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In this work, the exact travelling wave solutions to the forced Korteweg–de Vries (fKdV) equation with different force terms are studied with the help of symbolic computations. This equation is derived from a straightforward mathematical model that describes the behaviour of a shallow fluid layer when influenced by external forces. The fKdV equation has many applications in diverse fields, including fluid dynamics, plasma physics, soliton theory and mathematical physics, for modeling wave propagation and nonlinear phenomena under the influence of external forces. Solitary wave solutions for this equation have been derived using three distinct techniques: the extended ((G^prime / G))-expansion method, the Kudryashov method and the ((1/G^prime ))-expansion method. As a result, several new solutions have been achieved which are in the form of hyperbolic, trigonometric, rational and exponential functions. Finally, the effects of different time-dependent external forces have been studied by presenting 3D, 2D and contour plots. It can be seen that the external forces affect the background and speed of solitary waves. The results could be expected to be helpful in understanding the propagation of solitary waves subjected to external forces.

Growth of 4-N-N-dimethylamino-4(^prime )-N(^prime )-methyl-stilbazolium tosylate (DAST), 4-chloro-N-methyl 4-stilbazolium tosylate (CMST) and 4-bromo-N-methyl 4-stilbazolium tosylate (BMST) crystals by slope nucleation technique using mixed solvents are reported. Investigation on compositional, structural, thermal, luminescent and dielectric properties of these crystals were studied. Purity and the crystal quality are analysed using NMR and XRD. The thermal stability of the crystals is studied in detail from the TG-DTA. Emission characteristics are examined by photoluminescence spectra. Finally, 800 nm wavelength of 140 and 50 fs duration of pulses obtained from Ti:sapphire oscillator and amplifier were used for the measurement of refractive indices and absorption coefficients and generation of terahertz (THz) radiation. The conversion efficiency of DAST, CMST and BMST with respect to incident laser power of 150 mW were of the order of (0.67 times 10^{-4}), (0.826times 10^{-4}) and (0.947 times 10^{-4}), respectively. Finally, the significance of effective polarisability in THz generation has been demonstrated in terms of rotational angle (theta ).

Researchers have made many efforts to store energy in forms that can be turned into required forms. Energy storage minimises the gap between supply and demand for energy while increasing energy systems’ effectiveness and dependability. Latent heat storage (LHS) can be used to store energy efficiently. This article explores the numerical analysis of the solidification procedure for latent heat thermal energy storage (LHTES) in a triplex chamber. TiO(_2)–Al(_2)O(_3) nanoparticles were used as hybrid nanoparticles and water was used as a phase change material (PCM). FlexPDE, a general-purpose scripted finite-element software, was used to discretise and solve the partial differential governing equations. The study investigated the impact of various factors on the contour of solid fraction, temperature distribution, average temperature, solid fraction diagram and the overall energy of the system. These factors encompassed the volume fraction of nanoparticles, the presence of fins, thermal radiation and the shape factor of nanoparticles. Moreover, the optimal values for the full solidification time (FST) were established using the response surface methodology (RSM). The findings indicate that full solidification time is optimised when the hybrid nanoparticle volume fraction is 0.048, thermal radiation is 0.777 and shape factor is 15.29.

Theoretical analysis of electron transport behaviour in carbon nanotube/high-density polyethylene (CNT/HDPE) composites successfully predict the strain conduction behaviour in CNT/HDPE nanocomposites. The conductivity below the percolation threshold can well be explained by the tunnelling conduction mechanism which can be explained as follows: The potential field within the connection is determined by the effective potential of the ideal polymeric solid. Certain assumptions have been made, such as treating the electrons in CNT sheets as free particles. As a result, the potential within the CNT sheets is close to zero. Additionally, the polyethylene (PE) insulating layer in the CNT–PE–CNT junction is assumed to act as a rectangular potential barrier in one-dimensional electrical fields along the x-axis. This resulted in finding a direct correlation between strain and the separation distance of the carbon nanotubes (CNTs). As the strain level rises, the gap between the CNTs widens, eventually reaching a critical threshold where they become no longer conductive.

It is hard to explain low-mass strange stars. In this paper, we have modelled these low-mass strange stars using the Tolman IV metric in ((2+1)) dimensions. We found that the presence of attractive or positive anisotropic force is the cause for the lower mass of the strange stars in our model. We have also found that the cosmological constant has a significant role in the mass–radius relationship of the stars. We have used our model to predict the radius of a few low-mass strange stars. Our approach is helpful for predicting the crucial parameters of the low-mass strange stars.

Thermodynamical systems having negative heat capacity are characterised by peculiar behaviours, yet they have been reported in several systems ranging from large to nanoscales. We show that negative heat capacity may arise in low-dimensional/nano quantum oscillators due to strong electron correlations observed in underdoped cuprates and quantum wells with negative density of states which emerge in several quantum systems including mesoscopic systems.

The squeezing of an incompressible magnetohydrodynamic (MHD) fluid between two parallel plates is a primary type of flow that is commonly observed in several hydrodynamical tools and machines. Compression and injection molding, polymer processing and modelling of lubrication systems are several practical examples of squeezing flows. The aim of the present work is to compute the heat and mass transfer on MHD squeezing flow of a viscous fluid through a porous medium using Bernoulli wavelet numerical method. Mathematically simulating the flow results in a highly nonlinear coupled ordinary differential equation (ODE) by combining conservation laws and similarity transformations. Our outcome illustrates that the Bernoulli wavelet method is immensely capable and accessible for finding solutions to this type of coupled nonlinear ODEs. The results are in very good agreement for coupled nonlinear ODEs in engineering applications. The plots clarify and thoroughly illustrate the flow behaviour when the physical factors are involved. The normalisation of the flow behaviour by the magnetic field show that it may be utilised to control various flows. Moreover, the squeeze number affects the velocity, temperature and concentration profiles, which is a crucial factor in these kinds of issues.

We study exchange interaction between two magnetic impurities, i.e. the Ruderman–Kittel–Kasuya–Yosida (RKKY), in doped germanene layer by directly computing Green’s function within the full band method. Kane–Mele model Hamiltonian in the presence of spin–orbit coupling and longitudinal magnetic field has been applied to describe electron dynamics. The behaviour of RKKY interaction as a function of distance between the localised moments has been analysed for different values of magnetic field and spin–orbit coupling strength for electrons. Also, the effects of electron doping as the variation of chemical potential on behaviours of RKKY interaction have been investigated. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to an XXZ model interaction between two magnetic moments. The exchange interaction along the arbitrary direction between two magnetic moments has been obtained using the static spin susceptibilities of doped germanene layer in the presence of spin–orbit coupling. The effects of magnetic field, electron doping and spin–orbit coupling on the dependence of exchange interaction on distance between moments are investigated by calculating the correlation function of the spin density operators. Our results show that the electron doping impacts the spatial behaviour of RKKY interaction. Moreover, spin–orbit coupling effects on both longitudinal and transverse RKKY interactions have been investigated for doped germanene monolayer. Finally, we have studied in detail the temperature dependence of RKKY interactions for various amounts of spin–orbit coupling strengths.

The unsteady flow of fluids is crucial for real-world applications, efficiency and performance optimisation in various sectors, such as engineering, environmental impact research and developing technologies. Shape of nanoparticles in hybrid nanofluids is important for optimising energy applications and customising the performance of the nanofluid as it has effect on heat transport, material characteristics and stability. Considering the importance of unsteady flow and the shape factor of the nanoparticles, the present study aims to explore the solution of the unsteady flow problem of hybrid nanofluid over a stretching surface embedded within the porous medium. This study deals with the shape factor analysis by considering four shapes: brick, lamina, platelet and blade. The Legendre wavelet collocation technique is implemented to obtain the solution of the problem. It is revealed by creating a pie chart that the thermal conductivity is found to be maximum for lamina-shaped nanoparticles (i.e., 32%) while it is minimum for brick-shaped nanoparticles (i.e., 20%). The rate of heat transfer enhancement is also presented by the waterfall graph. The graph disclosed that on increasing the volume fraction of TiO(_2) from 1 to 10%, the rate of heat transfer is enhanced by 39.63%. The velocity profiles are inversely related to the temperature-dependent viscosity and velocity slip parameter.

The proper utilisation of the coating fluid is crucial for ensuring the effectiveness of the wire coating process. Its complexity and importance make it the central focus of the present study. Also, understanding wire coating processes is important for ensuring product performance, cost efficiency, regulatory compliance, customer satisfaction, innovation and environmental sustainability. By optimising the coating processes, manufacturers can produce high-quality wire products that meet market demands while minimising negative impacts on the environment and resources. The objective is to assess the quality and performance of the wire coating process by examining the fluid flow characteristics within the die. Therefore, a mathematical model is devised to study the rheological properties of Sisko fluid with a constant pressure gradient in an unsteady state. The governing equation with oscillating boundary constraints is converted into dimensionless form and solved numerically using the method of lines (MoL) technique. The findings are presented through 2D and 3D plots. Response surface methodology (RSM) is implemented to investigate the statistical significance and sensitivity of the parameters and to optimise the shear stress rate.