• Anil Kumar

      Articles written in Pramana – Journal of Physics

    • Impurity effects on the critical behaviour of the electrical resistance of binary liquid mixtures

      Anil Kumar E S R Gopal

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      The electrical resistance of the binary liquid system cyclohexane + acetic anhydride is measured, in the critical region, both in the pure mixture and when the mixture is doped with small amounts (≈ 100 ppm) of H2O/D2O impurities.Tc was approached to aboutt=3×10−6 wheret=(TTc)/Tc. The critical exponentb ≈ 0.35 in the fit of the resistance data to the equationdR/dTt−b does not seem to be affected appreciably by the impurities. There is a sign reversal ofdR/dt in the non-critical region. Binary liquid systems seem to violate the universality of the critical resistivity.

    • Flip angle dependence in two-dimensional multiple quantum coherencenmr spectroscopy

      N Murali Y V S Ramakrishna K Chandrasekhar M Albert Thomas Anil Kumar

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      The multiple-quantum pathway description developed earlier for two-dimensional single-quantum correlation spectroscopy (cosy), is generalized and applied to the two-dimensional multiple-quantum transitions (2Dmqt) spectroscopy. The connectivity classes ofcosy are also generalized tomqt spectroscopy. The pathway description allows a straightforward method of computation of the flip angle dependence of the intensity of various peaks in two-dimensional correlation spectroscopy. It is shown that a variation of flip angle allows distinction between various classes and types of transitions, as well as optimization of experiment for selective detection of certain classes of peaks in 2D spectroscopy.

    • Evaluation of one-centre electron interaction integrals over slater type atomic orbitals

      Anil Kumar P C Mishra

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      Simplified expressions for one-centre electron interaction integrals in general and Slater-Condon parameters as well as repulsion integrals of the type (aa|aa) in particular have been obtained over Slater-type atomic orbitals. Results calculated using these expressions are in agreement with those due to other authors.

    • Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm

      Arvind Kavita Dorai Anil Kumar

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      A scheme to execute an 𝑛-bit Deutsch-Jozsa (DJ) algorithm using 𝑛 qubits has been implemented for up to three cubits on an NMR quantum computer. For the one- and the two-bit Deutsch problem, the qubits do not get entangled, and the NMR implementation is achieved without using spin-spin interactions. It is for the three-bit case, that the manipulation of entangled states becomes essential. The interactions through scalar 𝐽-couplings in NMR spin systems have been exploited to implement entangling transformations required for the three bit DJ algorithm.

    • Developments in quantum information processing by nuclear magnetic resonance: Use of quadrupolar and dipolar couplings

      Anil Kumar K V Ramanathan T S Mahesh Neeraj Sinha KVRM Murali

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      Use of dipolar and quadrupolar couplings for quantum information processing (QIP) by nuclear magnetic resonance (NMR) is described. In these cases, instead of the individual spins being qubits, the 2n energy levels of the spin-system can be treated as an n-qubit system. It is demonstrated that QIP in such systems can be carried out using transition-selective pulses, in CH3CN, 13CH3CN, 7Li (I=3/2) and 133Cs (I=7/2), oriented in liquid crystals yielding 2 and 3 qubit systems. Creation of pseudopure states, implementation of logic gates and arithmetic operations (half-adder and subtractor) have been carried out in these systems using transition-selective pulses.

    • The kinetics of Cr layer coated on TiNi films for hydrogen absorption

      M Singh Vaibhav Kulsherstha Anil Kumar N K Acharaya Y K Vijay

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      The effect of hydrogen absorption on electrical resistance with temperature for TiNi and TiNi–Cr thin films was investigated. The TiNi thin films of thickness 800 Å were deposited at different angles ($\theta = 0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}$ and $75^{\circ}) under 10$^{−5}$ Torr pressure by thermal evaporation on the glass substrate at room temperature. A layer of Cr of thickness 100 Å was coated on the TiNi thin films. The changing rate of hydrogen absorption increases after Cr layer coating because Cr enhances the catalytic properties of hydrogen absorption in thin films. The rate of hydrogen absorption increases with temperature at lower range but at higher range of temperature it was found to decrease and also it was found that the hydrogen absorption increases with angle of deposition.

    • Effect of normal processes on thermal conductivity of germanium, silicon and diamond

      Banashree Saikai Anil Kumar

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      The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch – KK-S model and (b) between different phonon branches – KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.

    • Bianchi type-V string cosmological models in general relativity

      Anil Kumar Yadav Vineet Kumar Yadav Lallan Yadav

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      Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.

    • Real-time stand-off detection of improvised explosive materials using time-gated UV–Raman spectroscopy


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      A transportable, trolley-mounted stand-off explosive material detection system based on the time-gated Raman spectroscopy was developed and tested in our laboratory. This system is capable of identifying the explosives and improvised explosive materials located up to a distance of 30 m. A frequency tripled Nd:YAG, nanosecond pulsed laser (355 nm, 6 ns) operated at 10 Hz was used as an excitation source to induce Raman spectra of explosive materials under investigation. A reflected type 200 mm aperture telescope designed using Zemax opticaldesign software was used to collect the backscattered Raman signals. Raman signals were recorded using the gated intensified charge coupled device (ICCD) spectrograph. A LabVIEW-based data acquisition and analysis software for real-time identification of materials was developed and used. It gives audio as well as text alarm to the operatorabout threat identification.

    • Hybrid scheme for factorisation: Factoring 551 using a 3-qubit NMR quantum adiabatic processor


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      Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorisation. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given composite number. The main challenge in scaling it to larger numbers is the unavailability of large number of qubits. Here, we propose a hybrid scheme that involves both classical and quantum computation, based on the previous work of Peng et al, Phys. Rev. Lett. 101(22), 220405 (2008), which reduces the number of qubits required for factorisation. The classical part involves setting up and partially simplifying a set of bit-wise factoring equations and the quantum part involves solving these coupled equations using a quantum adiabatic process. We demonstrate the hybrid scheme by factoring 551 using a 3-qubit NMR quantum register.

    • Singularity-free non-exotic compact star in $f (R, T)$ gravity


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      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.

    • Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate


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      In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number. For stronger magnetic field, velocity decreases, while the temperature and concentration increase. It was also found that for shear thinning fluid the drag coefficient exhibits an increasing character when Weissenberg number increases, but for shear thickening fluid the drag coefficient shows the contrary nature. For small values of Dufour number, heat transfer rate enhances with increasing Soret number, but for higher values of Dufour number it slightly dies down with Soret number and the mass transfer rate reacts oppositely. In addition, due to increasing chemical reaction rate, the concentration and velocity decrease.

    • Bulk viscous accelerating Universe in $f (R, T)$ theory of gravity


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      In this paper, we propose that the late-time acceleration of the Universe is due to bulk viscous fluid and trace of energy–momentum tensor $T$ in $f (R, T )$ theory of gravity. We assume that $f (R, T ) = f (R)+2 f (T )$ with $f (R) = R$ and $f (T ) = \lambda T$ where $\lambda$ is a constant, $R$ and $T$ are the Ricci scalar and trace of energy–momentum tensor. First, we obtain an exact solution of the bulk viscous Universe in $f (R, T )$ gravity, then we use observational Hubble data (OHD), the baryon acoustic oscillation (BAO) distance ratio data as well as SN Ia data to constrain the parameters of the derived bulk viscous Universe. Our estimations show that in the model under consideration $H_{0} = 69.089$ km/Mpc/s which is in good agreement with recent astrophysical observations. We ascertain the present age of the derived Universe as well as the signature flipping behaviour of deceleration parameter. Some physical properties of the derived model are also discussed.

    • Entropy generation analysis of Falkner–Skan flow of Maxwell nanofluid in porous medium with temperature-dependent viscosity


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      Entropy generation analysis in steady two-dimensional, viscous, incompressible forced convective Falkner–Skan flow of Maxwell nanofluid over a static wedge embedded in a porous medium with temperature-dependent viscosity is examined. The Buongiorno’s model has been utilised, to get the flow governing higher-order coupled nonlinear partial differential equations (PDEs) from mass, momentum, energy and concentration conservations. Suitable transformations have been done to convert governing PDEs into the coupled non-linear ODEs along with no-slip boundary conditions, which are then solved using the MATLAB programme bvp4c. The influences of diverse flow governing parameters on various flow properties and quantities of physical interest are displayed in graphical mode and discussed. It is found that entropy generation reduces only with Eckert number (Ec), while more entropy is generated for pressure gradient parameter $(m)$, local Deborah number ($\beta$), variable viscosity parameter ($\delta$) and permeability parameter ($K$). Entropy generation due to heat transfer irreversibility is prominent with increase in $m$ and $\delta$, but it is not so for other parameters. The drag force on the wedge surface become stronger with $\beta$ and $m$, but it reduces with $\delta$. Rates of heat transfer and mass transfer enhance with $m$ and $\delta$. In addition, surface drag force and heat transfer rate diminish with Brownian motion parameter ($Nb$) and thermophoresis parameter ($Nt$).

    • Improved tests for non-linearity using network-based statistics and surrogate data


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      We report the results of studies of improved tests for non-linearity based on time series-induced network statistics and surrogate data.We compare results from the network-based statistics with the earlier tests available in the literature and demonstrate the superiority of these tests over the previous tests for several systems. The method we propose is based on constructing a network from a time series and using easily computable parameters of the resulting network such as the average path length, graph density and clustering coefficient as test statistics for the surrogate data test. These statistics are tested for their ability to distinguish between nonlinear processes and linear noise processes, using surrogate data tests on time series obtained from the Rössler system, the Lorenz system,the Henon map, the logistic map and an actual experimental time series of wind speed data, and compared with popularly used time series associated statistics. The network-based statistics are found to distinguish between the nonlinear time series and surrogates derived from the data to a higher degree than the commonly used time series based statistics, even in the presence of measurement noise and dynamical noise. These statistics may thus prove tobe of value in distinguishing between time series derived from nonlinear processes and time series obtained from linearly correlated stochastic processes even in the presence of measurement noise and dynamical noise. The results also show that the efficiency of the network parameters is not exacerbated by the presence of outliers in the given time series.

    • Boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis


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      Two-dimensional forced convective steady boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving plate in a porous medium in the presence of a parallel free-stream is investigated. The governing coupled non-linear partial differential equations (PDEs) along with boundary conditions are transformed into a set of non-linear coupled ordinary differential equations (ODEs) by using appropriate transformations. The obtained non-linear ODEs with modified boundary conditions are converted into a system of first-order ODEs whichare solved using the classical and efficient shooting method. Dual solutions for velocity, temperature and nanoparticle concentration distributions for Eying–Powell fluids similar to Newtonian fluid in some special flow situations are obtained, when the plate and free-stream are moving along mutually opposite directions. The stability analysis of the obtained solutions is performed and it is found that the upper branch solutions are physically stable, while lowerbranch solutions are unstable. The impacts of different dimensionless physical parameters on velocity, temperature and nanoparticle concentration are reported in the form of graphs and tables. An important result is obtained and itreveals that the ‘dual solutions’ character has been destroyed if resistance due to the porous medium is raised up to a definite level (i.e., permeability parameter K > 0.07979), though the range of existence of unique solution becomes larger with further increase of resistance due to porous medium. It is also observed that heat transfer rate diminishes with increasing thermophoresis parameter, Brownian diffusion parameter and Lewis number in all the cases, whereas mass transfer rate enhances with thermophoresis parameter (for dual solutions), Brownian diffusionparameter (for unique solutions) and Lewis number (for unique solutions). Further, skin-friction coefficient, i.e., the surface drag force, increases with permeability parameter, suction/injection parameter and decreases with Eyring–Powell fluid parameter. Also, increments in permeability parameter and the suction/injection parameter lead to the delay in the boundary layer separation. The critical values of velocity ratio parameter beyond which the boundarylayer separation appears are − 0.5476432, − 0.5987132, − 0.704862, − 0.816944, − 0.9365732, − 0.96179102, − 1.057104, − 1.062004, − 1.09222, − 1.115824, − 1.193413, − 1.591023 and − 1.898366 for K = 0, 0.01, 0.03, 0.05, 0.07, 0.074, 0.08, 0.082, 0.085, 0.09, 0.1, 0.15 and 0.2, respectively.

    • Optical and terahertz characterisation of efficient NLO single crystal: (E)-2-(4-(dimethyl amine) styryl)-1,1,3-trimethyl-1Hbenzo[ e]indol-3-ium iodide (P-BI)


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      We report the terahertz (THz)-based characterisation of a highly efficient non-linear optical compound (E)-2-(4-(dimethyl amino) styryl)-1,1,3-trimethyl-1H-benzo[e]indol-3-ium iodide (P-BI) single crystal. The crystallographic structure of the grown crystal was confirmed by single-crystal X-ray diffraction analysis. Based on the obtained diffraction analysis, the title crystal belongs to the space group P2$_1$ and possesses good optical transmission between 700 and 1500 nm. The most important impedance spectroscopy-based parameters such as dielectric constant and dielectric losses show lower values which are an essential requirement for general non-linear optical (NLO) materials. The femtosecond oscillator has helped us to ascertain the transmission/absorption and generation in the 0.2–2.0 THz range. The obtained experimental data were used for the measurement of real and imaginary parts of the refractive index and absorption coefficients of the crystal. Finally, the crystal was subjected to the femtosecond laser amplifier for measuring the efficiency, maximum generated power and effect of vertical rotation of the crystal on THz radiation. The output power was measured using a pyroelectric detector and the generated maximum power was of the order of 1.9 μW at 150 mW incident pump power. The corresponding efficiency of the generated THz signal is of the order of 1.26 × 10$^{–3}$%.

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