• Volume 93, Issue 1

July 2019

• Adaptive synchronisation of complex networks with non-dissipatively coupled and uncertain inner coupling matrix

In this paper, the adaptive synchronisation of time-varying perturbed complex networks with non-dissipatively coupled and uncertain inner coupling matrix is studied. In order to describe the actual network better, the out-coupling configuration matrix is not limited by the dissipatively coupled conditions. It is also worth pointing out that the drive system and the response system described in this paper are uncertain, and uncertainty arises in linear inner coupling matrix and unavoidable uncertain external disturbances, which is different from the past. On the basis of Lyapunov stability theory, adaptive law can be obtained and at the same time unknown bounded disturbances can be overcome.

• Analytical evaluation of cesium emission lines using laser-induced breakdown spectroscopy

A laser-induced breakdown spectroscopy-based method has been successfully developed to quantify cesium (Cs) in solution using spectroscopically pure graphite planchets as a sample support. As Cs is a line-poor system, only five usable Cs atomic emission lines could be found and characterised by employing high-resolution system. The calibration curves of these emission lines were constructed under optimised experimental conditions. The analytical properties of these calibration curves were evaluated based on the usable dynamic range, $R^{2}$ of fitting, root mean square error cross-validation and limit of detection (LOD). The dynamic ranges of these five lines were found to be in correlation with the energy level involved in the transition. An LOD of 4 ppm was obtained using Cs(I) 852.11-nm line, which corresponds to 0.16 $\mu$g of Cs on the planchet. Based on the cross-validation approach, the best accuracy and precision ($\sim$6%) were obtained for 852.11 nm in >3000 ppm solutions, and the same is $\sim$8% for 672.33 nm and 697.33 nm in high concentrated solution of Cs.

• Analytical behaviour of lump solution and interaction phenomenon to the Kadomtsev–Petviashvili-like equation

In this paper, we use the generalised Hirota bilinear method (GHBM). With the help of symbolic calculations and applying the used method, we solve the Kadomtsev–Petviashvili (KP)-like equation with $p$ = 3 to obtain some new lump, periodic kink-wave and solitary wave solutions. All solutions have been verified with their corresponding equations with the aid of the Maple package program.

• Pfaffians of B-type Kadomtsev–Petviashvili equation and complexitons to a class of nonlinear partial differential equations in (3+1) dimensions

The aim of this paper is to investigate a class of generalised Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations, which include many important nonlinear evolution equations as its special cases.By applying the fundamental Pfaffian identity, a general Pfaffian formulation is established and all the involved generating functions for Pfaffian entries need to satisfy a system of combined linear partial differential equations. The illustrative examples of the presented Pfaffian solutions are given for the (3+1)-dimensional generalised KP, Jimbo–Miwa and BKP equations. Moreover, we use the linear superposition principle to generate exponential travelling wave solutions and mixed resonant solutions of the considered equations.

• A new efficient technique for solving fractional coupled Navier–Stokes equations using q-homotopy analysis transform method

In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series.The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm.

• Statistical distribution of adsorption of quantum particles

There is a need to compute and work out the theoretical relationship between the single fermion cell and single fermion particle and the single boson cell and more than one boson particle in the assumed processes for developing the theory of adsorption, simply by maximising the entropy of the system for both types of particles. In this work, the reduction of the general expression of adsorption to the special case of the Langmuir adsorption isotherm and closely related family of curves or types of adsorption isotherms in dimensionless form have been derived using statistical mechanics for an adsorbate. The classification of the laboratory data, for adsorption distribution concept, power of generalised method in terms of nonlinear parameter least square fits by selecting different sets of derived functional form one by one is demonstrated.

• Monte Carlo simulation of charge transport in disordered organic systems using buffer lattice at the boundary

In this paper, we present an alternative method for simulating the charge transport in disordered organic materials by using a buffer lattice at the boundary. This method does not require careful tracking of the carrier’s hopping pattern across boundaries. The suitability of this method is established by reproducing the field dependence of mobility, carrier relaxation and carrier diffusion in disordered organic systems obtained by simulating the charge transport in a lattice without implementing any boundary conditions along the electric field direction. The significance of the buffer lattice is emphasised by simulating the field dependence of mobility without using a buffer lattice, which results in negative field dependence of mobility (NFDM) at low field regime due to the extra bias the carrier gains from the neglected hops at the boundaries along the direction of the electric field.

• Density functional theory of influence of methane adsorption on the electronic properties of a PbS cluster

The effect of methane adsorption on the electronic properties of a lead sulphide (PbS) cluster is investigated using density functional theory (DFT) when an oxygen molecule was previously adsorbed to the cluster. This paper studies how the pre-adsorption of oxygen influences the tendency of PbS cluster to adsorb $\rm{CH}_{4}$ and variations of its electronic properties due to $\rm{CH}_{4}$ adsorption. Further investigation on how these variations occur was carried out by charge transfer calculations. The discussion based on the results of this study succeeded in explaining the previously reported experimental observations.

• Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves

We investigated the new exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, auxiliary equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs.We used the Mathematica program to show these solutions in two and three dimensions graphically.

• Quantum coupling and electrothermal effects on electron transport in high-electron mobility transistors

Based on the energy and momentum balance equations and three-dimensional Schrödinger equations, a physical model of the quantum coupling and electrothermal effects on the electron transport in GaN transistors is proposed. Quantum coupling and electrothermal effects in GaN transistors cause a reduction in the barrier height, changes in the quantised energy levels of the two-dimensional electron gas, and a decrease in the electron densityand source–drain current. This model predicts that the current collapse in GaN transistors can occur under channel electrons with large transverse energy and it can be alleviated by optimising the physical device parameters. The gate length-dependent resistance predicted by the proposed model agrees well with the experimental data reported in the literature. Not only the physical mechanism but also the possibility to improve the reliability of high-electron mobility (HEMT) GaN transistors by optimising its physical parameters has been given in this model due to its analytic nature.

• Coexistence of attractors in integer- and fractional-order three-dimensional autonomous systems with hyperbolic sine nonlinearity: Analysis, circuit design and combination synchronisation

This paper reports the results of the analytical, numerical and analogical analyses of integer- and fractional-order chaotic systems with hyperbolic sine nonlinearity (HSN). By varying a parameter, the integer order of the system displays transcritical bifurcation and new complex shapes of bistable double-scroll chaotic attractorsand four-scroll chaotic attractors. The coexistence among four-scroll chaotic attractors, a pair of double-scroll chaotic attractors and a pair of point attractors is also reported for specific parameter values. Numerical results indicate that commensurate and incommensurate fractional orders of the systems display bistable double-scrollchaotic attractors, four-scroll chaotic attractors and coexisting attractors between a pair of double-scroll chaotic attractors and a pair of point attractors. Moreover, the physical existence of chaotic attractors and coexisting attractors found in the integer-order and commensurate fractional-order chaotic systems with HSN is verified using PSIM software. Numerical simulations and PSIM results have a good qualitative agreement. The results obtained in this work have not been reported previously in three-dimensional autonomous system with HSN and thus represent an enriching contribution to the understanding of the dynamics of this class of systems. Finally, combination synchronisation of such three-coupled identical commensurate fractional-order chaotic systems is analysed usingthe active backstepping method.

• Comment on “New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel (G' /G)-expansion method”

This comment deals with the new auxiliary equation method (Khater method) introduced by MostafaM A Khater, Aly R Seadawy and Dianchen Lu in Pramana – J. Phys. 90, 59 (2018). By simple calculation, it is shown that this method is wrong. The exact solutions obtained in this paper are also wrong. In this comment, the errors in the above paper are pointed out and modified. The right method (amended Khater method) has been introduced.

• Assessment of the mass attenuation coefficients of granite, basalt, andesite and tuff stones with the Geant4 model of a high-purity germanium detector

In this work, the radiation shielding properties of various natural stones, such as granite, basalt, andesite and tuff, were determined by using Monte-Carlo simulations performed with the Geant4 model of a high-purity germanium (HPGe) detector.Mass attenuation coefficients were calculated for $\gamma$ -ray energies of 80.9, 140.5, 356.5, 661.6, 1173.2 and 1332.5 keV and for the sample thicknesses between 1 and 7 cm. The results of this study indicate that the stone samples have lower mass attenuation values varying in the range from −28.8% to −3.7% compared to lead. Among the measured stone samples, the mass attenuation values of tuff stone are closest to lead (above661.6 keV).

• Design of a spiral inflector and transverse beam matching for K130 cyclotron at the Variable Energy Cyclotron Centre

This paper describes the design of a spiral inflector for inflecting heavy ion beams into the existing central region of the K = 130 Variable Energy Cyclotron at Kolkata. Simulation results of transverse beam dynamics through the spiral inflector and the effect of the fringe field on beam phase ellipses at its exit have been discussed in the absence of space charge effect. We have also made an effort to minimise the effect of inflector fringe field by properly adjusting the inflector voltage. The proper matching conditions in the central region have been obtained by optimising the system parameters of the existing axial injection line of K130 cyclotron. The tracking of particles that belong to the boundary of the optimised phase ellipses at the matching point has also been carried out in the computed electric and magnetic fields in the central region. Simulation results confirm that the optimised beam condition reduces beam losses for further acceleration in the cyclotron.

• The Weyl equation under an external electromagnetic field in the cosmic string space–time

In this paper we have considered a massless spinor Dirac particle in the presence of an external electromagnetic field in the cosmic string space–time. To study the Weyl equation in the cosmic string framework using the general definition of Laplacian in the curved space, elements of covariant derivative have been constructed and the Weyl equation has been rewritten in the considered framework. Then we have obtained the equation ofenergy eigenvalues by using the Nikiforov–Uvarov (NU) method. The wave function has been obtained in terms of Laguerre polynomials. An important result obtained is that the degeneracy of the Minkowski space spectral is broken in the transition from Minkowski to cosmic string space.

• General electrodynamics of non-abelian vector bosons of $SU(2)$

Generalised Dirac–Maxwell equations (GDM) are extended to describe non-abelian vector bosons by forming $SU(2)$ multiplet. Noether’s conserved current is investigated by forming suitable Lagrangian for thetheory. General electrodynamics (GED) equations are obtained as Euler–Lagrange equations. Higgs mechanism leads to eigenvalue problem with masses of the bosons as eigenvalues. The sources of the fields have only improper conservation. Analogous to abelian vector bosons, non-abelian vector bosons also are seen to have nuclear structure with massive nucleus. There occur two types of $SU(2)$ sheets, each of three non-abelian vector bosons: one group contains one bradyon and two tachyon vector bosons, whereas the other group contains one tachyon and two bradyon vector bosons. Physical $Z$ and $W$ bosons are formed from the eigenvectors of $U(1)$ and $SU(2)$. The $Z$ and $W$ bosons do not have the same coupling strengths in $SU(2)$.

• # Pramana – Journal of Physics

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