Article ID 0039 Published: 10 February 2020 Research Article
HADI REZAZADEH DIPANKAR KUMAR AHMAD NEIRAMEH MOSTAFA ESLAMI MOHAMMAD MIRZAZADEH
This paper examines new travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) model with Kerr nonlinearity using Bäcklund transformation method based on Riccati equation, Kudryashov method and a new auxiliary ordinary differential equation (ODE). The three methods are adequately utilised, and some new rational-type hyperbolic and trigonometric function solutions are derived in different shapes for the aforementioned model. We confirm that our methods are more efficient than the other methods and it might be used in many other such types of nonlinear equations arising in the basic fabric of communications network technology and nonlinearoptics.
Article ID 0038 Published: 10 February 2020 Research Article
Fundamental goal of the present communication is to analyse the viscous electrically conducting nanofluid flow near a stagnation region past a stretching sheet. Investigation of single-wall carbon nanotubes (SWCNTs) are done and water is employed as the base fluid. Combinations of the effects of heat generation, thermal radiation, viscous dissipation and Joule heating are considered. Mathematical modelling and examinations are done in the presence of magnetic field. Similarity variables are introduced to convert nonlinear partial differential equations into nonlinear ordinary differential equations. Numerical solutions of the governing modelled equations are collected by applying Galerkin finite-element method. Impacts of distinct influential parameters such as velocity ratio parameter, solid volume fraction, magnetic parameter, radiation parameter, heat generation parameter and Brinkmann number on velocity, temperature, surface shear stress and surface heat flux are obtained and discussed. Furthermore, comparison of the results of the current analysis is made with the earlier published data.
Article ID 0037 Published: 10 February 2020 Research Article
YESIM SAGLAM ÖZKAN EMRULLAH YASAR
In this paper, the improved tan($\varphi/2$)-expansion method (ITEM) is proposed to obtain more general exact solutions of the nonlinear evolution equations (NLEEs). This method is applied to the generalised Hirota–Satsuma coupled KdV (HScKdV) equation and (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) system. We have obtained four types of solutions of these equations such as hyperbolic, trigonometric, exponential and rational functions as an advantage of this method. These solutions include solitons, rational, periodic and kink solutions. Moreover, modulation instability is used to establish stability of the obtained solutions.
Article ID 0036 Published: 30 January 2020 Research Article
A lump-type solution of the (2 + 1)-dimensional generalised fifth-order Korteweg–de Vries (KdV) equation is obtained from the two-soliton solution by applying the parametric limit method. Some theorems and corollaries about the superposition behaviour between lump solutions and different forms of $N$-soliton ($N \rightarrow\infty$) solutions are constructed, and detailed proofs are given. Besides,we give a large number of examples and spatial evolution graphics to illustrate the effectiveness of the described theorems and corollaries. Some new nonlinear phenomena and superposition behaviour, such as rational-exponential type, rational-cosh-cos type, rational-sin type, rational-logarithmic type etc., are simulated and shown for the first time. Finally, we also illustrate the superposition between high-order lump-type solutions and $N$-soliton solutions.
Article ID 0035 Published: 30 January 2020 Research Article
HAJAR F ISMAEL HASAN BULUT HACI MEHMET BASKONUS
The purpose of this study is to find some novel soliton solutions of Fokas–Lenells (FL) equation where the perturbation terms are taken into account with nonlinearity. The sine-Gordon expansion method (SGEM) and the $(m + (G'/G))$-expansion method are used in this context. The dark, bright, dark–bright and singular optical soliton solutions are successfully obtained. Moreover, the constraint conditions for guaranteeing the existence of solutions are also given.
Article ID 0034 Published: 30 January 2020 Research Article
SHUANG ZHOU YIXUAN HONG YIMING YANG LING LÜ CHENGREN LI
In this paper, the problem of finite-time synchronisation of uncertain delay spatiotemporal networks via unidirectional coupling technology is investigated. Based on Lyapunov theorem and finite-time stability theory, an effective finite-time synchronisation scheme is designed to achieve finite-time synchronisation between uncertain delay spatiotemporal networks, and adaptive estimations of coupling coefficient, unknown parameter and uncertain network topology are realised. Then, the Fisher–Kolmogorov spatiotemporal model is used as the state equation of the network node for numerical simulation. The simulation results show that the finite-time synchronisation scheme is effective.
Article ID 0033 Published: 30 January 2020 Research Article
TAPAS DAS UTTAM GHOSH SUSMITA SARKAR SHANTANU DAS
$D$-dimensional fractional Klein–Gordon equation with fractional vector and scalar potential has been studied. Both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely $v$ and $s$. Jumarie-type definitions for fractional calculus have been used. We have succeeded in achieving Whittaker-type classical differential equation in fractional mode for the required eigenfunction. Fractional Whittaker equation has been manipulated using the behaviour of the eigenfunction at asymptotic distance and origin. This manipulation delivers fractional-type confluent hypergeometric equation to solve. Power series method has been employed to do the task. All the obtained results agree with the existing results in literature when fractional parameter $\alpha$ is unity. Finally, we furnish numerical results with a few eigenfunction graphs for different spatial dimensions and fractional parameters.
Article ID 0032 Published: 30 January 2020 Research Article
Analysis of imprecisely defined fuzzy space-fractional telegraph equations
SMITA TAPASWINI DIPTIRANJAN BEHERA
Telegraph equations are very important in physics and engineering due to their importance in modelling and designing frequency or voltage transmission. Moreover, uncertainty present in the system parameters plays a vital role in the designing process. Also it is known that it is not always easy to find exact solution of fractionally ordered system. Taking these factors into consideration, here space-fractional telegraph equations with fuzzy uncertainty have been analysed. A new technique to represent fuzzy number using two different parameters in the same domain has been used along with a semianalytic approach known as Adomain decomposition method (ADM) for the solution. Gaussian and triangular shaped fuzzy numbers are considered to model the uncertainties in initial as well as boundary conditions. The obtained results are compared with the existing solution in special cases for the validation.
Article ID 0031 Published: 25 January 2020 Research Article
KAPIL BHATT SANDEEP KUMAR C C TRIPATHI
Exploiting the advantages of additive patterning process over complex fabrication processes, herein we report the fabrication of field-effect transistor (FET) using the screen-printing method. The graphene conductive composite dielectric ink as the channel and the dielectric layer respectively was screen printed on cellulose paper substrate. The fabricated device shows the hole and electron mobility of $\rm{135 cm^{2}/V s}$ and $\rm{98 cm^{2}/V s}$ respectively with an ultra-low leakage current of $\sim 25 \rm{nA}$. The proposed technique can be used for large-scale roll-to-roll commercial manufacturing of disposable FET-based sensors such as temperature and IR sensors, health monitoring devices etc.
Article ID 0030 Published: 25 January 2020 Research Article
Binding energy of excitons in an infinitely deep spherical quantum dot under intense THz laser field
A OUADGUI J DIOURI J KHAMKHAMI
We study the effects of intense THz laser field on the ground-state binding energy of heavy hole excitons confined in GaAs spherical quantum dots. The calculation is performed using the variational method in the framework of the single band effective mass theory. Our results show that (i) the laser electric field lowers the binding energy for all quantum dot radii, making the exciton clustered near the centre of the dot, (ii) the binding energy is mainly due to the dressed potential making the kinetic part insensitive to the field and (iii) the behaviour of the exciton, under the approximations used, can be modelled by a unique set of plots, depending on the material only via its excitonic units.
Article ID 0029 Published: 25 January 2020 Research Article
Optical travelling wave solutions for the Biswas–Arshed model in Kerr and non-Kerr law media
MUHAMMAD TAHIR AZIZ ULLAH AWAN
This paper scrutinises the newly proposed Biswas–Arshed model for soliton propagation through optical fibres,with small group velocity dispersion and in the absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered to balance with group velocity dispersion. First integral and functional variable methods are employed to recover solitary wave, shock wave, singular wave and singular periodic wave solutions for the two nonlinear forms of the model through Kerr law and power-law nonlinearity. The constraint relations are also figured for the manifestation of these optical solutions.
Article ID 0028 Published: 25 January 2020 Research Article
Computational soliton solutions to (2 + 1)-dimensional Pavlov equation using Lie symmetry approach
SACHIN KUMAR MUKESH KUMAR DHARMENDRA KUMAR
In this work, Lie symmetry analysis and one-dimensional optimal system for Pavlov equation are presented. All the possible vector fields, their commutative and adjoint relations are carried out under invariance property of Lie group theory. On the basis of optimal system, similarity reductions of Pavlov equation are obtained. A repeated process of similarity reductions transforms the Pavlov equation into ordinary differential equations, which generate invariant solutions. The obtained invariant solutions are supplemented by numerical simulation toanalyse the physical behaviour. Thus, their parabolic, multisoliton, nonlinear, kink and antikink wave profiles are traced in results and discussions sections.
Article ID 0027 Published: 25 January 2020 Research Article
ELIF EBRU ERMIS CUNEYT CELIKTAS
The objective of this study is to improve the time resolution value of a coincidence spectrometer used in a time-of-flight–positron emission tomography (TOF–PET) system. This spectrometer is used in medical imaging systems. The coincidence spectrometer is manufactured by using a BC420-type plastic scintillator and R1828-01-type photomultiplier tube, and the time resolution value of the manufactured spectrometer is determined. The accuracy of the experimental results is determined using the FLUKA Monte Carlo simulation program. Detectors are first manufactured in this program. Experimental and simulation results are compared and are found to be in good agreement. Optimal positions of the detectors are investigated to improve the coincidence time resolution of the spectrometer. Time resolution improvement of the optimal detector positions enables higher time-of-flight (TOF) gain and spatial resolution, leading to better image quality, reduction in patient doses and detection of small lesions.
Article ID 0026 Published: 10 January 2020 Research Article
Bose–Einstein condensation of an imperfect Bose gas using cluster expansion
Bose–Einstein condensations (BEC) for an ideal Bose gas and an imperfect Bose gas are presented using cluster expansion method by using a new generating function obtained by Ushcats. The saturation density is calculated from the known values of virial coefficients for both ideal and uniform hard-sphere imperfect Bose gas. The values of saturation densities are found for some experimentally observed Bose–Einstein condensates and the fractional shift in the saturation densities are also calculated using this method, which are found to be positive.
Article ID 0025 Published: 10 January 2020 Research Article
ARCHANA DIXIT RASHID ZIA ANIRUDH PRADHAN
We investigate a new class of LRS Bianchi type-II cosmological models by revisiting the paper of Mishra et al (Int. J. Theor. Phys. 52, 2546 (2013)) by considering a new deceleration parameter (DP) depending on the time in string cosmology for the modified gravity theory suggested by Sáez–Ballester (Phys. Lett. 113, 467 (1986)). We have considered the energy–momentum tensor proposed by Letelier (Phys. Rev. 28, 2414 (1983)) for bulk viscous and perfect fluid under some assumptions. To make our models consistent with recent astronomical observations, we have used the scale factor (Sharma et al, Astron Astrophys. 19, 55 (2018), Garg et al, Int. J. Geo. Meth. Mod. Phys. 16, 1950007 (2019)) $a(t) = \rm{exp} [ \frac{1}{\beta}\sqrt{2\beta t + k}]$, where $β$ and $k$ are positive constants and it provides a time-varying DP. By using the recent constraints ($H_{0} = 73.8$ and $q_{0} = −0.54$) from SN Ia data in combination with BAO and CMB observations (Giostri et al, JCAP 3, 27 (2012), arXiv:1203.3213v2[astroph. CO]), we affirm $\beta = 0.0062$ and $k = 0.000016$. For these constraints, we have substantiated a new class of cosmological transit models for which the expansion takes place from the early decelerated phase to the current accelerated phase. Also, we have studied some physical, kinematic and geometric behaviour of the models, and have found them consistent with observations and well-established theoretical results. We have also compared our present results with those of Mishra et al (Int. J. Theor. Phys. 52, 2546 (2013)) and observed that the results in this paper are much better, stable under perturbation and in good agreement with cosmological reflections.
Article ID 0024 Published: 10 January 2020 Research Article
Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models
The present paper studies the impact of applied uniform transverse magnetic field on the flow of incompressible conducting fluid around a weakly permeable spherical particle bounded by a spherical container. Analytical solution of the problem is obtained using Happel and Kuwabara cell models. The concerned flow is parted in two regions, bounded fluid region and internal porous region, to be governed by Stokes and Darcy’s law respectively. At the interface between the fluid and the permeable region, the boundary conditions used are continuity of normal component of velocity, Saffman’s boundary condition and continuity of pressure. For the cellsurface, Happel and Kuwabara models together with continuity in radial component of the velocity has been used. Expressions for drag force, hydrodynamic permeability and Kozeny constant acting on the spherical particle under magnetic effect are presented. Representation of hydrodynamic permeability for varying permeability parameters, particle volume fraction, slip parameter and Hartmann numbers are represented graphically. Also, the magnitude of Kozeny constant for weakly permeable and semipermeable sphere under a magnetic effect has been presented. In limiting cases many important results are obtained.
Article ID 0023 Published: 10 January 2020 Research Article
Lie symmetries and invariant solutions of (2 + 1)-dimensional breaking soliton equation
The present article deals with the symmetry reductions and invariant solutions of breaking soliton equation by virtue of similarity transformation method. The equation represents the collision of a Riemann wave propagating along the $y$-axis with a long wave along the $x$-axis. The infinitesimal transformations under one parameter for the governing system have been derived by exploiting the invariance property of Lie group theory. Consequently, the number of independent variables is reduced by one and the system remains invariant. A repeated application transforms the governing system into systems of ordinary differential equations. These systems degenerate well-known soliton solutions under some limiting conditions. The obtained solutions are extended with numerical simulation resulting in dark solitons, lumps, compactons, multisolitons, stationary and parabolic profiles and are shown graphically.
Article ID 0022 Published: 10 January 2020 Research Article
J A LAOYE T O ROY-LAYINDE K A OMOTESO O O POPOOLA U E VINCENT
In our recently published paper [Pramana – J. Phys.93: 102 (2019), https://doi.org/10.1007/s12043-019- 1865-5] one of the author’s affiliation (O O Popoola) was wrongly indicated. The correct affiliation is Depart- ment of Physics, University of Ibadan, Ibadan, Nigeria.
Article ID 0021 Published: 10 January 2020 Research Article
In this paper, a (2+1)-dimensional nonlinear evolution equation (NLEE), namely the generalised Camassa–Holm–Kadomtsev–Petviashvili equation (gCHKP) or Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation (KP-BBM), is examined. After applying the newly developed generalised exponential rational function method (GERFM), 14 travelling wave solutions are formally generated. It is worth mentioning that by specifying values to free parameters some previously obtained solutions can be recovered. The simplest equation method (SEM) is used to prove that the solutions obtained by GERFM are good. With the aid of a symbolic computation system, we prove that GERFM is more efficient and faster.
Article ID 0020 Published: 1 January 2020 Research Article
A JANA S K SINGH A GUPTA S DAS K BASU S SAMANTA R RAUT S S GHUGRE A K SINHA
A zero-cost multichannel analyser (MCA) system based on the digital signal (pulse) processing (DSP) convenient for $\gamma$ -ray spectroscopy with conventional detectors such as scintillators and high-purity germanium (HPGe) has been implemented. The in-built high-performance analog-to-digital converter (ADC) in the sound card, an integral component of the present day personal computers, was used to digitise the signals from the radiation detectors. These pulses were then shaped using the established digital signal processing recursive algorithms. The filtered data were then displayed as histograms which then could be subjected to the traditional analysis to obtain peak parameters and the associated quantities were deduced. The developed system combines the performance of the sound card hardware with the flexibility allowed by the DSP to achieve a versatile MCA.
Article ID 0019 Published: 1 January 2020 Research Article
Dynamic analysis and synchronisation control of a novel chaotic system with coexisting attractors
CHENGQUN ZHOU CHUNHUA YANG DEGANG XU CHAOYANG CHEN
In this paper, a novel four-dimensional continuous chaotic system is constructed from the simplified Lorenz-like system. The novel system has three equilibria, strange attractors, coexisting attractors, and performs Hopf bifurcation with the variation of system parameters. The coexisting attractors, which are the most remarkable dynamic features of the system, are numerically studied. The coexisting attractors show that the system coexists as a pair of point, periodic, and chaotic attractors. Some basic dynamic behaviours are studied as well. The synchronisation control problem of the system is analysed. The theoretical and numerical analyses demonstrate that the system can easily achieve synchronisation by using the passive control technique.
Article ID 0018 Published: 1 January 2020 Research Article
Exact solution of perturbed nonlinear Schrödinger equation using $(G'/G, 1/G)$-expansion method
By constructing auxiliary equations and combining the expansion method of $(G'/G, 1/G)$, we study a class of nonlinear Schrödinger equation with perturbation terms which describes the propagation of the waves in optical metamaterials. More types of exact solutions, particularly solitary wave solutions, are obtained for the first time.
Article ID 0017 Published: 1 January 2020 Research Article
ALY R SEADAWY DAVID YARO DIANCHEN LU
This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.
Article ID 0016 Published: 1 January 2020 Research Article
Physical origins of the ideality factor of the current equation in Schottky junctions
After the carrier drift velocity at the semiconductor/metal interface is considered, current transport in Schottky diodes under a forward electric field is physically modelled. This model reveals that the ideality factor can be physically originated from the drift velocity and the drift velocity can also reduce the effective Schottky barrier height. This proposed model predicts that both the ideality factor and the Schottky barrier height depend on temperature, voltage and doping density, which agree well with the experimental results reported in the literature. The proposed diode current model also predicts a linear dependent relation between the reciprocal of the ideality factor and the effective Schottky barrier height, which is validated by experimental results. Such a model is useful to better understand the thermionic emission current physically in semiconductor/metal contact. It is also useful to characterise the material properties by using the ideality factor.
Article ID 0015 Published: 1 January 2020 Research Article
Influence of magnetic field and Coulomb field on the Rashba effect in a triangular quantum well
The influence of magnetic field and Coulomb field on the Rashba spin–orbit interaction in a triangular quantum well was studied using Pekar variational method. We theoretically derived the expression of the boundmagnetopolaron ground-state energy. The energy of the bound magnetopolaron splits under the influence of the Rashba effect. From this phenomenon, it is concluded that the effects of orbital and spin interactions on the polaron energy in different directions must be considered. Because of the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Compared to the bare electron, the bound polaron is more stable, and the energy of bound polaron split is more stable.
Article ID 0014 Published: 1 January 2020 Research Article
Mixed-mode oscillations and the bifurcation mechanism for a Filippov-type dynamical system
MIAO PENG ZHENGDI ZHANG ZIFANG QU QINSHENG BI
In this paper, mixed-mode oscillations and bifurcation mechanism for a Filippov-type system including two time-scales in the frequency domain are demonstrated. According to classic Chua’s system, we investigate a non-smooth dynamical system including two time-scales. As there exists an order gap between the exciting frequency and the natural one, the whole external excitation term can be considered as a slow-changing parameter, which results in two smooth subsystems divided by the non-smooth boundary. In addition, the critical condition about fold bifurcation (FB) is studied, and by applying the Hopf bifurcation (HB) theorem, specific formulas for determining the existence of HBs are presented. By introducing an auxiliary parameter via differential inclusions theory, the non-smoothbifurcations on the boundary are discussed. Then, the equilibrium branches and the bifurcations are derived, and two typical cases associated with different bifurcations are considered. In light of the superposition between the bifurcation curve and the transformed phase portrait, the dynamical behaviours of the mixed-mode oscillations as well as sliding movement along the non-smooth boundary are obtained, which reveal the corresponding dynamical mechanism.
Article ID 0013 Published: 1 January 2020 Research Article
Ion-acoustic waves in magnetised plasma with nonthermal electrons and positrons
J K CHAWLA P C SINGHADIYA R S TIWARI
Zakharov–Kuznetsov (ZK) equation for ion-acoustic waves (IAWs) is derived using the reductive perturbation method (RPM) in magnetised plasma consisting of ions, positrons and nonthermal electrons in small but finite amplitude limit. Propagation characteristics of ion-acoustic solitary waves (IASWs) in three-dimensional space are analysed to determine their region of existence. Investigations reveal that ion-acoustic solitary pulses (IASPs) may exist in such plasmas and presence of nonthermal electrons significantly affects the amplitude and width of solitary pulses. Dependence of velocity, amplitude and width of solitary pulses on plasma parameters arepresented graphically. The amplitude of soliton increases with increase in ion temperature ratio ($\sigma$) and positron concentration ($\alpha$). However, it decreases with increase in nonthermal electron parameter ($\beta$) keeping other plasma parameters constant. Width of the soliton increases with increase in $\beta$, $\sigma$ and $\alpha$. Phase velocity of ion-acoustic wave ($\lambda$) increases with increase in nonthermal $\beta$ and $\sigma$. In our analysis, we found that magnetisation of plasma affect the width of the soliton but not the amplitude.
Article ID 0012 Published: 1 January 2020 Research Article
Numerical and microcontroller simulations, and electronic circuit realisation of Minorsky’s equation
NGOUABO ULRICH GAËL NOUBISSIE SAMUEL FOTSIN HILAIRE BERTRAND WOAFO PAUL
This work deals with the mathematical analysis, numerical and microcontroller simulations and electronic circuit realisation of the dynamics of Minorsky’s equation.We consider the model including the nonlinear derivative feedback with delay. The study of stability is done by linearising the equation. An alternation between the zones of stability and instability as a function of the values of the delay is found. The bifurcation diagrams allowed us to validate the analytical predictions. These bifurcation diagrams show Hopf bifurcations and complex dynamics of the system. The analog and microcontroller simulations together with the experimental analysis were carried out in order to validate the theoretical analysis.
Article ID 0011 Published: 1 January 2020 Research Article
A ASKIN C MUTUWONG T NUTARO M DAL
In this study, mass attenuation coefficient ($\mu_{\rm{m}}$), transmission fractions ($T$), effective atomic numbers ($\rm{Z_{eff}}$) and half-value layer (HVL) of the $\rm{xPbO–(50 − x)BaO–50B_{2}O_{3}}$ (where x = 10, 20, 30, 40 mol%) glass system have been determined from the Monte Carlo simulations carried out with Geant4 and Fluka simulation toolkits and WinXCOM database software. The calculated results were compared with the experimentally obtained $\mu_{m}$ values of the selected glass in order to validate the Geant4 model of HPGe detector and Fluka model of NaI(Tl) detectors. $T$, $\rm{Z_{eff}}$ and $\rm{HVL}$ shielding parameters of the studied glass system indicate that increase of PbO content from 10 to 40% results in a better shielding behaviour thanks to the high atomic number of lead.
Article ID 0010 Published: 1 January 2020 Research Article
Rogue wave solutions of the chiral nonlinear Schrödinger equation with modulated coefficients
L FERNAND MOUASSOM ALAIN MVOGO C BIOUELE MBANE
The research of rogue wave solutions of the nonlinear Schrödinger (NLS) equations is still an open topic. NLS equations have received particular attention for describing nonlinear waves in optical fibres, photonics, plasmas, Bose–Einstein condensates and deep ocean. This work deals with rogue wave solutions of the chiral NLS equation. We introduce an inhomogeneous one-dimensional version, and using the similarity transformation and direct ansatz, we solve the equation in the presence of dispersive and nonlinear coupling which are modulated in time and space. As a result, we show how a simple choice of some free functions can display a lot of interesting rogue wave structures and the interaction of quantum rogue waves. The results obtained may give the possibility of conducting relevant experiments in quantum mechanics and achieving potential applications.
Article ID 0009 Published: 1 January 2020 Research Article
MARWAN AL-RAEEI MOUSTAFA SAYEM EL-DAHER
A comment on an article by Khater et al published in Pramana – J. Phys. 90: 59 (2018) is presented here. We represent two quotes on the article, the two quotes about the space-dependent fractional Schrödinger equation type and about one of the constants used by the authors.
Article ID 0008 Published: 1 January 2020 Research Article
S DZHUMANOV B L OKSENGENDLER SH S DJUMANOV
So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like ($s-$ or $d-$wave) pairing theory is adequate for explaining high-$T_{c}$ superconductivity in doped cuprates from underdoped to overdoped regime.We show that the doped cuprates, depending on the Fermi energy ($\varepsilon_{F}$) and the energy ($\varepsilon_{A}$) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios $\varepsilon_{A}/\varepsilon_{F}$ and $\Delta/\varepsilon_{F}$ (where $\Delta$ is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high-$T_{c}$ superconductivity is quite different from the BCS-type ($s-$ or $d-$wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature ($T_{c}$) and the peculiar oxygen and copper isotope effects on $T_{c}$ in overdoped cuprates.
Article ID 0007 Published: 1 January 2020 Research Article
We have enumerated new and exact general wave solutions, along with multiple exact soliton solutions of space–time nonlinear fractional differential equations (FDE), namely Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM), foam drainage and symmetric regularised long-wave (SRLW) equations, by employing a relatively new technique called (G'/G, 1/G)-expansion method. Also, based on fractional complex transformation and the properties of the modified Riemann–Liouville fractional-order operator, the fractional partial differential equations transform into a form of ordinary differential equation (ODE). This method is a recollection of the commutation of the well-appointed (G'/G)-expansion method introduced by Wang et al, Phys. Lett. A 372, 417 (2008) In this paper, it is mentioned that the two-variable (G'/G, 1/G)-expansion method is more legitimate, modest, sturdy and effective in the sense of theoretical and pragmatical point of view. Lastly, the peculiarities of these analytic solutions are illustrated graphically by utilising the computer symbolic programming Wolfram Mathematica.
Article ID 0006 Published: 1 January 2020 Research Article
BRAHIM MARFOUA BRAHIM LAGOUN HAMZA LIDJICI ALI BENGHIA AHMED GUEDDOUH
Based on the density functional theory and the Boltzmann transport theory, the thermoelectric properties of $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with $x = 0.25, 0.5$ and $075$ were investigated. The calculated structural parameters were in good agreement with the previous work and the mechanical and dynamical stabilities were confirmed. The electronic band structure computed using the Tran-Blaha-modified Becke and Johnson (TB-mBJ) exchange potential indicated that the band gap can be tuned by the alloy effect. We combined first-principles calculations and the semiclassical Boltzmann transport theory by considering the electronic transport in the $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution to determine the effect of varying the Sn composition on the thermoelectric performance. Our results have shown exceptionally high electrical conductivity for $\rm{Mg_{2}Sn}$ and higher Seebeck coefficient for $\rm{Mg_{2}Si}$. The highest figure of merit (ZT) was predicted for $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with x = 0.5 where ZT has reached 0.55 with carrier concentration charge $n = 10^{20} \rm{cm}^{−3}$ (p-type doping) at intermediate temperatures. Consequently, the alloying system with p-type doping may improve the thermoelectric properties compared to the $\rm{Mg_{2}Si}$ and $\rm{Mg_{2}Sn}$ pristine compounds.
Article ID 0005 Published: 1 January 2020 Research Article
RACHITA MOHAPATRA PRADIPTA DUTTA
An aluminium gallium nitride/gallium nitride ($\rm{Al_{0.3}Ga_{0.7}N/GaN}$) high electron mobility transistor (HEMT) is designed at a gate length ($L_{G}$) of 0.1 $\mu$m, drain-to-source spacing ($L_{SD}$) of 3 $\mu$m and drain length to source length ratio ($L_{D}:L_{S}$) of 1. The HEMT is investigated by considering four different heterostructures, namely single channel, single channel with back-barrier, double channel and double channel with back-barrier. A two-dimensional electron gas (2DEG) is formed at the interface of AlGaN/GaN HEMT (DC HEMT). The physical importance of indium gallium nitride (InGaN) as back-barrier is to increase carrier confinement by raising the conduction band of GaN buffer. The double-channel HEMT (DC HEMT) with back-barrier shows the highest current drive. There is an improvement of 3.16% in drain current and an improvement of 4.58% in cut-off frequency at a gate-to-source voltage of −0.5 V for the DC HEMT with back-barrier compared to the DC HEMT without back-barrier. For further improvement in transconductance and cut-off frequency, the structure of DC HEMT with back-barrier is modified by increasing the drain contact length and decreasing the source contact length, that is $L_{D}:L_{S} = 3$, keeping the drain-to-source spacing unchanged, i.e. $L_{SD} = 3 \mu m$. There is 32.55% improvement in transconductance and 14.03% improvement in cut-off frequency at a gate-to-source voltage of −0.5 V for the DC HEMT with back-barrier at $L_{D}:L_{S} = 3$ compared to the DC HEMT with back-barrier at $L_{D}:L_{S} = 1$.
Article ID 0004 Published: 1 January 2020 Research Article
J PRAKASH ASHISH SHARMA D TRIPATHI
An analytical study to investigate the double diffusive convection in peristaltic pumping of ionic nanofluids through asymmetric microchannel under the influence of electromagnetohydrodynamics (EMHD) is presented. Thermal radiation effect is also considered. Velocity slip and convective boundary conditions are employed at the permeable channel walls. Debye Hückel linearisation is considered to simplify the Poisson–Boltzmann equation. The normalised two-dimensional conservation equations formass, momentum, energy, solutal concentration and nanoparticle fraction are reduced when long wavelength and low Reynolds number are assumed. Analytical solutions are computationally illustrated with MATLAB software to describe the pumping, flow and thermal characteristics under the effects of relevant parameters like Biot number, slip parameters, thermal radiation, Debye length, Hartmann number and Grashof numbers. Furthermore, solutal concentration, nanoparticle fraction and heat transfer coefficient are also analysed to see the influences of pertinent parameters. Such observations may be applicable to develop electro-osmotically actuated bio-microfluidic systems for smart drug delivery andmicrolevel physiological transport.
Article ID 0003 Published: 1 January 2020 Research Article
Chirped solitons in optical monomode fibres modelled with Chen–Lee–Liu equation
The paper studies the extraction of chirped soliton to Chen–Lee–Liu equation (CLLE) with the group velocity dispersion (GVD) and self-steeping coefficients that describe pulse transmission through optical monomode fibres. The chirped bright, dark and singular optical solitons are obtained and the results show that nonlinear chirp parameters strongly vary on self-steeping, GVD and spreading effects. The constraint conditions for the existence of solitons are also derived during the derivation. The results are helpful and important for understanding the propagation of optical pulses.
Article ID 0002 Published: 1 January 2020 Research Article
Single and multiband THz metamaterial polarisers
BAGVANTH REDDY SANGALA ARVIND NAGARAJAN PRATHMESH DESHMUKH HARSHAD SURDI GOUTAM RANA VENU GOPAL ACHANTA S S PRABHU
We report single and multiband linear polarisers for terahertz (THz) frequencies using cut-wire metamaterials (MM). The MMs were designed by finite-element method (FEM), fabricated by electron beam lithography, and characterised by THz time-domain spectroscopy. The MM unit cells consist of single or multiple length cut-wire pads of gold on semi-insulating gallium arsenide (GaAs) for single or multiple band polarisers. For example, a MM with a square unit cell of 50 $\mu$m size on 1 mm GaAs substrate with a gold cut wire of 65 $\mu$m length, 2 $\mu$m width, and 150 nm height gives a resonance around 1.05 THz. The dependence of the resonance frequency of the single-band polariser on the length of the cut-wires was explained based on transmission line model.
Article ID 0001 Published: 1 January 2020 Research Article
Quantisation of particle motion in dissipative harmonic environment
In this work, the quantisation of particle propagating in a dissipative harmonic medium will be investigated using the creation and annihilation operator formalism, which is more appropriate in some fields of physics. Modelling the problem as damped harmonic oscillator, the equations of motion are then written in terms of Poisson brackets, and the Heisenberg equations are written in terms of the quantum counterpart of the Poisson bracket, known as commutators. The creation and annihilation operators are introduced and used to obtain the energy and eigenstates. Our results are in exact agreement with different quantisation approaches as in Serhan et al, J. Math. Phys. 59, 082105 (2018). The normalisable coherent states are obtained as eigenstates of the annihilation operator, which overcome the non-normalisability of these states that appeared via the dual coordinate method.
Volume 94, 2020
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