• Volume 88, Issue 1

January 2017

• General editorial on publication ethics

• Periodic Hamiltonian hierarchies and non-uniqueness of superpotentials

In this article, a family of periodic quantum Hamiltonians, that is subject to a closure condition is considered. In the context of the factorization method, we address the question of non-uniqueness of the governing superpotentials and study an alternative factorization to generate new hierarchies of potentials.

• Observation of multilayer graphene sheets using terahertz phase contrast microscopy

Although it is important for the study of graphene, identifying and characterizing the number of graphene layers is challenging. In this paper, we calculate graphene’s transmission.The result shows that the phase change is more sensitive than the intensity change when light passes through graphene in some THz frequencies. Based on this fact, a simple route is presented for identifying the single or few layers of graphene sheets by using terahertz phase contrast microscopy (TPCM). The route is fast, and easy to be carried out.

• Modelling of capacitance and threshold voltage for ultrathin normally-off AlGaN/GaN MOSHEMT

A compact quantitative model based on oxide semiconductor interface density of states (DOS) is proposed for Al$_{0.25}$Ga$_{0.75}$N/GaN metal oxide semiconductor high electron mobility transistor (MOSHEMT). Mathematical expressions for surface potential, sheet charge concentration, gate capacitance and threshold voltage have been derived. The gate capacitance behaviour is studied in terms of capacitance–voltage (CV) characteristics. Similarly, the predicted threshold voltage ($V_T$) is analysed by varying barrier thickness and oxide thickness. The positive $V_T$ obtained for a very thin 3 nm AlGaN barrier layer enables the enhancement mode operation of the MOSHEMT. These devices, along with depletion mode devices, are basic constituents of cascode configuration in power electronic circuits. The expressions developed are used in conventional long-channel HEMT drain current equation and evaluated to obtain different DC characteristics. The obtained results are compared withexperimental data taken from literature which show good agreement and hence endorse the proposed model.

• On quantum harmonic oscillator being subjected to absolute potential state

In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as ‘like-potential’ energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remainsdormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity – this needs further research. The more the QOE, the greaterwill be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.

• The properties of $C$-parameter and coupling constants

We present the properties of the C-parameter as an event-shape variable. We calculate the coupling constants in the perturbative and also in the non-perturbative parts of the QCD theory, using the dispersive as wellas the shape function models. By fitting the corresponding theoretical predictions to our data, we find $\alpha_{s}(M_{Z^{0}} ) = 0.117 \pm 0.014$ and $\alpha_{0}(\mu_{I} ) = 0.491 \pm 0.043$ for dispersive model and $\alpha_{ s}(M_{Z^{0}} ) = 0.124 \pm 0.015$ and $\lambda_{1} = 1.234 \pm 0.052$ for the shape function model. Our results are consistent with the world average value of $\alpha_{s}(M_{Z^{0}} ) = 0.118 \pm 0.002$. All these features are explained in the main text.

• Dielectric relaxation and optical properties of 4-amino-3-mercapto-6-(2-(2-thienyl)vinyl)-1,2,4-triazin-5(4$H$)-one donor

Structural, optical, electrical conductivity and dielectric relaxation properties of bulk 4-amino-3-mercapto-6-(2-(2-thienyl)vinyl)-1,2,4-triazin-5(4H)-one donor (AMT) are studied. The structure of AMT in its powder form was analysed by X-ray diffraction (XRD), infrared spectroscopy (FT-IR) and atomic forcemicroscopy (AFM). AC measurements (impedance, capacitance and phase angle) are done over the temperature range 303–373 K and in the frequency range from 42 Hz to 5 MHz. Analytical approaches for the experimentalresults of the $\sigma_{AC}(\omega,T)$ and the temperature behaviour of the frequency exponent show that the correlated barrier hopping (CBH) model is a good model to explain the AC electrical conductivity of bulk AMT organic semiconductor material. Application of the dielectric modulus formulism gives a simple method for evaluating the activation energy of the dielectric relaxation. The activation energy from the DC conductivity and the relaxation time are quite similar suggesting a hopping mechanism for AMT. The optical band gap of AMT is investigated using spectrophotometric measurement of transmittance at normal incidence of light in the wavelength range 300–1100 nm.

• Lie symmetry analysis and soliton solutions of time-fractional $K(m, n)$ equation

In this note, method of Lie symmetries is applied to investigate symmetry properties of timefractional $K(m, n)$ equation with the Riemann–Liouville derivatives. Reduction of time-fractional $K(m, n)$ equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α. Thensoliton solutions are extracted by means of a transformation.

• Hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation

The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble’s parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter $K$ occurring in the metric of the space–time. The model for $K = 0$ corresponds to an accelerating Universe with isotropic dark energy. The other two models for $K = 1$ and $−1$ represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.

• Robust control of a class of chaotic and hyperchaotic driven systems

This paper proposes new conditions which are sufficient for robust control of a class of chaotic and hyperchaotic driven systems. The drive–driven systems are characterized by non-identical uncertain complex dynamics where complexities are mainly introduced by the switching nature of their vector fields. The controllerdesign is achieved using linear matrix inequalities (LMIs) and the so-called S-procedure and then validated using two numerical examples. To illustrate the robustness of the proposed approach, a comparative study is also established with regard to a related approach.

• Rotational quenching of H$_2$CO by molecular hydrogen – Suggestion on the work ofWiesenfeld & Faure

Wiesenfeld and Faure investigated rotational quenching of H$_2$CO by molecular hydrogen where they considered 40 rotational levels of $o$-H$_2$CO and 41 rotational levels of $p$-H$_2$CO. Data on energies of rotationallevels of the molecule are fundamental in the investigation. We have found that the sequence of levels reported by Wiesenfeld and Faure is not as per convention of molecular physics. Their results are also available on the website: http://home.strw.leidenuniv.nl/∼moldata/datafiles/ph2co-h2.dat, where the collisional transitions are shown even between the levels having equal energies. Data for such transitions should not be there.

• Dielectric relaxation of amides and tetrahydrofuran polar mixture in C$_{6}$H$_{6}$ from conductivity measurement under 9.90 GHz electric field

Dielectric relaxation studies of binary ($jk$) polar mixtures of tetrahydrofuran with $N$-methyl acetamide, $N,N$-dimethyl acetamide, $N$-methyl formamide and $N,N$-dimethyl formamide dissolved in benzene(i) for different weight fractions ($w_{jk}$’s) of the polar solutes and mole fractions ($x_{j}$ ’s) of tetrahydrofuran at 25◦C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time ($\tau_{jk}$’s) and dipole moment ($\mu_{jk}$’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of $\tau_{jk}$ and $\mu_{jk}$ against $x_{j}$ of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto $x_{j} = 0.3$ of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto $x_{j} = 1.0$ for all systems except tetrahydrofuran + $N,N$-dimethyl acetamide.

• Achieving ultrahigh vacuum in an unbaked chamber with glow discharge conditioning

Glow discharge conditioning (GDC) has long been accepted as one of the basic wall conditioning techniques for achieving ultrahigh vacuum in an unbaked chamber. As a part of this fundamental experimental study, a test chamber has been fabricated from stainless steel 304 L with its inner surface electropolished on which a detailed investigation has been carried out. Both helium and hydrogen gases have been employed as discharge cleaning medium. The discharge cleaning was carried out at 0.1 A/m$^{2}$ current density with workingpressure maintained at $1.0 \times 10^{−2}$ mbar. It was experimentally observed that the pump-down time to attain the base pressure $∼10−8$ mbar was reduced by 62% compared to the unbaked chamber being pumped to this ultimate vacuum. The results were similar irrespective of whether the discharge cleaning medium is either hydrogen or helium. It was also experimentally established that a better ultimate vacuum could be achieved as compared to theoretically calculated ultimate vacuum with the help of discharge cleaning.

• Analysis of the $B^{+}_{c} \rightarrow D^{+}_{s} \bar{K}^{0\ast}$ decay

We analysed the process of $B^{+}_{c} \rightarrow D^{+}_{s} \bar{K}^{0\ast}$ using QCD factorization (QCDF) and final-state interaction (FSI) effects. First, the $B^{+}_{c} \rightarrow D^{+}_{s} \bar{K}^{0\ast}$ decay is calculated using QCDF method. The value found by using theQCDF method is less than the experimental value. Then we considered FSI effect as a sizable correction wherethe intermediate state $D^{+}^{\ast}$ mesons via the exchange of $K^{0}(K^{0}^{\ast}$) are produced. To consider the amplitudes ofthis intermediate state, the QCDF approach was used. The experimental branching ratio of $B^{+}_{c} \rightarrow D^{+}_{s} \bar{K}^{0\ast}$ decayis less than $0.4 \times 10^{-6}$ and our results are $(0.21 \pm 0.04) \times 10^{7}$ and $(0.37 \pm 0.05) \times 10^{6}$ from QCDF and FSI,respectively.

• Detection of bubble nucleation event in superheated drop detector by the pressure sensor

Superheated drop detector consisting of drops of superheated liquid suspended in polymer or gel matrix is of great demand, mainly because of its insensitivity to β-particles and γ -rays and also because of the low cost. The bubble nucleation event is detected by measuring the acoustic shock wave released duringthe nucleation process. The present work demonstrates the detection of bubble nucleation events by using the pressure sensor. The associated circuits for the measurement are described in this article. The detection of events is verified by measuring the events with the acoustic sensor. The measurement was done using drops of various sizes to study the effect of the size of the drop on the pressure recovery time. Probability of detection of events has increased for larger size of the superheated drops and lesser volume of air in contact with the gel matrix. The exponential decay fitting to the pressure sensor signals shows the dead time for pressure recovery of such a drop detector to be a few microseconds.

• Effects of non-extensive electrons and positive/negative dust particles on modulational instability of dust-ion-acoustic solitary waves in non-planar geometry

The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational instability (MI) of DIA waves governed by the NLS equation is also presented. The effects of different ranges of the non-extensive parameter $q$ on the MI are studied. The growth rate of the MI is also given for different values of $q$. It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the netdust-charge number density and non-planar geometry.

• Symbolic computation and abundant travelling wave solutions to KdV–mKdV equation

In this article, the novel $(G'/G)$-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometricand rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

• Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation

By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

• Face-to-face interaction of multisolitons in spin-1/2 quantum plasma

We investigate the face-to-face collision between multisolitons in spin-1/2 quantum plasma. It is studied in the framework of the model proposed by Marklund et al in {\it Phys. Rev.} E 76, 067401 (2007). This studyis done with the help of the extended Poincare–Lighthill–Kno (PLK) method. The extended PLK method is also used to obtain two Korteweg–de Vries (KdV) equations and the phase shifts and trajectories during the head-oncollision of multisolitons. The collision-induced phase shifts (trajectory changes) are also obtained. The effects of the Zeeman energy, total mass density of the charged plasma particles, speed of the wave and the ratio of the sound speed to Alfvén speed on the phase shifts are studied. It is observed that the phase shifts are significantly affected by all these parameters.

• Separable metrics and radiating stars

We study the junction condition relating the pressure to heat flux at the boundary of an accelerating and expanding spherically symmetric radiating star. We transform the junction condition to an ordinary differential equation by making a separability assumption on the metric functions in the space–time variables. The condition of separability on the metric functions yields several new exact solutions. A class of shear-free models is found which contains a linear equation of state and generalizes a previously obtained model. Four new shearing models are obtained; all the gravitational potentials can be written explicitly. A brief physical analysis indicates that the matter variables are well behaved.

• On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel’s equation

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel’s equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel’s equation into the normal form ‘via the suggested change of independent variable’. JWKB approximation of the first-order Bessel functions $(ν = 1)$ of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders $(ν = 0$ and $2)$ by the recursion relations. The required initial values are also being studied anda quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normallyused for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.

• Pramana – Journal of Physics

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Volume 93 | Issue 5
November 2019

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019