Pramana,

Analysing the stability of a delay differential equation involving two delays Abstract Analysis of systems involving delay is a popular topic among the applied scientists. In the present work, we analyse the generalised equation \(D^{\alpha } x(t) = g\left( x(t-\tau _1), x(t-\tau _2)\right) \) involving two delays, viz. \(\tau _1\ge 0\) and \(\tau _2\ge 0\) . 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.

Asymptotic iteration method applied to new confining potentials Abstract 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 effect of thermal expansion coefficient on unsteady non-Newtonian supercritical Casson fluid flow past a vertical cylinder Abstract 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 and compressibility 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.

Extreme multistable synchronisation in coupled dynamical systems Abstract 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.

Modulational instability and dynamics of rational soliton solutions for the coupled Volterra lattice equation associated with $$4\times 4$$ 4 × 4 Lax pair Abstract 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.

Symmetry analysis of some nonlinear generalised systems of space–time fractional partial differential equations with time-dependent variable coefficients Abstract 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.

Ab initio study of the fundamental properties of $$\hbox {Zn}_{1-x} \hbox {TM}_{x} \hbox {Se}$$ Zn 1 - x TM x Se (TM $$=$$ = Mn, Co and Fe) Abstract The structural, electronic, magnetic, thermal and elastic properties of 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 Zn \(_{1-x}\) Mn \(_{x}\) Se and Zn \(_{1-x}\) Co \(_{x}\) Se and a half-metallic behaviour for 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 \(\mu \) \(_{\mathrm{B}}\) , 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.

General electrodynamics of non-abelian vector bosons of SU (2) Abstract Generalised Dirac–Maxwell equations (GDM) are extended to describe non-abelian vector bosons by forming SU(2) multiplet. Noether’s conserved current is investigated by forming suitable Lagrangian for the theory. General electrodynamics (GED) equations are obtained as Euler–Lagrange equations. Higgs mechanism leads to eigenvalue problem with masses of the bosons as eigenvalues. The sources of the fields have only improper conservation. Analogous to abelian vector bosons, non-abelian vector bosons also are seen to have nuclear structure with massive nucleus. There occur two types of SU(2) sheets, each of three non-abelian vector bosons: one group contains one bradyon and two tachyon vector bosons, whereas the other group contains one tachyon and two bradyon vector bosons. Physical Z and W bosons are formed from the eigenvectors of U(1) and SU(2). The Z and W bosons do not have the same coupling strengths in SU(2).

The Weyl equation under an external electromagnetic field in the cosmic string space–time Abstract In this paper we have considered a massless spinor Dirac particle in the presence of an external electromagnetic field in the cosmic string space–time. To study the Weyl equation in the cosmic string framework using the general definition of Laplacian in the curved space, elements of covariant derivative have been constructed and the Weyl equation has been rewritten in the considered framework. Then we have obtained the equation of energy eigenvalues by using the Nikiforov–Uvarov (NU) method. The wave function has been obtained in terms of Laguerre polynomials. An important result obtained is that the degeneracy of the Minkowski space spectral is broken in the transition from Minkowski to cosmic string space.

Design of a spiral inflector and transverse beam matching for K130 cyclotron at the Variable Energy Cyclotron Centre Abstract This paper describes the design of a spiral inflector for inflecting heavy ion beams into the existing central region of the \(\text {K} = 130\) Variable Energy Cyclotron at Kolkata. Simulation results of transverse beam dynamics through the spiral inflector and the effect of the fringe field on beam phase ellipses at its exit have been discussed in the absence of space charge effect. We have also made an effort to minimise the effect of inflector fringe field by properly adjusting the inflector voltage. The proper matching conditions in the central region have been obtained by optimising the system parameters of the existing axial injection line of K130 cyclotron. The tracking of particles that belong to the boundary of the optimised phase ellipses at the matching point has also been carried out in the computed electric and magnetic fields in the central region. Simulation results confirm that the optimised beam condition reduces beam losses for further acceleration in the cyclotron.