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The primary aim of the present paper is to analyse the Reiner–Philippoff hybrid nanofluid (HNF) flow over a stretching(/)shrinking sheet under the influence of thermal radiation and suction. A set of partial differential equations is used to describe the model, which is then reduced to non-dimensional ordinary differential equations through similarity transformations and solved computationally with the help of the bvp4c function. A graphical investigation examines the effects of various parameters, including the magnetic parameter, suction, Philippoff fluid parameter, Eckert number, radiation parameter, porosity parameter and Bingham number on velocity, temperature, skin friction and the local Nusselt number. The results show that as the Bingham number, Philippoff fluid parameter and stretching(/)shrinking parameter increase, the velocity profiles exhibit an upward trend. In addition, increasing the magnetic, porosity and suction parameters leads to higher absolute values of the skin friction coefficient. It is also noted that the rate of heat transfer increases up to 14.11% with an increase in the radiation parameter. The novel findings of this study provide a deeper understanding of HNF behaviour, which can facilitate the optimisation of heat transfer systems in industrial and engineering applications.

This research reveals the novel types of exact wave solutions of the nonlinear Gardner–Kawahara (G–K) model in the concept of truncated M-fractional derivative. The G-K model, which is also called the extended Korteweg–de Vries (KdV) model, explains the solitary wave propagation in media, notation in plasmas, notation in shallow-water waves along surface tension and notation of magneto-acoustic waves. For our purpose, two techniques, the unified and the Sardar sub-equation techniques are applied. As a result, new types of exact wave solitons having periodic, dark–bright, periodic, kink are obtained. Some of the obtained solutions are represented through two- and three-dimensional and contour plots. The effect of the truncated M-fractional derivative (TMFD) is explained by plots. Stability of a concerned equation is checked by applying stability analysis. Moreover, the modulation instability analysis of the governing equation is also performed, which proves that the model and the obtained results are stable as well as exact.

The magnetic behaviour of a three-electron quantum dot(/)ring system is analytically investigated with electron–electron (e–e) interaction taking into account the Rashba effect and magnetic field. The Jacobi transformation has been employed to separate the Hamiltonian of the system into relative motion and the centre of mass. The Schrödinger equation is analytically solved and energy spectra are obtained. Then, the magnetisation and susceptibility are calculated. The magnetisation decreases by rising the magnetic field without and with spin–orbit interaction (SOI) and also without e–e interaction. The Rashba effect slightly modifies the magnetisation of the system without e–e interaction. The susceptibility displays a peak structure as the magnetic field changes from low values to high values. The susceptibility sign is negative by considering e–e interaction and without the Rashba effect and its value decreases by rising the magnetic field. The susceptibility displays a transition from diamagnetic to paramagnetic by considering the e–e term and the Rashba effect.

We have demonstrated that the relationship between the deep inelastic scattering structure functions remains stable for a nuclear target with mass number A at (x{le }10^{-3}). Numerical results have been provided for the specific nuclei (^{12})C and (^{208})Pb using the nuclear PDF parametrisations incorporated in the HIJING2.0 model. These findings are within the electron–ion collider kinematic acceptance for heavy ion running. The ratio (R^{A}_{F_{L}}) is determined as the ratio (R^{A}_{F_{2}}) based on the HIJING2.0 model.

In the present work, the capture and fission dynamics of (Z=) 102 and 103 nuclear systems are investigated. The coupled channel model and the extended Wong model are used to address nuclear capture as well as fission cross-sections of (^{48})Ca(+) (^{208})Pb (leading to the composite system (^{256}_{102})No(^*)) and (^{50})Ti(+^{208})Pb (resulting in (^{258}_{104})Rf(^*)) reactions in reference to the available experimental data. Furthermore, the isotopic analysis of the (Z =) 102 nucleus is performed by changing the mass of the projectile–target (p–t) nuclei that leads to the synthesis of (^{252,254,256})No(^*) composite systems. The study suggests relatively higher cross-sections and compound nucleus formation probability ((P_{textrm{CN}})) values for the reactions in which (^{48})Ca projectile is involved with (^{208})Pb. Also, with a decrease in neutron number for Ca projectile (i.e., (^{48,46,44})Ca with (^{208})Pb target) the fission cross-sections drop by 40(%) which otherwise for Pb target ((^{208,206,204})Pb with (^{48})Ca projectile) is 10(%). Subsequently, an attempt is made to predict the nuclear capture and fission data of (Z=) 103 (Lr(^*)) nucleus within the mass domain of 249u to 261u (i.e., (^{249,253,257,261})Lr(^*)) using various heavy-ion fusion reactions. Along with this, the decay profiles of (^{249-261})Lr(^*) composite systems are examined within the framework of the dynamical cluster decay model (DCM) in reference to the fragmentation potential, preformation probability and average total kinetic energy ((langle mathrm TKErangle )) distribution. Apart from traditional Pb-valley, an additional dip around the entrance channel mass asymmetry of (eta approx 0.4) and (eta approx ) 0.2 is also noted for the reactions under consideration.

This study aims to apply two highly effective and precise analytical methods: the Aboodh residual power series method and the Aboodh transform iterative method. These enhanced techniques are utilised to analyse and solve two types of fractional physical evolutionary wave equations including the planar fractional Kawahara equation and the planar fifth-order Korteweg–de Vries (FKdV) equation. The mentioned approaches are a mixed form of the standard Aboodh transform with the standard residual power series method and iterative method. Some highly accurate analytical approximate solutions are derived using the two proposed approaches. In these techniques, the generated approximations are expressed as convergent series solutions. All generated approximations are analysed both graphically and numerically to gain insight into the dynamics of the nonlinear phenomena they represent, including planar solitary waves. The absolute error is also computed to assess the generated approximations’ precision and validate the efficacy of the proposed approaches. The fractional evolutionary wave equations (EWEs) under study are widely used to analyse and model various nonlinear structures that emerge and propagate in fluid mechanics, plasma physics and optical physics. Consequently, the derived approximations are expected to reveal some behaviours not shown by the exact solutions of these equations in their integer cases.

Our approach in the present work is concerned with a novel study involving a sampled-data controller for hybrid nanofluid in a time-delay nonlinear Brinkman system with randomly occurring uncertainties. The time-delay error system is described by utilising a hybrid nanofluid in nonlinear system and the looped Lyapunov–Krasovskii functional with a splitting sampling interval. In order to ensure that the resulting closed-loop system is reliable, it is asymptotically stable and has the required dissipative efficiency. A master/slave synchronisation technique is employed to synchronise the hybrid nanofluid in nonlinear system. In addition, we employed a sampling interval ([t_{k}, t_{k+1}]) and the fractional parameter ({tilde{beta }}) in the interval [0,1] has split into ([t_{k}, t_{k} +{tilde{beta }} varsigma _{1}(t)], [ t_{k} +{tilde{beta }} varsigma _{1}(t), t], [t, t +{tilde{beta }} varsigma _{2}(t)]) and ( [ t +{tilde{beta }} varsigma _{2}(t), t_{k+1}]). Then, the synchronised hybrid system utilises the looped Lyapunov stability theory and positive definite matrix. The simulation results not only confirm the theoretical predictions but also demonstrate enhanced control performance, improved synchronisation accuracy and robust dynamic stability. Furthermore, this study highlights the impact of time-delay, uncertainty and fractional parameter variations on system stability. The proposed approach provides a new direction for advanced control strategies in nanofluid-based nonlinear systems, offering potential applications in engineering and industrial processes. Finally, certain simulation results verify the effectiveness and correctness of the analytical results.

In recent years, nanoplastics have attracted increasing attention due to their widespread presence in the environment and potential harm to living organisms. To provide a theoretical basis for using surface-enhanced Raman spectroscopy (SERS) mechanism to detect nanoplastics of different sizes, this work employed lasers to irradiate the substrate composed of a bowl-shaped particle-in-cavity structure and nanoplastics. Then, the electric field distribution was obtained using the finite-difference time-domain (FDTD) method. By altering the curvature of the Ag nanobowl and the size of gold nanoparticles (AuNPs), the electric field enhancement capability of this SERS structure can be ameliorated. It is found that when the diameter of AuNPs is 30 nm, the larger the nanoplastics, the more suitable the structure with smaller curvature as a substrate. But when the diameter of AuNPs is 40 nm, the larger the nanoplastics, the more suitable the structure with larger curvature as a substrate. AuNPs with a size of 40 nm are generally superior to those with a size of 30 nm. To verify the feasibility of this SERS structure for detecting various nanoplastics, we tested a range of nanoplastic materials. The results prove that the materials of nanoplastics will not have a significant impact on the detection. Moreover, a multi-hot-spot system is analysed to reveal the SERS signal enhancement mechanism. A laser of 785 nm can produce stronger ‘localised hot spots’ (LHSs) and weaker ‘volume hot spots’ (VHSs) than a laser of 532 nm. The issue of nanoplastic detection is optimistically poised for resolution, as the hot spots within the bowl-shaped particle-in-cavity structure can effectively approach and surround nanoplastics, stimulating highly intense SERS signals that demonstrate their promising application in nanoplastic detection.

Bell–Kochen–Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional Hilbert space of two spin-1/2 particles. Peres’ argument is enormously simpler than that of Kochen and Specker. Peres contextuality demonstrates a logical contradiction between quantum mechanics and non-contextual hidden variable models by showing an inconsistency when assigning non-contextual definite values to a certain set of quantum observables. In this work, we present a similar proof in time with a temporal version of the Peres-like argument. In analogy with the two-particle version of Peres’ argument in the context of spin measurements at two different locations, we examine here single-particle spin measurements at two different times (t=t_1) and (t=t_2). We adopt three classical assumptions for time-separated measurements, which are demonstrated to conflict with quantum mechanical predictions. Consequently, we provide a non-probabilistic proof of certified quantumness in time, without relying on inequalities, demonstrating that our approach can certify the quantumness of a device through single-shot, time-separated measurements. Our results can be experimentally verified with the present quantum technology.

A five-level microwave-driven X-type scheme is used to study the influence of various field parameters on the absorption and nonlinear dispersion of probe light. In the proposed system, the cross-Kerr nonlinearity can be enhanced by optimum setting of the field strength and detunings. Our calculation reveals that the amplitude and position of the cross-Kerr peaks can be manipulated by tuning the microwave Rabi frequency and relative phase parameter. This proposed scheme has potential applications in the realm of multichannel quantum gates.