• Articles written in Pramana – Journal of Physics

    • L subshell fluorescent $X$-ray measurements to study $CK$ transitions in the $66\leqZ\leq83$ region


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      L subshell fluorescent X-rays in Dy, Ho, Er, Lu, Ta, W, Pt, Au, Hg, Pb and Bi have been measured using synchrotron with selective creation of electron vacancies in individual subshells. Coster--Kronig (CK) yields were derived from the measured intensities. Present measurements have been made at photon energies above the edges where differences between measured and theoretical attenuation coefficients are almost negligible. Parametric trends for the results with $Z$ were developed to cover all $Zs$ in the range of 66--83. The trends predict the switching-off of L1--L2, N1 transition at Z = 67. The extent of fall/rise of $f_Lij$ values corresponding to off/on of certain transitions is found inversely proportional to the difference in binding energies of two consecutive subshells involved in the transition. For $Zs$ above/below these rises/falls, $fL_13$ and $fL_12$ values are almost constants. $f_L23$ values involving no break at $Zs$ follow the general photoionization behaviour that ionization probability is highest at the edge energy and decreases with photon energy. Yield measurements with synchrotron radiation for Dy, Ho, Lu, Hg and Bi and experimental values for $f_L23$, $f_L12$ in Lu and for $f_L13$ in Ta are being quoted for the first time.

    • Root mean square radii of heavy flavoured mesons in a quantum chromodynamics potential model


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      We report the results of root mean square (r.m.s.) radii of heavy flavoured mesons in a QCD model with the potential $V (r) = −(4\alpha_{s}/3r) + br + c$. As the potential is not analytically solvable, we first obtain the results in the absence of confinement and Coulomb terms respectively. Confinement and Coulomb effects are then introduced successively in the approach using the Dalgarno’s method of perturbation. We explicitly consider the following two quantum mechanical aspects in the analysis: (a) The scale factor $c$ in the potential should not effect the wave function of the system even while applying the perturbation theory. (b) Choice of perturbative piece of the Hamiltonian (confinement or linear) should determine the effective radial separation between the quarks and antiquarks. The results are then compared with the available theoretical values of r.m.s. radii.

    • Effects of slip on Cu–water or $\rm{Fe_{3}O_{4}}$–water nanofluid flow over an exponentially stretched sheet

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      This study aims to report the boundary layer flow of nanofluid over an exponentially stretched sheet in the presence of velocity slip as well as thermal slip. Utilising similarity transformations, the governing momentum and temperature equations are converted into ordinary differential equations and then solved numerically by shooting technique. An interesting behaviour of the solution for the converted self-similar equations is noted: dual solutions are obtained for some particular range of values of the governing parameters for the flow past an extended sheet. A comparison is made between the boundary layer flow of Cu–water and $\rm{Fe_{3}O_{4}}$–water nanofluids. Both fluid velocity and temperature increase due to the enhancement in the velocity slip parameter. With the rising values of solid volume fraction, velocity diminishes but temperature increases.

    • Dynamic response of the e-HR neuron model under electromagnetic induction


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      Due to the fluctuation of membrane potential of neuron, there are complex time-varying electromagnetic fields in nervous systems, and the exciting electromagnetic field will further regulate the discharge activities of neurons. In this paper, the coupling of magnetic flux variables to the membrane potential is realised by using a magnetron memristor, and then a 5D extended Hindmarsh–Rose (e-HR) neuron model is established. With the help of Matcont software, the distribution and bifurcation properties of the equilibrium point in the e-HR model is analysed. It is found that there are subcritical Hopf bifurcation, coexisting oscillation modes and hidden limit cycle attractors with period 1 and period 2. In addition, by applying the washout controller, the subcritical Hopf bifurcation point can be transformed into the supercritical Hopf bifurcation point. Thus, the hidden oscillation behaviour of the model can be effectively eliminated. In order to analyse the influence of various parameters on the bifurcation behaviour, numerical simulation of two-parameter bifurcation, single-parameter bifurcation, maximum Lyapunov exponential and time response are given. It is found that the e-HR neuron has a complex bifurcation structure, i.e., the bifurcation structure with period-doubling bifurcations, inverse period-doubling bifurcations, period-adding bifurcations with and without chaos. At the same time, the study also finds that the coexistence behaviour of the periodic cluster discharge and the mixed-mode oscillations (MMOs) can be observed from the bifurcation structure with unique ‘periodic dislocation layer’ on the two-parameter plane. Interestingly, the bursting mode of the system is converted into MMOs when the system parameters are randomly perturbed. The results of this study provide useful insights into the complex discharge patterns and hidden discharge behaviours of neurons under electromagnetic induction.

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