliton ($N \rightarrow\infty$) solutions are constructed, and detailed proofs are given. Besides,we give a large number of examples and spatial evolution graphics to illustrate the effectiveness of the described theorems and corollaries. Some new nonlinear phenomena and superposition behaviour, such as rational-exponential type, rational-cosh-cos type, rational-sin type, rational-logarithmic type etc., are simulated and shown for the first time. Finally, we also illustrate the superposition between high-order lump-type solutions and $N$-soliton solutions.

    • Optical soliton solutions to the Fokas–Lenells equation via sine-Gordon expansion method and $(m + (G'/G))$-expansion method


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      The purpose of this study is to find some novel soliton solutions of Fokas–Lenells (FL) equation where the perturbation terms are taken into account with nonlinearity. The sine-Gordon expansion method (SGEM) and the $(m + (G'/G))$-expansion method are used in this context. The dark, bright, dark–bright and singular optical soliton solutions are successfully obtained. Moreover, the constraint conditions for guaranteeing the existence of solutions are also given.

    • Finite-time synchronisation of uncertain delay spatiotemporal networks via unidirectional coupling technology


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      In this paper, the problem of finite-time synchronisation of uncertain delay spatiotemporal networks via unidirectional coupling technology is investigated. Based on Lyapunov theorem and finite-time stability theory, an effective finite-time synchronisation scheme is designed to achieve finite-time synchronisation between uncertain delay spatiotemporal networks, and adaptive estimations of coupling coefficient, unknown parameter and uncertain network topology are realised. Then, the Fisher–Kolmogorov spatiotemporal model is used as the state equation of the network node for numerical simulation. The simulation results show that the finite-time synchronisation scheme is effective.

    • Analytical study of $D$-dimensional fractional Klein–Gordon equation with a fractional vector plus a scalar potential


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      $D$-dimensional fractional Klein–Gordon equation with fractional vector and scalar potential has been studied. Both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely $v$ and $s$. Jumarie-type definitions for fractional calculus have been used. We have succeeded in achieving Whittaker-type classical differential equation in fractional mode for the required eigenfunction. Fractional Whittaker equation has been manipulated using the behaviour of the eigenfunction at asymptotic distance and origin. This manipulation delivers fractional-type confluent hypergeometric equation to solve. Power series method has been employed to do the task. All the obtained results agree with the existing results in literature when fractional parameter $\alpha$ is unity. Finally, we furnish numerical results with a few eigenfunction graphs for different spatial dimensions and fractional parameters.

    • Analysis of imprecisely defined fuzzy space-fractional telegraph equations


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      Telegraph equations are very important in physics and engineering due to their importance in modelling and designing frequency or voltage transmission. Moreover, uncertainty present in the system parameters plays a vital role in the designing process. Also it is known that it is not always easy to find exact solution of fractionally ordered system. Taking these factors into consideration, here space-fractional telegraph equations with fuzzy uncertainty have been analysed. A new technique to represent fuzzy number using two different parameters in the same domain has been used along with a semianalytic approach known as Adomain decomposition method (ADM) for the solution. Gaussian and triangular shaped fuzzy numbers are considered to model the uncertainties in initial as well as boundary conditions. The obtained results are compared with the existing solution in special cases for the validation.

    • High-performance ultra-low leakage current graphene-based screen-printed field-effect transistor on paper substrate


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      Exploiting the advantages of additive patterning process over complex fabrication processes, herein we report the fabrication of field-effect transistor (FET) using the screen-printing method. The graphene conductive composite dielectric ink as the channel and the dielectric layer respectively was screen printed on cellulose paper substrate. The fabricated device shows the hole and electron mobility of $\rm{135 cm^{2}/V s}$ and $\rm{98 cm^{2}/V s}$ respectively with an ultra-low leakage current of $\sim 25 \rm{nA}$. The proposed technique can be used for large-scale roll-to-roll commercial manufacturing of disposable FET-based sensors such as temperature and IR sensors, health monitoring devices etc.

    • Binding energy of excitons in an infinitely deep spherical quantum dot under intense THz laser field


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      We study the effects of intense THz laser field on the ground-state binding energy of heavy hole excitons confined in GaAs spherical quantum dots. The calculation is performed using the variational method in the framework of the single band effective mass theory. Our results show that (i) the laser electric field lowers the binding energy for all quantum dot radii, making the exciton clustered near the centre of the dot, (ii) the binding energy is mainly due to the dressed potential making the kinetic part insensitive to the field and (iii) the behaviour of the exciton, under the approximations used, can be modelled by a unique set of plots, depending on the material only via its excitonic units.

    • Optical travelling wave solutions for the Biswas–Arshed model in Kerr and non-Kerr law media


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      This paper scrutinises the newly proposed Biswas–Arshed model for soliton propagation through optical fibres,with small group velocity dispersion and in the absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered to balance with group velocity dispersion. First integral and functional variable methods are employed to recover solitary wave, shock wave, singular wave and singular periodic wave solutions for the two nonlinear forms of the model through Kerr law and power-law nonlinearity. The constraint relations are also figured for the manifestation of these optical solutions.

    • Computational soliton solutions to (2 + 1)-dimensional Pavlov equation using Lie symmetry approach


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      In this work, Lie symmetry analysis and one-dimensional optimal system for Pavlov equation are presented. All the possible vector fields, their commutative and adjoint relations are carried out under invariance property of Lie group theory. On the basis of optimal system, similarity reductions of Pavlov equation are obtained. A repeated process of similarity reductions transforms the Pavlov equation into ordinary differential equations, which generate invariant solutions. The obtained invariant solutions are supplemented by numerical simulation toanalyse the physical behaviour. Thus, their parabolic, multisoliton, nonlinear, kink and antikink wave profiles are traced in results and discussions sections.

    • Effects of the positions of scintillation detectors with fast scintillators and photomultiplier tubes on TOF–PET performance


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      The objective of this study is to improve the time resolution value of a coincidence spectrometer used in a time-of-flight–positron emission tomography (TOF–PET) system. This spectrometer is used in medical imaging systems. The coincidence spectrometer is manufactured by using a BC420-type plastic scintillator and R1828-01-type photomultiplier tube, and the time resolution value of the manufactured spectrometer is determined. The accuracy of the experimental results is determined using the FLUKA Monte Carlo simulation program. Detectors are first manufactured in this program. Experimental and simulation results are compared and are found to be in good agreement. Optimal positions of the detectors are investigated to improve the coincidence time resolution of the spectrometer. Time resolution improvement of the optimal detector positions enables higher time-of-flight (TOF) gain and spatial resolution, leading to better image quality, reduction in patient doses and detection of small lesions.

    • Bose–Einstein condensation of an imperfect Bose gas using cluster expansion


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      Bose–Einstein condensations (BEC) for an ideal Bose gas and an imperfect Bose gas are presented using cluster expansion method by using a new generating function obtained by Ushcats. The saturation density is calculated from the known values of virial coefficients for both ideal and uniform hard-sphere imperfect Bose gas. The values of saturation densities are found for some experimentally observed Bose–Einstein condensates and the fractional shift in the saturation densities are also calculated using this method, which are found to be positive.

    • Anisotropic bulk viscous string cosmological models of the Universe under a time-dependent deceleration parameter


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      We investigate a new class of LRS Bianchi type-II cosmological models by revisiting the paper of Mishra et al (Int. J. Theor. Phys. 52, 2546 (2013)) by considering a new deceleration parameter (DP) depending on the time in string cosmology for the modified gravity theory suggested by Sáez–Ballester (Phys. Lett. 113, 467 (1986)). We have considered the energy–momentum tensor proposed by Letelier (Phys. Rev. 28, 2414 (1983)) for bulk viscous and perfect fluid under some assumptions. To make our models consistent with recent astronomical observations, we have used the scale factor (Sharma et al, Astron Astrophys. 19, 55 (2018), Garg et al, Int. J. Geo. Meth. Mod. Phys. 16, 1950007 (2019)) $a(t) = \rm{exp} [ \frac{1}{\beta}\sqrt{2\beta t + k}]$, where $β$ and $k$ are positive constants and it provides a time-varying DP. By using the recent constraints ($H_{0} = 73.8$ and $q_{0} = −0.54$) from SN Ia data in combination with BAO and CMB observations (Giostri et al, JCAP 3, 27 (2012), arXiv:1203.3213v2[astroph. CO]), we affirm $\beta = 0.0062$ and $k = 0.000016$. For these constraints, we have substantiated a new class of cosmological transit models for which the expansion takes place from the early decelerated phase to the current accelerated phase. Also, we have studied some physical, kinematic and geometric behaviour of the models, and have found them consistent with observations and well-established theoretical results. We have also compared our present results with those of Mishra et al (Int. J. Theor. Phys. 52, 2546 (2013)) and observed that the results in this paper are much better, stable under perturbation and in good agreement with cosmological reflections.

    • Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models


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      The present paper studies the impact of applied uniform transverse magnetic field on the flow of incompressible conducting fluid around a weakly permeable spherical particle bounded by a spherical container. Analytical solution of the problem is obtained using Happel and Kuwabara cell models. The concerned flow is parted in two regions, bounded fluid region and internal porous region, to be governed by Stokes and Darcy’s law respectively. At the interface between the fluid and the permeable region, the boundary conditions used are continuity of normal component of velocity, Saffman’s boundary condition and continuity of pressure. For the cellsurface, Happel and Kuwabara models together with continuity in radial component of the velocity has been used. Expressions for drag force, hydrodynamic permeability and Kozeny constant acting on the spherical particle under magnetic effect are presented. Representation of hydrodynamic permeability for varying permeability parameters, particle volume fraction, slip parameter and Hartmann numbers are represented graphically. Also, the magnitude of Kozeny constant for weakly permeable and semipermeable sphere under a magnetic effect has been presented. In limiting cases many important results are obtained.

    • Lie symmetries and invariant solutions of (2 + 1)-dimensional breaking soliton equation


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      The present article deals with the symmetry reductions and invariant solutions of breaking soliton equation by virtue of similarity transformation method. The equation represents the collision of a Riemann wave propagating along the $y$-axis with a long wave along the $x$-axis. The infinitesimal transformations under one parameter for the governing system have been derived by exploiting the invariance property of Lie group theory. Consequently, the number of independent variables is reduced by one and the system remains invariant. A repeated application transforms the governing system into systems of ordinary differential equations. These systems degenerate well-known soliton solutions under some limiting conditions. The obtained solutions are extended with numerical simulation resulting in dark solitons, lumps, compactons, multisolitons, stationary and parabolic profiles and are shown graphically.

    • Correction to: Vibrational resonance in a higher-order nonlinear damped oscillator with rough potential


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      In our recently published paper [Pramana – J. Phys.93: 102 (2019), https://doi.org/10.1007/s12043-019- 1865-5] one of the author’s affiliation (O O Popoola) was wrongly indicated. The correct affiliation is Depart- ment of Physics, University of Ibadan, Ibadan, Nigeria.

    • Exact solitary wave solutions to the (2 + 1)-dimensional generalised Camassa–Holm–Kadomtsev–Petviashvili equation


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      In this paper, a (2+1)-dimensional nonlinear evolution equation (NLEE), namely the generalised Camassa–Holm–Kadomtsev–Petviashvili equation (gCHKP) or Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBM), is examined. After applying the newly developed generalised exponential rational function method (GERFM), 14 travelling wave solutions are formally generated. It is worth mentioning that by specifying values to free parameters some previously obtained solutions can be recovered. The simplest equation method (SEM) is used to prove that the solutions obtained by GERFM are good. With the aid of a symbolic computation system, we prove that GERFM is more efficient and faster.

    • Development of a zero-cost multichannel analyser based on digital signal processing for $\gamma$ -ray spectroscopy using the PC sound card


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      A zero-cost multichannel analyser (MCA) system based on the digital signal (pulse) processing (DSP) convenient for $\gamma$ -ray spectroscopy with conventional detectors such as scintillators and high-purity germanium (HPGe) has been implemented. The in-built high-performance analog-to-digital converter (ADC) in the sound card, an integral component of the present day personal computers, was used to digitise the signals from the radiation detectors. These pulses were then shaped using the established digital signal processing recursive algorithms. The filtered data were then displayed as histograms which then could be subjected to the traditional analysis to obtain peak parameters and the associated quantities were deduced. The developed system combines the performance of the sound card hardware with the flexibility allowed by the DSP to achieve a versatile MCA.

    • Exact solution of perturbed nonlinear Schrödinger equation using $(G'/G, 1/G)$-expansion method


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      By constructing auxiliary equations and combining the expansion method of $(G'/G, 1/G)$, we study a class of nonlinear Schrödinger equation with perturbation terms which describes the propagation of the waves in optical metamaterials. More types of exact solutions, particularly solitary wave solutions, are obtained for the first time.

    • Propagation of nonlinear waves with a weak dispersion via coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky dynamical equation


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      This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.

    • Physical origins of the ideality factor of the current equation in Schottky junctions


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      After the carrier drift velocity at the semiconductor/metal interface is considered, current transport in Schottky diodes under a forward electric field is physically modelled. This model reveals that the ideality factor can be physically originated from the drift velocity and the drift velocity can also reduce the effective Schottky barrier height. This proposed model predicts that both the ideality factor and the Schottky barrier height depend on temperature, voltage and doping density, which agree well with the experimental results reported in the literature. The proposed diode current model also predicts a linear dependent relation between the reciprocal of the ideality factor and the effective Schottky barrier height, which is validated by experimental results. Such a model is useful to better understand the thermionic emission current physically in semiconductor/metal contact. It is also useful to characterise the material properties by using the ideality factor.

    • Influence of magnetic field and Coulomb field on the Rashba effect in a triangular quantum well


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      The influence of magnetic field and Coulomb field on the Rashba spin–orbit interaction in a triangular quantum well was studied using Pekar variational method. We theoretically derived the expression of the boundmagnetopolaron ground-state energy. The energy of the bound magnetopolaron splits under the influence of the Rashba effect. From this phenomenon, it is concluded that the effects of orbital and spin interactions on the polaron energy in different directions must be considered. Because of the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Compared to the bare electron, the bound polaron is more stable, and the energy of bound polaron split is more stable.

    • Mixed-mode oscillations and the bifurcation mechanism for a Filippov-type dynamical system


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      In this paper, mixed-mode oscillations and bifurcation mechanism for a Filippov-type system including two time-scales in the frequency domain are demonstrated. According to classic Chua’s system, we investigate a non-smooth dynamical system including two time-scales. As there exists an order gap between the exciting frequency and the natural one, the whole external excitation term can be considered as a slow-changing parameter, which results in two smooth subsystems divided by the non-smooth boundary. In addition, the critical condition about fold bifurcation (FB) is studied, and by applying the Hopf bifurcation (HB) theorem, specific formulas for determining the existence of HBs are presented. By introducing an auxiliary parameter via differential inclusions theory, the non-smoothbifurcations on the boundary are discussed. Then, the equilibrium branches and the bifurcations are derived, and two typical cases associated with different bifurcations are considered. In light of the superposition between the bifurcation curve and the transformed phase portrait, the dynamical behaviours of the mixed-mode oscillations as well as sliding movement along the non-smooth boundary are obtained, which reveal the corresponding dynamical mechanism.

    • Ion-acoustic waves in magnetised plasma with nonthermal electrons and positrons


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      Zakharov–Kuznetsov (ZK) equation for ion-acoustic waves (IAWs) is derived using the reductive perturbation method (RPM) in magnetised plasma consisting of ions, positrons and nonthermal electrons in small but finite amplitude limit. Propagation characteristics of ion-acoustic solitary waves (IASWs) in three-dimensional space are analysed to determine their region of existence. Investigations reveal that ion-acoustic solitary pulses (IASPs) may exist in such plasmas and presence of nonthermal electrons significantly affects the amplitude and width of solitary pulses. Dependence of velocity, amplitude and width of solitary pulses on plasma parameters arepresented graphically. The amplitude of soliton increases with increase in ion temperature ratio ($\sigma$) and positron concentration ($\alpha$). However, it decreases with increase in nonthermal electron parameter ($\beta$) keeping other plasma parameters constant. Width of the soliton increases with increase in $\beta$, $\sigma$ and $\alpha$. Phase velocity of ion-acoustic wave ($\lambda$) increases with increase in nonthermal $\beta$ and $\sigma$. In our analysis, we found that magnetisation of plasma affect the width of the soliton but not the amplitude.

    • Numerical and microcontroller simulations, and electronic circuit realisation of Minorsky’s equation


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      This work deals with the mathematical analysis, numerical and microcontroller simulations and electronic circuit realisation of the dynamics of Minorsky’s equation.We consider the model including the nonlinear derivative feedback with delay. The study of stability is done by linearising the equation. An alternation between the zones of stability and instability as a function of the values of the delay is found. The bifurcation diagrams allowed us to validate the analytical predictions. These bifurcation diagrams show Hopf bifurcations and complex dynamics of the system. The analog and microcontroller simulations together with the experimental analysis were carried out in order to validate the theoretical analysis.

    • Investigation of the radiation shielding capability of $\rm{xPbO–(50 − x)BaO–50B_{2}O_{3}}$ glass system using Geant4, Fluka, WinXCOM and comparison of data with the experimental data


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      In this study, mass attenuation coefficient ($\mu_{\rm{m}}$), transmission fractions ($T$), effective atomic numbers ($\rm{Z_{eff}}$) and half-value layer (HVL) of the $\rm{xPbO–(50 − x)BaO–50B_{2}O_{3}}$ (where x = 10, 20, 30, 40 mol%) glass system have been determined from the Monte Carlo simulations carried out with Geant4 and Fluka simulation toolkits and WinXCOM database software. The calculated results were compared with the experimentally obtained $\mu_{m}$ values of the selected glass in order to validate the Geant4 model of HPGe detector and Fluka model of NaI(Tl) detectors. $T$, $\rm{Z_{eff}}$ and $\rm{HVL}$ shielding parameters of the studied glass system indicate that increase of PbO content from 10 to 40% results in a better shielding behaviour thanks to the high atomic number of lead.

    • Rogue wave solutions of the chiral nonlinear Schrödinger equation with modulated coefficients


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      The research of rogue wave solutions of the nonlinear Schrödinger (NLS) equations is still an open topic. NLS equations have received particular attention for describing nonlinear waves in optical fibres, photonics, plasmas, Bose–Einstein condensates and deep ocean. This work deals with rogue wave solutions of the chiral NLS equation. We introduce an inhomogeneous one-dimensional version, and using the similarity transformation and direct ansatz, we solve the equation in the presence of dispersive and nonlinear coupling which are modulated in time and space. As a result, we show how a simple choice of some free functions can display a lot of interesting rogue wave structures and the interaction of quantum rogue waves. The results obtained may give the possibility of conducting relevant experiments in quantum mechanics and achieving potential applications.

    • On: 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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      A comment on an article by Khater et al published in Pramana – J. Phys. 90: 59 (2018) is presented here. We represent two quotes on the article, the two quotes about the space-dependent fractional Schrödinger equation type and about one of the constants used by the authors.

    • Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting transition temperature


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      So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like ($s-$ or $d-$wave) pairing theory is adequate for explaining high-$T_{c}$ superconductivity in doped cuprates from underdoped to overdoped regime.We show that the doped cuprates, depending on the Fermi energy ($\varepsilon_{F}$) and the energy ($\varepsilon_{A}$) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $\varepsilon_{A}/\varepsilon_{F}$ and $\Delta/\varepsilon_{F}$ (where $\Delta$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high-$T_{c}$ superconductivity is quite different from the BCS-type ($s-$ or $d-$wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ($T_{c}$) and the peculiar oxygen and copper isotope effects on $T_{c}$ in overdoped cuprates.

    • Exact solitary wave solutions for a system of some nonlinear space–time fractional differential equations


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      We have enumerated new and exact general wave solutions, along with multiple exact soliton solutions of space–time nonlinear fractional differential equations (FDE), namely Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM), foam drainage and symmetric regularised long-wave (SRLW) equations, by employing a relatively new technique called (G'/G, 1/G)-expansion method. Also, based on fractional complex transformation and the properties of the modified Riemann–Liouville fractional-order operator, the fractional partial differential equations transform into a form of ordinary differential equation (ODE). This method is a recollection of the commutation of the well-appointed (G'/G)-expansion method introduced by Wang et al, Phys. Lett. A 372, 417 (2008) In this paper, it is mentioned that the two-variable (G'/G, 1/G)-expansion method is more legitimate, modest, sturdy and effective in the sense of theoretical and pragmatical point of view. Lastly, the peculiarities of these analytic solutions are illustrated graphically by utilising the computer symbolic programming Wolfram Mathematica.

    • Theoretical investigation of structural, electronic and thermoelectric properties of $p−n$ type $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ system


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      Based on the density functional theory and the Boltzmann transport theory, the thermoelectric properties of $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with $x = 0.25, 0.5$ and $075$ were investigated. The calculated structural parameters were in good agreement with the previous work and the mechanical and dynamical stabilities were confirmed. The electronic band structure computed using the Tran-Blaha-modified Becke and Johnson (TB-mBJ) exchange potential indicated that the band gap can be tuned by the alloy effect. We combined first-principles calculations and the semiclassical Boltzmann transport theory by considering the electronic transport in the $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution to determine the effect of varying the Sn composition on the thermoelectric performance. Our results have shown exceptionally high electrical conductivity for $\rm{Mg_{2}Sn}$ and higher Seebeck coefficient for $\rm{Mg_{2}Si}$. The highest figure of merit (ZT) was predicted for $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with x = 0.5 where ZT has reached 0.55 with carrier concentration charge $n = 10^{20} \rm{cm}^{−3}$ (p-type doping) at intermediate temperatures. Consequently, the alloying system with p-type doping may improve the thermoelectric properties compared to the $\rm{Mg_{2}Si}$ and $\rm{Mg_{2}Sn}$ pristine compounds.

    • Improvement of transconductance and cut-off frequency in $\rm{In_{0.1}Ga_{0.9}N}$ back-barrier-based double-channel $\rm{Al_{0.3}Ga_{0.7}N/GaN}$ high electron mobility transistor by enhancing the drain source contact length ratio


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      An aluminium gallium nitride/gallium nitride ($\rm{Al_{0.3}Ga_{0.7}N/GaN}$) high electron mobility transistor (HEMT) is designed at a gate length ($L_{G}$) of 0.1 $\mu$m, drain-to-source spacing ($L_{SD}$) of 3 $\mu$m and drain length to source length ratio ($L_{D}:L_{S}$) of 1. The HEMT is investigated by considering four different heterostructures, namely single channel, single channel with back-barrier, double channel and double channel with back-barrier. A two-dimensional electron gas (2DEG) is formed at the interface of AlGaN/GaN HEMT (DC HEMT). The physical importance of indium gallium nitride (InGaN) as back-barrier is to increase carrier confinement by raising the conduction band of GaN buffer. The double-channel HEMT (DC HEMT) with back-barrier shows the highest current drive. There is an improvement of 3.16% in drain current and an improvement of 4.58% in cut-off frequency at a gate-to-source voltage of −0.5 V for the DC HEMT with back-barrier compared to the DC HEMT without back-barrier. For further improvement in transconductance and cut-off frequency, the structure of DC HEMT with back-barrier is modified by increasing the drain contact length and decreasing the source contact length, that is $L_{D}:L_{S} = 3$, keeping the drain-to-source spacing unchanged, i.e. $L_{SD} = 3 \mu m$. There is 32.55% improvement in transconductance and 14.03% improvement in cut-off frequency at a gate-to-source voltage of −0.5 V for the DC HEMT with back-barrier at $L_{D}:L_{S} = 3$ compared to the DC HEMT with back-barrier at $L_{D}:L_{S} = 1$.

    • Convective heat transfer and double diffusive convection in ionic nanofluids flow driven by peristalsis and electromagnetohydrodynamics


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      An analytical study to investigate the double diffusive convection in peristaltic pumping of ionic nanofluids through asymmetric microchannel under the influence of electromagnetohydrodynamics (EMHD) is presented. Thermal radiation effect is also considered. Velocity slip and convective boundary conditions are employed at the permeable channel walls. Debye Hückel linearisation is considered to simplify the Poisson–Boltzmann equation. The normalised two-dimensional conservation equations formass, momentum, energy, solutal concentration and nanoparticle fraction are reduced when long wavelength and low Reynolds number are assumed. Analytical solutions are computationally illustrated with MATLAB software to describe the pumping, flow and thermal characteristics under the effects of relevant parameters like Biot number, slip parameters, thermal radiation, Debye length, Hartmann number and Grashof numbers. Furthermore, solutal concentration, nanoparticle fraction and heat transfer coefficient are also analysed to see the influences of pertinent parameters. Such observations may be applicable to develop electro-osmotically actuated bio-microfluidic systems for smart drug delivery andmicrolevel physiological transport.

    • Chirped solitons in optical monomode fibres modelled with Chen–Lee–Liu equation


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      The paper studies the extraction of chirped soliton to Chen–Lee–Liu equation (CLLE) with the group velocity dispersion (GVD) and self-steeping coefficients that describe pulse transmission through optical monomode fibres. The chirped bright, dark and singular optical solitons are obtained and the results show that nonlinear chirp parameters strongly vary on self-steeping, GVD and spreading effects. The constraint conditions for the existence of solitons are also derived during the derivation. The results are helpful and important for understanding the propagation of optical pulses.

    • Single and multiband THz metamaterial polarisers


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      We report single and multiband linear polarisers for terahertz (THz) frequencies using cut-wire metamaterials (MM). The MMs were designed by finite-element method (FEM), fabricated by electron beam lithography, and characterised by THz time-domain spectroscopy. The MM unit cells consist of single or multiple length cut-wire pads of gold on semi-insulating gallium arsenide (GaAs) for single or multiple band polarisers. For example, a MM with a square unit cell of 50 $\mu$m size on 1 mm GaAs substrate with a gold cut wire of 65 $\mu$m length, 2 $\mu$m width, and 150 nm height gives a resonance around 1.05 THz. The dependence of the resonance frequency of the single-band polariser on the length of the cut-wires was explained based on transmission line model.

    • Quantisation of particle motion in dissipative harmonic environment


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      In this work, the quantisation of particle propagating in a dissipative harmonic medium will be investigated using the creation and annihilation operator formalism, which is more appropriate in some fields of physics. Modelling the problem as damped harmonic oscillator, the equations of motion are then written in terms of Poisson brackets, and the Heisenberg equations are written in terms of the quantum counterpart of the Poisson bracket, known as commutators. The creation and annihilation operators are introduced and used to obtain the energy and eigenstates. Our results are in exact agreement with different quantisation approaches as in Serhan et al, J. Math. Phys. 59, 082105 (2018). The normalisable coherent states are obtained as eigenstates of the annihilation operator, which overcome the non-normalisability of these states that appeared via the dual coordinate method.

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