Volume 72, Issue 4

The study of new integrable defects leads to new type of Bäcklund transformations named as the type-II Bäcklund transformations. In this article, we show, for the MKdV hierarchy, that the type-II Bäcklund transformation is the compound type-I Bäcklund transformation.

The influence of pressure on the elastic and mechanical properties of the hexagonal transition-metal dichalcogenide WS 2 is investigated using the first-principles calculations. With the increase in pressure, the lattice parameters and the volume of WS 2 decrease, which is exactly in agreement with the available experimental data and other calculated results. The elastic constants C ij , bulk modulus B , shear modulus G , Young’s modulus E , and Poisson’s ratio σ of WS 2 also increase with pressure. At last, for the first time, the band gaps of energy, the partial density of states, and the total density of states under three different pressures are obtained and analysed. It is found that the band gap of WS 2 decreases from 0.843 to 0 eV when the external pressure varies from 0 to 20 GPa, which implies that WS 2 may transform from semiconductors to semimetal phase at a pressure about 20 GPa.

For the first time, it has been proposed to study the processes of caking nonmetallic powders containing quadrupole nuclei using the distribution of the spin–lattice and spin–spin relaxation times in NQR. The results of experimental studies of the effect of caking samples on the distributions of relaxation times of T 1 and T 2 for the 14 N NQR in powders of NaNO 2 and C 6 H 12 N 4 are presented.

The rational and semirational solutions in the Boussinesq equation are obtained by the Hirota bilinear method and long wave limit. It is shown that the rational solutions contain dark and bright rogue waves, and their typical dynamics are analysed and illustrated. The semirational solutions possess a range of hybrid solutions, and the hybrid of rogue wave and solitons are demonstrated in detail by the three-dimensional figures. Under certain parameter conditions, a new kind of semirational solutions consisted of rogue waves, breathers and solitons is discovered, which describes the dynamics of the rogue waves interacting with the breathers and solitons at the same time.

The investigation of liquid bridge force acting between wet particles has great significance in many fields. In this article, the exact solution of capillary force between two unequal-sized spherical particles is investigated. Firstly, The Young-Laplace equation with moving boundary is converted into a set of ordinary differential equations with two fix point boundary using variable substitution technique, in which the gravity effects have been neglected. The geometry of the liquid bridge between two particles is solved by shooting method. After that, the gorge method is applied to calculate the capillary-bridge force that is consists of contributions from the capillary suction and surface tension. Finally, the effect of various parameters including distance between two spheres, radii of spheres, and contact angles on the capillary force are investigated. It is shown that the presented approach is an efficient and accurate algorithm for capillary force between two particles in complex situations.

The structural stabilities of cobalt mononitride (CoN) and nickel mono-nitride (NiN) were investigated among the crystal structures, namely, NaCl (B1), CsCl (B2), and zinc blende (B3). It was found that the zinc blende (B3) phase was the most stable phase for both nitrides. A pressure-induced structural phase transition from B3 to B1 phase was predicted in these nitrides. The computed lattice parameter values were in agreement with the experimental values and other theoretical values. The electronic structures reveal that these nitrides are metallic at zero pressure. The computed elastic constants indicate that CoN and NiN are mechanically stable in the B1 and B3 phases. The variations of the elastic constants, bulk modulus, shear modulus, Poisson’s ratio, and elastic anisotropy factor with pressure were investigated. The Debye temperature θ D values are reported for both the nitrides in their B1 and B3 phases. The high-pressure NaCl phase of both CoN and NiN were found to be ferromagnetic.

The Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

Abstract: In this article, a generalized Darboux transformation for the fourth-order nonlinear Schrödinger equation is constructed in terms of Darboux matrix method. Subsequently, breathers and the Nth-order rogue wave solutions of this equation are explicitly given in the light of the obtained Darboux transformation. Finally, we concretely discuss the dynamics of the obtained rogue waves, which are also demonstrated by some figures.

In this article, we propose an approach to measure solution concentrations by using photonic crystal cavities. Based on the experimental data, the refractive index of a NaCl solution is proportional to the concentration. Filling the proposed photonic crystal cavity with a NaCl solution, we calculate the spectral transmission using the transfer matrix method. We found that the cavity transmittance was proportional to the refractive index of the NaCl solution, and thus we obtained a linear relationship between cavity transmittance and the concentration of the NaCl solution. The formula was found by fitting the simulation results with experimental data. Such a formula can be applied to the measurement of an unknown concentration of NaCl solution utilizing a photonic crystal cavity.

Abstract: The potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere have been investigated. The multiplier approach yields two local conservation laws for the Prandtl boundary layer equations on the surface of a sphere. Two potential variables ψ and ϕ are introduced corresponding to first and second conservation law. Moreover, another potential variable p is introduced by considering the linear combination of both conservation laws. Two level one potential systems involving a single nonlocal variable ψ or ϕ are constructed. One level two potential system involving both nonlocal variables ψ and ϕ is established. The nonlocal variable p is utilised to derive a spectral potential system . The nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere are derived by computing the local conservation laws of its potential systems. The nonlocal conservation laws are utilised to derive the further nonlocally related systems.

The adiabatic compressibility, β , of the immiscible liquid mixture 0.52 LiCl+0.48 AgBr (the top of the miscibility gap) was experimentally investigated in the temperature range from the melting point to the critical mixing temperature using the sound velocity values, u , measured by the pulse method, and the density quantities, ρ , which were determined using the hydrostatic weight procedure based on the relationship β=u − 2 ρ − 1 . It is shown that the coefficients of the temperature dependencies for the compressibility and density of the upper and lower equilibrium phases have opposite signs because of the superposition of the intensity of the thermal motion of the ions and the change in the composition of the phases. The differences, ∆β and ∆ρ , in the magnitudes of the compressibility and density for the equilibrium phases decrease with temperature elevation. The temperature dependencies of the compressibility and density difference are described using the empirical equations ∆ β ≈( T c – T ) 0.438 and ∆ ρ ≈( T c – T ) 0.439 .

Abstract: The authors considered the bulk viscous fluid in f ( R , T ) gravity within the framework of Kaluza–Klein space time. The bulk viscous coefficient ( ξ ) expressed as ξ=ξ0+ξ1a˙a+ξ2a¨a˙,$\xi = {\xi _0} + {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}},$ where ξ 0 , ξ 1 , and ξ 2 are positive constants. We take p =( γ −1) ρ , where 0≤ γ ≤2 as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of f ( R , T )= R +2 f ( T ), where f ( T )= λT , λ is constant. We studied the cosmological model in two stages, in first stage: we studied the model with no viscosity, and in second stage: we studied the model involve with viscosity. The cosmological model involve with viscosity is studied by five possible scenarios for bulk viscous fluid coefficient ( ξ ). The total bulk viscous coefficient seems to be negative, when the bulk viscous coefficient is proportional to ξ2a¨a˙,${\xi _2}{{\ddot a} \over {\dot a}},$ hence, the second law of thermodynamics is not valid; however, it is valid with the generalised second law of thermodynamics. The total bulk viscous coefficient seems to be positive, when the bulk viscous coefficient is proportional to ξ=ξ1a˙a,$\xi = {\xi _1}{{\dot a} \over a},$ξ=ξ1a˙a+ξ2a¨a˙$\xi = {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}}$ and ξ=ξ0+ξ1a˙a+ξ2a¨a˙,$\xi = {\xi _0} + {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}},$ so the second law of thermodynamics and the generalised second law of thermodynamics is satisfied throughout the evolution. We calculate statefinder parameters of the model and observed that it is different from the ∧CDM model. Finally, some physical and geometrical properties of the models are discussed.

Tungsten sulfide (WS 2 ) nanoflakes were successfully prepared via electrospinning with polyvinylpyrrolidone (PVP) as organic solvent. In addition, Ag-deposited WS 2 (Ag-WS 2 ) was obtained by chemical blending/calcination method. The structure and morphology of as-prepared materials were characterised by powder X-ray diffraction (XRD) and scanning electron microscope (SEM), respectively. The XRD result shows that the prepared WS 2 has a graphene-like structure with P 63/mmc space group symmetry. The SEM illuminates that the sensing samples have nanoflake appearance. Furthermore, heater-type gas sensors were fabricated based on WS 2 and Ag-WS 2 nanomaterials. The sensing responses of WS 2 and Ag-WS 2 on the ammonia (NH 3 ), ethanol (C 2 H 5 OH), and acetone (C 3 H 6 O) were investigated at about 220°C. The results indicate that gas sensor based on WS 2 and Ag-WS 2 nanoflakes has 60 ppm sensing threshold value for ammonia. One possible gas sensing mechanism of WS 2 and Ag-WS 2 gas sensors is surface control via charge transfer.

In this article, structural properties and bonding behaviours of codoped lanthanum chromites (La 0.8 Ca 0.2 )(Cr 0.9− x Co 0.1 Cu x )O 3 ( x =0.00, 0.03, and 0.12) were investigated in detail. Polycrystalline chromite samples (La 0.8 Ca 0.2 )(Cr 0.9− x Co 0.1 Cu x )O 3 ( x =0.00, 0.03, and 0.12) were prepared by a standard solid-state reaction process. The synthesised samples were characterised for their structural, morphological, optical, and magnetic properties using powder XRD, SEM/EDS, UV–Vis, and VSM. XRD data showed that the samples were crystallised into a single phase with orthorhombic structure. Powder profile refinement analysis suggested the reduction in lattice parameters and cell volume with the addition of Cu. The electron density distributions and the bonding features of the prepared samples have been investigated using maximum entropy method (MEM). The mid bond electron density values revealed the enhancement of ionic nature between lanthanum and oxygen ions and a reduction in covalent nature between chromium and oxygen ions. Heterogeneous distribution of particles with different sizes was observed through SEM micrographs. EDS spectra confirms the presence of constituent elements in the prepared samples. Optical band gap values are decreasing with the addition of Cu. Antiferromagnetic ordering was observed from M–H curves obtained at room temperature. The structural and the magnetic properties are correlated.