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The hybrid nanofluids (HNFs) have superior thermal impact and stability than traditional nanofluids, making them more suitable for peak thermal results in thermal systems and solar energy. Furthermore, artificial neural network (ANN) improves the accuracy and thermal aspects of HNF with optimised results. This analysis presents optimised thermal results associated with the flow of HNF due to the permeable porous surface with mass suction effects. Hybrid nanofluid properties are accounted for by using the suspension of gold (Au) and silver (Ag) nanoparticles with blood as the base liquid. The nonlinear applications of radiated phenomenon have been considered. The modification in heat and concentration equations are done by following the Cattaneo–Christov model. The concentration of HNF is observed using chemical reaction. Artificial neural network (ANN) simulations are performed to validate and optimise thermal results. Convective heat constraints are implemented to observe the thermal simulations. Computations are numerically simulated with the help of shooting scheme. The results for mono-nanofluid (MNF) and HNF are compared. It is observed that the suspension of HNF is more suitable for enhancing heat transfer systems. Temperature profile increases using suction phenomenon and porous media.

We show that the inverted versions of the Mathews–Lakshmanan and Higgs oscillator systems admit closed-form bound states within the Dunkl formalism. Conditions for the existence and number of bound states are derived.

The current study explores a fascinating plasma system in which ion-acoustic cnoidal waves arise and their dynamics is shaped by the interaction of positron, thermal and quantum processes. Degenerate electrons, positrons and warm ions in an unmagnetised environment make up the present plasma system. The Korteweg–de Vries (KdV) equation is developed using the reductive perturbation technique and modified for periodic waves by applying suitable boundary conditions. A preference for compressive ion-acoustic cnoidal waves is shown by the system’s support for hump-shaped (positive potential) periodic structures. Wave amplitude, frequency and wavelength correlations are shown by periodic solutions. The influence of several variables, including the ion temperature (sigma _{i}), positron temperature (sigma _{p}), positron density p and quantum parameter H, is examined in this work. The effects of these variables on the dispersion and nonlinear behaviour of the plasma system are investigated. When positron density (p), positron temperature ((sigma _{p})), thermal effects through ion temperature ((sigma _{i})) and quantum effects (H) are included, the amplitude of the cnoidal wave increases. It has been observed that the amplitude of moving waves increases both their frequency and wavelength. This implies that in this plasma structure, higher frequencies and longer wavelengths are linked to waves with bigger amplitudes.

This study examines the Painlevé integrability and complex dynamics of a dispersive coupled Burgers system, focussing on its fractal and chaotic structures. The Painlevé test is performed to determine the system’s integrability. Analytical solutions are derived using the Riccati method, while logarithmic, sine, cosine and Jacobi elliptic functions are employed to investigate the emergence of fractal structures. The chaotic nature of the system is further analysed through Poincaré section and Lyapunov exponent computations. The results provide valuable insights into the nonlinear wave interactions, pattern formation and turbulence modelling. This system has potential applications in fluid dynamics, particularly in describing shock waves and turbulence in compressible flows. Moreover, understanding the integrability, fractality and chaos in the present system can lead to advancement in predictive modelling across various scientific and engineering disciplines.

The E-gamma over spin (E-GOS) ratio, defined as (R_{mathrm {E-GOS}}(I)=E_{gamma }(Irightarrow I-2)/I), serves as a powerful tool in examining the transitions between vibrational and rotational structures. The mass region (100 le A le 112) has been recognised as a region of interest for such transitions, especially from (gamma )-soft/vibrational to rotational structures. However, recent studies of nuclei, such as (^{104})Pd and (^{106,108,110})Cd, have revealed an exotic interesting phenomenon: a transition from (gamma )-soft/vibrational to antimagnetic rotational behaviour along the yrast line. To explore this transition in a systematic manner, we have calculated two quantities: the average of the E-GOS ratio (({overline{R}}_{mathrm{E-GOS}})) and the gradient of the E-GOS ratio ((g=frac{triangle R_{mathrm{E-GOS}}}{triangle I})) at the band-head for both (gamma )-soft/vibrational and antimagnetic rotational modes within a specific spin range.

Processes that take place in the participant and spectator regions of interacting nuclei poses a significant obstacle to comprehend the nucleus–nucleus (A–A) interactions, given the central character of the reactions. An essential parameter for gaining a thorough understanding of the response processes in A–A interactions is the analysis of angular distributions (ADs) in the final-state particles in the target fragmentation zone. By offering a full 4(pi ) angular coverage, nuclear emulsion detectors (NEDs) enable almost thresholdless detection of shower, black and grey particles, referred to as fast target protons (FTP). The ADs of the FTP released in contact with emulsion nuclei at 1 A GeV of (^{84})Kr are reported. These ADs are examined using the modified Maxwell–Boltzmann statistical (MBS) model for a range of (N_{h})-values (target sizes) and Q-values (projectile spectator charges). It is evident that the ADs of these target protons satisfy the nuclear limiting fragmentation (NLF) theory, which is unaffected by the (N_{h})-values and Q-values. It is also observed that all event group ADs have maxima located at around (60^{circ }). For each collection of events, the forward–backward asymmetry ratio (F/B) is examined together with the computed statistical moments ((M=langle theta rangle ), (sigma ^{2}), (chi _{0}), (omega )) of the distributions. Results presented by other physicists are compared with the ADs of FTP.

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.