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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.

This article aims to derive optical soliton solutions for the ((4+1))-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) problem using the generalised exponential rational function method and the ((m+F))-expansion method. Both techniques yield various soliton solutions, including bright and dark solitons. The behaviour of these solitons may be further analysed using three-dimensional, two-dimensional and contour graphs. The effect of temporal parameter on the obtained soliton solutions is illustrated using two-dimensional graphs. The study emphasises the significance of solitons in optical fibre technology, signal processing and quantum systems, while also paving the way for applying the proposed techniques to more complex nonlinear models, such as fractional and higher-order systems. These findings contribute to a deeper theoretical understanding of soliton dynamics and support their practical implementation in advanced nonlinear optics and engineering applications.

This paper analyses the performance of a new fin field-effect transistor (FinFET) for two undesirable effects, such as self-heating and hot carrier effects. Two effects often degrade the device performance. This paper proposes a new FinFET architecture as dual gate dielectrics heterodielectric buried-oxide (HDB) FinFET. The HDB consists of SiO₂ and HfO₂ dielectrics, placed laterally. The use of HfO₂ with SiO₂ in the buried-oxide (BOX) increases the thermal conductivity, due to which the introduced structure demonstrates less self-heating effect on device characteristics. Similarly, the incorporation of HfO₂ beneath the drain lowers the band gap narrowing in the channel(/)drain region, resulting in reduced hot carrier degradation effect. To analyse the performance, the self-heating effect and the hot carrier effect is compared between the conventional and HDB FinFET. The proposed HDB FinFET is found to be better than the conventional FinFET and hence, a detailed analysis on self-heating and the hot carrier effects is performed by varying the different dimensions of the BOX, fin and work function of gate material.

The flow of a non-Newtonian Jeffrey fluid over a pulsating plate in a rotating frame is analysed. The effects of the Coriolis force and a constant magnetic field are also studied. The velocity of the plate is periodically pulsed, while the remaining part of the rotating fluid exhibits unsteady motion. Exact solutions for each case are obtained using the Laplace transform method with Mallin’s integral inversion formula. The graphical analysis shows how rotation, elasticity and magnetic field influence the fluid velocity during plate pulsation. It is found that the longitudinal component of velocity decreases with higher values of the Jeffrey parameter and magnetic field, while the transverse component of velocity shows the opposite behaviour.

Particle tracking passive microrheology in the 8CB liquid crystals is used to redefine the precessional motion of the orientation of nematic director in liquid crystals. Physical origin of the tumbling director in the presence of presmectic clusters under zero shear conditions is discussed. Different structural properties (pure nematic phase, presmectic (smectic C and smectic A clusters)) were differentiated with characteristic dependence of (G') on (omega ) in the nematic phase of the 8CB liquid crystals. Also, dynamic viscosity is observed with a cross-over between parallel and perpendicular components as the smectic A phase is approached.

Nanotechnology offers innovative and sustainable solutions for environmental remediation. However, enhancing photocatalytic efficiency remains a significant challenge. In this study, we developed a cost-effective method for synthesising carbon quantum dot (CQD)-incorporated cerium oxide (CeO₂) nanocomposites for efficient methyl orange (MO) degradation under direct sunlight. CeO₂ nanosols and CQDs were synthesised via sol–gel and hydrothermal processes, respectively, and combined using a hydrothermal route with sonication-assisted mixing. The nanocomposites were calcinated at 600 °C and characterised using XRD, FTIR, Raman, PL spectroscopy, SEM and EDX to analyse their structural, morphological and surface properties. The specific surface area of the CQDs(/)CeO₂ composites was determined to be 72.3 m²(/)g from the sol–gel method and 96.7 m²(/)g from the hydrothermal method, as measured by Brunauer–Emmett–Teller (BET) analysis. The optimised CQDs(/)CeO₂ (1:100 ratio) exhibited enhanced MO degradation, with the MO degradation rate constant for the hydrothermal composite. The energy band gap of the sol–gel composite was found to be 2.78 eV, while the hydrothermal composite showed a band gap of 2.73 eV, facilitating improved light absorption. The degradation efficiency was further influenced by MO concentration, pH and catalyst loading. Additionally, CQDs(/)CeO₂ demonstrated excellent catalytic stability over multiple cycles. These findings highlight the potential of CQDs(/)CeO₂ nanocomposites for cost-effective water purification and disinfection applications.

Graphical abstract

The purpose of this paper is to study the trajectory controllability (which is said to be the strongest notion rather than other controllabilities) and null controllability of a control system commanded by fractional-order composite relaxation semi-linear differential equation. The linear control system under consideration addresses a classical problem in fluid dynamics, specifically focussing on the dynamics of a particle experiencing unsteady movement within a viscous fluid while subjected to gravitational forces. Initially, we derive the mild solution of the considered control system employing the results on (a, k)-regularised families of bounded linear operator (matrices). Under some appropriate assumptions regarding non-linear terms and by utilising the Gronwall’s inequality, we establish the trajectory controllability and null controllability with constrained controls via fixed point technique. Finally, a few examples are shown to illustrate and explore the applications of the obtained findings.