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In this study, we aim to present a deeper exploration of the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) for fluid dynamics. The travelling wave transformation, along with the semi-inverse method (SIM) are utilised to develop the variational principle (VP). In light of the VP, the Hamiltonian is found. Upon the planar dynamical system that is constructed through the Galilean transformation, the phase portraits are illustrated, and the conditions for the existence of solutions with different waveform structures are expounded by conducting the bifurcation analysis. Meanwhile, the system’s chaotic behaviours are also analysed. In the end, two robust schemes are employed to investigate various wave solutions: the variational approach (VA), which combines the VP and Ritz technique and the Hamiltonian-based approach (HBA), based on the energy conservation law. These different solutions include the kink solitary, anti-kink solitary and periodic wave solutions. Correspondingly, the waveforms of the obtained solutions are depicted graphically to exhibit the physical properties. To the author's knowledge, the quantitative analysis has not been reported yet and the VA and the HBA have not been used to explore the considered equation so far.

This work pioneers a universal framework for quantifying quantum entanglement in nuclear systems by innovatively integrating quantum distance metrics and machine learning. We introduce a framework for quantifying entanglement in nuclear spin systems using quantum distance measures (fidelity, trace distance and Bures distance ((D_textrm{B})) ). A universal scaling law (D_textrm{B} propto Gamma ^{-0.85}) links Bures distance to nuclear decay width, experimentally validated in (^{56}text {Fe}(n,gamma )) reactions ((D_textrm{B} = 0.62 pm 0.04)). Machine learning achieves 94% prediction accuracy, revealing 18% entanglement enhancement near shell closures. Three entanglement phases guide quantum technology applications: (^{56}text {Fe}) for memory ((D_textrm{B}>0.6), (tau _Dsim 10^{-25}) s) and (^{6}text {Li}) for sensing. The study bridges quantum information theory and nuclear physics, offering transformative tools for both fields.

This study examines the linear instability of double-diffusive rotational convection in a horizontal layer of Navier–Stokes–Voigt fluid with stress-free boundary conditions. The onset condition for convection is derived in closed form using normal mode analysis. Double-diffusive convection in the presence of rotation serves as an example of a triple-diffusive fluid system, exhibiting convective behaviours not observed in double-diffusive Kelvin–Voigt fluid models. Numerical calculations reveal several novel and significant phenomena under specific parametric conditions: (i) the emergence of a closed and disconnected oscillatory neutral stability curve from its stationary counterpart, necessitating three Rayleigh numbers to characterise the onset of instability, unlike the classical single-parameter framework; (ii) the destabilisation of a double-diffusive Navier–Stokes–Voigt fluid layer under the influence of rotation and (iii) the destabilisation of rotating convection in a Navier–Stokes–Voigt fluid layer due to the addition of a stable solute concentration gradient. These findings highlight the complex interplay between rotation, solutal stratification and viscoelasticity, offering fresh insights with implications for industrial processes, geophysical flows and astrophysical environments. Validation against established benchmarks affirms the accuracy of the analysis and demonstrates how, even within the Navier–Stokes–Voigt framework, traditionally stabilising factors can collectively act as catalysts for convective instabilities under specific conditions.

This paper examines the fractional Klein–Gordon–Zakharov system using the conformable fractional derivative, both quantitatively and qualitatively. Wielding the semi-inverse method (SIM) and travelling wave transformation (TWT), the variational principle is developed. Correspondingly, the Hamiltonian function is established based on the variational principle. Utilising the Galilean transformation, we derive the planar dynamical system, conduct a bifurcation analysis and discuss the existence of various wave solutions. In addition, the chaotic phenomenon is investigated by introducing an external perturbed term and the sensitivity analysis is presented in detail. Finally, two effective methods, namely the variational method that is based on the variational principle and the Ritz approach and the Hamiltonian-based method, are utilised to construct diverse wave solutions, including the bell-shaped solitary wave, anti-bell-shaped solitary wave, M-shaped wave (double bell-shaped solitary wave), W-shaped wave (double anti-bell-shaped solitary wave) and periodic wave solutions. The outlines of the obtained wave solutions are unfolded graphically and the impact of the fractional order (alpha ) on the extracted wave solutions is elaborated. As we all know, the findings of this exploration are new and have not been investigated before, which enables us to gain a deeper insight into the dynamics of the system under consideration.

This study examines the production of (tau ) lepton pairs ((e^+ + e^- rightarrow Z rightarrow tau ^+ + tau ^-)) through the collision of electrons and positrons. This process is important for understanding the generation of fermion pairs and confirming the accuracy of the Standard Model at high energy levels. We used data from the LEP program to investigate (tau ) lepton production in resonance with the Z boson, both with and without a circularly polarized monochromatic laser field. In our theoretical model, (tau ) leptons are considered free Dirac states, while electrons and positrons are described by Dirac–Volkov states altered by the laser field. Our analysis involved using Mathematica to calculate the differential cross-section (DCS) and total cross-section (TCS). Our findings indicate that the TCS increases with laser frequency and stabilizes at specific thresholds, revealing significant effects of the laser field on the interaction dynamics. To validate our theoretical approach, we compared it with data from OPAL and Muijs (2001) and found excellent agreement in the absence of laser effects. Additionally, we examined how various laser parameters, such as the strength of the electric field and the number of exchanged photons, impact the scattering process.

A breaking soliton equation is considered and its solutions are obtained via Hirota bilinear derivative method. Then, utilising the auxiliary function, the different-order complex solitonary solutions including soliton, breather and hyperbolic soliton solutions are derived. The results validate that the proposed method is useful.

The combination–combination synchronisation (CCS) of fractional-order ecological systems is studied in this paper using two distinct approaches. By designing an appropriate controller, we attain CCS among chaotic systems. In addition, calculating the bounds of a chaotic system is a significant task in chaos theory. It reveals fundamental features of the system. We also estimated the ultimate bound, Mittag–Leffler positive invariant set and globally attracting set of the ecological system using fractional-order and complex system. The chaotic system’s bounds are demonstrated using simulation. Finally, the numerical results confirm the efficacy of the suggested scheme.

This study investigates the catalytic tangential hyperbolic flow of a C₂H₆O₂–H₂O-based hybrid Hartmann nanofluid over a stretching sheet, considering the effects of nonlinear thermal radiation and a non-uniform heat source. The influence of various physical parameters, including the Weissenberg number, magnetic parameter, radiation parameter, heat generation/absorption parameters and the thermal slip factor, on the velocity, induced magnetic field and temperature profiles are comprehensively analysed. Additionally, the study examines the homogeneous–heterogeneous reactions, skin friction coefficient and Nusselt number under varying physical constraints. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and the bvp4c solver in MATLAB and then used to solve the equations numerically. The results indicate that the axial velocity and Hall effect decrease with increasing stretching parameter and induced Prandtl number, whereas they improve as the Weissenberg number and magnetic parameter increase. The temperature profile is found to rise with an increase in heat generation, absorption and radiation parameters. Hybrid nanofluids outperform mono-nanofluids in terms of thermal performance. It is anticipated that the results of this study will offer important new information for designing effective thermal systems and may serve as a reference for future research on advanced heat transfer applications involving hybrid nanofluids and complex flow geometries.

High-intensity accelerators are designed with the zero-current phase advance per period ((varvec{sigma}_{0})) kept below 90° to avoid beam degradation. The 4^th order single-particle resonance and the 2^nd order envelope instability are triggered in a high current beam passing through a periodic channel for (varvec{sigma}_{0}>90^circ). The 4^th order resonance is a single-particle effect, whereas the latter is a collective effect of the entire beam. Both phenomena result in beam degradation, leading to increased beam size and emittance. Although they exhibit overlapping stopbands of emittance increase, there are distinct features that allow differentiation between the two effects. This paper presents a comparative analysis of these effects through detailed numerical simulations using TRACEWIN, employing both Gaussian and KV input beam distributions. Key distinguishing features such as differences in the root mean square (rms) and maximum beam size evolution, beam centroid oscillations, halo formation dynamics, 99.99% emittance growth, and the spatial characteristics of particles are explored. The paper also emphasizes how the choice of beam distribution, whether Gaussian or Kapchinsky-Vladimirsky (KV), affects the onset and severity of these instabilities. This analysis helps in developing a clearer understanding of these effects and their impact on beam dynamics in high-intensity accelerator systems.

This research paper focusses on the development of a triple stop-band frequency-selective surface (FSS) positioned on an FR4 dielectric material with the substrate dimension of (0.08lambda_{0} times 0.08lambda_{0}), where (lambda_{0}) is the free-space wavelength of the lowest resonance at 2.4 GHz. The triple stop-band phenomenon is simple and attractive considering the simple structure, size, design methodology and angular stability. (S_{21}) is the measure of the fabricated FSS for different elevation angles under transverse electric (TE) and transverse magnetic (TM) polarisations. The proposed polarisation-insensitive structure covers three valuable stop bands of 2.15–2.59 GHz, 4–5.65 GHz and 7.25–9.2 GHz at 2.4, 5.1 and 8.2 GHz for EM shielding. An angular stability of (80^{circ }) with a minimum frequency ratio of 1.62 is achieved. It can be used for WiFi, WLAN and X-band satellite applications.