The effect of two-loop correction in quark–gluon plasma (QGP) droplet formation is studied by introducing the two-loop correction factor in the mean-field potential. The correction factor leads to the stability in the droplet formations of QGP at different parametrisation factors of the QGP fluid. This also shows that the gluon parameter factor shifts to a larger value from its earlier value of one-loop correction in attaining the stability of the droplets. The results show a decrease in the observable QGP droplet sizes which are found to be 1.5–2.0 fm radii with the two-loop correction. It indicates that the dynamics of the QGP droplet and the stability of the droplet withthe two-loop correction factor can be controlled by the fluid parameter in the model.

The degenerate coupled multi-Korteweg–de Vries equations for coupled multiplicity $l = 3$ are studied. The equations, also known as three-field Kaup–Boussinesq equations, are considered for invariant analysis and conservation laws. The classical Lie’s symmetry method is used to analyse the symmetries of equations. Based on the Killing’s form, which is invariant of adjoint action, the full classification for Lie algebra is presented. Further, one-dimensional optimal group classification is used to obtain invariant solutions. Besides this, using general theorem proved by Ibragimov, we find several non-local conservation laws for these equations. The conserved currents obtained in this work can be useful for the better understanding of some physical phenomena modelled by the underlying equations.

In this paper, a numerical technique for solving the regularised long wave equation (RLW) is presented using a wavelet Galerkin (WG) method in space and a fourth-order Runge–Kutta (RK) technique in time.We study the convergence analysis of the obtained numerical solutions and investigate the results for the motions of doubleand single solitary waves, undular bores and conservation properties of mass, energy and momentum in order to verify the applicability and performance of the proposed method. Simulation results are further compared with the known analytical solutions and some previous published numerical results. It is concluded that the present method remarkably improves the accuracy of the Galerkin-based methods for numerically solving a large class of nonlinear and weakly dispersive ocean waves.

A novel criterion for achieving synchronisation in fractional-order chaotic and hyperchaotic systems is presented. Here, it is proved that the existence of a Lyapunov function in the integer-order differential system implies local stability of the steady state in its fractional-order counterpart. So, our criterion is based on computations of suitable linear feedback controllers of the fractional-order systems according to an appropriate choice of Lyapunov function. Furthermore, a new fractional-order hyperchaotic system is introduced here. The case of hyperchaos in the proposed system is verified by computing its greatest two Lyapunov exponents which are shown to be positive. The new synchronisation criterion is successfully applied to the fractional Liu system, the fractional Samardzija–Greller system, the fractional financial system and a novel fractional-order hyperchaotic system. Numerical results are used to verify the analytical results.

The effects of Soret and variable porosity on an unsteady magnetohydrodynamic flow of an upper convected Maxwell fluid through an expanding or contracting channel are explored in this article. The temperature and concentration at the walls are maintained at different values. The gravitational forces arising from temperature and concentration gradients are also considered. The behaviour of velocity components, skin friction, temperature and concentration with respect to various non-dimensional parameters has been numerically computed by using anefficient shooting method. Newtonian case has been studied using the current algorithm and the present results are compared with earlier literature. At the boundaries, the heat and mass transfer rates are studied using local Nusseltand Sherwood numbers. The results show that both the variable permeability and wall expansion have dominant effects on skin friction at the plates. The Prandtl and Soret numbers have dominating effect on mass transfer when compared with variable permeable parameter.

The main thrust of this paper is to consider a delayed q-deformed discrete susceptible–infected–susceptible (SIS) epidemic model. Parametric conditions on the local stability of the disease-free fixed point and the endemic fixed points are obtained. A codimension-one bifurcation analysis at the fixed points of the model is discussed. The model has a variety of bifurcations such as flip, transcritical, and pitchfork bifurcations. Numerical simulations including trajectories, bifurcation diagrams, maximal Lyapunov exponent, and phase portraits are illustrated to verify the obtained analytical results. It has been noticed that introducing the delay in the absence of deformations recovers the chaotic behaviour of the model. Meanwhile, introducing both deformations and delay suppress the chaotic behaviour of the model. The disease will be eradicated by increasing the value of bothdeformation and delay strength parameters.

This paper generalises an earlier result by the author based on the well-established embedding theorems that connect the classical theory of relativity to higher-dimensional space–times. In particular, an n-dimensional Riemannian space is said to be of class $m$ if $m + n$ is the lowest dimension of the flat space in which the given space can be embedded. To study traversable wormholes, we concentrate on spacetimes that can be reduced to embedding class one by a suitable transformation. It is subsequently shown that the extra degrees of freedom from the embedding theory provide the basis for a complete wormhole solution in the sense of obtaining both the redshift and shape functions.

We demonstrate a technique based on optical heterodyne detection to measure the Rydberg population in the thermal atomic vapour. The technique used a probe beam far off-resonant to the D2 line of rubidium along with a reference beam with frequency offset by 800 MHz in the presence of a coupling laser that couples to Rydberg state via two-photon resonance. The polarisation of the probe, reference and coupling beams are suitably chosen such that only the probe beam goes through a nonlinear phase shift due to the two-photon process which is measured relative to the phase shift of the reference beam using optical heterodyne detection technique. We show that the technique has a sensitivity to measure the minimum phase shift of the order of a few $\mu$rad. We have used a suitable model of two-photon excitation of a three-level atom to show that the minimum phase shift measured in our experiment corresponds to the Rydberg population of the order of $10^{−5}$. The corresponding probe absorption for the given laser parameters is of the order of $10^{−7}$. We demonstrate that this technique is insensitive to polarisation impurity or fluctuations in the beams. The technique is particularly useful in measuring the Rydberg population via two-photon excitation in thermal vapour where microchannel plates (MCP) could be relatively difficult to implement. It can also be used in the ultracold atomic sample with suitable laser parameters.

Based on Routh–Hurwitz criterion, this paper reports on synchronisation of two coupled 3D Josephson junctions via cyclic coupling. Analytical conditions which lead to stable synchronisation through the cyclic coupling were derived. Numerical and microcontroller-based circuit simulations are employed to verify the feasibility and effectiveness of the derived analytical criteria. The cyclic coupling has potential applications in neural information transmission and communication in natural systems.

Electrostatic ion cyclotron instability pertaining to the higher harmonics of proton and helium cyclotron modes is investigated in three-component magnetised plasma consisting of beam electrons, protons and doubly charged helium ions. The effect of different plasma parameters, namely, angle of propagation, number density andtemperature of helium ions and electron beam speed, has been studied on the growth of proton and helium cyclotron harmonics. It is found that an increase in angle of propagation leads to the excitation of fewer harmonics of proton cyclotron waves with decreased growth rates and higher number of helium harmonics with decreased growth rates.Also, largely odd helium harmonics are excited, except for one particular case where the second harmonic also becomes unstable. The number density and temperature of ions have significant effect on the helium cyclotron instability compared to the proton cyclotron instability. Further, as the speed of electron beam is increased, the peak growth rate increases. Our results are relevant to laboratory and space plasmas where field-aligned currents exist.

In this paper, we have studied the locally rotationally symmetric (LRS) Bianchi type-I cosmological model filled with a bulk viscous cosmological fluid in $f(R)$ gravity in the presence of time-varying gravitational and cosmological constant. We have used the power-law and intermediate scenario for scale factor to obtain thesolution of the field equations. The evolution of temperature of a viscous Universe is also analysed.

Carbon materials possessing photoluminescence properties are considered as potential candidates in a wide range of photonic and optoelectronic applications. In this work, the cellulose derived from the natural source, Pandanus, is autoclave-treated for the synthesis of fluorescent carbon. The natural fibres are greatly preferred over synthetic ones due to their cost-effectiveness, easy processability, non-abrasivity, non-toxic and environment-friendly characteristics along with high mechanical strength and damage tolerance. These properties enable them to be used as templates for synthesis, as important reinforcement materials for commercial thermoplastics and for making value-added products. In this study, the synthesised sample is subjected to structural, morphological, elemental and optical characterisations. These studies reveal that the sample can be used as a low-cost tunable light-emitting source for photonic, biomedical and biosensing applications.

The interaction of intense femtosecond laser pulses with argon nanoclusters is studied using nanoplasma model. Based on the dynamic simulations, ionisation process, heating, and expansion of an argon nanocluster irradiated by an intense femtosecond laser pulse are investigated. The analytical calculation provides ionisation ratefor different mechanisms and time evolution of hydrodynamic pressure for various pulse shapes. In this work, the dependence of laser intensity, initial ion density and pulse shape on the electron pressure, the density of electrons and electron temperature are presented. It is noticed that the negative and positive chirped pulses and initial iondensity implement some modifications on the current calculation models. It is found that reducing the initial ion density at a laser intensity of about $1\times10^{16}W/hboxcm^{2}$ increases the energy of electrons. By applying a positive chirp laser pulse during interaction with nanoclusters, both electron density and ultimately electron pressure are improved by about 22%.

The objective of this paper is to study the nonlinear coupled dynamical fractional model of romantic and interpersonal relationships using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). These procedures inspect the dynamics of love affairs among couples. Sufficient conditions for their convergence and error estimates are established. Obtained results are compared with the existing and recently developed methods. It is interesting to observe that these methods also work for those fractional models that do not have an exact solution. Results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes. Results divulge those schemes that are attractive, accurate, easy to use and highly effective.

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase space using statistical methodology. The adopted perspective leads to obtainingwithin the framework of its theory the fundamental quantum-mechanical equation without recourse to the other formulations of quantum mechanics, and gives the idea for operators pertaining to dynamical quantities. The derivation of this equation starts with the ensemble in phase space and, as a result, reproduces Liouville’s theorem and virial theorem for quantum mechanics. We have explained with the help of this equation the structure of quantum mechanics in phase space and the approximation to the Schrödinger equation. Furthermore, we have shown that this formalism provides reasonable results of quantisation such as the quantisation of harmonic oscillation, the two-slit interference and the uncertainty relation. In particular, we have demonstrated that this formalism can easily give the relativistic wave equation without using the linearisation of the Hamiltonian operator.The ultimate outcome this formalism produces is that primary and general matters of quantum mechanics can be studied reasonably within the framework of statistical mechanics.