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      Volume 93, Issue 6

      December 2019

    • Representation of the inverse momentum operator in curved space

      JAFARI MATEHKOLAEE MEHDI

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      After a detailed report on the representation of the momentum operator in curved space, we straightforwardly obtain the representation of the inverse momentum operator in a curved space.

    • Commissioning and validation of the injector and electron beam transport systems for the IR-FEL at RRCAT

      SONA CHANDRAN BHASKAR BISWAS SHANKAR LAL ARVIND KUMAR R S SAINI M KHURSHEED SAKET KUMAR GUPTA PRAVIN NERPAGAR R K PANDIT K K PANT

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      The first observation of lasing in an infra-red free electron laser (IR-FEL) at the Raja Ramanna Centre for Advanced Technology has been reported recently with a measured power output, i.e. $\sim10^{5}$ times higher than the expected spontaneous radiation power for the electron beam parameters used in the experiment. IR-FEL design simulations, however, estimate a power gain of $10^{7}$ which is three orders of magnitude higher than the experimentally achieved value. To understand this difference between the measured and the expected power output from the IR-FEL, the electron beam used in the experiments has been characterised and FEL simulations have been repeated after considering the measured electron beam parameters. A reasonably good agreement is obtained between the measured results and those predicted by FEL simulations. Experiments have also been performed to study the expected variation in electron beam properties over a macropulse, which should be minimum for an oscillator FEL like the IR-FEL. This paper reports the results from the experiments for characterisation of the electron beam in the IR-FEL set-up and the results from FEL simulations, considering these measured electron beam parameters.

    • Influence of non-uniform heat source/sink on the three-dimensional magnetohydrodynamic Carreau fluid flow past a stretching surface with modified Fourier’s law

      B RAMADEVI K ANANTHA KUMAR V SUGUNAMMA N SANDEEP

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      The combined influence of heat and mass transfer on the boundary layer flow of Carreau fluid across a bidirectional stretching surface has many applications such as heat exchangers, transportation, making of paper plates, fibre coating, and some metal-working procedures in engineering and industrial applications. In this paper,we present a three-dimensional (3D) numerical study on the magnetohydrodynamic (MHD) Carreau fluid flow driven by a stretching surface influenced by heat and mass transfer. This examination further sees the impacts of variable thermal conductivity, Joule heating, irregular heat source/sink and chemical reaction. The improved Fourier’s model is considered in view of the response of heat transfer. The flow equations are transformed into dimensionless equations with suitable similarity transformations. The fourth-order Runge–Kutta-based shooting method is used to resolve the converted nonlinear coupled equations. Influences of various physical aspects on the flow fields are shown through graphs and friction factor, local Nusselt and Sherwood numbers are presented in a separate table. The results predict that the fluid temperature is an escalating factor of the thermal relaxation parameter and Eckert number. Also, the rates of thermal and mass transport and the Weisenberg numbers are proportional to each other.

    • Counterstreaming beams in magnetised Vlasov plasma

      L PALODHI F CALIFANO M E DIECKMANN F PEGORARO

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      In this paper, we investigate nonrelativistic, kinetic, linear phase of the filamentation instability when an external magnetic field is present in the direction of the counterstreaming electron beams using Vlasov simulations in 1D-3V space.We first investigate the growth rate of instability. In the linear growth regime, our results correspondto the previous conclusions that with the increase in strength of the ambient magnetic field, there is a suppression of instability. Interestingly, we established that at a critical/threshold magnetic field, Vlasov simulations and particle-in-cell (PIC) simulations differ in their instability behaviour. At this particular magnetic field, there is a complete suppression of the growth of instability in Vlasov results compared to PIC simulations, where a strong growth of instability is shown. It is believed that thermal noise in the PIC leads to the growth. However, Vlasov simulations show wave–wave coupling which stabilises the modes. In this work, our focus is to demonstrate the difference in this behaviour and to thoroughly analyse the spectra and wave generation for the same.

    • Simultaneous influence of thermo-diffusion and diffusion-thermo on non-Newtonian hyperbolic tangent magnetised nanofluid with Hall current through a nonlinear stretching surface

      M M BHATTI MAJEED A YOUSIF S R MISHRA A SHAHID

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      In this article, the effect of thermo-diffusion and diffusion-thermo on hyperbolic tangent magnetised nanofluid with Hall current past a nonlinear porous stretching surface has been analysed numerically. The impact of thermal slip and chemical reaction are also examined in our current analysis. Runge–Kutta–Merson method and shooting method have been successfully employed to obtain numerical results for the governing nonlinear differentialequations. The impact of Hartmann number, Hall parameter, porosity parameter, fluid parameter, Weissenberg number, Richardson number, concentration buoyancy parameter, Schmidt number, Dufour parameter, Soret number, Prandtl number, chemical reaction parameter, and power-law exponent are discussed and demonstrated graphicallyfor the flow phenomena. Furthermore, the description for Sherwood number, rate of shear stress, and Nusselt number are displayed using tables against all the pertinent parameters. A detailed numerical comparison for the power-law exponent and Prandtl number has been elaborated via tables.

    • Friedmann–Robertson–Walker accelerating Universe with interactive dark energy

      G K GOSWAMI ANIRUDH PRADHAN A BEESHAM

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      In this work, we study a cosmological model based on the cosmological principle which exhibits a transition from deceleration to acceleration. We consider baryonic matter dark energy (DE), and ‘curvature’ energy. Both baryonic matter and DE have variable equations of state. It is assumed that DE interacts with and transforms energy to baryonic matter. A Friedmann–Robertson–Walker (FRW) Universe filled with two fluids has been discussed. The model is shown to satisfy current observational constraints. This Universe is at present in a phantom phase after passing through a quintessence phase in the past. Various cosmological parameters regarding the accelerating Universe have been presented. The evolution of DE, Hubble, deceleration parameters, etc. have been described with the aid of figures. Our theoretical results have been compared with the SNe Ia related Union 2.1 compilation 581 data and we have observed that our derived model is in good agreement with the current observational constraints. We have also explored the physical properties of the model.

    • All-optical NAND/NOR logic gates using bistable switching

      ALI RAHMATI MOHAMMAD ALI AMANDADI

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      A logical NAND and NOR gate was simulated using bistability behavior in nonlinear medium of Fabry–Perot cavity based on the inverse trend of output intensity vs. input intensity. The gate was optimised relative to different cavity parameters, sharp edges between the ON and OFF modes and threshold switching intensity. The real and imaginary parts of the refractive index of the nonlinear medium were utilised to compute numerical results. Finally, gate speed was calculated to be 9.2Gb/s.

    • High polarisation extinction ratio of the TM-pass polariser with silicon carbide/graphene/silicon multilayers

      XINYU WANG WEI SU XINGYU LIU

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      We propose a compact TM-pass polariser, consisting of silicon (Si)/silicon carbide (SiC)/Si layers. Two graphene sheets are sandwiched between the Si and SiC layers as the interlayer to enhance the interaction with light. The loss characteristics have been investigated by using the finite-difference time-domain (FDTD) method. The proposed structure exhibits a low insertion loss (IL) of $\sim 0.25 \rm{dB}$ and a high polarisation extinction ratio (PER) of $\sim 57 \rm{dB}$. To verify the robustness of the proposed polariser, we analyse the fabrication tolerance of the waveguide width and the height of the Si and SiC layers. The polariser shows great fabrication error tolerance. In addition, by employing a $100 \mu\rm{m}$ long waveguide, a PER of 48.3–59.4 dB is obtained in the visible regime ranging from 400 to 600 nm.

    • Cooling of fermionic $^{83}\rm{Kr}$ and bosonic $^{84}\rm{Kr}$ isotopes in a magneto-optical trap

      S SINGH V B TIWARI S R MISHRA

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      Simultaneous laser cooling of two isotopes of krypton, $^{83}\rm{Kr}$ and $^{84}\rm{Kr}$, is reported here in a two-isotope magneto-optical trap (TIMOT). The number of cold metastable $^{83}\rm{Kr}$ atoms in this TIMOT is dependent on the power of the repumping laser beams used, which is maximised for our set-up by varying the powers of repumping lasers. These studies may be useful to investigate cold collisions between fermionic $^{83}\rm{Kr}$ and bosonic $^{84}\rm{Kr}$ atoms in the metastable state.

    • Some exactly solvable $\mathcal{PT}$ -invariant potentials with real spectra via the (extended) Nikiforov–Uvarov method

      M ABUSINI M SERHAN MOHAMMAD F AL-JAMAL AHMED AL-JAMEL EQAB M RABEI

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      The (extended) Nikiforov–Uvarov method is employed to find exact solutions of the Schrödinger operator for three $\mathcal{PT}$ -invariant potentials (periodic exponential, cotangent and $\mathcal{PT}$ -symmetric harmonic plus centrifugal). It is shown that their corresponding Schrödinger operators can exhibit real energy eigenvalues. The results are compared with similar works but with different methods. The comparisons led to Rodrigues formulas of some functions of interest. The eigenfunctions of these examples are expressed in terms of Hankel functions, Romanovski polynomials and Heun functions. The method is proved to be felicitous and leads to closed energy formulas for the potentials under study.

    • Multipartite quantum discord and quantum coherence in Heisenberg–Ising bond alternating chain

      WAJID JOYIA

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      The behaviour of multipartite quantum discord and quantum coherence in Heisenberg–Ising bond alternating spin-1/2 chain are computed by exploiting the method of quantum renormalisation group (QRG). At larger number of iterations, both quantum coherence and quantum discord have found to exhibit quantum phase transition (QPT) between the spin fluid phase and the Neel phase. In addition, at the critical point, the first derivative of both quantum coherence and quantum discord have shown a non-analytical behaviour. Finally, the scaling behaviour of both quantum coherence and quantum discord has been investigated.

    • Consequences of chemical reaction in temperature-dependent thermal conductivity fluid flow by a rotating disk with variable thickness

      MARIA IMTIAZ FIZA SHAHID TASAWAR HAYAT AHMED ALSAEDI

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      This paper examines the steady flow due to a rotating disk with variable thickness. Equations are modelled by considering the homogeneous–heterogeneous reactions and variable thermal conductivity. Themodified Von Karman transformations are utilised to convert the governing partial differential equations into dimensionless nonlinear ordinary differential equations. Convergent series solutions are computed. The impactof relevant parameters on flow fields is computed and interpreted. It is predicted that an increase in disk thickness index decreases the axial velocity while increases the radial and tangential velocities. The Nusselt number enhances by increasing the thickness parameter of a disk.

    • Entropy generation minimisation: Nonlinear mixed convective flow of Sisko nanofluid

      TASAWAR HAYAT FARIA MASOOD SUMAIRA QAYYUM AHMED ALSAEDI

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      Two-dimensional magneto-Sisko nanofluid flow bounded by nonlinearly stretching sheet is studied. Thermophoretic diffusion and Brownian motion effects are also scrutinised. Additionally, impacts of activation energy, chemical reaction and nonlinear convection are considered. The purpose of this study is to analyse entropy generation in the Sisko fluid model. Suitable transformations are used to reduce the governing equation of motion, concentration and temperature. Effects of some pertinent variables on skin friction coefficient, temperature, velocity, concentration and Nusselt number are graphically presented. Clearly, for larger Brownian and thermophoresis parameters, the temperature increases while concentration distribution decreases with Brownian parameter. Bejan number is maximum away from the sheet in the case of shear thickening fluids while it approaches zero for shear thinning fluids.

    • Chemically reactive flow of thixotropic nanofluid with thermal radiation

      MADIHA RASHID TASAWAR HAYAT KIRAN RAFIQUE AHMED ALSAEDI

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      This article addresses the flow of a thixotropic liquid with nanomaterials due to a stretching sheet of variable thickness. The stimulus effects of the heat source/sink and first-order chemical reaction are retained. Convective conditions of heat and mass transfer are also considered at the boundary. Unlike the classical consideration, the linear thermal radiation aspect is examined. The influence of emergent flow, heat and mass parameters on velocity, concentration and temperature fields are shown graphically. It is also noted that the velocity of the fluid significantly favours the non-Newtonian parameters. For higher values of radiation and heat source/sink parameter, the temperature rises.Moreover, a novel investigation on heat and mass transfer rates subject to nanomaterials (i.e. Brownian motion and thermophoresis) in the liquid has been carried out. Nonlinear systemsare solved by the optimal homotopy analysis method (OHAM). Convergence analysis has been executed and the optimal values are computed. The main advantage of the proposed technique is that it can be directly utilised inhighly nonlinear systems without using discretisation, linearisation and round-off errors. The table shows the results of the error analysis.

    • Switching from sub- to superluminal light in a Y-type atomic system using wavelength mismatching

      KAVITA YADAV AJAY WASAN

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      We study the optical properties of a four-level Y system theoretically in $^{87}\rm{Rb}$ atoms using density matrix formalism. On account of wavelength mismatching effects in the system transparency window splits and enhanced absorption regions are observed on either side of the line centre. This enhanced absorption is associated with anomalous dispersion resulting in superluminal light propagation. We also explore the dressed state analysis in the system. The effect of mismatching factor on the group index and group velocity is discussed.

    • Combined effects of free convection and chemical reaction with heat–mass flux conditions: A semianalytical technique

      RAM PRAKASH SHARMA S R MISHRA

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      This paper discusses the effect of heat and mass flux on the natural convective laminar flow of a viscous incompressible fluid under the influence of radiation, magnetic field and Joule heating. The partial differentialequations related to the problem have been changed as a set of ordinary differential equations employing non-dimensional quantities. Semianalytical approach such as the Adomian decomposition method (ADM) is employedto solve the system of ordinary differential equations. The behaviour of characterising parameters on the velocity, heat and mass transfer profiles, and the engineering quantities of interest, i.e. skin friction, heat and mass transfer rates and other indices are presented through graphs

    • Lie symmetry analysis for the coupled integrable dispersionless equations

      YAO ZHANG BEN GAO

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      In this paper, we primarily investigate Lie symmetry analysis and exact solutions for the coupled integrable dispersionless equations. First of all, based on the Lie symmetry analysis, an optimal system of one dimensional subalgebras is constructed. Furthermore, similarity reductions and group invariant solutions are given. Next, exact solutions of the reduced equations have been derived by the method of power series. Finally, by means of Ibragimov’s method, conservation laws are obtained.

    • Global stability analysis of axisymmetric boundary layer: Effect of axisymmetric forebody shapes

      RAMESH BHORANIYA VINOD NARAYANAN

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      This paper presents the effect of axisymmetric forebody shapes on the global stability characteristics of axisymmetric boundary layer developed on a circular cylinder. Axisymmetric forebodies like sharp-cone, ellipsoid,and paraboloid with a fineness ratio (FR) of 2.5, 5.0 and 7.5 are considered. The boundary layer starts to develop at a stagnation point on the forebody geometry and grows in spatial directions. The inflow velocity component is parallel to the axis of the cylinder, and hence the angle of attack is zero. The base flow is axisymmetric, nonparallel and non-similar. The linearised Navier–Stokes equations are derived in the cylindrical polar coordinates for the disturbance flow components. The discretised linearised Navier–Stokes equations along with appropriate boundary conditions form a general eigenvalue problem and it has been solved using Arnoldi’s algorithm. The global temporal modes have been computed by solving the two-dimensional eigenvalue problem. The extent of a favourable pressure gradient developed in streamwise direction depends on the shape of axisymmetric forebody. The temporal and spatial growth of the disturbances has been computed for axisymmetric ($N = 0$) mode for different Reynolds numbers (Re). The forebody shapes have a significant effect on the base flow and stability characteristics at low Re.

    • Vibrational resonance in a higher-order nonlinear damped oscillator with rough potential

      J A LAOYE T O ROY-LAYINDE K A OMOTESO O O POPOOLA U E VINCENT

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      We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medium with a harmonically perturbed potential consisting of a background smooth triple-well potential superimposed by a fast oscillating periodic function and subjected to weak and high-frequency (HF) driving forces. The combined effects of the nonlinear damping inhomogeneity and roughness induced by the harmonic perturbation on the phenomenon of VR were theoretically and numerically analysed. It was found that damping inhomogeneity contributed significantly to the enhancement of resonant states, while potential roughness can be optimised by the HF signal to assist resonance enhancement. Furthermore, the traditional smooth VR shapes occurring in the absence of roughness experienced significant distortion occasioned by potential roughness manifesting as spikes that could ultimately be optimised by large amplitudes of the fast signal to energetically facilitate the potential barrier crossing process, thereby enabling VR enhancement.

    • Study of entropy generation in transient hydromagnetic flow of couple stress fluid due to heat and mass transfer from a radiative vertical cylinder

      G JANARDHANA REDDY MAHESH KUMAR H P RANI

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      Radiative–convective flow studies find wide range of applications in furnace design, solar fans, photochemical reactors, turbid water bodies, etc. The present article focusses on unsteady radiative–convective hydromagnetic couple stress fluid (CSF) flow from a vertical cylinder using the thermodynamic concept. The obtained governing equations of the present model are resolved by a well-organised numerical scheme. The unsteady nature of friction, entropy, coefficients of heat and mass transfer (HMT) along with the time-independent state pattern of flow-field profiles, are shown graphically for distinct values of governing radiation parameter, magnetic parameter, concentration parameter, and constant parameter to display important aspects of the solution. To analyse the HMT process in a 2D domain, Bejans flow visualisation is considered along with isotherms, streamlines, andisoconcentration lines. The Bejans HMT flow visualisation shows that the heat and mass function contours are denser in the foremost verge of the hot surface of the cylinder compared to other contours. The result indicatesthat the entropy generation (EG) parameter increases with decreasing values of radiation and magnetic parameters. Also, the entropy parameter increases for increasing values of concentration parameter or constant parameter.

    • Retraction Note to: Singular vs. non-singular memorised relaxation for basic relaxation current of the capacitor

      SHANTANU DAS

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