The structural, electronic, magnetic, thermal and elastic properties of $\rm{Zn_{1−x}TM_{x}Se (TM=Mn, Co \, and \, Fe)}$ ternary alloys are investigated at $x$ = 0, 0.25, 0.50, 0.75 and 1.00 in the zincblende (B3) phase. The calculations are performed using all-electron full-potential linearised augmented plane-wave (FP-LAPW) method within the framework of the density functional theory (DFT) and the generalised gradient approximation (GGA). The electronic and magnetic properties were performed using the modified Becke–Johnson potential combined with the GGA correlation (mBJ-GGA). The electronic structures are found to exhibit a semiconducting behaviour for $\rm{Zn_{1−x}Mn_{x}Se}$ and $\rm{Zn_{1−x}Co_{x}Se}$ and a half-metallic behaviour for $\rm{Zn_{1−x}Fe_{x}Se}$ alloys at all concentrations, while CoSe with $x = 1.00$ is found to exhibit a metallic behaviour. The calculated magnetic moment per substituted transition metal (TM) Mn, Co and Fe atoms for half-metallic compounds are found to be 2.5, 1.5 and 2 $\mu_{B}$, respectively. The p–d hybridisation between the TM d- and Se p-states reduces the local magnetic moment of Mn, Co and Fe and induces small local magnetic moments on Zn and Se sites. In addition, we discuss the mechanical behaviour of binary and ternary compounds and all compounds studied here are mechanically stable.

A rule for designing extreme multistable synchronised systems by coupling two identical dynamical systems has been proposed in this paper. The basic idea behind the proposed scheme is the existence of chaos in the coupled system in the presence of initial condition-dependent constants of motion. A new conjecture has been introduced according to which an extreme multistable synchronised system can be designed if all states of one system will synchronise with the corresponding states of the other system (of the two coupled systems) and the basin of the synchronised state depends on the difference between the initial conditions of the corresponding states of the individual systems. The proposed scheme has been illustrated with the help of coupled Rössler systems, coupled Hénon maps and coupled logistic maps. Moreover, the existence of flip bifurcation with the variation of initial conditions has been shown analytically as well as numerically in the case of coupled Hénon maps. Numerical results are reported to show the proficiency of the proposed scheme to design extreme multistable synchronisation behaviour. This work establishes a theoretical foundation for constructing extreme multistable synchronised continuous as well as discrete dynamical systems.

A new thermodynamic computational model has been proposed for the current study, which deals with the free convective supercritical Casson fluid flow past a vertical cylinder. In this model, pressure, temperature andcompressibility factor are the critical parameters to govern the thermal expansion coefficient. The present model is based on the Redlich–Kwong equation of state. Comparisons with experimental results and determined values of thermal expansion coefficient for the choice of chemical compound (isobutene) from the present study show great similarity. The chemical compound isobutane has many industrial applications. For instance, in geothermal power plant, supercritical isobutane is employed as a working fluid, it is used in the deactivated (USY alkylation) catalyst regeneration, it is used in heat pumps and many other industrial processes. Furthermore, isobutane finds extensive application as a propellant in foam products and aerosol cans, as a refrigerate gas in freezers and refrigerators, as a feedstock in industries of petrochemical importance, for standardisation of gas mixtures and emission monitoring, etc. In addition, the Casson fluid flow model can be used to study the blood flow rheology, slurry flows, etc. The numerical scheme such as Crank–Nicolson type is demonstrated to simplify the governing nonlinear coupled partial differential equations. The transient results of flow-field variables, coefficients of heat and momentum transport for a Casson fluid under supercritical condition for various values of reduced pressure and reduced temperature are computed and discussed through graphs.

In this paper, the Lie group analysis method is applied to carry out the Lie point symmetries of some space–time fractional systems including coupled Burgers equations, Ito’s system, coupled Korteweg–de-Vries(KdV) equations, Hirota–Satsuma coupled KdV equations and coupled nonlinear Hirota equations with time-dependent variable coefficients with the Riemann–Liouville derivative. Symmetry reductions are constructed using Lie symmetries of the systems. To the best of our knowledge, nobody has so far derived the invariants of space–time nonlinear fractional partial differential equations with time-dependent coefficients.

This work intends to evaluate the energy spectrum of a particle influenced by the new type of confined interactions introduced in our previous work [Assi and Sous, Eur. Phys. J. Plus 133(5), 175 (2018); Assi et al,Mod. Phys. Lett. 33(32), 1850128 (2018)]. We have used the asymptotic iteration method (AIM) to carry out numerical computations and our results agree to a high degree of accuracy with those obtained by other researchers using different methods as shown in the tables.

The coupled Volterra lattice equation associated with $4 \times 4$ Lax pair is under investigation, which is an integrable discrete form of a coupled KdV equation applied widely in fluids, Bose–Einstein condensation and atmospheric dynamics. First, we explore the conditions for modulational instability (MI) of the constant seed background for this equation. Secondly, we present the discrete Darboux transformation (DT) and generalised DT based on the new $4 \times 4$ Lax pair. Through the resulting discrete DT, the bell-shaped and anti-$N$-shaped soliton solutions of the coupled Volterra lattice equation are derived. Moreover, we derive the $M$-shaped and $N$-shaped rational solitons and bell-shaped and $N$-shaped semirational soliton solutions of the coupled Volterra lattice equation via the discrete generalised DT. Finally, we numerically study the dynamical behaviours of such soliton solutions and find that the rational and semirational soliton solutions have better numerical stability than the usual soliton solution, although three types of solutions are robust against a small noise. The results may be helpful for understanding the two-layered fluid waves near ocean shores described by the coupled Korteweg–de Vries (KdV) equation.

Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation $D^{\alpha}x(t) = g(x(t − \tau_{1}), x(t − \tau_{2}))$ involving two delays, viz. $\tau_{1} \geq 0$ and $\tau_{2} \geq 0$. We use stability conditions to propose the critical values of delays.Using examples,we show that the chaotic oscillations are observed in the unstable region only. We also propose a numerical scheme to solve such equations.

In this study, the effects of the type of the cage, the bias and gate voltages on spin transport properties of electrons in magnetic tunnel junction (MTJ) of $B_{n}N_{n}(n = 12, 24)$ cages were investigated by theoretical methods. For a gate voltage $(V_{g})$ more than 0.5V, the device became electrically conductive at $V_{b} = 0.5 V$. The electric current increased linearly for bias voltages more than $|V_{b}|$ = 1 V at $V_{g}$ = 0.0 V. The maximum value of the tunnel magnetic resistance (TMR) ratio was $\sim 75%$ for $\rm{B_{12}N_{12}}$ and 60% for $\rm{B_{24}N_{24}}$ molecules. The maximum values of TMR against the bias voltage $(V_{b})$ were seen at 1.6V (−1.6V) for $\rm{B_{12}N_{12}}$ and 0.0V for $\rm{B_{24}N_{24}}$. At $V_{b}$ = 0.5 V, the TMR ratio was changed by varying the gate voltage. Finally, the spin transport properties of the $\rm{B_{12}N_{12}}$ cage were compared with those of the $\rm{B_{24}N_{24}}$ and $\rm{C_{60}}$ cages.

The main objective of this paper is to introduce an analytical study for the water wave solutions of coupled fractional variant Boussinesq equation, which is modelled to investigate the waves in fluid dynamics. Wave transformation in fractional form is applied to convert the original fractional-order nonlinear partial differential equation into another nonlinear ordinary differential equation. The strategy here is to use the unified method to obtain a variety of exact solutions. The unified method works well and reveals distinct exact solutions which are classified into two different types, namely polynomial function and rational function solutions. The results are also depicted graphically for different values of fractional parameter. These findings are highly encouraging and have significant importance for some special physical phenomena in fluid dynamics

The nonlinear evolution equation describing the propagation of waves in thin-film ferrroelectric materials is investigated in detail. The modified extended tanh method is used for the purpose and, as a result, novel soliton solutions are derived analytically which show the shape and the width of the waves. In the construction of the solutions obtained, it appears that bright and singular waves can be propagated in thin-film ferroelectric materials.

In this paper, a reliable numerical scheme, the q-fractional homotopy analysis transform method (q-FHATM), is proposed to examine the Helmholtz equation of fractional order arising in seismic wave propagation, imaging and inversion. Sufficient conditions for its convergence and error estimates are established. The q-FHATMprovides a solution in a rapidly convergent series. Results for different fractional values of space derivatives are compared with the existing methods and discussed with the help of figures. A proper selection of parameters yields approximations identical to the exact solution. Parameter $\bar{h}$ offers an expedient way of controlling the region of convergence of the solution. Test examples are provided to illustrate the accuracy and competency of the proposed scheme. The outcomes divulge that our scheme is attractive, user-friendly, reliable and highly effective.

A method to construct the multi-indexed exceptional Laguerre polynomials using the isospectral deformation technique and quantum Hamilton–Jacobi (QHJ) formalism is presented. For a given potential, the singularity structure of the quantum momentum function, defined within the QHJ formalism, allows us to find its solutions. We show that this singularity structure can be exploited to construct the generalised superpotentials, which lead to rational potentials with exceptional polynomials as solutions. We explicitly construct such rational extensions of the radial oscillator and their solutions, which involve exceptional Laguerre orthogonal polynomials having two indices. The weight functions of these polynomials are also presented. We also discuss the possibility of constructing more rational potentials with interesting solutions.

We report a refractive index sensor consisting of a gold-coated nanoporous anodic alumina membrane on aluminium substrate that can distinguish between different kinds of alcohols such as methanol and ethanol due totheir different refractive indices. The nanoporous volume allows the loading of liquids with low surface energy into its nanopores. Upon dipping one end of the membrane into the alcohol, the entire nanoporous surface experiences wetting. The wavelength shift of the Fabry–Perot resonating modes formed between the gold-coated nanoporous alumina surface and aluminium on the other side due to the changed effective refractive index form the basis of the sensor. The sensitivity of the nanosensor to the refractive index of the loaded liquid is sufficient to distinguish between different alcohols such as methanol, ethanol and isopropanol, and to detect about 5–10% of methanol in a methanol–ethanol mixture.

In the current study, the flow of Casson liquid thin film, together with heat transfer towards a stretching surface extracting out from a narrow slit in the presence of a magnetic field, viscous dissipation and thermal radiation effects, is examined. The contribution of nanoparticles is investigated by employing the Buongiorno model. Mathematical modelling is carried out in the Cartesian coordinate system and similarity analysis is opted for simplification. The numerical analysis is performed in the reduced system using the shooting method. The effects of the prominent parameters are discussed using line and bar graphs. The key finding is that the temperature drop is prominent in the case of Casson nanofluid compared to the nanofluid.

A series of tin oxide $\rm{(SnO_{2})}$/polyaniline (PANI) nanocomposites with loading of different wt% of PANI were synthesised using a solution-based processing method for improving the structural and physical properties of tin oxide. The effect of PANI loading on the gross structure, surface morphology, optical properties and electrical properties of $\rm{(SnO_{2})}$/PANI nanocomposites was investigated. The scanning electron micrographs (SEM) show congruent dispersal of PANI in the tin oxide matrix where the gross/average structure is unchanged as revealed by powder X-ray diffraction (PXRD). A slight change in the lattice parameter of the pristine rutile crystalline structure $\rm{(SnO_{2})}$and its nanocomposites has been recorded. However, the crystallite size has been found to decrease from 60 to 40 nm with different wt% loading of PANI. The presence of characteristic Fourier transform infrared (FT-IR) peaks dovetail to $\rm{C–H, C=C, NH_{2}, C–C}$ and the energy-dispersive analysis of X-rays (EDAX) confirm the development of the PANI nanocomposite. Photoluminescence (PL) spectroscopic study shows the gradual decrement in the intensity of the emission peak at 611 nm due to the disappearance of surface defects associated with oxygen vacancies. The uniform dispersion of PANI at the nanoscale significantly enhanced the electrical properties, e.g. four orders of magnitude changes in electrical conductivity and carrier mobility.