Article ID 0097 Published: 8 July 2020 Research Article
In this study, fast neutron removal cross-section and $\gamma$-ray shielding capabilities in terms of mass attenuation coefﬁcient ($\mu_{m}$), transmission fractions ($T$), effective atomic numbers ($Z_{{\rm eff}}), half-value layer (HVL) and exposure build-up factors (EBF) of the 64TeO$_{2}$ + 15ZnO + (20 − $x$)CdO + $x$BaO + 1V$_{2}$O$_{5}$\, ($x$ = 0, 5, 10, 15, 20 mol%) glass system have been evaluated using Monte Carlo simulations carried out with Geant4 model of the high-purity germanium (HPGe) detector and Phy-X database software. The results of this study revealed that $\gamma$-ray shielding capability of the studied glass system increases with the increase of BaO content and decrease of CdO content in the chemical structure due to the high atomic number (Z) of Ba compared to Cd. The results also showed that increase of BaO fraction in the glass structure weakens the neutron shielding ability and by the use of low Z elements in the composites better shielding performance against neutrons can be obtained.
Article ID 0096 Published: 8 July 2020 Research Article
Control-based veriﬁcation of multiatoms in a cavity
In this paper, we study a model of two two-level atoms interacting with a quantum ﬁeld. An analytical solution is obtained which is used to study the information entropy of the system. It is shown that the nonlinear term plays a signiﬁcant role in the behaviour of the minimum uncertainty (MU) compared with the concurrence (C). Our extensive study of information entropy of atoms–ﬁeld interaction demonstrates that using the coupling strength between the atoms and the ﬁeld as a controller parameter, one can control the dynamics of the system by increasing the lower bound of the entropic uncertainty relation or decreasing the entanglement.
Article ID 0095 Published: 8 July 2020 Research Article
Bursting oscillations with boundary homoclinic bifurcations in a Filippov-type Chua’s circuit
ZHIXIANG WANG CHUN ZHANG ZHENGDI ZHANG QINSHENG BI
A modiﬁed version of the typical Chua’s circuit, which possesses a periodic external excitation and a piecewise nonlinear resistor, is considered to investigate the possible bursting oscillations and the dynamical mechanism in the Filippov system. Two new symmetric periodic bursting oscillations are observed when the frequency of external excitation is far less than the natural one. Besides the conventional Hopf bifurcation, two non-smooth bifurcations, i.e., boundary homoclinic bifurcation and non-smooth fold limit cycle bifurcation, are discussed when the whole excitation term is regarded as a bifurcation parameter. The sliding solution of the Filippov system and pseudo-equilibrium bifurcation of the sliding vector ﬁeld on the switching manifold are analysed theoretically. Based on the analysis of the bifurcations and the sliding solution, the dynamical mechanism of the bursting oscillations is revealed. The external excitation plays an important role in generating bursting oscillations. That is, bursting oscillations may be formed only if the excitation term passes through the boundary homoclinic bifurcation. Otherwise, they do not occur. In addition, the time intervals between two symmetric adjacent spikes of the bursting oscillations and the duration of the system staying at the stable pseudonode are dependent on the excitation frequency.
Article ID 0094 Published: 8 July 2020 Research Article
This article studies a class of ﬁn problems with two nonlinear terms arising from thermal conductivity and convection heat transfer coefﬁcient. A one-dimensional convective straight ﬁn is analysed for exponentially temperature-dependent thermal conductivity and exponentially temperature-dependent heat transfer coefﬁcient. The exact ﬁn temperature excess, heat transfer rate and ﬁn efﬁciency are obtained and presented graphically. The obtained results show the strong inﬂuences of exponent indexes of thermal conductivity and convection transfer coefﬁcient as well as thermogeometric ﬁn parameter on the ﬁn efﬁciency and heat ﬂow.
Article ID 0093 Published: 8 July 2020 Research Article
Novel fractional-order chaotic systems of different order and multiswitching synchronisation
NEETU ANEJA P TRIPATH SHARMA BINAY KUMAR
This paper gives multiswitching synchronisation scheme for a class of fractional-order chaotic systems by combining active and adaptive control theories. Adaptive controllers have been designed by using different laws of switching and fractional-order Lyapunov stability theory. We have also constructed a new fractional-order Dufﬁng system. The fractional-order Dufﬁng system and fractional-order Rabinovich–Fabrikant system have been taken as the drive system and the response system respectively. Applications have been demonstrated. Theoretical analysis and numerical simulations are also given to verify the robustness of the proposed controllers.
Article ID 0092 Published: 8 July 2020 Research Article
FATMA EL-GHENBAZIA BOUZENNA MOHAMMED TAYEB MEFTAH MOSBAH DIFALLAH
In this work, we solve time, space and time-space fractional Schrödinger equations based on the non-singular Caputo–Fabrizio derivative deﬁnition for 1D inﬁnite-potential well problem. To achieve this, we ﬁrst work out the fractional differential equations deﬁned in terms of Caputo–Fabrizio derivative. Then, the eigenvalues and the eigenfunctions of the three kinds of fractional Schrödinger equations are deduced. In contrast to Laskin’s results which are based on Riesz derivative, both the obtained wave number and wave function are different from the standard ones. Moreover, the number of solutions is ﬁnite and dependent on the space derivative order. When the fractional orders of derivatives become integer numbers (one for time derivative or/and two for space), our ﬁndings collapse to the standard results.
Article ID 0091 Published: 8 July 2020 Research Article
Probabilistic solution of nonlinear ship rolling in random beam seas
WEN-AN JIANG XIU-JING HAN LI-QUN CHEN QIN-SHENG BI
In this paper, the probability density function (PDF) and the mean up-crossing rate of nonlinear ship rolling in random beam seas are investigated. The excitation of stationary random sea waves is approximated as a second-order linear ﬁltered white noise. The Fokker–Planck–Kolmogorov (FPK) equation governing the probability density function of ship rolling is a four-dimensional linear partial differential equation with varying coefﬁcients, and obtaining its exact solution is much more sophisticated. The exponential-polynomial closure (EPC) method is applied to solve the corresponding FPK equation of the system. In numerical examples, linear-plus-cubic damping model and linear-plus-quadratic damping model with three different sea states are further examined. Comparison with the equivalent linearisation (EQL) method and Monte Carlo simulated results show that the proposed procedure is effective to obtain a satisfactory probability density function solution, especially in the tail region.
Article ID 0090 Published: 8 July 2020 Research Article
Singularity-free non-exotic compact star in $f (R, T)$\, gravity
ANIL KUMAR YADAV MONIMALA MONDAL FAROOK RAHAMAN
In the present work, we have searched for the existence of anisotropic and non-singular compact star in the $f (R, T)$\, gravity by taking into account the non-exotic equation of state (EoS). In order to obtain the solutions of the matter content of the compact object, we assume the well-known barotropic form of EoS that yields the linear relation between pressures and energy density. We propose the existence of non-exotic compact star which shows the validation of energy conditions and stability within the perspective of\, $f (R,T)$\, extended theory of gravity. The linear material correction in the extended theory and matter content of compact star can remarkably satisfy energy condition. We discuss various physical features of the compact star and show that the proposed model of the stellar object satisﬁes all regularity conditions and is stable as well as singularity-free.
Article ID 0089 Published: 8 July 2020 Research Article
Analysis of solution trajectories of fractional-order systems
The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw light on the relation between two trajectories $X (t)$ and $Y (t)$ of such a system, where the initial point $Y$ (0) is at some point X (t1) of the trajectory $X (t)$. In contrast with classical systems, these trajectories $X$ and $Y$ do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect.
Article ID 0088 Published: 25 June 2020 Research Article
Doppler narrowing of EIT linewidth in closed-loop systems
NAWAZ SARIF MALLICK KANHAIYA PANDEY
We theoretically investigate a five-level closed-loop M-type atomic system and a three-level closed-loop $\Lambda$-system in hot atomic vapour. In contrast to closed-loop $\Lambda$-system, two unpopulated ground states of the M-system are coupled by a microwave field. We find that thermal averaging in the M-system causes many interesting modification of probe absorption lineshape including narrowing, splitting and absorption enhancement. In M-system, the linewidth of probe absorption after thermal averaging becomes remarkably narrow (100 times smaller) with respect to the linewidth of stationary atoms. On the contrary, the closed-loop $\Lambda$-system generates only 1.6 times smaller linewidth in thermal vapour. The absence of population transfer through the microwave field leads to this significant narrowing effect in the M-system which is unachievable in closed-loop $\Lambda$-systems. Hence, M-system has potential application in high-resolution spectroscopy, generation of ultra slow light, phase-dependent optical switching, and in microwave electro- and magnetometry.
Article ID 0087 Published: 18 June 2020 Research Article
ADIL JHANGEER NAUMAN RAZA HADI REZAZADEH ALY SEADAWY
The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic detailsof the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.
Article ID 0086 Published: 18 June 2020 Research Article
Structural, magnetic and electrical properties of Ni–Co–Cu–Mn ferrite + PZT composite thick films
P S JADHAV K K PATANKAR V L MATHE Y D KOLEKAR R C KAMBALE VIJAYA PURI
$\rm{Ni–Co–Cu–Mn\,Ferrite+PZT (PbZr_{0.52}Ti_{0.48}O_{3})}$ ferroelectric: composite thick filmswere prepared by the screen-printing method. The normal XRD and the low glancing angle XRD confirm the presence of both phases in the composite thick films. Back-scattered SEM shows 0-3 and 3-3 types of connectivity. The magnetic ordering of the ferrite phase was confirmed from $M–H$ hysteresis loop whereas the electric ordering of the ferroelectric phase was confirmed from $P–E$ hysteresis curve. Various measurable parameters from the loop were studied as a function of the mole percent of constituent phases. PUND (positive up negative down) analysis was done to determine the resultant polarisation contributed by the participating phases in the composites. Dielectric and magnetoelectric (ME) measurements were analysed in the light of PUND measured data.
Article ID 0085 Published: 11 June 2020 Research Article
PUSHPLATA SHUKLA SADHNA SINGH SANKAR P SANYAL
First-principle computations on structural and electronic properties of cubic rare-earth $\rm{ErX_{3} (X = Ga, In\,and\,Sn)}$ intermetallic compounds have been accomplished using the full-potential linearised augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). For the exchange correlation, we used local spin density approximation (LSDA) plus Hubbard parameter $U (LSDA+U)$ approach because of the strong on-site Coulomb repulsion between the localised $\rm{RE}-4 f$ states. Calculated ground-state properties such as lattice constant ($a_{0}$) and other parameters with exchange correlation functional are found compatible with the experimental results. The electronic properties have been determined in terms of band structures, total and partial density of states (DOSs) and Fermi surfaces, which demonstrate the metallic behaviour of all the compounds. Also, the effect of Hubbard potential on this is discussed in detail. The bonding descriptions of these compounds have also been evaluated from charge density difference plots, which display the presence of metallic and mixed covalent–ionic bonding. The determined magnetic moments explain the ferromagnetic behaviour of these compounds.
Article ID 0084 Published: 11 June 2020 Research Article
Electric charge quantisation in 331 models with exotic charges
DAVID ROMERO ABAD JOSE REYES PORTALES ELMER RAMIREZ BARRETO
The extensions of the Standard Model based on the $SU(3)_{C} \otimes SU(3)_{L} \otimes U(1)_{X}$ gauge group are known as 331 models. Different properties such as the fermion assignment and the electric charges of the exotic spectrum, that define a particular 331 model, are fixed by a $\beta$ parameter. In this article, we study the electric charge quantisation in two versions of the 331 models, set by the conditions $\beta = 1/(3\sqrt{3})$ and $\beta = 0$. In these frameworks, arise exotic particles, for instance, new leptons and gauge bosons with a fractional electric charge. Additionally, depending on the version, quarks with non-standard fractional electric charges or even neutral appear. Considering the definition of electric charge operator as a linear combination of the group generators that annihilates the vacuum, classical constraints from the invariance of the Lagrangian, and gauge and mixed gauge-gravitational anomalies cancellation, the quantisation of the electric charge can be verified in both versions.
Article ID 0083 Published: 11 June 2020 Research Article
We present first-principles calculations on the structural, mechanical, electronic, thermodynamic, lattice dynamic and magnetic properties of RbN in the CsCl, rocksalt (Rs) and zinc-blende (ZB) structures centred on spin-polarised density functional theory (DFT). It was established that in all the three structures, ferromagnetic (FM) state is more stable than the non-magnetic (NM) state. The results show that RbN exhibits half-metallic characteristics at the equilibrium lattice parameters and have small energy gaps of 1.205, 1.092 and 1.364 eV for CsCl, Rs and ZB structures respectively. We find that only the CsCl and Rs structures are mechanically, lattice dynamically and thermodynamically stable. Furthermore, the structures exhibit equal integer magnetic moment of $2 \mu_\rm{B}$ approximately.
Article ID 0082 Published: 11 June 2020 Research Article
Pseudopotential study of wide band-gap GaN at high pressures
N BOUARISSA H ALGARNI M AJMAL KHAN O A AL-HAGAN T F ALHUWAYMEL
A pseudopotential approach is used to study the lattice and elastic properties of the wide band-gap GaN at zero and high pressures up to 120 kbar. When the pressure is 0 kbar, our findings are generally in agreement with the data reported in the literature. The pressure dependence of lattice constant, polarity, transverse effective charge, elastic constants and their related mechanical parameters, and microhardness has been examined and discussed. Our results show that all these features exhibit a monotonic behaviour against pressure. Upon compression up to 120 kbar, our results suggest that the material in question remains mechanically stable with higher stiffness, becomes more resistant to the deformations or deflections and its chemical bond and rigidity become stronger.
Article ID 0081 Published: 4 June 2020 Research Article
LEANDRE KAMDJEU KENGNE JACQUES KENGNE JUSTIN ROGER MBOUPDA PONE
We investigate the impact of a constant force excitation on the dynamics of a simple jerk system with piecewise quadratic nonlinearity.We demonstrate that in the presence of the forcing term, the model is asymmetric yielding more complex and striking bifurcation patterns such as parallel bifurcation branches, coexisting multiple asymmetric attractors, hysteretic dynamics, crises, and coexisting asymmetric bubbles of bifurcation. Accordingly, the coexistence of two, three, four, or five asymmetric periodic and chaotic attractors are reported by changing the model parameters and initial conditions. The control of multistability is investigated by using the method of linear augmentation. We demonstrate that the multistable system can be converted to a monostable state by smoothly adjusting the coupling parameter. A very good agreement is observed between PSpice simulation results and the theoretical study.
Article ID 0080 Published: 23 May 2020 Research Article
P C SINGHADIYA J K CHAWLA S K JAIN
Ion-acoustic solitary waves (IASWs) in plasma consisting of ions, positrons and superthermal electrons in two distinct temperatures have been studied. The reductive perturbation method (RPM) has been employed to derive the Korteweg–de Vries and modified KdV equation. Numerical and analytical studies show that compressive and rarefactive solitons exist for the selected parametric range depending on the spectral indexes, $κ (κ_{h},κ_{c})$ and their respective densities ($\nu,\mu$). It is found that spectral indexes ($κ_{h},κ_{c}$) and their relative densities have significant impact on the basic properties, i.e., amplitude and width as well as on the nature of IASWs. Variations of amplitude and width for the compressive and rarefactive solitary waves have been analysed graphically with different plasma parameters like spectral indexes of cold and hot electrons ($k_{c}, k_{h}$), their respective densities, ionic temperature ratio, positron temperature ratio as well as with the temperature ratio of the two-electron species. The amplitude of the compressive (rarefactive) solitary waves increases (decreases) on increasing $k_{h}$. However, the amplitude of the compressive (rarefactive) solitary waves decreases (increases) on increasing $k_{c}$. The investigations of such solitary waves may be helpful for the critical understanding of space where superthermal electrons with two different temperatures exist along with positrons and ions (e.g. Saturn’s magnetosphere, pulsar magnetosphere).
Article ID 0079 Published: 23 May 2020 Research Article
New wave patterns to the doubly dispersive equation in nonlinear dynamic elasticity
This study aims to obtain travelling wave solutions of the doubly dispersive equation in nonlinear dynamic elasticity by the sine-Gordon expansion method. We give physical explanation of the presented solutions under suitable parameters via the 3D, 2D and contour simulations.
Article ID 0078 Published: 23 May 2020 Research Article
M SATHISH ARAVINDH R GOPAL A VENKATESAN M LAKSHMANAN
We investigate the effect of two aperiodic square waves in a quasiperiodically-driven Murali–Lakshmanan–Chua circuit. It is found that the response of the circuit produces logical output in both strange nonchaotic and chaotic regions. Changing the biasing of the circuit changes the response of the circuit into another kind of logic operation and SR flip flop. Further, we show how this circuit produces two logical elements as its outputs which are complementary to each other. It is also shown that the logical nature of the circuit persists even when experimental noise is present. Thus, we confirm that both the dynamical behaviours, namely strange nonchaos and chaos, can be efficient tools to construct computer architecture.
Article ID 0077 Published: 22 May 2020 Research Article
NATALIIA ATAMAS DMYTRO GAVRYUSHENKO VITALY BARDIK KIRILL TARADII MAXIM LAZARENKO OLEKSANDER ALEKSEEV JULIE RENEA GEARHEART ANNA MIROSHNICHENKO GENNADIY TARANYIK
The influence of radiation on the thermodynamic properties of liquid systems that are governed by the radiation-induced change in the chemical potentials of the liquid and its components has been studied. The irradiation of coexisting phases in the stationary state is shown to result in a shift of the phase transition point parameters. The temperature shift of the first-order phase transition under the influence of radiation is evaluated with regard to both the entropy and interaction factors in the chemical potential of the system. The results obtained from the MD simulation of the radiation influence on 10% saline quantitatively confirm the predictions of the introduced theoretical model of the irradiation process. To verify our theoretical assumptions concerning modifications in the local structure of the examined saline (water solution of NaCl at 10% concentration), experiments under the influence of irradiation were done.
Article ID 0076 Published: 20 May 2020 Research Article
KINNARI PAREKH HARSHIDA PARMAR VINAY SHARMA
The influence of metal ion to hydroxide ion ($\rm{Me^{2+} /OH^{−}}$) ratio on the synthesis of $\rm{Mn_{0.5}Zn_{0.5}Fe_{2}O_{4}}$ (MZ5) ferrite nanoparticles is reported. The aim of this low-temperature co-precipitation technique is to produce MZ5 nanoparticles with different sizes in single domain range. The variation in $\rm{Me^{2+} /OH^{−}}$ ratio affects the growth and shape of the particles. The mechanism of nucleation and growth of the particles is discussed. EDX and XPS measurements show the change in stoichiometry of the composition when $\rm{Me^{2+} /OH^{−}}$ ratio changes. When the ratio is 0.52, Zn ion was found to be absent and the structure resembles $\rm{Mn_{x}Fe_{3−x}O_{4}}$. The defect in the composition changes magnetic properties such as saturation magnetisation and Curie temperature of the samples. 119 nm crystalline size with highest magnetisation ($\rm{80 Am^{2}/kg}$) is obtained which shows quite good response to induction heating (specific absorption rate (SAR) = 78 W/g). Moreover, SAR and intrinsic loss power (ILP) are higher for MZ5 ferrite than that are reported earlier. This shows the potential of magnetic induction heating in the treatment of cancer.
Article ID 0075 Published: 15 May 2020 Research Article
Chaos in a cyclic three-species predator–prey system with a partial consumption of superpredator
M KRISHNADAS P P SARATCHANDRAN K P HARIKRISHNAN
This paper aims at the detailed numerical analysis of a cyclic three species predator–prey model where the prey consumes only a part of the super-predator population. Such a model exists only when the prey acts as an omnivore. Here, we have investigated the dynamical behaviour of the prey, middle predator and super-predator. All the possible equilibrium points of the model are computed and the existence and stability condition of the equilibrium states are determined. The phase portraits are generated for different sets of parameter values. The long term behaviour of the system is investigated by studying the bifurcation structure and nature of the attractors, thereby identifying the domain of chaos, as each of the control parameter is varied independently. Finally, we show that a transition from chaotic domain to escape or vice-versa of the predator in a small region of the parameter plane leads to a fractal structure.
Article ID 0074 Published: 7 May 2020 Research Article
Non-contact excitation of piezoelectric components through bidirectional energy transfer system
T NAYAK D PATNAIK B R SWAIN D P KAR P P NAYAK S BHUYAN
The non-contact excitation of multiple piezoelectric components (PZT) through bidirectional electric field transmission system has been explored. In the proposed technique, two parallel plate capacitor-like structures have been designed with a pair of ground copper electrodes along with a live copper electrode, and two PZT plates are equidistantly placed in between each live and ground electrode. Experimentally, it has been observed that piezoelectric plates are wirelessly energised as a result of both electric and piezoelectric resonances. Maximum vibrational displacement can be obtained over the piezoelectric plates at a point,when the operating frequency of the E-field generator matches with the frequency of the mechanical resonance of the PZT plate. The maximum output power (Pout) across the non-contact stimulated piezoelectric plates principally depends on resonance, resistive load, vibration mode, driving frequency, position of PZT component etc. The output power obtained across the excited piezoelectric device by bidirectional non-contact energy transfer has been appreciably higher than that of the single PZT component excited by simple parallel-plate capacitor structure. The maximum output power of 0.271mW and 0.298 mW are acquired across piezoelectric plates at a resonance frequency of 924 kHz and 350 $\Omega$ optimal loads with 50 V input, when the live and ground electrodes are separated by 4 mm. By enacting the proposed wireless excitation technique, multiple piezoelectric devices can be energised together.
Article ID 0073 Published: 7 May 2020 Research Article
ANAND BHARADVAJA SAVINDER KAUR K L BALUJA
The amines are major source of environment pollutants emitted in atmosphere from variousanthropogenic sources. The non-thermal plasma (NTP)-based technology has proved successful in controlling the emitted amines reaching the atmosphere. The efficient NTP reactors rely on accurate electron–molecule collision data. The electron impact cross-sections are thus obtained for a few amines from ionisation threshold to 5000 eV using the single centre expansion (SCE) formalism. Themolecular wave function of each target is obtained from themulticentre expansion of the Gaussian-type orbitals within a single determinant Hartree–Fock self-consistent field scheme. The expansion of wave function, density and potential is carried out at the centre of mass of the molecules. The interaction potential included to model the electron interaction in the target comprises static, correlation polarisation and exchange types of potentials. The elastic cross-sections are obtained after solving the coupled scattering equations using Volterra integral form. The inelastic effects contributing to electron–molecule scatteringare approximated by the ionisation cross-sections. The total cross-sections obtained after summing the elastic and ionisation cross-sections are in good agreement with the available data. We have also tried to explain the effect of polarisation potential on scattering cross-sections. A semiempirical formula based on the spatial extent of the molecule is proposed to estimate the cross-sections for the homologous series of amine molecules.
Article ID 0072 Published: 22 April 2020 Research Article
Numerical study of multidimensional fractional time and space coupled Burgers’ equations
HODA F AHMED M S M BAHGAT MOFIDA ZAKI
This paper declares a new spectral collocation technique to provide accurate approximate solutions of the one- and two-dimensional time and space fractional coupled Burgers’ equations (TSFCBEs) in which the fractional derivatives are defined according to Caputo’s definition. The suggested method is based on the shifted Gegenbauer polynomials (SGPs) for approximating the solution of TSFCBEs. The suggested technique reduces the considered problems to the solution of nonlinear algebraic equations (NLAEs). Moreover, the accuracy and reliability of the proposed method are confirmed through numerical examples. Finally, the obtained numerical results are compared with those previously reported in the literature.
Article ID 0071 Published: 22 April 2020 Research Article
Execution of Fredkin gate by a set of free fermions
It is not a trivial task to answer whether a free fermion-based architecture for a quantum computer can efficiently execute basic gates such as the Fredking gate. We show that a set of free fermions can efficiently execute Fredkin gate.
Article ID 0070 Published: 22 April 2020 Research Article
Systematics of multinucleon transfer in heavy-ion reactions
S SANILA A M VINODKUMAR B R S BABU
One-neutron pickup reactions for 52 projectile–target combinations were analysed using a systematics between transfer cross-sections and ground-state $Q$-values. One-neutron pickup transfer shows a good correlation between reduced transfer cross-sections and ground-state $Q$-values ($Q_{gg}$) if one separate the systems into two groups based on their $\rm{Z_{p} Z_{t}}$ product. Also, similar kind of systematics is applied to 2n, 3n and 4n pickup transfer and a good correlation is obtained between reduced transfer cross-sections and $Q_{gg}$ values, where no $\rm{Z_{p} Z_{t}}$ dependenceis seen.
Article ID 0069 Published: 22 April 2020 Research Article
The present study investigates the heat and mass transfer of magnetohydrodynamic (MHD) free convection through two infinite plates embedded with porous materials. In addition to that the combined effect of viscous dissipation, heat source/sink considered in energy equation and thermodiffusion effect is taken care of in the mass transfer equation. Using suitable non-dimensional variables, the expressions for the velocity, temperature, species concentration fields, as well as shear stress coefficient at the plate, rate of heat and mass transfer, i.e. Nusselt number (Nu) and Sherwood number (Sh) are expressed in the non-dimensional form. These coupled nonlinear differential equations are solved using perturbation technique and their behaviour is demonstrated via graphs for various values of pertinent physical parameters namely, Hartmann number (Ha), Reynolds number (Re), Schmidt number (Sc), Soret number (So), permeability parameter etc. In a particular case, the present result was compared with earlier established results and the results are found to be in good agreement. However, major findings are elaborated in the results and discussion section.
Article ID 0068 Published: 22 April 2020 Research Article
NASSER S ELGAZERY ASMAA F ELELAMY
We have explored multiple solutions for non-Newtonian Casson nanofluid flowpast a moving extending sheet under the influence of variable thermal conductivity and nonlinear radiation through a permeable medium with convective boundary conditions. The governing equations are transformed to ODEs by similarity transformations and then solved numerically by the Chebyshev pseudospectral (CPS) method. Dual solutions are obtained for velocity, temperature and nanoparticle concentration distributions with different values of physical parameters. Inthe present analysis, it was found that, the nonlinearity formula for thermal radiation gives a realistic description of nanofluid mathematical model depending on the existence of nanoscale particles. Furthermore, the concentration of nanoparticles is highly influenced by nonlinear thermal radiation due to the sizes of nanofluid, where linear radiation has a weak effect on the concentration distributions of nanoparticles. These results are very important in medicine, and more specifically for reinforcing the delivery of drugs through the skin, as the nanoparticle entrapment of drugs enhances delivery to, or absorption by, target cells. The transdermal drug delivery system offers huge clinical advantages over other dosage forms. As transdermal drug delivery offers controlled as well as predetermined rate of release of the drug into the patient, it can keep up steady-state nanofluid concentration.
Article ID 0067 Published: 22 April 2020 Research Article
This article addresses the heat and mass transport phenomena by performing a theoretical analysis of three-dimensional viscous fluid flow containing gyrotactic micro-organisms over a nonlinear stretched surface. Variable magnetic field is considered normal to the stretched surface to control the fluid flow. Thermal transportation is discussed in view of variable thermal conductivity. Variable characteristics of mass diffusion along with chemicalreaction are incorporated in mass transportation. Darcy–Forchheimer expression is used to characterise the porous medium. Also, Brownian motion and thermophoresis are incorporated to enhance the diffusion. The governing partial differential equations (PDEs) are derived using boundary layer analysis by assuming small magnetic Reynolds number. Appropriate transformation is used to convert complex system of coupled PDEs into nonlinearordinary differential equations (ODEs). Transformed problem is then tackled analytically using optimal homotopic procedure. Reliability of the suggested scheme is presented through error reduction table and also by comparing the obtained solution with the published ones. Graphs and tables are prepared to observe the impact of parameters on physical variables. Dimensionless stresses and rate of heat transfer are computed numerically. It has been observed that larger values of Brownian diffusion and thermophoresis increase the fluid temperature. Moreover, dimensionless stresses and rate of heat transfer are computed to check the reliability of the proposed procedure. These values are clearly in an excellent agreement with the previous findings reported in literature.
Article ID 0066 Published: 15 April 2020 Research Article
FARBOD BAHRAMI SAMANEH BARADARAN MEHRAN TAHERI FEREIDOUN MIANJI
In this study, a new detector is designed based on CR-39, and separately calibrated for protons, neutrons and $\alpha$-particles under the same etching condition. To that end, an americium–beryllium standard source ($^{241}$Am–Be) and a plexiglass phantom for neutron irradiation, brass collimators and an americium standard source ($^{241}\rm{Am}$) for alpha irradiation, as well as a Van de Graaff accelerator for proton irradiation were employed. Sodium hydroxide solution of 6.25 N at $85^{\circ}\rm{C}$ was also used for CR-39 chemical etching. Considering the detection principle of the device, different filters were designed to help distinguish between fast neutron particles, thermal neutrons, albedo neutrons, protons and $\alpha$-particles in mixed radiation fields. Moreover, both the contribution of each particle and the ability of the designed detector to discriminate energy of charged particles were quantified.
Article ID 0065 Published: 15 April 2020 Research Article
Long-lived quantum coherence in a two-level semiconductor quantum dot
In this paper, we present an analytical solution for the system of two-level semiconductor quantum dot. In addition, we discuss the rates of the photon radiative and phonon radiationless transitions fromthe excited state ($\alpha_{12}, \alpha_{21}$), the rate of processes of pure dephasing ($\gamma$ ), the detuning parameter ($\Delta$) and the Rabi frequency ($\Omega$), on the atomic occupation probabilities ($\rho_{11}(t)$ and $\rho_{22}(t)$), the atomic population inversion ($\rho_{z}(t)$), the purity ($P_{A}(t)$), the von Neumann entropy ($S(t)$) and the information entropies ($H(\sigma_{x}), H(\sigma_{y})$ and $H(\sigma_{z})$). We clearly observe the emergence of long-lived quantum coherence phenomenon in all the curves for some special cases of $\alpha_{12}, \alpha_{21}, \gamma, \Delta$ and $\Omega$. Besides, the decay phenomenon is quite evident in the purity curves, which can be simply controlled by changing the values of $\alpha_{12}, \alpha_{21}$ and $\gamma$.
Article ID 0064 Published: 9 April 2020 Research Article
Features of Jeffrey fluid flow with Hall current: A spectral simulation
V K SINHA B KUMAR G S SETH R NANDKEOLYAR
The Hall current in MHD flow stimulates substantial interest of researchers because of its wide rolein many geophysical, astrophysical and fluid engineering situations (construction of turbines, Hall accelerator and centrifugal machines). Motivated by such wide applications, the present work reports the influence of Hall current and thermal radiation on the three-dimensional Jeffrey fluid flow over a stretching surface. In order to achieve similar solution of the governing equations, transformation technique is adopted. The mathematical model is numerically solved by using a spectral technique, namely successive linearisation method (SLM). To explore the feature of various factors, e.g. Hall current and thermal radiation, the variation of flow dominant parameters on the obtained profiles are carefully elucidated with graphs. It can be sensed from the obtained graphs that primary and secondary velocity increase, but, temperature reduces with the enhancement in Hall current. Radiation parameter has the tendency to increase the temperature of the fluid.
Article ID 0063 Published: 5 April 2020 Research Article
A wide range of two-dimensional nonlinear wave is described by Kadomtsev–Petviashvili (KP) equation. We obtained the classification of travelling wave patterns to the generalised KP equation with high-ordernonlinear dispersive and dissipative terms. Among these patterns, some new phenomena can be acquired for the first time. Representations of wave propagation patterns were achieved by taking specific values of parameters. This means that all these patterns can be realised under appropriate physical conditions.
Article ID 0062 Published: 5 April 2020 Research Article
Coexisting chaotic attractors in a memristive system and their amplitude control
HONGYAN ZANG ZHENYU GU TENGFEI LEI CHUNBIAO LI SAJAD JAFARI
A memristive chaotic system of rotational symmetry is constructed and analysed. The dynamical behaviour of the system is demonstrated by phase trajectories, Lyapunov exponents and bifurcation diagrams. Coexisting attractors are observed and a simple approach for amplitude control is proposed according to the specific structure. It shows that this symmetric memristive system has partial amplitude control when a control function is introduced. The corresponding circuit implementation is given by generating a symmetric pair of chaotic attractors. Circuit results agree well with the theoretical analysis and numerical simulation.
Article ID 0061 Published: 5 April 2020 Research Article
SUDIPTA GHOSH SWATI MUKHOPADHYAY
This article aims to present the flow and heat transfer characteristics of a nanofluid past an elastic sheet having variable thickness in the presence of a magnetic field. Vanishing nanoparticle flux at the boundary has been taken into account for the passive control of nanoparticles. Two-phase model for the nanofluid has been considered. With the help of similarity transformations, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations along with the appropriate boundary conditions. The reduced equations are then solved numerically. The effects of buoyancy parameter,magnetic parameter, Brownian motion, thermophoresis parameter etc. on velocity, temperature and nanoparticle volume fraction are presented graphically and analysed in detail. Velocity, temperature and nanoparticle volume fraction are decreasing functions of wall thickness parameter for decelerated flow. Due to increasing values of thermophoresis parameter, the rate of heat transfer at the surface reduces while with the increase in the Brownian motion parameter the mass transfer rate at the surface increases.
Article ID 0060 Published: 5 April 2020 Research Article
SUSHILA DEVI P K AHLUWALIA SHYAM CHAND
A systematic generalised approach to find transport observables for a linear array of different quantum dot (QD) systems has been discussed, using non-equilibrium Green function (NEGF) formalism, in the presence of on-dot Coulomb interaction and inter-dot tunnelling. The equation of motion (EOM) method has been used to derive expressions for Green functions (GFs) within the simplest mean-field approximation to tackle the Coulomb correlation term. Starting from the mathematical structures of GFs for single, double and triple quantum dot systems, the expressions for GFs and transport observables have been generalised for the quantum dot systems containing N number of quantum dots in series as well as parallel linear array of dots. Further, the formulae so obtained have been used for numerical calculations of transmission probability and the I –V characteristics of linear arrays of quantum dots in series as well as parallel configuration containing up to three dots. The results show that, with the increase in number of dots in the scattering region, transmission probability and electron current decrease in series case, while both quantities increase in parallel configuration of dots. The inter-dot tunnelling leads to the splitting of transmission peaks in double QD system in series case whereas, it induces Fano effect in triple QD system in parallel configuration.
Article ID 0059 Published: 15 March 2020 Research Article
In this study, we are going to obtain the energy spectrum and the corresponding solution of the noncentral Makarov potential. In this case, we consider the arbitrary angular momentum with quantum number l. In order to calculate the energy spectrum and eigenfunction we use the factorisation method. The factorisation methodleads us to discuss the shape-invariance condition with respect to any index as $n$ and $m$. Here, we also achieve the shape invariance with respect to the main quantum number $n$. It leads to the quantum-solvable models on real forms of the homogeneous manifold $SL(2,\mathbb{C})/GL(1,\mathbb{C})$ with infinite-fold degeneracy for $\gamma\upsilon = 0$ and $\gamma\upsilon \neq 0$. These processes also help us to obtain raising and lowering operators of states on the above-mentioned homogeneous manifold.
Article ID 0058 Published: 15 March 2020 Research Article
Dust-acoustic rogue waves in non-thermal plasmas
S K PAUL N A CHOWDHURY A MANNAN A A MAMUN
The nonlinear propagation of dust-acoustic waves (DAWs) and associated dust-acoustic rogue waves (DARWs), which are governed by the nonlinear Schrödinger equation, is theoretically investigated in a four componentplasma medium containing inertial warm negatively charged dust grains and inertialess non-thermal distributed electrons as well as isothermal positrons and ions. The modulationally stable and unstable parametric regimes of DAWs are numerically studied for the plasma parameters. Furthermore, the effects of temperature ratios of ion-to-electron and ion-to-positron, and the number density of ion and dust grains on the DARWs are investigated. It is observed that physical parameters play very crucial roles in the formation of DARWs. These results may be useful in understanding the electrostatic excitations in dusty plasmas in space and laboratory situations.
Article ID 0057 Published: 15 March 2020 Rapid communication
Likelihood theory in a quantum world: Tests with quantum coins and computers
ARPITA MAITRA JOSEPH SAMUEL SUPURNA SINHA
By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence.We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.
Article ID 0056 Published: 10 March 2020 Research Article
Modified multiple scale technique for the stability of the fractional delayed nonlinear oscillator
In the present proposal, the familiar method of the parameter expansion is combined with the multiple scales to study the stability behaviour of the Riemann–Liouville fractional derivative applied to the cubic delayed Duffing oscillator. The analysis of the modified multiple scale perturbation leads to a system of nonlinear differential-algebraic equations governing the solvability conditions. The nonlinear differential equation was reduced to the linear differential equation with the help of the algebraic one. The stability attitude of the periodic motion is determined by the steady-state analysis. Such a periodic motion is needed to better understand the dynamics of the fractional cubic delayed Duffing oscillator.
Article ID 0055 Published: 12 March 2020 Research Article
Analysis of the evolution equation of a hyperbolic curve flow via Lie symmetry method
In this paper, based on the classical symmetry method, the group-invariant solutions of the evolution equation of a hyperbolic curve flow are investigated. The optimal system of the obtained symmetries is found, and the reduced equations and exact solutions of the evolution equation are discussed. Then explicit solutions are obtained by the power series method. In addition, the convergence of the power series solutions is proved. Theobjective shapes of the solutions of the evolution equation are performed.
Article ID 0054 Published: 12 March 2020 Research Article
Analysis of ferrite nanoparticles in liquid
SOHAIL NADEEM SHAFIQ AHMAD NOOR MUHAMMAD
The foremost aim of the present paper is to explore the impact of heat transport phenomenon in a ferrofluid via magnetic dipole. Three distinct ferrite nanoparticles are discussed in the present study with water as the base fluid. Magnetic dipole existing in ferrite nanoparticles plays a significant role in controlling the momentum and thermal boundary layers. The partial differential equations (PDEs) are changed into nonlinear coupled ordinary differential equation (ODEs) by utilising similar transformations. Flow occurs due to linear stretching sheet. For the evaluation of heat flux, Fourier’s law of heat conduction is employed. Effects of rising parameters on the magneto-thermomechanical coupling are examined numerically. The results indicate that the property of magneto-thermomechanical cooperation slows the motion of liquid particles, and accordingly, strengthen the heat transfer rate at the surface and skin friction coefficient. Further, Nusselt number enhances with larger solid volume fraction. A magnificent comparison with accessible results for definite cases has been made.
Article ID 0053 Published: 12 March 2020 Research Article
YI HENG WU KE YAN MA FEI CHENG XUE YUAN CAI
Shell-model calculations are performed using NuShellX code in the model space $\pi( f_{5/2}, p_{3/2}, p_{1/2}, g_{9/2}) \otimes \nu(g_{9/2}, g_{7/2}, d_{5/2}, h_{11/2})$, which probe the proton core excitation from the interior of $Z = 38$ semiclosed shell and neutron core excitation from the interior of $N = 56$ semiclosed shell for the level structure of $^{89}Sr$. Our calculations show that the excitation of a single $d_{5/2}$ neutron across $N = 56$ semiclosed shell into the $h_{11/2}$ orbit should have great effects on the excited states of $^{89}Sr$. In addition, the systematic features of proton core excitation across $Z = 38$ semiclosed shell into the $g_{9/2}$ orbit and neutron core excitation across $N = 56$ semiclosed shell into the $g_{7/2}, s_{1/2}, d_{3/2}, h_{11/2}$ orbits in $N = 51$ isotones are discussed.
Article ID 0052 Published: 12 March 2020 Research Article
SEYED MEHDI MIRHOSSEINI-ALIZAMINI HADI REZAZADEH KUMBINARASAIAH SRINIVASA AHMET BEKIR
In this paper, we apply the new extended direct algebraic method (NEDAM) to solve new exact solutions of the new coupled Konno–Oono (CKO) equation, and construct exact solution expressed in terms of hyperbolic functions and trigonometric functions with arbitrary parameters. A comparison between our established results and the results obtained by the existing ones is also presented. As a newly developed mathematical tool, the proposedmethod is an effective and straightforward technique to work out new solutions of various types of nonlinear partial differential equations (NLPDEs) in applied sciences and engineering.
Article ID 0051 Published: 12 March 2020 Research Article
Zakharov–Kuznetsov–Burgers equation in a magnetised non-extensive electron–positron–ion plasma
In this paper, we have studied the three-dimensional (3D) electron-acoustic waves (EAWs) in a three component complex plasma containing $q$-non-extensive distributed hot electrons and positrons. The propagation characteristics of the 3D electron-acoustic (EA) shock waves under the influence of magnetic field have been studied. Our present plasma model supports the negative potential shocks. Combined action of dissipation ($\eta$), nonextensivity ($q$), concentration of positrons ($\beta$), temperature ratio of cold electrons to positrons ($\sigma$) and magnetic field ($\omega_{c}$) on the EA shock waves has been studied in detail and the findings obtained here will be beneficial in future astrophysical investigations.
Article ID 0050 Published: 28 February 2020 Research Article
RABAH DJEGHIOUR BACHIR MEZIANI OUERDIA OURRAD
In this study, free surface evolution of a magnetic fluid in a finite size tank which is subjected to an external magnetic field was investigated. The physical problem and equations governing fluid motion and magnetic field were given with boundary conditions. Using proper selection of variables, dimensionless equation system governing magnetic fluid sloshing were written. Resolution method based on multiple scale variables was presented and solution of the linear problem was given. The dispersion relation obtained in the finite depth case was compared with that corresponding to an infinite depth calculated with the same assumptions. Direction and magnitude of the external magnetic field, magnetic permeability ratio and surface tension effects on magnetic fluid free surface stability were analysed and important results were discussed.
Article ID 0049 Published: 28 February 2020 Research Article
ZAKIR HUSSAIN MEHBOOB ALI MUHAMMAD SHAHZAD FAISAL SULTAN
In this work, linear stability of an electrically conductive fluid experiencing Poiseuille flow for minimum Reynolds value under a normal magnetic field is analysed using the Chebyshev collocation method. The neutral curves of linear instability are derived by utilising Qualitat and Zuverlassigkeit (QZ) method. Instability of the magnetohydrodynamics for plane Poiseuille flowis introduced by solving the generalised Orr–Sommerfeld equation to determine the growth rates, wave number and spatial shapes of the eigenmodes. To solve linear problems, we use numerical methods which help us at each time step of the simulation, uncoupled by physical processes, which can improve the computational performance. This article provides the stability and error analysis, presents a concise study of the Poiseuille flow, and produces computational tests to support the given theory.
Article ID 0048 Published: 28 February 2020 Research Article
Soret and Dufour effects in the flow of viscous fluid by a curved stretching surface
MARIA IMTIAZ HIRA NAZAR TASAWAR HAYAT AHMED ALSAEDI
The main focus in this study is to study the flow of a viscous fluid through a curved stretched surface. Soret and Dufour effects along with Joule heating are incorporated. Appropriate transformations yield the nonlinear ordinary differential system. Convergent series solutions of velocity, temperature and concentration are constructed. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. Skin friction coefficient, Nusselt and Sherwood numbers are also obtained and discussed graphically. Current computations reveal that the radial velocity experience decline with the increase of Hartman number. Further, fluid temperature declines for higher Prandtl and Soret numbers.
Article ID 0047 Published: 28 February 2020 Research Article
Models for membrane curvature sensing of curvature generating proteins
T V SACHIN KRISHNAN SOVAN L DAS P B SUNIL KUMAR
The curvature-sensitive localisation of proteins on membranes is vital for many cell biological processes. Coarse-grained models are routinely employed to study the curvature-sensing phenomena and membrane morphology at the length scale of a few micrometres. Two prevalent phenomenological models exist for modelling the experimental observations of curvature sensing: (1) the spontaneous curvature (SC) model and (2) the curvature mismatch (CM) model, which differ in their treatment of the change in elastic energy due to the binding of proteins on the membrane. In this work, the prediction of sensing and generation behaviour by these two models are investigated using analytical calculations as well as dynamic triangulation Monte Carlo simulations of quasispherical vesicles. While the SC model yields a monotonically decreasing sensing curve as a function of the vesicle radius, the CM model results in a non-monotonic sensing curve. We highlight the main differences in the interpretation of the protein-related parameters in the two models. We further propose that the SC model is appropriate for modelling peripheral proteins employing the hydrophobic insertion mechanism, with minimal modification of membrane rigidity, while the CM model is appropriate for modelling curvature generation using scaffolding mechanism where there is significant stiffening of the membrane due to protein binding.
Article ID 0046 Published: 28 February 2020 Research Article
In this work, the direct method and the linear differential scattering method were used to detect the experimental effective atomic numbers of some potassium compounds ($\rm{KH_{2}PO_{4}, KNO_{3}, K_{2}S_{2}O_{8}, KOH, K_{2}HPO_{4}, K_{2}SO_{4}, KCl, KIO_{3}}$ and $\rm{KI}$). The experiment has been done by using $^{241}\rm{Am}$ radioactive source, a Si(Li) detector and an energy-dispersive X-ray fluorescence spectrometer (EDXRFS). The experimental effective atomic numbers were compared with the effective atomic numbers obtained using WinXCom, FFAST, non-relativistic theory (NRT)and relativistic theory (RT).
Article ID 0045 Published: 28 February 2020 Research Article
Possible effects of galactic cosmic ray flux and low-cloud amounts on global surface temperature
M A EL-BORIE A A THABET E S EL-MALLAH M ABD EL-ZAHER A A BISHARA
The solar variations, solar–climate interactions, and the mechanisms controlling the response of Earth’s climate system are important to understand the effect of solar variability on climate change. The solar magnetic field is directly/indirectly disturbing the interplanetary space, the ionosphere, the magnetosphere, and even the atmosphere. To investigate the contribution of varying galactic cosmic flux, the role of sunspot number (Rz), galactic cosmic ray (GCR) rates, cloud condensation nuclei (CCN), total solar irradiance (TSI), $\rm{CO}_{2}$ concentration and the global surface temperature (GST) is examined. The variations of TSI can partially explain the global increase in temperature, and it accounts for about $0.5^{0}\rm{C}$ warming experienced from 1950 to 2016. Therefore, the future predictions of global warming should take into account the effects due to long-term changes in the galactic CRs, the low-level cloud condensation (LLC), etc. The concentrations of $\rm{CO}_{2}$ increased in the upper atmosphere by 19% during the last 65 years. A strong correlation between LLC and GST suggests a linear relationship between these parameters. These observations are suggestive of the possible role of GCRs in global climate.
Article ID 0044 Published: 28 February 2020 Research Article
MUBBASHAR NAZEER NASIR ALI FAYYAZ AHMAD MADIHA LATIF
The steady flow of a third-grade fluid due to pressure gradient is considered between parallel plane walls which are kept at different temperatures. The space between the plane walls is assumed to be a porous medium of constant permeability. The viscosity of the fluid is taken as constant as well as a function of temperature. It is further assumed that the fluid may slip at the wall surfaces. The consequence of this assumption results in non-linear boundary conditions at the plane walls. The temperature field is also supposed to satisfy thermal slip condition at the walls. The governing equations are modelled under these assumptions and the approximate solution is obtained using the perturbation theory. The skin friction coefficient is a decreasing function of slip parameters in the case of temperature-dependent viscosity models while no variation is noted for the case of constant viscosity via boundary slip parameter. The heat transfer rate increases with the boundary slip parameter and decreases with the thermal slip parameter. The validity of the approximated solution is checked by calculating the numerical solution as well. The absolute error is calculated and listed in tabular form in the case of constant and temperature-dependent viscosity via boundary and thermal slip parameters. The influence of various emerging parameters on flow velocity and temperature profile is discussed through graphs.
Article ID 0043 Published: 28 February 2020 Research Article
Lump solutions with higher-order rational dispersion relations
This paper aims to explore a kind of lump solutions in nonlinear dispersive waves with higher-order rational dispersion relations.We show that the second member in the commuting Kadomtsev–Petviashvili hierarchy is such an example, and construct its lump solutions, based on a Hirota trilinear form. The presented lump solutions have one peak and two valleys, where the global maximum and minimum values are achieved. A few three dimensional plots and contour plots are made for a specific example of the lumps.
Article ID 0042 Published: 13 February 2020 Research Article
We present results on the bonding nature, structural, electronic, magnetic and elastic properties of $\rm{REIr}_{3}$ ($\rm{RE = Gd, Tb}$ and $\rm{Ho}$) intermetallic compounds adopting simple cubic $\rm{AuCu_{3}}$-type structure obtained using the full-potential linearlised augmented plane wave (FP-LAPW) method based on density functional theory. The local spin density approximation (LSDA) with Hubbard parameter ($\rm{LSDA} +U$) has been used for exchange and correlation effects to get accurate results because of the presence of highly localised $4 f$ electrons of rare-earth $\rm{(RE) (RE = Gd, Tb}$ and $\rm{Ho}$) atoms. The calculated lattice parameter is found to be consistent with the experimental results. The calculated magnetic moments predict ferromagnetic behaviour of these compounds. The electronic and bonding properties have been solved in terms of band structure, density of states (DOS) and charge density plots. These results confirm the metallic nature of these compounds. The bonding appearances of these compounds have also been interpreted from charge density plots. The elastic constants, shear modulus and Cauchy’s pressure are computed and they reveal that $\rm{GdIr_{3}}$ and $\rm{TbIr_{3}}$ compounds are ductile while $\rm{HoIr_{3}}$ shows brittle character.
Article ID 0041 Published: 13 February 2020 Research Article
Joint remote state preparation of an arbitrary eight-qubit cluster-type state
LING-YUN CAO MIN JIANG CHEN CHEN
In this paper, we put forward a scheme to realise joint remote state preparation (JRSP) of an arbitrary eight-qubit cluster-type state with two non-maximally entangled Greenberger–Horne–Zeilinger (GHZ) states in a recursive manner. The senders begin by helping the remote receiver to construct one intermediate state which is related to the target state closely. Then, the receiver introduces auxiliary qubits and applies appropriate local operations to obtain the target eight-qubit cluster-type state. It is shown that one new GHZ channel can be distributed among three participants with a certain probability if the initial attempt fails.Moreover, compared with the previous protocols, in our scheme both quantum resources and classical communications are considerably reduced.
Article ID 0040 Published: 13 February 2020 Research Article
Vibrational resonance is studied in a fractional Mathieu–Duffing oscillator with two types of time delays: fixed and distributed delays. The theoretical expression of the response amplitude is obtained by utilising the methodof direct partition of slow and fast motions. Relative errors between the theoretical prediction and the numerical simulation are introduced to verify the validity of analytical approaches. The relative error of the displacement andthe relative error of the response amplitude are calculated. Small relative errors show that the theoretical analysis is statistically correct. Therefore, the effects of fractional order, linear stiffness coefficient, low-frequency signal, time delay intensity and damping coefficient on the Mathieu–Duffing oscillator with distributed delay are studied successively. In order to better illustrate the impact of distributed time delay on the model, the case of fixed time delay is analysed and compared, and it can be found that the distributed delay has more significant influence than fixed delay on the system. In addition, the influence of distributed delay on the system is more significant than that of the fixed delay.
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 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.
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