Volume 71, Issue 9

We first introduced a linear stationary equation with a quadratic operator in ∂ x and ∂ y , then a linear evolution equation is given by N -order polynomials of eigenfunctions. As applications, by taking N =2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N =3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N =2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N =3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

In this article, we present results of the first-principle study of the structural, electronic, and optical properties of the InN, InP binary compounds and their related ternary alloy InN x P 1– x in the zinc-blend (ZB) phase within a nonrelativistic full potential linearised augmented plan wave (FP-LAPW) method using Wien2k code based on the density functional theory (DFT). Different approximations of exchange–correlation energy were used for the calculation of the lattice constant, bulk modulus, and first-order pressure derivative of the bulk modulus. Whereas the lattice constant decreases with increasing nitride composition x . Our results present a good agreement with theoretical and experimental data. The electronic band structures calculated using Tran-Blaha-modified Becke–Johnson (TB-mBJ) approach present a direct band gap semiconductor character for InN x P 1– x compounds at different x values. The electronic properties were also calculated under hydrostatic pressure for ( P =0.00, 5.00, 10.0, 15.0, 20.0, 25.0 GPa) where it is found that the InP compound change from direct to indirect band gap at the pressure P ≥7.80 GPa. Furthermore, the pressure effect on the dielectric function and the refractive index was carried out. Results obtained in our calculations present a good agreement with available theoretical reports and experimental data.

In this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method. N -soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.

We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G ′/ G -expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.

In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens’s nonlocal-in-time kinetic energy approach, which is motivated from Feynman’s kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.

The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.

Transition-metal light-element compounds are currently raising great expectations for hard and superhard materials. Using the widely attracting osmium (Os) and its borides (OsB, Os 2 B 3 and OsB 2 ) as prototypes, we demonstrate by first-principles calculations that heavy transition metals, which possess high stiffness but low hardness, can be converted into highly hard materials by incorporating of light elements to form compounds. Such a crossover is a manifestation that the underlying sources of high stiffness and high hardness are fundamentally different. The stiffness is related to elastic deformation that is closely associated with valence electron density, whereas the hardness depends strongly on plastic deformation that is determined by bonding nature. Therefore, the incorporation of light atoms into transition metal should be a valid pathway of designing hard and superhard materials. This strategy is in principle also applicable to other transition-metal borides, carbides, and nitrides.

The present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

Propagation of magnetoplasma waves at an angle to a static magnetic field is studied for a random distribution of spherical metallic nanoparticles. A general analytical expression for dispersion relation of the system is derived and useful expressions are obtained in the limiting cases. It is found that the interaction between longitudinal and transverse modes leads to coupled modes in the vicinity of the frequency f + ξωp,$\sqrt {f\, + \,\xi } {\omega _p},$ where ξ is the ratio of the volume occupied by all the nanoparticles to the entire volume, ω p the plasma frequency of electrons inside a nanoparticle, and f a geometrical factor of order unity (1/3 for spherical nanoparticles).

We construct the differential invariants of Lie symmetry pseudogroups of the (2+1)-dimensional breaking soliton equation and analyze the structure of the induced differential invariant algebra. Their syzygies and recurrence relations are classified. In addition, a moving frame and the invariantization of the breaking soliton equation are also presented. The algorithms are based on the method of equivariant moving frames.

By the homotopy renormalisation method, the global approximate solutions to Falkner-Skan equation and Von Kármá’s problem of a rotating disk in an infinite viscous fluid are obtained. The homotopy renormalisation method is simple and powerful for finding global approximate solutions to nonlinear perturbed differential equations arising in mathematical physics.

We investigate the reflection of massive particles from moving mirrors. The adoption of the formalism based on the energy-momentum allowed us to derive the most general set of formulas, valid for massive and, in the limit, also for massless particles. We show that the momentum change of the reflecting particle always lies along the normal to the mirror, independent of the mirror speed. The subject is interesting not only to physicists designing concentrators for fascicles of massive particles and electron microscopes but also to computer scientists working in raytracing operating in the photon sector. The paper, far from being only theoretical, has profound and novel practical applications in both domains of engineering design and computer science.