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      Volume 93, Issue 3

      September 2019

    • On physical limitations of mathematical constructions used in mathematical models


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      Physical limitations of mathematical constructions are discussed, which should be taken into account in developing or modifying mathematical models. We begin with consideration of the method of describing physical objects using numbers and restrictions followed from this method. Next, we formulate some general recommendations concerning procedures for modifying mathematical models. Since models of physical phenomena are considered, it is natural to provide a physical interpretation for each stage of the model development. Unfortunately, some of transformations used are treated as purely technical tricks, and therefore the question of the physical meaning is not raised in such cases. The lack of physical meaning of some mathematical procedures does not make them unambiguously unacceptable. However, this marks out the place that requires a reasonable interpretation because the final result should possess the physical meaning. Finally, we discuss the issues related to the dimensionality of the space of places of a model. The above-mentioned physical limitations often are left without necessary attention. Sometimes this leads to various undesirable consequences, which may include excessive complication of the problem, an implicit substitution of the declared problem with another one or, finally, the absence of solution of the formulated problem.

    • Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: An application to upgrade industrial sieves/filters


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      The peristaltic transport of Jeffrey fluid through the rectangular duct is investigated. The effect of porosity under the influence of partial slip is also taken into consideration. The equations describing the flow transport along with boundary conditions are first made dimensionless using appropriate transformations and are then solved to get the exact solutions. The role of pressure rise generated by the fluid is also presented. The obtained results are examined graphically through pertinent parameters affecting the flow. The streamlines have also beendisplayed to analyse the trapping phenomenon.

    • The electronic and transport properties of Li-doped graphene nanoribbons: An ab-initio approach


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      The metal-to-semiconductor transition has been noticed in graphene nanoribbons (GNRs) with various novel electronic and structural characteristics. The prospective and scope of GNRs for an array of implications could be spread significantly by this transition. Based on density functional theory (DFT) calculations, we studied the electronic and transport properties of zig-zag GNRs doped with lithium (Li) along with different edge morphology. Zig-zag nanoribbons are known to exhibit metallic behaviour without using spin. The structural properties, namely, edge state, doping and ribbon width, can be considered to affect the electronic properties of GNR structures. In this study, the changes in the electronic properties by doping a Li atom with various atomic percentages (16.6%, 33.3%, 50% and 66.6%) were investigated. Calculations were done by employing the local density approximation (LDA) based on DFT. In the presence of unique edge states, the edge-modified systems exhibit a noticeable change with prominent and better Li mobility. As a result, it has been observed that substituting two Li atoms at the carbon edges is more predominant compared to other doping configurations. We expect that our peculiar results will have potential applications in energy conversion, solar cells and thermoelectric devices.

    • Uranium(IV) incorporation into inverse spinel magnetite $\rm{(FeFe_{2}O_{4})}$: A charge-balanced substitution case analysis


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      Magnetite has gained significant attention owing to its good radionuclide solid solution and recovery capacity. In this paper, first-principle calculations are adopted to evaluate and analyse the formation energies, mechanical stabilities, bonding behaviours and magnetic properties of U(IV) ions incorporated into the magnetite lattice with different charge-balanced cases. The case indicated by $B_{1}$, adding a U(IV) ion in an octahedron site and generating an octahedron Fe(III) ion vacancy, is most favourable for U(IV) incorporation into the magnetite lattice. Moreover, the corresponding models (named $B_{1}$, $C_{1}$ and $D$) for different amounts of U(IV) incorporation satisfy mechanical stability. The bond population and Mulliken charge population calculations show that the ionic bonding strength of $\rm{Fe–O}$ and $\rm{U^{IV}–O}$ bonds is stronger in pure magnetite compared to the mentioned U(IV)-doped magnetite models. The spin-polarised density of states of U(IV)-doped magnetites are asymmetrical for the spin-up part and the spin-down part, indicating that the mentioned U(IV)-doped magnetites have good magnetic properties. Our work is expected to provide new ideas for the disposal of U(IV).

    • Thermal properties of $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes in the back-shifted Fermi gas model with temperature-dependent pairing energy


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      Thermodynamic properties of $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes are investigated using the back-shifted Fermigas(BSFG) model with the energy-dependent level density parameter and the temperature-dependent pairing energy. The temperature dependency of pairing energy is applied using the mean order parameter of the exact Ginzburg–Landau (EGL) theory. The level density, entropy, temperature and heat capacity of $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes are calculated using these approaches and the results are compared with each other as well as with experimental data to examine the validity of these models. The results obtained by the present study indicate that the BSFG model with the temperature-dependent pairing energy is in better agreement with the experimental data, compared to the BSFG model with the energy-dependent level density parameter, for $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes.

    • Lie symmetries, conservation laws and solitons for the AB system with time-dependent coefficients in nonlinear optics or fluid mechanics


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      In this paper, the AB system with time-dependent coefficients for the ultrashort pulses in an inhomogeneous optical fibre or the marginally unstable baroclinic wave packets in an atmospheric or oceanic system is investigated via the Lie symmetry analysis. We obtain the Lie symmetries, reduced equations and groupinvariant solutions. The nonlinear self-adjointness of the AB system is proved, and the conservation laws associated with the Lie symmetries are constructed. For the amplitude of the electric field in the inhomogeneous optical fibre or the amplitude of the wave packet in the atmospheric or oceanic system, and for the quantity associated with the occupation number which gives a measure of the atomic inversion in the inhomogeneous optical fibre or the quantity measuring the correction of the basic flow in the atmospheric or oceanic system, we get some solitons through the Lie symmetry transformations, whose amplitudes,widths, velocities and backgrounds are different from those of the given ones and can be adjusted via the Lie group parameters. We find a family of the ultrashort pulses propagating in the inhomogeneous optical fibre or a family of the marginally unstable baroclinic wave packets propagating in the atmospheric or oceanic system.

    • Theoretical studies on the fine structure of $\alpha$ decay for even–odd and even–even isotopes of Cm, Cf, Fm and No nuclei


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      Using the cubic plus Yukawa plus exponential model (CYEM), half-lives of $\alpha$ decay from the ground state of the parent nuclei to the ground state of the daughter nuclei and from the ground state to an excited state of the daughter nuclei have been systematically investigated for even–odd and even–even isotopes of Cm, Cf, Fm and No nuclei by incorporating centrifugal potential term, rotational energy term, deformation effects ($\beta_{2}$ and $\beta_{4}$) of the parent and daughter nuclei and spin–parity effects.We have done our calculations by considering the Coulomb, centrifugal and Yukawa plus exponential potentials as an interacting barrier for separated fragments and the cubic potential for the overlapping region. The calculated half-lives are compared with the available data. Our results are found to be in good agreement with each other. The effect of the centrifugal potential on half-life was evaluated. The branching ratio, hindrance factor and standard deviation of half-lives from the ground state of the parent nuclei to the ground state of the daughter nuclei have been calculated.

    • Numerical treatment of activation energy for the three-dimensional flow of a cross magnetonanoliquid with variable conductivity


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      This research demonstrates the diverse characteristics of the cross fluid in the presence of Lorentz’s forces. Moreover, this work reviews the characteristics of variable diffusivity and variable conductivity. Mathematical modelling of the presented physical model is carried out in the Cartesian coordinate system and the formulated system of partial differential equations (PDEs) is simplified in ordinary differential equations (ODEs). Numerical algorithm leads to solution computations. Velocity, temperature and concentration are numerically analysed for the cross fluid. Outcomes of the current physical model are presented through graphical data and in tabular form. It is noted that variable conductivity and variable diffusivity significantly affect heat–mass transport mechanisms. Furthermore, graphical analysis reveals that the concentration of the cross nanofluid increase for increased values of variable diffusivity. Furthermore, this research reveals that concentration distribution is a reducing function of chemical reaction parameters.

    • An analytical approach to the metal and metallic oxide properties of Cu–water and $\rm{TiO_{2}}$–water nanofluids over a moving vertical plate


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      An analysis was carried out to study the flow phenomena of an unsteady, electrically conducting, water-based nanofluid embedded with a porous matrix over a moving/stationary plate. The effects on the nanofluid flow were observed by taking copper (Cu) and titanium oxide ($\rm{TiO_{2}}$) nanoparticles. The crux of the investigation is to examine the influence of thermal radiation, radiation absorption parameter accounted for in the energy equation. The first-order chemical reaction was also taken care of by incorporating it into the solutal transfer equation. Closed form solution holds good for nonlinear coupled partial differential equations. Solutions of these equations are obtained by employing Laplace transform technique. The effects of parameters such as magnetic parameter, porous matrix, thermal and mass buoyancy parameters, thermal radiation, heat absorption parameter, radiation conduction parameter, Prandtl and Schmidt numbers and the homogeneous chemical reaction are shown via graphs. The results for the physical quantities of interest such as the rate of shear stress and the rate of heat and mass transfer coefficients are also obtained and presented through graphs. Observing these, the emerging role of a few parameters is elaborated in the results and discussion section.

    • A third-order memristive Wien-bridge circuit and its integrable deformation


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      In this paper, a novel passive memristor model and its equivalent circuit model are designed, analysed and realised to investigate the memristor characteristics and their applications in nonlinear circuits. By employing this memristor model, a new third-order memristive Wien bridge is set up. Dynamical behaviours of the system are studied in detail, and multiscroll attractors, coexisting bifurcation modes, coexisting attractors, antimonotonicity and transient chaotic bursting are observed in this system by using theoretical analysis, simulation analysis and circuit experiment. Integrable deformation of the memristive Wien-bridge system is analysed. The circuit experiment is performed by replacing the memristor with its equivalent circuit model in the proposed memristor-based Wien-bridge circuit.

    • Multiple vibrational resonance and antiresonance in a coupled anharmonic oscillator under monochromatic excitation


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      We examine the existence of multiple vibrational resonance (VR) and antiresonance in two coupled overdamped anharmonic oscillators where each one is individually driven by a monochromatic sinusoidal signal with widely separated frequencies ($\Omega \gg \omega$). In contemporary VR, superposed periodic waves are adopted to infer resonance, but herein we employ non-superposed periodic waves to acquire the elevated response. We study two coupling schemes namely, unidirectional and bidirectional, to substantiate the occurrence of multiple VR and antiresonance. Such occurrences have been shown and the results were ascertained with supportive numerical and experimental outcomes. We also illustrate the effect of coupling strength on the observed phenomenon.

    • Soliton solutions of the generalised third-order nonlinear Schrödinger equation by two mathematical methods and their stability


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      The generalised nonlinear Schrödinger equation (NLSE) of third order is investigated, which accepts one-hump embedded solitons in a single-parameter family. In this paper, we constructed analytical solutions in the form of solitary waves and solitons of third-order NLSE by employing the extended simple equation method and exp($−\Phi(\xi)$)-expansion method. In applied physics and engineering, the obtained exact solutions have important applications. The stability of the model is examined by employing modulational instability which verifies that all the achieved exact solutions are stable. The movements of exact solitons are also presented graphically, which assist the researchers to know the physical interpretation of this complex model. Several such types of problems arising in engineering and physics can be resolved by utilising these reliable, influential and effective methods.

    • Effect of strain on the structural and electronic properties of transition metal-doped arsenene nanoribbons: An ab-initio approach


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      Recently, arsenene, having a monolayer honeycomb structure of grey arsenic, has been manufactured successfully. Motivated by this, here we have calculated the electronic properties and stability of arsenene by employing the first-principles method for calculations. We have considered two different structures, namely planar and puckered. Based on the analysis, the puckered structure was found to be semiconducting in nature. Additionally, we have estimated the electronic properties of different 3d transition metal (TM) atoms doped in arsenene. Here, straining the nanoribbons also modulates the band gap. It closes the band gap for puckered arsenene under the 8% strain application. Specifically, a 4% strain is considerably sufficient to transform metallic arsenene to a directband-gap semiconductor. Also, the bond angle between the nearest atoms becomes almost equal. We have observed that Ni-doped arsenene is the most stable. We have also studied the electronic band structures of the pristine and TM-doped antimonene. Planar antimonene is metallic while rhombohedral antimonene is semiconducting. Our results will play vital roles in sensors and various nanoelectronics applications.

    • Soliton, Wronskian and Grammian solutions to the generalised (3 + 1)-dimensional Kadomtsev–Petviashvili equation

      YUE KAI

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      In this paper, a generalised (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation is considered. By transforming it into the bilinear form, one-, two- and multisoliton solutions are obtained. What is more, the Wronskian and Grammian solutions are also presented according to the Plücker relation and the Jacobi identity for determinants. In order to have an in-depth understanding of the dynamical properties of the equation, examples of each solution are given and some of them are plotted.

    • The impact of magnetohydrodynamics and heat transfer on the unsteady flow of Casson fluid in an oscillating cylinder via integral transform: A Caputo–Fabrizio fractional model


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      Casson fluid flow has numerous functional applications in food processing, metallurgy, drilling and bio-engineering operations. The significance of Casson fluid in cylindrical coordinates has recently attracted researchersbecause of the numerical and experimental analyses of the fluid. Due to the lack of fractional analytical approaches, this paper is trying to examine the magnetic effect and thermal effect on Casson fluid with oscillatory boundary conditions in cylindrical coordinates. The constitutive model of Casson fluid is solved by using the Caputo–Fabrizio time fractional derivative approach. The fluid moves in the vertical oscillating cylinder under the influence of a transverse applied magnetic field. Closed-form solutions are obtained via integral transforms (Laplace and Hankel transformations) for velocity and temperature distributions. Graphical results are shown for various physical parameters such as the Casson fluid parameter $\beta$, magnetic parameter $M$, Grashoff number Gr, Prandtl number Pr and fractional parameter $\alpha$. The corresponding expressions for Nusselt number are also evaluated for various embedded parameters in a tabular form.

    • Excitation performance of $\rm{Ba_{0.8}Mg_{0.2}(Zr_{0.1}Ti_{0.8}Ce_{0.1})O_{3}}$ materials in an electrical field


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      Dense and stoichiometric $\rm{Ba_{0.8}Mg_{0.2}(Zr_{0.1}Ti_{0.8}Ce_{0.1})O_{3} (BMZTCO)}$ ceramics have been synthesised and their excitation was experimentally evaluated by applying an electric field. The processed sample exhibits superior frequency-independent and temperature-dependent dielectric parameters. The prepared sample has combined the tetragonal and cubic phases of $\rm{BaTiO_{3}}$ and $\rm{Ce_{2}O_{3}}$. The Bode plots suggest non-Debye type of relaxation mechanism and positive temperature coefficient-type behaviour. The excitation intensity reaches a peak when the driving frequency matches with the natural frequency of the prepared sample.

    • The synchronisation of two floating memristor-based oscillators and the circuit design


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      The synchronisation between two floating memristor-based Colpitts oscillators is studied in this paper. Firstly, the mathematical and circuit models of Colpitts oscillator based on a floating memristor with a diodebridge structure are built. On this basis, numerical simulations on the features of both the independent memristor and the floating memristor are conducted and compared using MATLAB software. Secondly, circuit simulation is made on the synchronisation of two floating memristor-based systems by using MULTISIM software. Finally, the physical circuit on the synchronisation of the two coupling Colpitts systems based on the diode bridge memristors is implemented by using the linear error feedback scheme and improved by the capacitor coupling scheme and the adaptive nonlinear feedback control scheme, respectively. The experimental results by the oscilloscope and simulation results show that approximate synchronisation is achieved.

    • Effective optical properties of the one-dimensional periodic structure of $\rm{TiO_{2}}$ and $\rm{SiO_{2}}$ layers with a defect layer of nanocomposite consisting of silver nanoparticle and E7 liquid crystal


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      In this work, the dielectric property of a nanocomposite (NC) consisting of silver nanoparticle and E7 liquid crystal (LC) has been investigated theoretically at different temperatures. The study shows that the surface plasmon resonance (SPR) and filling fraction of the silver nanoparticle significantly change the dielectric property of the NC. To study the optical property of the defective periodic structure, the NC was considered as a defect layer in a semifinite one-dimensional periodic structure (1DPS) of $\rm{TiO_{2}}$ and $\rm{SiO_{2}}$ layers, i.e. $\rm{(TiO_{2}|SiO_{2})^{5}|NC|(TiO_{2}|SiO_{2})^{5}}$. The optical properties of the 1DPS with the NC as the defect layer have been studied by the simple transfer matrix method (TMM). Moreover, the transmission and absorption characteristics of the 1DPS in the presence of silver nanoparticle in the NC have been studied with different orientations of the LC molecule.

    • Influence of material parameters on the performance of niobium-based superconducting radiofrequency cavities


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      A detailed thermal analysis of a niobium (Nb)-based superconducting radio-frequency (SRF) cavity in a liquid helium bath is presented, by taking into account the temperature and magnetic field dependence of surface resistance and thermal conductivity in the superconducting state of the starting Nb material (for SRF cavity fabrication) with different impurity levels. The drop in SRF cavity quality factor ($\mathcal{Q}_{0}$) in the high acceleration gradient regime (before the ultimate breakdown of the SRF cavity) is studied in detail. It is argued that the highfield $\mathcal{Q}_{0}$-drop in SRF cavity is considerably influenced by the intrinsic material parameters such as electrical conductivity and thermal diffusivity. The detailed analysis reveals that the current specification on the purity of Nb material for SRF cavity fabrication is somewhat over-specified, as also inferred by the experimental work reported by some of the laboratories in the recent past. In line with these encouraging experimental results, in this paper, based on a rigorous calculation, we show that the Nb material with relatively low purity can very well serve the purpose for the accelerators dedicated for spallation neutron source (SNS) or accelerator-driven sub-critical system(ADSS) applications, where the required accelerating gradient is typically up to $\rm{20 MV m^{−1}}$. This information will have important implication towards the cost reduction of superconducting technology-based particle accelerators for various applications. We think this theoretical work will be complementary to the experimental efforts performed in various laboratories at different corners of the globe.

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