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Different deterministic solution methods are being used to solve the criticality problem of the reflected systems with different anisotropic behaviours for both fission neutrons and neutrons undergoing scattering. In the present study, the criticality problem is simulated using the developed Monte Carlo algorithm. Different angular distributions, such as Inönü, Anlı–Güngör and tetra-anisotropic kernels are taken into account. For each anisotropic kernel, the sampling method of the direction cosine of either newborn fission neutrons or scattered neutrons is presented by extracting the required probability distribution function (PDF). The simulation starts with an initial guess and following the presented procedure, the criticality thickness of the system is estimated with a certain convergence criterion. Different variance reduction methods, such as implicit capture, Russian-roulette and splitting, are also implemented to get more precise results with a reasonable computational time cost. The validity of the presented method is verified by comparing with the results of different deterministic methods. Finally, using an exact scattering function, the three considered kernels are compared with each other. It is seen that the tetra-anisotropic kernel is the best among the considered kernels.

The current article has identified dual solutions and their stability for the Ti-alloy/water nanofluid over an exponentially shrinking sheet, while taking into consideration the presence of magnetic fields, radiation and thermal buoyancy forces. The Tiwari and Das model has been utilised to formulate mathematical equations, which have subsequently been transformed from partial differential equations to ordinary differential equations using suitable similarity transformations. The transformed equations have been solved using the shooting method incorporated with the Runge–Kutta technique. Through the application of these techniques, it has been ascertained that multiple solutions have emerged for this problem. To assess the stability of these solutions, the eigenvalue approach has been employed. The eigenvalue approach has revealed that only the first solution is physically viable in laboratory settings, while the second solution is not. The effects of radiation on temperature, skin friction, velocity and heat transfer rate have been elaborated upon in detail. Furthermore, flow separation points have been identified and the rationale behind the delay in flow separation has been expounded upon. Streamlined patterns have been drawn and explained to enhance our understanding of the fluid flow behaviour. Finally, it is worth noting that these types of studies have significant applications in the medical and aerospace industries.

Manufacturing of several products with better quality and features in industries depends upon the cooling processes. Based on the thermal properties, this research aims to investigate the effect of dissipative heat in non-Newtonian Jeffrey nanofluid flow along horizontal channels embedded in a porous matrix. Due to cross-diffusion, the time-dependent electrically conducting fluid presents the role of Brownian motion and thermophoresis. Further, the conjunction of binary chemical reactions encourages the flow phenomena. The appropriate choice of the similarity variables helps to transform a dimensional system of the governing equations into their non-dimensional form. Further, the shooting-based Runge–Kuta–Fehlberg method is used to solve the transformed governing equations. The structural behaviour of the characterising constraints is presented via graphs and described briefly. The validation with the earlier result is presented in a particular case showing a good correlation.

In this study, by making use of the direct integral method and the complete discrimination system for the polynomial method, all the travelling wave solutions to the two-component Dullin–Gottwald–Holm (DGH2) system are obtained, including solitary wave solutions, singular periodic solutions and Jacobian elliptic function double periodic solutions. Some of them are initially given. Moreover, concrete examples are presented to make sure that several solutions can be realised, and the corresponding figures are also given to show their nature. This means every solution in the paper may reflect the corresponding natural phenomenon, such as tidal waves and tsunami waves.

The primary goal of this paper is to study a few advantages of bulk nanoparticles of Cu-doped SnO₂ using the solid-state reaction method. Many innovative methods were employed to evaluate the special tuning of the bandgap and other structural and morphological properties of the material. X-ray diffractometer (XRD) confirmed that tin oxide has a rutile-type tetragonal-shaped structure with space group P4₂(/)_mnm. The average crystallite size was calculated which was found to increase from 53 to 80 nm by increasing the Cu-doping from x (=) 0 to x (=) 0.30. SEM images specified that nanoparticles are inhomogeneous and densely close to each other and the average particle size was found to be in the range of ~225–430 nm. Transmission electron microscopy (TEM) images showed the grains present in a few cubic and spherical shapes and grain size was increased (~20–90 nm) with doping of copper in the SnO₂ lattice. UV–Vis spectroscopy showed that the band gap increased from 3.531 to 3.701 eV for pure SnO₂ and Cu-doped SnO₂, respectively. XPS identified the electronic state of Sn as well as Cu atoms as (4^{+}) and (2^{+}), respectively. Raman spectroscopy showed that only three vibrational modes, i.e., A_1g, B_2g and doubly degenerate E_g, exist in a sample.

We investigate quantum non-equilibrium refrigerators with one- and two-qubit systems in a squeezed thermal bath. We characterise their performances in the presence of squeezed heat baths, in terms of their coefficients of performance, cooling rates and figures of merit. Our results show that the performance of the refrigerators is strongly influenced by the squeezing parameter and the number of qubits. The performance of the two-qubit refrigerator (TQR) is found to be better than that of the one-qubit refrigerator (OQR) under the same operating conditions. Our findings suggest that a squeezed thermal bath can be a promising resource for the design of efficient quantum refrigerators in the non-equilibrium regime.

The physical properties of pure and defected ZnSe wurtzite systems were theoretically investigated. From the first-principle study, the wide band gap is 2.7 eV and ZnSe is a non-magnetic direct band-gap semiconductor. The ferromagnetic and antiferromagnetic states are also studied for Fe-doped ZnSe systems. Investigations show that adding iron and the presence of a single Zn vacancy defect leads to the magnetisation of ZnSe. The total energy calculations show that a ferromagnetic state is favourable when Zn is replaced with Fe. The ferromagnetic alignment in the Fe-doped ZnSe wurtzite compound allows it to be in high-spin and half-metallic states. In cases of Zn interstitial and Se vacancy defect in the ZnSe system does not lead to magnetisation. Defect formation energies and Curie temperature of Fe-doped ZnSe systems are estimated from ab-initio calculations.