• Volume 78, Issue 3

March 2012,   pages  335-498

• A highly accurate method to solve Fisher’s equation

In this study, we present a new and very accurate numerical method to approximate the Fisher’s-type equations. Firstly, the spatial derivative in the proposed equation is approximated by a sixth-order compact ﬁnite difference (CFD6) scheme. Secondly, we solve the obtained system of differential equations using a third-order total variation diminishing Runge–Kutta (TVD-RK3) scheme. Numerical examples are given to illustrate the efﬁciency of the proposed method.

• Nonlinear resonance in Dufﬁng oscillator with ﬁxed and integrative time-delayed feedbacks

We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Dufﬁng oscillator with two types of time-delayed feedbacks, namely, ﬁxed and integrative. Particularly, we analyse the effect of the time-delay parameter 𝛼 and the strength 𝛾 of the time-delayed feedback. Applying the perturbation theory we obtain a nonlinear equation for the amplitude of the periodic response of the system. For a range of values of 𝛾 and 𝛼, the response amplitude is found to be higher than that of the system in the absence of delayed feedback. The response amplitude is periodic on the parameter 𝛼 with period $2\pi /\omega$ where 𝜔 is the angular frequency of the external periodic force. We show the occurrence of multiple branches of the response amplitude curve with and without hysteresis.

• Robust chaos synchronization based on adaptive fuzzy delayed feedback $\mathcal{H}_{\infty}$ control

In this paper, we propose a new adaptive $\mathcal_{\infty}$ synchronization strategy, called an adaptive fuzzy delayed feedback $\mathcal_{\infty}$ synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback $\mathcal_{\infty}$ control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed $\mathcal_{\infty}$ performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.

• Multiple ($G'/G$)-expansion method and its applications to nonlinear evolution equations in mathematical physics

In this paper, an extended multiple ($G'/G$)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefﬁcients’ nonlinear evolution equations.

• Fragmentation and momentum correlations in heavy-ion collisions

The role of momentum correlations in the production of light and medium mass fragments is studied by imposing momentum cut in the clusterization of the phase space. Our detailed investigation shows that momentum cut has a major role to play in the emission of fragments. A comparison with the experimental data is also presented. The calculations showed better agreement with the experimental data when momentum cut is imposed.

• The second Born approximation of electron–argon elastic scattering in a bichromatic laser ﬁeld

We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser ﬁeld in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix elements numerically. The dependence of differential cross-section on the relative phase between the two laser components is presented. The results obtained in the ﬁrst and second Born approximations are compared and analysed.

• Vector wave diffraction pattern of slits masked by polarizing devices

Polarization property is important to the optical imaging system. It has recently been understood that the polarization properties of light can be fruitfully used for improving the characteristics of imaging system that includes polarizing devices. The vector wave imagery lends an additional degree of freedom that can be utilized for obtaining results that are unobtainable in scalar wave imagery. This calls for a systematic study of diffraction properties of different apertures using polarization-sensitive devices. In the present paper, we have studied the Fraunhofer diffraction pattern of slits masked by different kinds of polarizing devices which introduce a phase difference between the two orthogonal components of the incident beam.

• Performances of different metals in optical ﬁbre-based surface plasmon resonance sensor

The capability of various metals used in optical ﬁbre-based surface plasmon resonance (SPR) sensing is studied theoretically. Four metals, gold (Au), silver (Ag), copper (Cu) and aluminium (Al) are considered for the present study. The performance of the optical ﬁbre-based SPR sensor with four different metals is obtained numerically and compared in detail. The performance of optical ﬁbre-based SPR sensor has been analysed in terms of sensitivity, signal-to-noise (SNR) ratio and quality parameter. It is found that the performance of optical ﬁbre-based SPR sensor with Au metal is better than that of the other three metals. The sensitivity of the optical ﬁbre-based SPR sensor with 50 nm thick and 10 mm long Au metal ﬁlm of exposed sensing region is 2.373 𝜇m/RIU with good linearity, SNR is 0.724 and quality parameter is 48.281 RIU-1. The thickness of the metal ﬁlm and the length of the exposed sensing region of the optical ﬁbre-based SPR sensor for each metal are also optimized.

• Free convection effects and radiative heat transfer in MHD Stokes problem for the ﬂow of dusty conducting ﬂuid through porous medium

The present note deals with the effects of radiative heat transfer and free convection in MHD for a ﬂow of an electrically conducting, incompressible, dusty viscous ﬂuid past an impulsively started vertical non-conducting plate, under the inﬂuence of transversely applied magnetic ﬁeld. The heat due to viscous dissipation and induced magnetic ﬁeld is assumed to be negligible. The governing linear partial differential equations are solved by ﬁnite difference technique. The effects of various parameters (like radiation parameter 𝑁, Prandtl number Pr, porosity parameter 𝐾) entering into the MHD Stokes problem for ﬂow of dusty conducting ﬂuid have been examined on the temperature ﬁeld and velocity proﬁle for both the dusty ﬂuid and dust particles.

• Modulation instability of an intense laser beam in an unmagnetized electron–positron–ion plasma

The modulation instability of an intense circularly polarized laser beam propagating in an unmagnetized, cold electron–positron–ion plasma is investigated. Adopting a generalized Karpman method, a three-dimensional nonlinear equation is shown to govern the laser ﬁeld. Then the conditions for modulation instability and the temporal growth rate are obtained analytically. In order to compare with the usual electron–ion plasmas, the effect of positron concentration is considered. It is found that the increase in positron-to-electron density ratio shifts the instability region towards higher vertical wave numbers but does not cause displacement along the parallel wave number direction, and the growth rate increases as the positron-to-electron density ratio increases.

• Effective atomic number, electron density and kerma of gamma radiation for oxides of lanthanides

An attempt has been made to estimate the effective atomic number, electron density (0.001 to 10$^5$ MeV) and kerma (0.001 to 20 MeV) of gamma radiation for a wide range of oxides of lanthanides using mass attenuation coefﬁcient from WinXCom and mass energy absorption coefﬁcient from Hubbell and Seltzer. The values of these parameters have been found to change with energy for different oxides of lanthanides. The lanthanide oxides ﬁnd remarkable applications in the ﬁeld of medicine, biology, nuclear engineering and space technology. Nano-oxides of lanthanide ﬁnd applications in display and lighting industry.

• Phonon heat transport in gallium arsenide

The lifetimes of quantum excitations are directly related to the electron and phonon energy linewidths of a particular scattering event. Using the versatile double time thermodynamic Green’s function approach based on many-body theory, an ab-initio formulation of relaxation times of various contributing processes has been investigated with newer understanding in terms of the linewidths of electrons and phonons. The energy linewidth is found to be an extremely sensitive quantity in the transport phenomena of crystalline solids as a collection of large number of scattering processes, namely, boundary scattering, impurity scattering, multiphonon scattering, interference scattering, electron–phonon processes and resonance scattering. The lattice thermal conductivities of three samples of GaAs have been analysed on the basis of modiﬁed Callaway model and a fairly good agreement between theory and experimental observations has been reported.

• Electronic structures of the F-terminated AlN nanoribbons

Using the ﬁrst-principles calculations, electronic properties for the F-terminated AlN nanoribbons with both zigzag and armchair edges are studied. The results show that both the zigzag and armchair AlN nanoribbons are semiconducting and nonmagnetic, and the indirect band gap of the zigzag AlN nanoribbons and the direct band gap of the armchair ones decrease monotonically with increasing ribbon width. In contrast, the F-terminated AlN nanoribbons have narrower band gaps than those of the H-terminated ones when the ribbons have the same bandwidth. The densityof-states (DOS) and local density-of-states (LDOS) analyses show that the top of the valence band for the F-terminated ribbons is mainly contributed by N atoms, while at the side of the conduction band, the total DOS is mainly contributed by Al atoms. The charge density contour analyses show that Al–F bond is ionic because the electronegativity of F atom is much stronger for F atom than for Al atom, while N–F bond is covalent because of the combined action of the stronger electronegativity and the smaller covalent radius.

• Theoretical studies of the g factors and local structure for Pt3+ in 𝛼-Al2O3

The anisotropic 𝑔 factors and local structure for the trigonal Pt3+ centre in 𝛼-Al2O3 are theoretically investigated from the perturbation formulas of the 𝑔 factors for a $5d^7$ ion in trigonal symmetry. The Pt3+ impurity is found to experience an outward displacement by about 0.18 Å away from the centre of the oxygen octahedron along the $C_3$-axis. The calculated g factors based on the above axial displacement show good agreement with the observed values. Importantly, the pending problem of $+3$ valence state of the doped Pt in 𝛼-Al2O3 is theoretically clariﬁed, and the possibility of Pt+ ($5d^9$) is thus excluded in this work.

• Magnetic response of split-ring resonator metamaterials: From effective medium dispersion to photonic band gaps

On systematically investigating the electromagnetic response of periodic split-ring resonator (SRR) metamaterials as a function of the size-to-wavelength ($a/\lambda$) ratio, we ﬁnd that the stop bands due to the geometric resonances of the SRR weaken with increasing ($a/\lambda$) ratio, and are eventually replaced by stop bands due to Bragg scattering. Our study traces the behaviour of SRR-based metamaterials as the resonance frequency increases and the wavelength of the radiation ﬁnally becomes comparable to the size of the unit cell of the metamaterial. In the intermediate stages, the dispersion of the SRR metamaterial can still be described as due to a localized magnetic resonances while Bragg scattering ﬁnally becomes the dominant phenomenon as $a/\lambda \sim 1/2$.

• Measurement of peak ﬂuence of neutron beams using Bi-ﬁssion detectors

Fission fragments and other charged particles leave tracks of permanent damage in most of the insulating solids. Damage track detectors are useful for personal dosimeters and for ﬂux/dose determination of high-energy particles from accelerators or cosmic rays. A detector that has its principal response at nucleon energy above 50 MeV is provided by the ﬁssion of Bi-209. Neutrons produce the largest percentage of hadron dose in most high-energy radiation ﬁelds. In these ﬁelds, the neutron spectrum is typically formed by low-energy neutrons (evaporation spectrum) and high-energy neutrons (knock-on spectrum). We used Bi-ﬁssion detectors to measure neutron peak ﬂuence and compared the result with the calculated value of neutron peak ﬂuence. For the exposure to 100 MeV we have used the iThemba Facility in South Africa.

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