Volume 71, Issue 5

Two new phases of Si 8 C 4 and Si 4 C 8 with the P4 2 /mnm symmetry are proposed. Using first principles calculations based on density functional theory, the structural, elastic, and electronic properties of Si 8 C 4 and Si 4 C 8 are studied systematically. Both Si 8 C 4 and Si 4 C 8 are proved to be mechanically and dynamically stable. The elastic anisotropies of Si 8 C 4 and Si 4 C 8 are studied in detail. Electronic structure calculations show that Si 8 C 4 and Si 4 C 8 are indirect semiconductors with the band gap of 0.74 and 0.15 eV, respectively.

Quantum ion-acoustic oscillations in single-walled carbon nanotubes are studied by employing a quantum hydrodynamics model. The dispersion equation is obtained by Fourier transformation, which exhibits the existence of quantum ion-acoustic wave affected by change of density balance due to presence of positive or negative heavy species as stationary ion clusters and wave potential at equilibrium. The numerical results are presented, and the role of quantum degeneracy, nanotube geometry, electron exchange-correlation effects, and concentration and polarity of heavy species on wave dispersion is pointed out for typical systems of interest.

In this article, we study a relativistic DKP particle in a one-dimensional box. We prove that it is impossible that the wavefunction vanishes completely at the box walls and provides various boundary conditions for this problem.

In this study, the generalised velocity slip and the generalised temperature jump of nanofluid in the flow over a stretching sheet with variable thickness are investigated. Because of the non-adherence of the fluid to a solid boundary, the velocity slip and the temperature jump between fluid and moving sheet may happen in industrial process, so taking velocity slip and temperature jump into account is indispensable. It is worth mentioning that the analysis of the velocity v , which has not been seen in the previous references related to the variable thickness sheet, is presented. The thermophoresis and the Brownian motion, which are the two very important physical parameters, are fully studied. The governing equations are simplified into ordinary differential equations by the proper transformations. The homotopy analysis method (HAM) is applied to solve the reduced equations for general conditions. In addition, the effects of involved parameters such as velocity slip parameter, temperature jump parameter, Prandtl number, magnetic field parameter, permeable parameter, Lewis number, thermophoresis parameter, and Brownian motion parameter are investigated and analysed graphically.

A system proposed by Ito is reconsidered. The corresponding Darboux transformation is presented explicitly. The resulted Bäcklund transformation is shown to be equivalent to the one found by Hirota. Also, a nonlinear superposition formula, which is of differential-algebraic, is obtained.

In the present work, an exponential relationship for the volume dependence of the Anderson–Grüneisen parameter along isotherm and the formulation derived from Tallon’s model have been used to develop a simple theoretical model for the elastic constants as a function of pressure. Applying it to some materials of earth’s mantle at different pressure ranges, the calculated results are in good agreement with the earlier theoretical investigations and available experimental data and thus show that our theory can be applied for predicting the elastic behaviour of earth materials at high pressure.

In this article, we constructed formal Lagrangian of Phi-4 equation, and then via this formal Lagrangian, we found adjoint equation. We investigated if the Lie point symmetries of the equation satisfy invariance condition or not. Then we used conservation theorem to find conservation laws of Phi-4 equation. Finally, the exact solutions of the equation were obtained through the ( G ′/ G , 1/ G )-expansion method.

We study the fourth-order dynamic Euler-Bernoulli beam equation from the Noether symmetry viewpoint. This was earlier considered for the Lie symmetry classification. We obtain the Noether symmetry classification of the equation with respect to the applied load, which is a function of the dependent variable of the underlying equation. We find that the principal Noether symmetry algebra is two-dimensional when the load function is arbitrary and extends for linear and power law cases. For all cases, for each of the Noether symmetries associated with the usual Lagrangian, we construct conservation laws for the equation via the Noether theorem. We also provide a basis of conservation laws by using the adjoint algebra. The Noether symmetries pick out the special value of the power law, which is –7. We consider the Noether symmetry reduction for this special case, which gives rise to a first integral that is used for our numerical code. For this, we then find numerical solutions using an in-built function in MATLAB called bvp4c, which is a boundary value solver for differential equations that are depicted in five figures. The physical solutions obtained are for the deflection of the beam with an increase in displacement. These are given in four figures and discussed.

In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of Mars). The goal of this article has been achieved via using accurate analytical solution to Kepler’s equation in terms of Bessel function. The periodicity property of this solution and its particular values at specified times are discussed through some lemmas. The mathematical conditions of opposition and conjunction of the two planets are formulated. Moreover, the intervals of opposition and conjunction have been determined using the graphs of some defined functions. The calculations reveal that there are nine possible oppositions and conjunctions for Earth and Mars during 20 years started on August 28, 2003. The dates of such oppositions and conjunctions were approximately determined and listed in Tables. It is found that our calculations differ few days from the published real dates of Earth–Mars oppositions due to the neglected effects of the gravitational attraction of other planets in the Solar system on the motion of two planets. The period of 20 years can be extended for any number of years by following the suggested analysis. Furthermore, the current approach may be extended to study the opposition and conjunction of the Earth and any outer planet.

This article deals with the interactions between a central crack and a pair of outer cracks situated at the interface of orthotropic elastic half planes under thermo-mechanical loading. The mixed boundary value problem has been reduced to a pair of singular integral equations which has been solved numerically using Jacobi polynomial method. The interaction effects have been obtained in terms of stress magnification factors depending on the crack spacing and crack length. The phenomena of crack shielding and crack amplification have been depicted through graphs for different particular cases.

In this article, we established abundant local conservation laws to some nonlinear evolution equations by a new combined approach, which is a union of multiplier and Ibragimov’s new conservation theorem method. One can conclude that the solutions of the adjoint equations corresponding to the new conservation theorem can be obtained via multiplier functions. Many new families of conservation laws of the Pochammer–Chree (PC) equation and the Kaup–Boussinesq type of coupled KdV system are successfully obtained. The combined method presents a wider applicability for handling the conservation laws of nonlinear wave equations. The conserved vectors obtained here can be important for the explanation of some practical physical problems, reductions, and solutions of the underlying equations.