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      Volume 87, Issue 5

      November 2016

    • Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds


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      The ASD systems and manifolds have been studied via a number of approaches and their origins have been well documented. In this paper, we look at the symmetry structures, variational symmetries and related concepts around the associated conservation laws for a number of such manifolds.

    • Review: Characterizing and quantifying quantum chaos with quantum tomography


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      We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in informationgain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory inthe fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different classes of maps and show that these bounds are realized by fully chaotic quantum systems.

    • Space–time transformation for the propagator in de Broglie–Bohm theory


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      A linear space–time transformation proposed to calculate the propagator in the de Broglie–Bohm theory, is viewed as an expansion of the guiding wave function over the velocity space. It is shown that the quantum evolution is preserved in its semiclassical scheme through this change. The case of variable-frequencyharmonic oscillator is presented as an example.

    • Effect of Ar bombardment on the electrical and optical properties of low-density polyethylene films

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      The influence of low-energy Ar ion beam irradiation on both electrical and optical properties of low-density polyethylene (LDPE) films is presented. The polymer films were bombarded with 320 keV Ar ions with fuences up to $1 \times 10^{15}$ cm$^{−2}$. Electrical properties of LDPE films were measured and the effect of ion bombardment on the DC conductivity, dielectric constant and loss was studied. Optically, the energy gap, the Urbach’s energy and the number of carbon atoms in a cluster were estimated for all polymer samples using theUV–Vis spectrophotometry technique. The obtained results showed slight enhancement in the conductivity and dielectric parameters due to the increase in ion fluence. Meanwhile, the energy gap and the Urbach’s energyvalues showed significant decrease by increasing the Ar ion fluence. It was found that the ion bombardment induced chain scission in the polymer chain causing some carbonization. An increase in the number of carbonatoms per cluster was also observed.

    • Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders


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      We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota’s method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop generalized dispersion relations for the typical breaking soliton equations and the generalized negative-order breaking soliton equations. The results provide useful information on the dynamics of the relevant nonlinear negative-order equations.

    • Triple differential cross-sections for the ionization of metastable 2P-state hydrogen atoms by electrons with exchange effects


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      In this paper, triple differential cross-sections for the ionization of metastable 2P-state hydrogen atoms by 250 eV electron energy with exchange effects for various kinematic conditions are calculated. Multiple scattering theory proposed by Das and Seal in {\it Phys. Rev.} A 47, 2978 (1993) is utilized here. The computational results provide significant peak features that show good qualitative agreement with the hydrogenic ground-state experimental data and theoretical results and the present first Born results. In addition, physical origin of the peaks of the cross-section curves is investigated.

    • Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma


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      This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries(KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influenceof plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequencywaves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.

    • Spinning Earth and its Coriolis effect on the circuital light beams: Verification of the special relativity theory


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      Bilger et al (1995), Anderson et al (1994) and Michelson–Gale assisted by Pearson (1925) measure/mention Sagnac effect on the circuital light/laser beams on the spinning Earth. But from the consideration of classical electrodynamics, the effect measured/mentioned by those experimenters is the Coriolis effect, not theSagnac effect. A simple experiment is suggested here that can easily settle the problem.

    • Optical characteristics of transparent samarium oxide thin films deposited by the radio-frequency sputtering technique


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      Transparent metal oxide thin films of samarium oxide (Sm$_2$O$_3$) were prepared on pre-cleaned fused optically flat quartz substrates by radio-frequency (RF) sputtering technique. The as-deposited thin films were annealed at different temperatures (873, 973 and 1073 K) for 4 h in air under normal atmospheric pressure. The topological morphology of the film surface was characterized by using atomic force microscopy (AFM). The optical properties of the as-prepared and annealed thin films were studied using their reflectance and transmittance spectra at nearly normal incident light. The estimated direct optical band gap energy (E$^{d}_{g}$ ) values were found to increase by increasing the annealing temperatures. The dispersion curves of the refractive index of Sm$_2$O$_3$ thin films were found to obey the single oscillator model.

    • Heavy quarkonium properties from Cornell potential using variational method and supersymmetric quantum mechanics


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      Using the variational method and supersymmetric quantum mechanics we calculated, in an approximate way, the eigenvalues, eigenfunctions and wave functions at the origin of the Cornell potential. We compared results with numerical solutions for heavy quarkonia $c \bar {c}, b \bar{b}$ and $b \bar{c}$.

    • Physics design of a 10 MeV, 6 kW travelling wave electron linac for industrial applications


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      We present the physics design of a 10 MeV, 6 kW S-band (2856 MHz) electron linear accelerator (linac), which has been recently built and successfully operated at Raja Ramanna Centre for Advanced Technology, Indore. The accelerating structure is a $2\pi/3$ mode constant impedance travelling wave structure, which comprises travelling wave buncher cells, followed by regular accelerating cells. The structure is designed to accelerate 50 keV electron beam from the electron gun to 10 MeV. This paper describes the details of electromagnetic design simulations to fix the mechanical dimensions and tolerances, as well as heat loss calculations in the structure. Results of design simulations have been compared with those obtained using approximate analytical formulae. The beam dynamics simulation with space charge is performed and the required magnetic field profile for keeping the beam focussed in the linac has been evaluated and discussed. An important feature of a travelling wave linac (in contrast with standing wave linac) is that it accepts the RF power over a band of frequencies. Threedimensional transient simulations of the accelerating structure along with the input and output couplers have beenperformed using the software CST-MWS to explicitly demonstrate this feature.

    • Photodetachment of H$^−$ ion in crossed gradient electric and magnetic fields


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      We study the photodetachment of H$^−$ ion in crossed gradient electric and magnetic fields and put forward an analytical formula for calculating the photodetachment cross-section. Compared to the photodetachmentof H$^−$ ion in a gradient electric field, the Hamiltonian of the detached electron has three degrees of freedom, which makes the dynamical behaviour of the detached electron complex. Photodetachment cross-section for variousexternal fields and the laser polarization are calculated and displayed. A comparison with the photodetachment cross-section in crossed uniform electric and magnetic fields or in a single gradient electric field has been made.The agreement of our results with the above two special cases suggests the correctness of our calculation. Our study may have some potential applications in the photodetachment microscopy experiment or in ion detection.

    • Nonlinear interaction of ultraintense laser pulse with relativistic thin plasma foil in the radiation pressure-dominant regime


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      We present a study of the effect of laser pulse temporal profile on the energy/momentum acquired by the ions as a result of the ultraintense laser pulse focussed on a thin plasma layer in the radiation pressuredominant(RPD) regime. In the RPD regime, the plasma foil is pushed by ultraintense laser pulse when the radiation cannot propagate through the foil, while the electron and ion layers move together. The nonlinear character of laser–matter interaction is exhibited in the relativistic frequency shift, and also change in the wave amplitude as the EM wave gets reflected by the relativistically moving thin dense plasma layer. Relativistic effects in a highenergy plasma provide matching conditions that make it possible to exchange very effectively ordered kineticenergy and momentum between the EM fields and the plasma. When matter moves at relativistic velocities, the efficiency of the energy transfer from the radiation to thin plasma foil is more than 30% and in ultrarelativisticcase it approaches one. The momentum/energy transfer to the ions is found to depend on the temporal profile of the laser pulse. Our numerical results show that for the same laser and plasma parameters, a Lorentzian pulse canaccelerate ions upto 0.2 GeV within 10 fs which is 1.5 times larger than that a Gaussian pulse can.

    • Bifurcations and new exact travelling wave solutions for the bidirectional wave equations


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      By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of {\it Maple} software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional waveequations. The results presented in this paper improve the related previous studies.

    • Formation of ground and excited hydrogen atoms in proton–potassium inelastic scattering


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      The inelastic scattering of proton with a potassium atom is treated for the first time as a three channel problem within the framework of the improved coupled static approximation by assuming that the ground (1s state) and the excited (2s state) hydrogen formation channels are open for seven values of total angularmomentum, $l (0 \leq l \leq 6)$ at energies between 50 and 500 keV. The Lipmann–Swinger equation and the Green’s function iterative numerical method are used to calculate iterative partial and total cross-sections. This can be doneby calculating the reactance matrix at different values of the considered incident energies to obtain the transition matrix that gives partial and total cross-sections. Present results are in reasonable agreement with previous results.

    • New analytical solutions for nonlinear physical models of the coupled Higgs equation and the Maccari system via rational exp$(−\psi(\eta)$)-expansion method


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      In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp$(−\psi(\eta)$)-expansion method is implemented tofind exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effectiveand can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method providesadditional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order andcould be protracted to other physical phenomena.

    • Phenomenological approach to describe logistic growth and carrying capacity-dependent growth processes


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      In this communication, different classes of phenomenological universalities of carrying capacity dependent growth processes have been proposed. The logistic as well as carrying capacity-dependent West-type allometry-based biological growths can be explained in this proposed framework. It is shown that logistic and carrying capacity-dependent West-type growths are phenomenologically identical in nature. However, there is a difference between them in terms of coefficients involved in the phenomenological descriptions. Involuted Gompertz function, used to describe biological growth processes undergoing atrophy or a demographic and economic system undergoing involution or regression, can be addressed in this proposed environment-dependent description. It is also found phenomenologically that the energy intake of an organism depends on carrying capacity whereas metabolic cost does not depend on carrying capacity. In addition, some other phenomenologicaldescriptions have been examined in this proposed framework and graphical representations of variation of different parameters involved in the description are executed.

    • Analysis of tokamak plasma confinement modes using the fast Fourier transformation


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      The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the ‘presenceof external field’ as well as in the ‘absence of external field’. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor $q$ were obtained by using the mode number of $q = m/n$ ($m$ is the mode number). The maximum MHD activity was obtained in 30–35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0–35 ms time was compared with each other in the presence and absence of theexternal field.

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