Volume 74, Issue 11

The bifurcation dynamics and pattern formation of a discrete-time three-species food chain system with Beddington–DeAngelis functional response are investigated. Via applying the centre manifold theorem and bifurcation theorems, the occurrence conditions for flip bifurcation and Neimark–Sacker bifurcation as well as Turing instability are determined. Numerical simulations verify the theoretical results and reveal many interesting dynamic behaviours. The flip bifurcation and the Neimark–Sacker bifurcation both induce routes to chaos, on which we find period-doubling cascades, invariant curves, chaotic attractors, sub–Neimark–Sacker bifurcation, sub–flip bifurcation, chaotic interior crisis, sub–period-doubling cascade, periodic windows, sub–periodic windows, and various periodic behaviours. Moreover, the food chain system exhibits various self-organized patterns, including regular and irregular patterns of stripes, labyrinth, and spiral waves, suggesting the populations can coexist in space as many spatiotemporal structures. These analysis and results provide a new perspective into the complex dynamics of discrete food chain systems.

The present study explores the effects of constant and space-dependent viscosity on Eyring–Powell fluid inside a circular pipe. The heat transfer analysis is also considered. Using the normalised quantities, the governing equations are transformed into dimensionless form, and then the solution of the constructed nonlinear differential equations is calculated. The perturbation method is used to find the analytical expressions of velocity and temperature profiles as a function of pipe radius. The perturbation solution is validated against explicit finite difference numerical method, and errors of each case are plotted. The accuracy in velocity and temperature of finite difference method relative to the perturbation method is of order 10 −2 and 10 −4 , respectively, in both cases of constant and space-dependent viscosity. The effects of various emerging parameters, namely, modified rheological parameter λ(=0.1)$\lambda\;\left({=0.1}\right)$, pressure gradient parameter G(−1≤G≤−0.4)$G\;\left({-1\leq G\leq-0.4}\right)$, rheological parameter ξ(=0.1)$\xi\;\left({=0.1}\right)$ and material parameter E(0.1≤E≤1)$E\;\left({0.1\leq E\leq 1}\right)$ on temperature and velocity fields, are discussed through plots. The heights of both profiles are maximal for the case of constant model as compared to the variable one. The numerical code is also validated with a previous study of Eyring–Powell fluid in a pipe.

The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 < n < 1) flows from the shear-thickening fluid ( n > 1) flows while the Newtonian fluid ( n = 1) flows remain unaffected by this parameter no matter what be the value of S .

In the first article of this series, we have introduced the concept of an atom of space-time-matter (STM), which is described by the spectral action of noncommutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a noncommutative space.

The present work encloses the deposition of three zinc selenide (ZnSe) thin films of thickness 175 nm, 243 nm, and 286 nm using thermal evaporation technique under a vacuum of 5 × 10 −5 mbar. The deposited ZnSe thin films are characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), surface profilometer, ultraviolet (UV)-visible (Vis)-near-infrared (NIR) spectrophotometer and Raman spectroscopic measurements. The structure and morphology measurements reveal that the deposited ZnSe material is nanocrystalline having a cubic structure whose crystallinity increases with an increase in film thickness/evaporation rate. The optical band gap estimated from the optical transmission spectra of the films is found to be 2.62 eV, 2.60 eV, and 2.57 eV, respectively, which decreases with an increase in film thickness. The estimation and polynomial curve fit analysis of refractive index, extinction coefficient, and dielectric constant indicates that these physical quantities are fifth-order polynomial function of wavelength. The obtained results are compared and analysed for justification and application of ZnSe thin films.

Citrate-capped gold nanoparticles (Gnps) have multiple applications in all optical devices and influence the properties of birefringence in liquid crystalline (LC) molecules. In the present paper, systematic studies have been carried out on LC compounds p - n -undecyloxy benzoic acid (11oba) and p - n -dodecyloxy benzoic acid (12oba) with dispersed citrate-capped Gnps in different low molar concentrations. The phase transition temperatures of the LC nanocomposites obtained from polarizing thermal microscopy (POM), differential scanning calorimetry (DSC) and modified spectrometry are found to be reduced with the increase in concentration of dispersed citrate-capped Gnps. The information was obtained from textural data utilizing the simple technique gradient measurement of standard deviation (GMSD) using the MATLAB tool, which is analogous to DSC. Further, the existence of citrate-capped Gnps in 11oba and 12oba was determined by spectroscopic techniques like ultraviolet-visible spectrometry and scanning electron microscopy. The birefringence measurements were carried out at different wavelengths (460, 500, 570 and 635 nm) using a wedge-shaped cell with a modified spectrometer. The birefringence ( δ n ) increases with increase in weight concentration of citrate-capped Gnps in the nematic thermal range. Further, the order parameter S values obtained from the Kuczynski internal field model, the Vuks model, the Haller extrapolation model and the effective geometry parameter methods are in good agreement. It is found that the order parameter S increases with increase in dispersion of concentration of citrate-capped Gnps. This is due to strong Van der Waal’s interaction between the LC molecules and citrate-capped Gnps, which increases the alignment of the LC molecules.

This study adopts density functional theory to predict and thoroughly investigate new types of perovskite compounds for solid state storage of hydrogen. CaTiH 3 and MgTiH 3 perovskite hydrides are chosen and investigated using density functional theory in terms of ground state properties, electronic, mechanical, and thermodynamic properties for solid state storage of hydrogen. Stability of compounds are verified by calculating formation energies. Several crucial parameters; elastic constants, bulk, Young, Shear modulus, and Cauchy pressures are computed and analysed in great detail. Mechanical stability evaluation indicated that both compounds are mechanically stable whereas MgTiH 3 is ductile whilst CaTiH 3 is a brittle material. In addition, mechanical anisotropy is analysed using 2D surfaces. Both compounds showed anisotropic behaviour in all directions except for linear compressibility. Electronic band structures and their corresponding density of states of compounds are obtained. The results indicate that both compounds have metallic nature. From the results presented here, it can be predicted that MgTiH 3 is a better material for hydrogen storage with a gravimetric density of ∼4.01 wt %.

In this article, we study about the absorption properties of terahertz (THz) wave in the magnetic plasma medium. Terahertz wave has strong transmission in plasma. Generally speaking, with the increase in THz wave frequency, the transmission in plasma is stronger. Thus, we can consider raising carrier frequency to THz band to solve the communication of “blackout.” We found that the absorption in magnetic plasma is greatly affected by magnetic field. The changes on the power absorption coefficient of the two kinds of eigen wave in magnetic plasma vary with how the outside magnetic field, incident angle, and the thickness of the plasma are obtained. The study found that following the increase in magnetic field, the absorption of left circularly polarised waves (L-wave) gradually reduces, and the right circularly polarised waves (R-wave) will produce two absorption peaks, and these two absorption peaks move to high frequency as a whole. With the increase in incident angle and the high spectrum absorption of L-wave enhancement, the reflection between the two absorption peaks of R-wave broadens. The reflection area on the left side of the low-frequency area to absorb has a little change. The absorption on the right side of the high-frequency area is enhancement. With the increase in the plasma thickness, the L-wave absorption peak on the right side of the high-frequency area absorbs enhancement; the R-wave reflection between the two absorption peak areas is impregnability, the second absorption peak absorption enhancement on the right side of the high-frequency area. The study has shown the different absorption mechanisms of the L-wave and the R-wave and shown different absorption features in magnetic plasma.

The mechanical and electronic properties of o -BC 6 N are studied by using first-principles calculations. The anisotropy studies of Young’s modulus, shear modulus and Poisson’s ratio show that o -BC 6 N exhibits a large anisotropy. Electronic structure study shows that o -BC 6 N presents metallicity under the conditions of zero and high pressure.