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The model of a stochastic Lorentz-correlated beam (SLCB) is produced, and the equations of such a beam in an anisotropic turbulent ocean are investigated. The properties of such beams in an anisotropic turbulent ocean are discussed based on the numerical results. The intensity of an SLCB with smaller (delta) will evolve into the Lorentz distribution faster, and such beams in an anisotropic turbulent ocean can evolve into Gaussian beams as (z) increases. The depolarisation effect of an SLCB in an anisotropic turbulent ocean is seen. The study can be useful in the study of the Lorentz-correlated beam in an anisotropic turbulent ocean.

This research utilises the Lie group method of point transformations to obtain generalised invariant solutions for the extended (3+1)-dimensional dispersive Kairat-X equation, initially formulated by Wazwaz, which models the trajectory of optical pulses in fibre optics. This study systematically determines the Lie point symmetries, the corresponding vector fields and commutation relations associated with the equation. Through various symmetry reductions, the equation was transformed into the governing nonlinear ordinary differential equations (ODEs). The derived solutions are more generalised, incorporate arbitrary functions and exhibit distinct characteristics compared to the previously established results. Additionally, a comparative analysis was conducted wherever applicable. Furthermore, this study explores the dynamic behaviour of these solutions, illustrating phenomena such as single-soliton annihilation, nonlinear wave evolution and curved multisoliton structures through their profiles.

This paper investigates families of novel exact soliton solutions in the form of hyperbolic, rational, exponential, trigonometric functions and their combinations for a continuous model of cold bosonic atoms in a zig-zag optical lattice via modified generalised exponential rational function method. The continuous model has been derived from the discrete model using the continuum approximation. The 3D, 2D and density graphs of the amplitude profile of the periodic, dark and bright singular solitons are plotted for analysing the effect of first-nearest-neighbour (FNN) hopping, second-nearest-neighbour (SNN) hopping, the strength of the boson–boson interaction, boson number and group velocity dispersion coefficient. As the value of FNN enhances, the soliton amplitude increases, while the shapes of the amplitude profile remain preserved. Further, modulation instability (MI) in the continuous model is investigated. The MI gain is studied against the wave number, FNN hopping, SNN hopping, boson number and initial incidence power. The effect of SNN hopping is higher than the effect of FNN hopping. It is observed that the proper choice of the parameters can manage the soliton solutions and MI for the continuous model.

The main cause of global warming is carbon dioxide ((hbox {CO}_2)) emissions, acting as a significant greenhouse gas. These emissions stem from various sources and significantly contribute to climate change. Fortunately, we have countermeasures like carbon taxes to curb (hbox {CO}_2) output. Carbon taxes incentivise a reduction in (hbox {CO}_2) production and a shift towards cleaner energy sources by placing a cost on emissions. This paper investigates the interplay between carbon tax policy, carbon emissions, economic output (GDP) and renewable energy consumption. A system of differential equations is constructed to model these relationships based on a comprehensive literature review. Parameter estimation based on real-world data yielded successful fits for the variables. However, the fit for the carbon tax equation is less conclusive, suggesting a more complex relationship with carbon emissions. Stability analysis and the boundedness of the system are carried out. Auto-regressive integrated moving average (ARIMA) forecasting is employed to predict future trends. The results suggest a projected increase in GDP and renewable energy consumption over the next ten years, indicating a potential for a cleaner energy transition. Furthermore, the forecasts anticipate a rise in carbon tax implementation. This analysis emphasises how important carbon taxes are for cutting emissions and advancing renewable energy. Results indicate that carbon taxes can promote decarbonisation and economic growth, despite the complicated link between them and (hbox {CO}_2) emissions. Both GDP growth and the use of renewable energy are anticipated to increase. However, policies must be improved to combat climate change effectively. Future studies should improve parameters and investigate other relevant elements to promote a low-carbon future.

The Ebola virus disease (EVD) poses a significant threat to public health due to its rapid transmission and high mortality rate. Accurate modelling for the comprehension of transmission of this malady is essential for planning effective containment and its outcome strategies. In this work, we analyse a four-dimensional compartmental model (susceptible, infectious, deceased, recovered) of EVD to understand its epidemiological behaviour. To enhance the predictive power and accuracy of the model, artificial intelligence (AI) technique, a specifically supervised neural network using Levenberg–Marquardt backpropagation recurrent neural network (L-MBRNN), is applied. Reference solutions are obtained using Runge–Kutta method. The AI-based approach is validated by comparing with numerical solutions, statistical analysis and absolute error assessment to confirm the reliability and precision of the applied method. This fusion of biological modelling and machine learning provides a robust framework for investigating the dynamics of Ebola.

In the present work, we made a comparative study of (f(R,{mathcal {T}})) gravity over general gravity regarding the parameter estimation of the strange star. For this purpose, we used the Durgapal IV metric as the inner space–time of the strange star. In this work, we applied (f(R,{mathcal {T}})=R+2beta {mathcal {T}}) where R is the Ricci scalar, ({mathcal {T}}) is the trace of the energy–momentum tensor and (beta ) is the coupling term between them. For the isotropic model of the compact star, the field equations were solved and the corresponding astrophysical aspects were discussed. We have shown that a sharp difference arise on the physical parameters like central density ((rho _{0})), central pressure ((p_{0})), surface redshift ((Z_{s})), compactness and radius of the compact stars 4U 1702-429, 2A 1822-371, PSR J1756-2251, PSR J1802-2124 and PSR (J1713+0747) in two distinct gravity theories.

The interest in zinc oxide (ZnO) has reached saturation; however, some issues remain overlooked. Specifically, activities in spintronics and optoelectronics involving doped ZnO are of particular interest, and the lack of consensus in the results obtained draws attention. Doping with Cu is unique because it has no vacancies in its 3d orbitals, but the presence of a single unoccupied state in the 4 s orbital offers intriguing properties. ZnO is known for its characteristic blue–green emission, but over the decades, there has been a significant shift towards more intense yellow–orange bands. Typically, ZnO emits blue–green spectra due to its large bandgap; however, a clear shift towards more intense spectral features requires explanation. The deconvoluted spectra of photoluminescence (PL) clearly reveal this characteristic, highlighting Cu's effect on the local electronic environment of Zn. To investigate the impact of Cu doping on the local electronic structures, X-ray absorption near-edge spectroscopy (XANES) was performed at the K-edge for both the transition element in the nanocrystalline powdered samples of Cu-doped ZnO (ZCO). The local electronic structures were modelled theoretically using Fourier-transformed extended X-ray absorption fine structures (FT-EXAFS) based on the XANES data. The EXAFS simulation achieved excellent agreement up to two shells of the Brillouin zone, confirming the substitutional effect of Cu and providing deeper insight into the local coordination geometry of ligand formation. Defects play a crucial role in determining and shifting emission bands in the visible spectrum, explicitly observed through oxygen vacancies (V_O). The correlation between different oxidation states of Cu significantly influences the percolation of defect formation, which could be crucial for understanding the desired emission bands.

This paper presents a piecewise Duffing map (PDM) model that introduces piecewise nonlinearity to the classic Duffing map and explores its rich dynamical behaviour, including bistable periodic oscillations, bistable periodic doubling and bistable(/)monostable chaotic characteristics. By incorporating two constant parameters in the PDM’s rate equations, the authors demonstrate the ability to flexibly control the amplitude of the chaotic sequences, with total amplitude control achieved by introducing an additional parameter. The dynamical characteristics of the PDM are validated through microcontroller implementation and the chaotic properties of the PDM are leveraged to develop a pseudo-random number generator (PRNG) with a linear feedback shift register (LFSR) as a post-processing unit. The randomness of the generated binary data is extensively tested using the NIST 800-22 test suite, confirming the suitability of the PDM-based PRNG for applications such as secure communication schemes and other chaos-based applications.

The applications of thermal transport through highly viscous fluids are observed in chemical and industrial engineering. With the inspiration of existing non-Newtonian fluids in chemical industries, the objective of the present study is to regulate the fluid temperature and improve the convective heat transfer in Carreau fluid by choosing a suitable power-law index and magnetic field. In this paper, two separate models of equations are presented based on the fluid phase and particle phase by using the Carreau fluid tensor. The dimensional equations are transformed into dimensionless form by applying the right transformation and the closed-form solution is generated through Mathematica 14.2. The computational results showed that the power-law index diminished the velocity and temperature fields. Moreover, the velocity and temperature of the pseudoplastic fluid are greater than those of the dilatant fluid. Further, the two-phase fluid model gives a higher heat transfer rate than the single-phase fluid model. It is observed that the dilatant fluid is the best option for the suspension of two-phase flow. The current computational results are expected to extend our understanding of two-phase flows of Carreau fluid and help to design innovative microfluidic devices with boosted performance for various industrial applications. Furthermore, this research will also be helpful for beginners to understand the basic idea of multiphase flow in non-Newtonian fluids.

We theoretically report on the acousto-electric direct current (ADC) generation in non-degenerate fluorine-doped single-walled carbon nanotubes (FSWCNTs). Our calculation on the carriers in the lowest miniband, where waves with commensurate frequencies (zero phase difference) mix in the hypersound region ((qell gg 1) where q is the acoustic phonon wave number and (ell ) is the carrier mean free path). The generated DC exhibits strong nonlinear and non-ohmic behaviour, dependent on the magnitude of the AC fields ((mathcal {E}_{1}) and (mathcal {E}_{2})), overlapping integral for leaps ((Delta _{s}) and (Delta _{z})), carrier concentration ((n_{0})), Bloch frequency ((Omega )), acoustic phonon frequency ((omega _{q})) and photon frequency ((omega _{i})). The non-ohmicity in the observed I–V characteristics likely originates from a combined non-parabolicity of the band relation, Stark effect, charge carrier heating, intraminiband carrier oscillation and parametric resonance. Notably, the generated DC corresponded to even instability regions in the FSWCNTs as promising candidates for ADC generation under bichromatic fields with commensurate frequencies.