• Volume 86, Issue 6

June 2016,   pages  1153-1428

• Exact solutions of the Drinfel’d–Sokolov–Wilson equation using Bäcklund transformation of Riccati equation and trial function approach

In this paper, two integration schemes are employed to obtain solitons, singular periodic waves and other types of solutions of the Drinfel’d–Sokolov–Wilson equation. The two schemes studied in this paper are the Bäcklund transformation of Riccati equation and the trial function approach. The corresponding constraint conditions of the solutions are also given.

• Hilbert space theory of classical electrodynamics

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

• Average weighted receiving time in recursive weighted Koch networks

Motivated by the empirical observation in airport networks and metabolic networks, we introduce the model of the recursive weighted Koch networks created by the recursive division method. As a fundamental dynamical process, random walks have received considerable interest in the scientific community. Then, we study the recursive weighted Koch networks on random walk i.e., the walker, at each step, starting from its current node, moves uniformly to any of itsneighbours. In order to study the model more conveniently, we use recursive division method again to calculate the sum of the mean weighted first-passing times for all nodes to absorption at the trap located in the merging node. It is showed that in a large network, the average weighted receiving time grows sublinearly with the network order.

• A generalized scheme for designing multistable continuous dynamical systems

In this paper, a generalized scheme is proposed for designing multistable continuous dynamical systems. The scheme is based on the concept of partial synchronization of states and the concept of constants of motion. The most important observation is that by coupling two mdimensional dynamical systems, multistable nature can be obtained if i number of variables of the two systems are completely synchronized and j number of variables keep a constant difference between them i.e., their differences are constants of motion, where $i+j = m$ and $1 \le i, j \le m−1$. The proposed scheme is illustrated by taking coupled Lorenz systems and coupled chaotic Lorenzlike systems. According to the scheme, two coupled systems reduce to single modified system withsome initial condition-dependent parameters. Time evolution plots, phase diagrams, variation of maximum Lyapunov exponent and bifurcation diagrams of the systems are presented to show the multistable nature of the coupled systems.

• Analytical treatment for synchronizing chaos through unidirectional coupling and implementation of logic gates

The idea of synchronization can be explicitly demonstrated by both numerical and analytical means on a nonlinear electronic circuit. Also, we introduce a scheme to obtain various logic gate structures, using synchronization of chaotic systems. By a small change in the response parameter of unidirectionally coupled nonlinear systems, one is able to construct various logic behaviours by both numerical and analytical methods.

• Hybrid synchronization of two independent chaotic systems on complex network

The real network nodes are always interfered by other messages. So, how to realize the hybrid synchronization of two independent chaotic systems based on the complex network is very important. To solve this problem, two other problems should be considered. One is how the same network node of the complex network was affected by different information sources. Another is how to achieve hybrid synchronization on the network. In this paper, the theoretical analysis andnumerical simulation on various complex networks are implemented. The results indicate that the hybrid synchronization of two independent chaotic systems is feasible.

• Robust adaptive synchronization of general dynamical networks with multiple delays and uncertainties

In this article, a general complex dynamical network which contains multiple delays and uncertainties is introduced, which contains time-varying coupling delays, time-varying node delay, and uncertainties of both the inner- and outer-coupling matrices. A robust adaptive synchronization scheme for these general complex networks with multiple delays and uncertainties is established and raised by employing the robust adaptive control principle and the Lyapunov stability theory. We choose some suitable adaptive synchronization controllers to ensure the robust synchronization of this dynamical network. The numerical simulations of the time-delay Lorenz chaotic system as local dynamical node are provided to observe and verify the viability and productivity of the theoretical research in this paper. Compared to the achievement of previous research, theresearch in this paper seems quite comprehensive and universal.

• Synchronization analysis of coloured delayed networks under decentralized pinning intermittent control

This paper investigates synchronization of coloured delayed networks under decentralized pinning intermittent control. To begin with, the time delays are taken into account in the coloured networks. In addition, we propose a decentralized pinning intermittent control for coloured delayed networks, which is different from that most of pinning intermittent controls are only appliedto the nodes from 1 to l or centralized nodes. Moreover, sufficient conditions are derived to guarantee the synchronization of coloured delayed networks based on Lyapunov stability theorem. Finally, numerical simulations are provided to verify the validity of the obtained results.

• Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients

Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.

• Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation

The (4+1)-dimensional Fokas equation is derived in the process of extending the integrable Kadomtsev–Petviashvili and Davey–Stewartson equations to higher-dimensional nonlinear wave equations. This equation is under investigation in this paper. Hirota’s bilinear method is, for the first time, used to solve such a higher-dimensional equation. In order to bilinearize the Fokas equation, some appropriate transformations are adopted. As a result, single-soliton solution,double-soliton solution and three-soliton solution are obtained. A new uniform formula of n-soliton solution is derived from this. It is shown that the transformations adopted in this work play a key role in converting the Fokas equation into Hirota’s bilinear form.

• Scattering chamber facility for double-differential cross-section measurement with 14 MeV DT neutron generator at IPR

Measurement of double-differential cross-sections of 14 MeV neutron-inducedcharged-particle productions is very important for estimating the nuclear heating and radiation damage of a fusion reactor. Only a few experimental data are available even though the nuclear reaction cross-section data of structural materials are important in fusion nuclear technology. In this context,general purpose scattering chamber facility has been developed for accelerator-based 14 MeV DT neutron generator to measure double-differential nuclear reaction cross-section at Fusion Neutronics Laboratory, IPR. It has been designed for experiments using silicon surface barrier detectors forthe online detection of charged particles. It offers flexibility in the arrangement of silicon surface barrier detectors.

• Analysis of the normal optical, Michel and molecular potentials on the $^{40}$Ca($^6$Li, d)$^{44}$ Ti reaction

Full finite-range (FFR) distorted-wave Born approximation (DWBA) method has been applied to analyse the angular distributions of cross-sections of the $^{40}$Ca($^{6}$Li, d)$^{44}$Ti reaction at 28 MeV incident energy for the 22 transitions involving both the bound and unbound states of $^{44}$Ti byusing the normal optical, Michel and molecular potentials. The extracted spectroscopic factors for the three optical potentials are compared with those of some previous studies of zero-range (ZR) calculations of the$^{40}$Ca($^{6}$Li, d)$^{44}$Ti reaction using the normal optical potential. The $\chi^{2}$ values of all the levels are obtained for the three optical potentials to estimate the quality of the fits. Molecular and Michel potentials have been used for the first time to analyse the four-nucleon transfer reaction and it seems that the molecular potential fits the experimental data more satisfactorily for some of the states than the normal optical and Michel potentials.

• 2$\pi$ proportional counting chamber for large-area-coated $\beta$ sources

Detection system for measuring absolute emission rate from large-area-coated $\beta$ sources has been indigenously developed. The system consists of a multiwire-based proportional counter with gas flow and a source mounted within the sensitive volume of the detector. Design of the counter enables efficient counting of emissions in $2\pi$ solid angle.A provision is made for change ofthe source and immediate measurement of source activity. These sources are used to calibrate the efficiency of contamination monitors at radiological facilities. Sensitive area of the detector covers 165◦ solid angle nearing $2\pi$ of emission from the source of size $100 \times 150$ mm. Performance of the chamber is tested using collimated $^{55}$Fe X-ray source and $^{90}$Sr / $^{90}$Y coated $\beta$ sources of various activities. The activity measurement system is established as a national primary standard for calibration of coated $\beta$ sources at Radiological Laboratory at BARC. Design and performanceof the chamber are presented.

• Spherical aberration from trajectories in real and hard-edge solenoid fields

For analytical, real and hard-edge solenoidal axial magnetic fields, the low-energy electron trajectories are obtained using the third-order paraxial ray equation. Using the particle trajectories, it is shown that the spherical aberration in the hard-edge model is high and it increases monotonously with hard edginess, although the focal length converges, in agreement with a recentfield and spherical aberration model. The model paved the way for a hard-edge approximation that gives correct focal length and spherical aberration, which is verified here by the trajectory method. In essence, we show that exact hard-edge fields give infinite spherical aberrations.

• Shift and broadening of emission lines in Nd$^{3+}$:YAG laser crystal influenced by input energy

Spectroscopic properties of the flashlamp-pumped Nd$^{3+}$:YAG laser as a function of input energy were studied over the range of 18–75 J. The spectral widths and shifts of quasi-three-level and four-level inter-Stark emissions within the respective intermanifold transitions of $^4$F$_{3/2}$ $\rightarrow$ $^{4}$I$_{9/2}$ and $^{4}$F$_{3/2}$ $\rightarrow$ $^{4}$I$_{11/2}$ were investigated. The emission lines of $^{4}$F$_{3/2}$ $\rightarrow$ $^{4}$I$_{9/2}$ shifted towards longer wavelength (red shift) and broadened, while the positions and linewidths of the $^{4}$F$_{3/2}$ $\rightarrow$ $^{4}$I$_{11/2}$ transition lines remained constant by increasing the pumping energy. This is attributed to the thermal population as well as one-phonon and multiphonon emission processes in the ground state. This phenomenon degrades the output performance of the lasers.

• Comparison of spectrum normalization techniques for univariate analysis of stainless steel by laser-induced breakdown spectroscopy

Analytical performance of six different spectrum normalization techniques, namelyinternal normalization, normalization with total light, normalization with background along with their three-point smoothing methods were studied using LIBS for quantification of Cr, Mn and Ni in stainless steel. Optimization of the number of laser shots per spectrum was carried out to obtain the best analytical results. Internal normalization technique model was used for selecting the bestemission lines having sufficient intensity and spectral purity for Cr, Mn and Ni for comparison of different normalization techniques. For detailed evaluation of these normalization techniques, under optimized experimental conditions, three statistical parameters i.e., standard error of prediction, relative standard deviation and average bias, were compared for these techniques using theselected emission lines. Results show that the internal normalization technique produces the best analytical results followed by total light normalization. The smoothing of the raw spectra reduces the random error and produces better analytical results provided the peak under study has sufficient $(\ge 7)$ number of pixels.

• Enhancement of nonlinear optical properties of compounds of silica glass and metallic nanoparticle

The aim of this paper is to introduce a method for enhancing the nonlinear optical properties in silica glass by using metallic nanoparticles. First, the T-matrix method is developed to calculate the effective dielectric constant for the compound of silica glass and metallic nanoparticles, both of which possess nonlinear dielectric constants. In the second step, the Maxwell–Garnetttheory is exploited to replace the spherical nanoparticles with cylindrical and ellipsoidal ones, facilitating the calculation of the third-order nonlinear effective susceptibility for a degenerate four-wave mixing case. The results are followed by numerical computations for silver, copper and gold nanoparticles. It is shown, graphically, that the maximum and minimum of the real part of thereflection coefficient for nanoparticles of silver occurs in smaller wavelengths compared to that of copper and gold. Further, it is found that spherical nanoparticles exhibit greater figure-of-merit compared to those with cylindrical or ellipsoidal geometries.

• Analytical solutions of coupled-mode equations for microring resonators

We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a $3 \times 3$ linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a $4 \times 4$ linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.

• Ultrasonic attenuation in rare-earth monoarsenides

The present paper deals with the theoretical calculation of mechanical and thermophysical properties of rare-earth monoarsenides, XAs (X: Np, Pu, Th and U) using elastic constants as the input parameters. These second- and third-order elastic constants (SOECs and TOECs) are determinedin the temperature range 100–500K using Coulomb and Born–Mayer potential upto second nearest neighbours. In order to provide the link between mechanical and dynamical behaviour of crystals, parameters such as Young’s modulus, bulk modulus, Poisson’s ratio etc. are also calculated.In addition, the Cauchy relationship is obeyed by the chosen monoarsenides and are fairly anisotropic, which results in the measurement of longitudinal and shear wave velocities along $\langle100 \rangle$, $\langle110\rangle$ and $\langle 111\rangle$ directions. The toughness/fracture $(G/BT)$ ratio is greater than 0.60, which implies that XAs compounds are brittle at room temperature. Further, the Debye temperature is computed using Debye average velocity as the input parameter. It helps in the characterization of lattice vibrations of a solid. In this work, ultrasonic attenuation due to phonon–phonon interaction$\alpha/f^2_{\rm p−p}$ and thermoelastic loss $\alpha/f ^{2}$th are computed for XAs from 100 to 500K using Mason’s theory. It further helps in evaluating the microstructural properties of the chosen materials. The obtained results indicate that XAs is mechanically stable and are compared with data availablein the literature.

• Thermal expansion behaviour and phase stability of AFe$_2$As$_2$ (A=Ca, Sr and Eu) using powder diffraction technique

The thermal expansibilities and phase stabilities of AFe$_2$As$_2$ (A = Ca, Sr and Eu) have been investigated by powder diffraction techniques in the temperature range 5–600 K.We found the anisotropic thermal expansivities with temperature for all the compounds. The lattice parameter in the tetragonal phase (AT) of CaFe$_2$As$_2$ contracts with increasing temperature, whereas CT expands. The rate of contraction in AT is lower than the rate of expansion in CT. Other compounds show normal thermal expansion behaviour along both a- and c-axes. In-plane expansion (i.e., along the a-axis) is found to be the smallest for EuFe$_2$As$_2$ and the highest for BaFe$_2$As$_2$. However, therate of change of thermal expansivities along out-of-plane (i.e., along the c-axis) is higher as we go from Ba, Sr, Eu and Ca, respectively. Above 600 K, we notice the appearance/disappearance of certain reflections which suggest that tetragonal phase is not stable above this temperature for these compounds.

• Low-temperature photoluminescence in CuIn$_5$S$_8$ single crystals

Photoluminescence (PL) spectra of CuIn$_5$S$_8$ single crystals grown by Bridgman method have been studied in the wavelength region of 720–1020 nm and in the temperature range of 10–34 K. A broad PL band centred at 861 nm (1.44 eV) was observed at $T$ = 10 K. Variations of emission band has been studied as a function of excitation laser intensity in the 0.5–60.2 mW cm$^{−2}$ range. Radiative transitions from shallow donor level located at 17 meV below thebottom of the conduction band to the acceptor level located at 193 meV above the top of the valence band were suggested to be responsible for the observed PL band. An energy level diagram showing transitions in the band gap of the crystal has been presented.

• Numerical method for a 2D drift diffusion model arising in strained n-type MOSFET device

This paper reports the calculation of electron transport in metal oxide semiconductor field effects transistors (MOSFETs) with biaxially tensile strained silicon channel. The calculation is formulated based on two-dimensional drift diffusion model (DDM) including strain effects. The carrier mobility dependence on the lateral and vertical electric field model is especially consideredin the formulation. By using the model presented here, numerical method based on finite difference approach is performed. The obtained results show that the presence of biaxially tensile strain enhances the current in the devices.

• The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule and a proper Lyapunov candidate function, the unknown coefficients of the system are estimated and the stabilization of the synchronizer system is demonstrated. Finally, the numerical simulation illustrates the efficiency of the proposed method in synchronizing two chaotic systems.

• On separation of exchange term from the coefficient of the magnetoelectromechanical coupling

The purpose of this analysis is to introduce the separated exchange coefficient and to graphically investigate it. This coefficient, depending on the electromagnetic constant plus two coefficients of the electromechanical and magnetomechanical couplings, form the coefficient of magnetoelectromechanical coupling (CMEMC), a very important characteristic used for analysingmagnetoelectroelastic smart (composite) materials. It was analytically and graphically demonstrated that the CMEMC can have a minimum due to the minimum of the exchange coefficient at a certain value of the electromagnetic constant. For graphical investigation, the frequently used transverselyisotropic (6$mm$) composite materials such as BaTiO$_3$–CoFe$_2$O$_4$ and PZT–5H–Terfenol–D are exploited.

• Erratum to: Robust adaptive synchronization of general dynamical networks with multiple delays and uncertainties

The affiliations of the authors were inaccurate in the original publication (DOI:10.1007/s12043-015-1182-6). The correct affiliation of all five authors are provided here.

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