Volume 70, Issue 9

The dynamics of a flat Friedmann–Robertson–Walker (FRW) cosmological model with a barotropic matter is studied, which is dominated by an oscillating scalar field conformally coupled to the gravity with a scalar potential characterised by multiple vacua. Several motivating consequences are observed and discussed accordingly.

We study a multiple pipe system filled with non-Newtonian fluid being in stationary regime and obeying the power law. Introducing the small parameter ε , being the ratio between the cross-section area and the length of the pipes, we find the effective flow via singular perturbation as ε tends to zero. The flow in each pipe of the system remains in the power-law Poiseuille form governed by the pressure drop between pipe’s end and the junction. Kirchhoff’s law providing the value of pressure at the junction point is derived, and its solvability is discussed. In the vicinity of junction, an interior layer appears, so we correct the asymptotic solution by introducing a non-Newtonian Leray’s problem. The error analysis is also provided.

The nonlinear propagation and interaction of dust acoustic multi-solitons in a four component dusty plasma consisting of negatively and positively charged cold dust fluids, non-thermal electrons, and ions were investigated. By employing reductive perturbation technique (RPT), we obtained Korteweged–de Vries (KdV) equation for our system. With the help of Hirota’s bilinear method, we derived two-soliton and three-soliton solutions of the KdV equation. Phase shifts of two solitons and three solitons after collision are discussed. It was observed that the parameters α , β , β 1 , μ e , μ i , and σ play a significant role in the formation of two-soliton and three-soliton solutions. The effect of the parameter β 1 on the profiles of two soliton and three soliton is shown in detail.

In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation, which describes the motion of a spin-1/2 particle in 1+1 dimensions for mixed scalar–vector–pseudoscalar linear potential are investigated. The Nikiforov–Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms.

Structural, electronic, and superconducting properties of carbides and nitrides of vanadium (V), niobium (Nb), and tantalum (Ta) (group V transition elements) have been studied by computing their electronic band structure characteristics. The electronic band structure calculations have been carried out based on the density functional theory (DFT) within the local density approximation (LDA) by using the tight binding linear muffin tin orbital method. The NaCl-type cubic structures of MN and MC (M=V, Nb, Ta) compounds have been confirmed from the electronic total energy minimum of these compounds. The ground state properties, such as equilibrium lattice constant ( a 0 ), bulk modulus ( B ), and Wigner–Seitz radius ( S 0 ) are determined and compared with available data. The electronic density of states reveals the metallic nature of the chosen materials. The electronic specific heat coefficient, Debye temperature, and superconducting transition temperature obtained from the band structure results are found to agree well with the earlier reported literature.

Applying the truncated Painlevé expansion to the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov (ANNV) system, some Bäcklund transformations (BTs) including auto BT and non-auto BT are obtained. The auto BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion and the related nonlocal symmetry group is presented with the help of the localization procedure. Further, it is shown that the ANNV system has a consistent Riccati expansion (CRE). Stemming from the consistent tan-function expansion (CTE), which is a special form of CRE, some complex interaction solutions between soliton and arbitrary other seed waves of the ANNV system are readily constructed, such as bight-dark soliton solution, dark-dark soliton solution, soliton-cnoidal interaction solutions, solitoff solutions and so on.

With the help of the conditional similarity reduction method, a new family of complex wave solutions with q = lx + my + kt + Γ( x , y , t ) for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on the derived solitary wave solution, some novel complex wave localised excitations are investigated.

Cu–water nanofluid with carbon nanotubes is considered for the peristaltic flow in an endoscope. The peristaltic flow for nanofluid is modelled considering that the peristaltic rush wave is a sinusoidal wave that propagates along the walls of the tube. The governing equations for the proposed model are simplified by using the assumptions of long-wavelength and low Reynolds number. Exact solutions have been evaluated for velocity, temperature, and pressure gradient. Graphical results for the numerical values of the flow parameters, i.e. Hartmann number M, the solid volume fraction ϕ of the nanoparticles, Grashof number Gr, heat absorption parameter β , and radius of the inner tube ε , have been presented for the pressure difference, frictional forces, velocity profile, and temperature profile, and trapping phenomena have been discussed at the end of the article.

Thermotropic hydrogen-bonded ferroelectric binary liquid crystal mixtures comprising of N -carbamyl- l -glutamic acid (CGA) and p-n-alkyloxy benzoic acids (BAO) are investigated. Variation in the molar proportion of X and Y (where X=CGA+5BAO and Y=CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO) comprising of four series yielded 36 binary mixtures. Optical and thermal properties of these mixtures are meticulously studied in the present article. In addition to the traditional phases, a novel smectic ordering namely smectic X* is observed in all the four series. The aim of the investigation is to obtain abundance occurrence of smectic X* with a large thermal span, and hence, the proportions of the binary mixtures are so chosen that the prelude task is accomplished. Optical tilt angle in smectic X* and smectic C* phases is experimentally determined, and a theoretical fit is performed. Phase diagrams of the four series are constructed from the data obtained from the differential scanning calorimetry and correlated with the phases recorded by the polarising optical microscope studies. Thermal stability factor and thermal equilibrium are also premeditated.

In this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n -wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.

In this study, we propose a boundary value problem that contains two arbitrary parameters in the differential equation and show that the results of a number of existing stretching problems (linear, power law, and exponential stretching) are the special cases of the proposed boundary value problem. A two-term analytic asymptotic solution of this problem is developed by introducing a small parameter in the differential equation. Interest lies in the finding of rare exact analytical solutions for the zeroth and first order systems. Surprisingly, only a two-term closed form of analytical solution shows an excellent match with the existing literature. The solution for second-order system is found numerically to improve the accuracy of the approximate solution. The generalised analytic solution is tested over a number of stretching problems for the velocity field and skin friction coefficient showing an excellent match. In conclusion, various stretching problems discussed in literature are special cases of this study.