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      Volume 92, Issue 3

      March 2019

    • Design of optical Mach–Zehnder interferometer phase shifter in silicon-on-insulator


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      A passive TE mode phase shifter-based compact structure of optical Mach–Zehnder interferometer(MZI) using silicon-on-insulator (SOI) platform is demonstrated by using BPM simulations. Insertion loss was found, that is 9 dB for 3 $\mu$m width, 16 dB for 1.55 $\mu$m wavelength, 0.9 dB for 2000 $\mu$m path length (arms), and 15 dB for 0.0055 index differences between the core and the cladding of SOI of the designed device. The Mach–Zehnder interferometer attains good phase shifts by changing the path lengths (arm) with TE mode polarisation.

    • All single travelling wave patterns to fractional Jimbo–Miwa equation and Zakharov–Kuznetsov equation


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      By the complete discrimination system of polynomial method, we obtain the classification and representation of all single travelling wave solutions to (3 + 1)-dimensional conformal fractional Jimbo–Miwa equation and fractional Zakharov–Kuznetsov equation. These solutions show rich evolution patterns of models described by these two equations.

    • Characteristics of solar microflares as seen in soft X-ray emission


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      In this paper, we present the thermal and non-thermal characteristics of solar plasma producing microflares in 4–12 keV energy range. The X-ray spectra of 10 B-class solar microflares observed by the silicon(Si) detector (4–25 keV) on-board solar X-ray spectrometer (SOXS) mission were analysed in 4–12 keV energy range. We employed forward fitting for the spectral modelling of thermal and non-thermal components of X-ray spectra with isothermal, multithermal and single power-law functions in order to determine flare parameters. The fit results obtained from the combination of isothermal and single power-law functions yield a weighted mean value of emission measure $\rm{(EM) \approx 0.0203×10^{49}cm^{−3}}$, plasma temperature [Case (1)] $T (1) \approx 10.24$MK and non-thermal spectral index $\gamma (1) \approx 3.90$. The fit results obtained from the combination of multithermal and single power-law functions yield a weighted mean value of differential emission measure, $\rm{(DEM) \approx 0.00116 × 10^{49} cm^{−3} keV^{−1}}$, plasma temperature [Case (2)], $T (2) \approx 12.90$MK, thermal spectral index, $\delta \approx 4.06$ and non-thermal spectral index, $\gamma (2) \approx 3.81$. Further, we obtained the mean value of conduction cooling time, $\tau_{c}(T) \approx 283$ s at 11.6 MK, thermal energy, $E_{th} \approx 0.50×10^{29}$erg and thermal–non-thermal cross-over energy, $\epsilon_{th} \approx 9.23$ keV. In this analysis, the obtained results were found to be compatible with the earlier analysis carried out for the microflares through Reuven Ramety High Energy Solar Spectroscopic Imager (RHESSI), Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) and NuSTAR observations. Here, we observed that EM decreases with increasing plasma temperature $(T)$. We find that $\tau_{c}(T)$ scale with plasma temperature $(T)$ with an inverse gradient exhibits time delay characteristic of the cooling process of plasma. The correlation of $E_{th}$ and temperature $(T)$ shows moderate anticorrelation. The present analysis demonstrates the multithermal plasma model and conduction cooling process during high temperature of microflares (similar to large flares) followed by radiative cooling in post-flare.

    • Truncated $q$-deformed fermion algebras and phase transition


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      In this paper, we apply the $q$-deformed fermion theory to the phase transition from the ordinary fermion into the truncated $q$-deformed fermion at the critical temperature $T_{c}$.

    • Thermodynamics analysis of Ricci dark energy models in bouncing Universe


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      Ricci dark energy (RDE) model in the framework of bouncing Universe is considered. Both the interacting and the non-interacting cases of the Ricci model of dark energy have been studied. Expressions for important cosmic parameters are reconstructed for the assumed model. It is noticed that the Universe undergoes a continuous expansion with a negative deceleration parameter for two scenarios. Also, Om diagnostic parameter has been established showing a type of quintessence-like behaviour over the given time range. The total entropy of the system is calculated and the validity of the generalised second law of thermodynamics is studied.

    • Test of isospin conservation in thermal neutron-induced fission of $^{245}Cm$


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      We have recently shown that the general trends of partition-wise fission fragment mass distribution in heavy-ion-induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using theconcept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [Jain et al, Nucl Data Sheets 120, 123 (2014); Garg and Jain, Phys. Scr. 92, 094001 (2017); Jain and Garg, EPJ Web of Conference 178, 05007 (2018); Garg et al, Phys. Scr. 93, 124008 (2018)]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-inducedCN fission reaction, $^{245}\rm{Cm}(n_{th}, f)$. As earlier, we use Kelson’s conjectures [I Kelson, Proceedings of the Conference on Nuclear Isospin (Academic Press, New York, 1969)] to assign isospin to neutron-rich fragments emitted in fission, which suggest the formation of fission fragments in isobaric analogue states. We calculate the relative yields of neutron-rich fragments using the concept of isospin conservation and basic isospin algebra. The calculated resultsreproduce the experimentally known partition-wise mass distributions quite well. This highlights the usefulness of isospin as an approximately good quantum number in neutron-rich nuclei. This also allows us to predict the fragment distribution of the most symmetric Cd–Cd partition and the heavier mass fragment distributions, both not measured so far.

    • Complexiton solutions and soliton solutions: (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation


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      In this work, we derive the complexiton solutions for Date–Jimbo–Kashiwara–Miwa (DJKM) equation using the extended transformed rational function algorithm that relies on the Hirota bilinear form of the considered equation. Additional solutions such as complex-valued solutions also fall out of this integration scheme. Multisoliton-type solutions, in other words one-soliton, two-soliton and three-soliton solutions, which comprise both wave frequencies and generic phase shifts are presented through the medium of the multiple exp-function methodology which falls out as a result of generalisation of Hirota’s perturbation technique.

    • The FDTD simulation of microring feedback bend-based coupling resonator system for electromagnetically-induced transparency-like effect


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      A microring feedback bend-based coupling resonant system is proposed and is finite difference time domain (FDTD)-simulated to generate electromagnetically-induced transparency (EIT)-like transmission and mode distribution. The coupling between the cross-section of the waveguides gives rise to EIT-like spectrum. Most of themode field energy is concentrated in the coupling region of the feedback bend. The full-width at half-maximum(FWHM) can be tuned by controlling the gap parameter between two feedback bends. The device enables integration with some photonic devices on a chip and shows great promise in applications such as fast–slow light and optical filters.

    • Analytical approaches to space- and time-fractional coupled Burgers’ equations


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      We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplace-variational iteration method (LVIM) and the reduced differential transform method (RDTM). The solutions are obtained as rapidly convergent series with simply calculable terms. Numerical studies of the application of theseapproaches for a number of sample problems are given and are illustrated graphically. With these methods, it is possible to investigate the nature of solutions when the fractional derivative parameters are changed. The numerical results reveal the effectiveness and the correctness of the proposed methods.

    • The effects of core polarisation on some even–even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions


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      Elastic and inelastic electron scattering from even–even $Z = N$ sd-shell ($^{28}Si, ^{32}S$ and $^{36}Ar$) nuclei has been studied using the nuclear shell-model configurations. The transition rates $B(C2\uparrow)$ from the ground $0^{+}$ state to the first excited $2^{+}_{1}$ state, the electric quadrupole moments $Q$, the elastic longitudinal $C0$ and inelastic longitudinal $C2$ form factors are calculated. SDBA and USDA model spaces have been used. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (HO) and Skyrme–Hartree–Fock (SHF) potentials. The configurations higher than the core and the model space are taken into account within a microscopic theory that includes one particle–one hole excitations from the core and model space orbits to higher allowed orbits with $2\bar{h}\omega$ excitations. These effects are defined as core polarisation (CP) effects. Two-body Michigan three-range Yukawa (M3Y) effective nucleon–nucleon interaction and the modified surface delta interaction (MSDI) have been used as residual interactions for the CP matrix elements. The calculations are performed using the shell-model code Nushell@MSU, where the deduced results, including CP, are more compatible with the available experimental and theoretical results.

    • Compact relativistic star with quadratic envelope


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      We consider an uncharged anisotropic stellar model with two distinct equations of state in general relativity. The core layer has a quark matter distribution with a linear equation of state. The envelope layer has a matter distribution which is quadratic. The interfaces between the core, envelope and the vacuum exterior regions are smoothly matched. We find radii, masses and compactifications for five different compact objects which are consistent with other investigations. In particular, the properties of the pulsar object PSR J1614-2230 are studied. The metric functions and the matter distribution are regular throughout the star. In particular, it is shown that the radii associated with the core and the envelope can change for different parameter values.

    • Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation


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      In this paper, we use the Hirota bilinear method. With the help of symbolic calculation and applying this method, we solve the (2 + 1)-dimensional bidirectional Sawada–Kotera (bSK) equation to obtain some new lump-kink, lump-solitons, periodic kink-wave, periodic soliton and periodic wave solutions.

    • A complete analytical study on the dynamics of simple chaotic systems


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      We report, in this paper, a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical solutions revealing several chaotic phenomena such as antimonotonicity, period-doubling sequences and Feignbaum remerging have been presented. Further, the analytical solutions are used to obtain basins of attraction, phase portraits and Poincare maps for different chaotic systems. Experimentally observed chaotic attractors in some of the systems are presented to confirm the analytical results. The bifurcations andchaotic phenomena studied through explicit analytical solutions are reported in the literature for the first time.

    • A parametric model to study the mass–radius relationship of stars


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      In static space–time, we solve the Einstein–Maxwell equations. The effective gravitational potential and the electric field for charged anisotropic fluid are defined in terms of two free parameters. For such configurations, the mass of the star as a function of stellar radius is found in terms of two aforementioned parameters subjected to certain stability criteria. For various values of these two parameters, one finds that such a mass–radius relationship can model stellar objects located at various regions of the Hertzsprung–Russel diagram.

    • Neutron star cooling via axion emission by nucleon–nucleon axion bremsstrahlung


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      Neutron stars generally cool off by the emission of $\gamma$-rays and neutrinos. But axions can also be produced inside a neutron star by the process of nucleon–nucleon axion bremsstrahlung. The escape of these axions adds to the cooling process of the neutron star.We explore the nature of cooling of neutron stars including the axion emission and compare our result with the scenario when the neutron star is cooled by only the emission of $\gamma$-rays and neutrinos. In our calculations we consider both the degenerate and non-degenerate limits for such axion energy loss rate and the resulting variation of luminosity with time and variation of surface temperature with time of the neutron star. In short, the thermal evolution of a neutron star is studied with three neutron star masses (1.0, 1.4 and 1.8 solar masses) and by including the effect of axion emission for different axion masses ($m_{a} = 10^{−5}, 10^{−3}$ and $10^{−2} eV$) and compared with the same when the axion emission is not considered. We compared theoretical cooling curve with the observational data of three pulsars PSR B0656+14, Geminga and PSR B1055-52 and finally gave an upper bound on axion mass limits $m_{a} \leq 10^{−3}$ eV which implies that the axion decay constant $f_{a} \geq 0.6×10^{10}$ GeV.

    • Mayer’s convergence and thermodynamics of ideal Bose gas


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      The equation of state for a collection of ideal bosons in both the low-density and high-density regions is found using the method of cluster expansion with a new generating function. The importance of the radius of convergence in the cluster expansion and its connection to the Bose–Einstein condensation phenomenon are studied. The radius of convergence of the partition function is calculated and the values of critical density, fugacity and other thermodynamic properties at condensation are obtained using Mayer’s convergence method.

    • Investigation on the electrical and optical properties of some zinc titanate ceramics


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      The ceramics of spinel zinc orthotitanate (SZT) and perovskite zinc metatitanate (PZT) sintered at $800^{\circ}$C have been prepared using the high-energy ball milling technique. The structural and optical characterisation of the prepared samples has been performed using X-ray diffraction and Fourier transformation of infrared (FT-IR)spectroscopy analysis. The measurements of frequency-dependent dielectric constant of the PZT and SZT ceramics sintered at $800^{\circ}$C have been performed in the $(50−600)^{\circ}$C temperature range. Impedance spectroscopy studies have been reported for the prepared nanocrystalline ceramics. The empirical vibrational frequencies observed from the FT-IR spectra have been compared using the computational method of ORCA program package. Constraints for symmetry, bonds, angles or dihedral angles have not been applied in the geometry optimisation calculations. Hybrid three-parameter exchange-correlation functional of Becke, Lee, Yang, Parr with 20% amount of exact exchange and Ahlrichs triple-zeta valence (def2-TZVP) basis set with polarisation function have been investigated for all atoms without considering the relativistic effects.

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