• Volume 76, Issue 4

April 2011,   pages  533-690

• Travelling wave solutions to nonlinear physical models by means of the ﬁrst integral method

This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully constructed for the equations considered.

• Bianchi type-I massive string magnetized barotropic perfect ﬂuid cosmological model in bimetric theory

Bianchi type-I massive string cosmological model for perfect ﬂuid distribution in the presence of magnetic ﬁeld is investigated in Rosen’s [Gen. Relativ. Gravit. 4, 435 (1973)] bimetric theory of gravitation. To obtain the deterministic model in terms of cosmic time, we have used the condition $A = (B C)^n$, where n is a constant, between the metric potentials. The magnetic ﬁeld is due to the electric current produced along the 𝑥-axis with inﬁnite electrical conductivity. Some physical and geometrical properties of the exhibited model are discussed and studied.

• Entropy of the Kerr–Sen black hole

We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the ﬁrst law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.

• A transformed rational function method for (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial differential equations.

• Investigation of $\Delta(3,3)$ resonance effects on the properties of neutron-rich double magic spherical ﬁnite nucleus, 132Sn, in the ground state and under compression

Within the framework of the radially constrained spherical Hartree–Fock (CSHF) approximation, the resonance effects of delta on the properties of neutron-rich double magic spherical nucleus 132Sn were studied. It was found that most of the increase in the nuclear energy generated under compression was used to create massive 𝛥 particles. For 132Sn nucleus under compression at 3.19 times density of the normal nuclear density, the excited nucleons to 𝛥s were increased sharply up to 16% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels were calculated and their behaviours under compression were examined. A meaningful agreement was obtained between the results with effective Hamiltonian and that with the phenomenological shell model for the low-lying single-particle spectra. The results suggest considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of 𝛥s in the nuclear dynamics.

• Vibrational analysis of Fourier transform spectrum of the $B^3 \Sigma^-_u (0^+_u) - X^3 \Sigma^-_g (0^+_g)$ transition of 80Se2 molecule

The emission spectra of $B^3 \Sigma^-_u (0^+_u) - X^3 \Sigma^-_g (0^+_g)$ transition of the isotopic species 80Se2, excited in an electrodeless discharge lamp by the microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and 𝑟-centroid values.

• Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reﬂection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no signiﬁcant distortion upon reﬂection. We report Goos–Hänchen shift for all the spots of a higherorder Hermite–Gaussian beam near the critical angle. The shift is shown to be insigniﬁcant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially ﬁnite, s-polarized, full 3D vector beam. We brieﬂy discuss the difﬁculties associated with the paraxial approximation pertaining to a vector Gaussian beam.

• Acoustic wave propagation in $Ni_3 R$ (𝑅 = Mo, Nb, Ta) compounds

The ultrasonic properties of the hexagonal closed packed structured $Ni_3$Mo, $Ni_3$Nb and $Ni_3$Ta compounds were studied at room temperature for their characterization. For the investigations of ultrasonic properties, the second-order elastic constants using Lennard–Jones potential were computed. The velocities $V_1$ and $V_2$ have minima and maxima respectively at 45° with the unique axis of the crystal, while $V_3$ increases with respect to angle with the unique axis of the crystal. The inconsistent behaviour of angle-dependent velocities is associated with the action of second-order elastic constants. Debye average sound velocities of these compounds increase with the angle and has maximum at $55^{\circ}$ with the unique axis at room temperature. Hence, when a sound wave travels at $55^{\circ}$ with the unique axis of these materials, the average sound velocity is found to be maximum. The results achieved are discussed and compared with the available experimental and theoretical results.

• Dielectric relaxation studies in 5CB nematic liquid crystal at 9 GH$_z$ under the inﬂuence of external magnetic ﬁeld using microwave cavity spectrometer

Resonance width, shift in resonance frequency, relaxation time and activation energy of 5CB nematic liquid crystal are measured using microwave cavity technique under the inﬂuence of an external magnetic ﬁeld at 9 GHz and at different temperatures. The dielectric response in liquid crystal at different temperatures and the effects of applied magnetic ﬁeld on transition temperatures are studied in the present work. The technique needs a small quantity (&lt; 0.001 cm3) of the sample and provides fruitful information about the macroscopic structure of the liquid crystal.

• Meyer–Neldel DC conduction in chalcogenide glasses

Meyer–Neldel (MN) formula for DC conductivity ($\sigma_{\text{DC}}$) of chalcogenide glasses is obtained using extended pair model and random free energy barriers. The integral equations for DC hopping conductivity and external conductance are solved by iterative procedure. It is found that MN energy ($\Delta E_{\text{MN}}$) originates from temperature-induced conﬁgurational and electronic disorders. Single polaron-correlated barrier hopping model is used to calculate $\sigma_{\text{DC}}$ and the experimental data of Se, As2S3, As2Se3 and As2Te3 are explained. The variation of attempt frequency $\upsilon_0$ and $\Delta E_{\text{MN}}$ with parameter $(r/a)$, where 𝑟 is the intersite separation and 𝑎 is the radius of localized states, is also studied. It is found that $\upsilon_0$ and $\Delta E_{\text{MN}}$ decrease with increase of $(r/a)$, and $\Delta E_{\text{MN}}$ may not be present for low density of defects.

• Magnetic behaviour of AuFe and NiMo alloys

We study the electronic structure and a mean-ﬁeld phase analysis based on the pair–pair energies derived from ﬁrst-principles electronic structure calculations of AuFe and NiMo alloys. We have used the tight-binding linear mufﬁn-tin orbitals-based augmented space recursion (TB-LMTO-ASR) method to do so. We investigate different behaviours of the two alloy systems by mapping the problems onto equivalent Ising models and then discuss the magnetic phase diagrams using the calculated pair energies. All three phases: paramagnetic, random ferromagnetic and spin glass, have been studied.

• Mismatch of dielectric constants at the interface of nanometer metal-oxide-semiconductor devices with high-𝐾 gate dielectric impacts on the inversion charge density

The comparison of the inversion electron density between a nanometer metal-oxidesemiconductor (MOS) device with high-𝐾 gate dielectric and a SiO2 MOS device with the same equivalent oxide thickness has been discussed. A fully self-consistent solution of the coupled Schrödinger–Poisson equations demonstrates that a larger dielectric-constant mismatch between the gate dielectric and silicon substrate can reduce electron density in the channel of a MOS device under inversion bias. Such a reduction in inversion electron density of the channel will increase with increase in gate voltage. A reduction in the charge density implies a reduction in the inversion electron density in the channel of a MOS device. It also implies that a larger dielectric constant of the gate dielectric might result in a reduction in the source–drain current and the gate leakage current.

• A simpliﬁed approach for the generation of projection data for cone beam geometry

To test a developed reconstruction algorithm for cone beam geometry, whether it is transmission or emission tomography, one needs projection data. Generally, mathematical phantoms are generated in three dimensions and the projection for all rotation angles is calculated. For non-symmetric objects, the process is cumbersome and computation intensive. This paper describes a simple methodology for the generation of projection data for cone beam geometry for both transmission and emission tomographies by knowing the object’s attenuation and/or source spatial distribution details as input. The object details such as internal geometrical distribution are nowhere involved in the projection data calculation. This simple approach uses the pixilated object matrix values in terms of the matrix indices and spatial geometrical coordinates. The projection data of some typical phantoms (generated using this approach) are reconstructed using standard FDK algorithm and Novikov’s inversion formula. Correlation between the original and reconstructed images has been calculated to compare the image quality.

• Bianchi type-V string cosmological models in general relativity

Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s ﬁeld equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s ﬁeld equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019