Abstract: The non-local symmetries for the generalised Broer–Kaup (BK) system are obtained with the truncated Painlevé expansion method. The non-local symmetries can be localised to the Lie point symmetries for the extended system by introducing auxiliary dependent variables. The finite symmetry transformations related to the non-local symmetries are computed. The consistent Riccati expansion and consistent tanh expansion integrability of the generalised BK system are proved, and the single soliton, two-resonant soliton and soliton–cnoidal wave interaction solutions are derived. PubDate: 2022-08-13

Abstract: This paper introduces modelling and simulation of signal distortions as well as intensity noise induced by two-tone direct intensity modulation of semiconductor lasers for use in radio-over-fibre (RoF) systems. The study develops a large-signal modulation of semiconductor laser simulations in the regime of high-frequency modulation by counting lasers with high modulation bandwidth. The temporal and spectral characteristics of the modulated laser output are investigated. The temporal characteristics include the fluctuations in the modulated signal waveforms, while the spectral characteristics include the frequency spectrum of the modulation response, second-order harmonic distortion (HD2) and second- and third-order intermodulation distortions, IMD2 and IMD3, respectively, as well as the relative intensity noise (RIN). The investigations are performed under three bias currents Ib of 2, 5 and 10 times the threshold value Ith over a wide range of modulation depth that covers regimes of small and large-signal modulation and at modulation frequencies as high as 8 and 25 GHz with a spacing of 10 MHz. The dynamic range of the linearity of the investigated laser is evaluated in terms of spurious-free dynamic range (SFDR). The results show that the nonlinear distortions increase as modulation depth increases. The highest distortion levels are observed when the modulation frequency approaches the laser relaxation frequency. The low-frequency RIN increases as the modulation depth and \(/\) or bias current increase and it has levels which are smaller when the modulation frequency is 8 GHz than when it is 25 GHz. PubDate: 2022-08-11

Abstract: The dynamic properties and the analytic solutions of high-order nonlinear time–space fractional Schrödinger equation are studied in this article. Based on a conserved Hamiltonian, the topological structure and the existence of the periodic and soliton solutions are studied by classifying the equilibrium points using the bifurcation method. Moreover, all exact travelling wave solutions are constructed to verify the prior estimation in the qualitative analysis by the complete discrimination system for the polynomial method. PubDate: 2022-08-11

Abstract: An investigation has been made relating the effect of UV radiations on etching parameters and activation energy of CR-39 (solid-state nuclear track detectors, (SSNTDs)). Corresponding changes in bulk etch rate (BER) (VB), track etch rate (TER) (VT), sensitivity (S), critical angle ( \(\theta_{{{\text{C}} }} )\) and efficiency ( \(\eta ) \) due to pre-irradiation and post-irradiation on CR-39 polycarbonate plastic detector have been reported and discussed in detail. Both bulk activation energy (BAE) (EB) and track activation energy (TAE) (ET) are reported to decrease with post-irradiation and are explained based on chain degradation, free radical formation, cross-linkage, chain scission and softening of the detector material. Further unusual decrease in BAE (EB) and TAE (ET) was observed for pre-irradiated CR-39 polycarbonate detectors, possibly due to the nature and density of the detector material. PubDate: 2022-08-10

Abstract: In this work, we successfully implemented the unified method and modified direct algebraic method (MDAM) to analyse the dynamical nonlinear wave structures of the predator–prey (PP) model using the conformable derivative that plays a significant role in biology. We secured some novel hyperbolic, trigonometric and rational function solutions. Modulation instability (MI) analysis of the PP model was also observed. Furthermore, the physical behaviours of some of the reported results are shown as three-dimensional, two-dimensional and contour profiles choosing suitable parameters. The computation software Mathematica was used to verify all the reported outcomes by substituting them back into the PP model. The results show that our mentioned methods are simple, efficient and precise to follow and can be used for a variety of further complex problems. The resulting solutions are novel, intriguing and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including biological sciences. The findings are exceptional and unique in comparison to previous findings in the literature. Furthermore, our findings are the first step towards understanding the structure and physical behaviour of complicated structures. These solutions define the wave performance of the governing model, actually. We feel that this work is timely and will be of interest to a wide spectrum of experts working on physics, engineering and biological models. PubDate: 2022-08-10

Abstract: The study reports the development of a continuously tunable excitation frequency-controlled cold atmospheric pressure plasma (CAP) device, its underlying physics and the associated unique discharge dynamics evolved under the variation of the external excitation frequency. The device is named as EFCAP to emphasise the ‘excitation frequency’ control aspect of the discharge. The absence of a dielectric barrier, very simple design, ability to operate with argon and ease of effective control via tuning of external driving frequency are some of the appealing features that drastically reduce device and operational cost. Significant controls achieved over dissipated power, discharge frequency, electron temperature, gas temperature and electronic excitation via tuning of frequencies are reported. While external excitation is in the kHz range, actual discharge dynamics were found to occur at a much higher frequency. Plasma–field interaction sets in complex interesting dynamics inside the torch, manifested in the form of spiral filaments and local hot spots. The evolution of the patterns by tuning the external excitation frequency is captured directly through fast photography and reported for the first time in CAP literature. The genesis of the patterns is examined from the synchronous time-domain behaviour of excitation pulse, discharge potential, discharge current and the corresponding frequency-domain behaviour. PubDate: 2022-08-04

Abstract: The cold fusion reactions with lead and bismuth as targets were used in the synthesis of superheavy elements (SHE) with mass number up to 113. Researchers ignored the cold fusion reactions in the synthesis of SHE>113. This may be due to the improper choice of projectiles. The present study focusses on cold fusion reactions leading to the formation of SHE from \(Z=112\) to 126. Suitable projectiles for the fusion reaction using \(^{208}\) Pb and \(^{209}\) Bi targets were identified. The fusion and evaporation residue cross-sections are evaluated using advance statistical model. The produced cross-sections were compared with the available experiments. Suitable projectiles for synthesising the superheavy elements with \(Z=104\) –126 using lead and bismuth targets are predicted. The predicted production cross-sections vary from nanobarn (nb) to picobarn (pb). The use of spherical–spherical projectile and target yields larger cross-sections than spherical–deformed or deformed–spherical projectile and target combination. PubDate: 2022-08-04

Abstract: The approximate phase-equivalent potentials to Manning–Rosen one are constructed using supersymmetric algebra. Using supersymmetric factorisation method, four SUSY transformations \(T_1\) , \(T_2\) , \(T_3\) and \(T_4\) are operated in pairs on Manning–Rosen potential to construct three different phase-equivalent potentials. These methodologies are verified by computing scattering phase shifts for different partial waves of nucleon–nucleon and \(\alpha \) –nucleon systems using the newly constructed phase-equivalent potentials. Good agreement with standard phase-shift data proves the merits of our approaches. PubDate: 2022-07-27

Abstract: We point out that PT-symmetric potentials \(V_{\mathrm {PT}}(x)\) having imaginary asymptotic saturation, \(V_{\mathrm {PT}}(x=\pm \infty ) =\pm i V_1, V_1 \in {\mathbb {R}}\) are devoid of scattering states and spectral singularity. We show the existence of real (positive and negative) discrete spectrum both with and without complex conjugate pair(s) of eigenvalues (CCPEs). If the eigenstates are arranged in the ascending order of the real part of the discrete eigenvalues, the initial states have few nodes but latter ones oscillate fast. Both real and imaginary parts of \(\psi _n(x)\) vanish asymptotically, and \( \psi _n(x) \) are nodeless. For the CCPEs, these are asymmetric and peaking on the left (right) and for real energies these are symmetric and peaking at the origin. For CCPEs \(E_{\pm }\) , the eigenstates \(\psi _{\pm }\) follow the interesting property, \( \psi _+(x) = N \psi _-(-x) , N \in {\mathbb {R}}^+\) . PubDate: 2022-07-26

Abstract: Superconducting behaviour of the fragile, pure, sub-milli-Kelvin temperature superconductor rhodium has been studied. Rhodium, a paramagnetic transition element, having free electron density, more than an order of magnitude larger (6.5×1023 cm−3) than a metallic monovalent superconductor, exhibits superconductivity at an extremely low temperature of a few hundred micro-Kelvin (10−6 K), at ambient pressure. Rhodium exhibits traditional BCS superconductivity brought about by the residual electron–phonon interaction and shows the characteristics of Type-I superconductivity. In this work, we have studied the effect of electron–phonon, electron–electron and electron–paramagnon interactions in rhodium. Further, we have evaluated the various characteristic parameters associated with rhodium. Finally, we conclude that rhodium is explained totally by the Bardeen–Cooper–Schrieffer (BCS) theory which corresponds fundamentally to the instantaneous nature of electron–phonon interaction along with the instantaneous electron–Coulomb interaction and instantaneous electron–spin interaction. PubDate: 2022-07-26

Abstract: In this study, an attempt is made to develop a model to analyse the anisotropic magnetoresistance in ferromagnetic metal films. In the model, the change in resistivity due to the changes in the scattering processes of the conduction electrons on applying an external magnetic field is proposed to be proportional to the spin–orbit interaction energy \(\Delta U_{\mathrm{SOI}}=\mu _{0}\mu M/2\) . Expressions are developed which relate the resistivity of the sample under an applied external magnetic field to its initial resistivity, current density, conduction electron magnetic moment, sample length, saturation magnetisation, remanence magnetisation, coercive field and external magnetic field. The equations obtained agree well with the experimental anisotropic magnetoresistance data of the ferromagnetic films. PubDate: 2022-07-26

Abstract: A model for cosmology that is conformal invariant from the beginning is presented. Breakdown of the conformal symmetry produces gravitation with parameters of mass. The system initially contains the Hilbert Lagrangian for general relativity plus quadratic terms in the Ricci tensor and in the scalar curvature. All these terms are supposed to create a space–time which cannot exist without gravity. So, masses appear when conformal invariance is broken. Massless Yang–Mills fields appear also as fundamental fields in the Lagrangian. An exact classical solution exists if a conformal scalar boson is introduced also in a conformal manner that couples gravity to the Yang–Mills sector. The paper claims that before the breakdown the model is renormalisable due to its conformal invariant nature. PubDate: 2022-07-20

Abstract: The current study deals with the linear stability of a fluid multilayered system in the presence of porous media. Fluids are subject to normal electric field, where there are insoluble surfactants contaminating the interfaces. The physical model consists of an inner layer sandwiched between two semi-infinite fluids. A single surface between two different fluid layers is studied as a limiting case, in which a small Reynolds number is covered. The objective of this work is to investigate the impact of viscosity and porosity properties on the linear growth rate and the sheet behaviour as a result of the interfacial surfactants. In the light of boundary constraints and geometry of the imposed system, the solutions of the hydrodynamic equations of motion lead to an implicit dispersion equation that basically depends on the growth rate along with the wave number. The physical parameters that control the fluid sheet strongly and significantly affect the shape of the waves, their amplitude and thus the stability profile of the liquid layers. Through the theoretical and analytical study, in addition to the numerical visualisations, the stability pictures are plotted and investigated. It is observed that both Marangoni and electric Weber numbers play opposite roles on the stability of the fluid sheet. This means that Marangoni number works to inhibit the growth rate while, the electric number encourages a stretching in the wave amplitude. PubDate: 2022-07-20

Abstract: We consider the attractive Bose–Einstein condensate (BEC) of Rb atoms, which is confined in a harmonic plus quartic trap \([ V(r)=\frac{1}{2}m\omega ^{2}r^{2}+\lambda r^{4}]\) . We slowly tune the coefficient of quartic term ( \(\lambda \) ) to see how the metastable region (MSR) in the outer part of the trap is modified. The MSR is always bounded by a left intermediate barrier (IB) and a deep but narrow attractive well (NAW) appears on the left of this barrier. For \(\lambda < 0\) , the MSR is bounded by an additional right IB. A dramatic behaviour (compared with the attractive BEC in a harmonic trap) of interaction energy, kinetic energy, trap energy along with the total ground-state energy of the condensate is observed in this different metastability. For \(\lambda \ge 0\) , the outer wall of the MSR increases steeply as \(\lambda \) increases. Dynamical responses of the zero point energies of the condensate are explored also. Observations are interesting as we find a critical value of anharmonicity ( \(\lambda _{\mathrm {cr}}\) ) to collapse the condensate. We slightly increase the strength of \(\lambda \) (close to \(\lambda _{\mathrm {cr}}\) ) and investigate the significant increase of the quantum tunnelling probability through the left IB into an inner core (NAW). PubDate: 2022-07-13

Abstract: The fast ignition (FI) scheme by energetic beams of light ions is one of the main approaches to increase the energy yield in an inertial fusion plasma. In this paper, the injection of a deuteron beam as a suitable laser-driven ignitor is suggested in a helium-3–lithium-6 ( \(^{3}\) He– \(^{6}\) Li) plasma for FI as well. The deuteron beam slows down and deposits its energy through Coulomb and nuclear interactions. The nuclear interaction effect caused by the deuteron beam is investigated on the slowing-down process of field ions. The deuterons can fuse with field ions (both \(^{3}\) He and \(^{6}\) Li) into plasma as they slow down and provide the added energy yield. The estimation of added energy yield and the evaluation of dependent parameters have a key role in the FI of this fuel with a high fusion yield. The curvature is created in the velocity distribution function due to the nuclear interaction of the deuteron beam in high energy. Reactivity improves at low electron density and high injection energy, compared with the Maxwellian state. Temperature increase reduces the share of nuclear interaction on the slowing-down process. The result indicates that the deuteron beam adds energy to the slowing down component through nuclear interaction. This enhancement of energy is more significant for low densities at high bulk temperature and injection energy. The added energy \(\hbox {yield}\) rises with the electron temperature and for \({E}_{\mathrm{D}} > 4000~\text{ keV }\) decreases with increasing deuteron injection energy. The added yield is high when the deuteron energy is low and the electron temperature is high. The maximum yield occurs with a deuteron beam energy of about 4 MeV. For \({E}_{\mathrm{D}} =4~\text{ MeV }\) , the total deposited energy \({E}_{\mathrm{total\, }{ }^{3}\mathrm{He}{+}{ }^{{6}}\mathrm{Li}}\) is about 5.4 \(\hbox {MeV}\) at \({T}_{\mathrm{e}} =200~\text{ keV }\) and is 6 MeV and 7.08 MeV at \({T}_{\mathrm{e}} =400~\text{ keV }\) and \({T}_{\mathrm{e}} =600~\text{ keV }\) , respectively. The application of deuteron beam decreases the ignition energy released in the \(^{3}\) He– \(^{6}\) Li fusion plasma. PubDate: 2022-07-13

Abstract: In quantum physics, plane and Airy waves are the only two known non-diffracting solutions in 1D. In this study, we perform numerical computation to find the other self-accelerating and non-diffracting waves. We construct the most general formula for self-accelerating waves in free space. We have found a new family of non-diffracting and self-accelerating waves in 2D and 3D. PubDate: 2022-07-13

Abstract: The singular surface theory is used for the planar and cylindrically symmetric flow of a dusty gas in radiative magnetogasdynamics to study the behaviour of different modes of wave propagation, and their culmination into a steepened form. We have considered one-dimensional steepening of waves. The transport equation for the jump discontinuity in the velocity gradient at the wave heads is determined and solved numerically. The effects of the van der Waals excluded volume of the medium, the mass concentration of solid particles, the ratio of densities, the ratio of specific heats, the radiation parameter and the magnetic field strength on the shock formation are analysed in detail. It is observed that the gradient of density, velocity, pressure and magnetic field are related to each other. PubDate: 2022-07-13

Abstract: This paper deals with the design of a numerical method for the Schnakenberg model. The patterns are nicely captured by way of the parameter values of the Schnakenberg model. The spatial integration of the equation is achieved by using a finite element method setting up the trigonometric quadratic B-spline collocation method over the subelements of the problem domain. The Crank–Nicolson technique is employed to get fully integrated Schnakenberg model. Numerical examples are given to show the good agreement with the Schnakenberg patterns. PubDate: 2022-07-13

Abstract: The propagation of a higher-order soliton in an ideal single-mode optical fibre under higher-order dispersion and higher-order nonlinearity is much affected by quintic nonlinearity, fourth-order dispersion and intrapulse Raman scattering. We use a compact split-step Padé scheme to numerically study the stabilisation of higher-order solitons by these effects in optical fibres. Our results show that the relative amplitudes of these two dispersive sideband waves, which originate from the fourth-order dispersion decrease or even eliminated by the increasing values of quintic nonlinear coefficient, in the presence of the intrapulse Raman scattering, and the higher-order soliton returns almost to its original shape. PubDate: 2022-07-07

Abstract: The present paper deals with flat Friedmann–Robertson–Walker (FRW) model with two-fluid sources in fractal cosmology. One fluid in this model represents the Universe’s matter content, while the other is a radiation field that models the cosmic microwave background. To obtain the deterministic model, we used the pressure–density relationship for matter via the gamma law equation of state \(p_{m} = (\gamma -1)\, \rho _{m}, \,\, 1\le \gamma \le 2\) . The solutions of fractal field equations are obtained in terms of Kummer’s confluent hypergeometric function of the first kind. Some physical parameters of the models are obtained and their behaviour is discussed in detail using graphs. PubDate: 2022-07-07