A parameter-uniform implicit approach for two-parameter singularly perturbed boundary value problems is constructed. Sharp bounds are derived for the derivatives of the solution. The solution is additionally divided into regular and singular components, bounding the derivatives of these components utilized in the convergence analysis. In the temporal direction, the system of ordinary differential equations obtained via the Crank-Nicolson scheme on a uniform mesh is further discretized in the spatial direction by employing a finite difference technique on a suitably chosen Shishkin mesh. Through a rigorous analysis, we establish the theoretical results for two cases: Case I. epsilon(1)/epsilon(2)(2) -> 0 as epsilon(2)-0, and Case II. epsilon(2)(2)/epsilon(1) -> 0 as epsilon(1) -> 0. In both cases, we prove that the proposed method is uniformly convergent with respect to the perturbation parameters. The order of accuracy is established as O((Delta t)(3/2)+ N-2(ln N)(2)). Three examples are presented to corroborate in practice the theoretical results.

This article presents the development and evaluation of a collocation-based, parameter-uniform numerical method tailored for a specific class of singularly perturbed convection-diffusion problems with a boundary turning point. A set of a priori bounds is established for both the exact solution and its derivatives to enable a comprehensive error analysis. These bounds are essential for ensuring the accuracy and stability of the proposed method, as they provide necessary constraints to evaluate the solution’s behavior across various parameters. The classical Crank-Nicolson method discretizes the time direction on a uniform mesh. At the same time, a collocation approach is applied to the spatial domain using an exponentially graded mesh, which is carefully refined in the boundary layer region. The proposed method demonstrates second-order, parameter-uniform convergence, as confirmed by a thorough investigation. Extensive numerical tests support the theoretical results, showing the approach’s accuracy and efficiency.

Ni 3In 2S 2 is a topological semimetal with endless nodal lines. Due to the linearly dispersive electronic structure near the Fermi level, Ni 3In 2S 2 exhibits the largest magnetoresistance (MR) among the Shandite Co 3Sn 2S 2 family of compounds. The prediction of band crossing just below and above the Fermi energy provides an opportunity to further improve the MR by accessing them using hole and electron doping. Therefore, in this work, we lightly hole-doped Ni 3In 2S 2 with cobalt and electron-doped the same using tin. As a result, a large MR% similar to 12000% was observed in Ni 3In 2S 2 at 2 K and 16 T magnetic field due to the near compensation of charge carriers and large carrier mobilities. In Ni 2.95 Co 0.05 In 2S 2, the MR% decreases to 940% at 2 K and 9 T. Cobalt doping causes deviation from charge compensation and enhances the carrier-defect scattering, which reduces the carrier mobilities, altogether resulting in lower MR. In Ni 3In 1.95 Sn 0.05 S 2, the mobility of electrons increases and the carrier density decreases as the chemical potential shifts towards the bands crossing. However, the MR is suppressed due to the large deviation of carrier densities from charge compensation. The MR in the Ni 3In 2S 2 series exhibits a strong dependence on the residual resistivity ratio. The Kohler scaling and the temperature dependence of differences in electron and hole mobility suggest that light Co/Sn doping significantly alters the temperature dependence of electron and hole scattering times. These findings have substantial implications for increasing MR in the Shandite family of kagome-based compounds.

The development of sodium-metal batteries (SMBs) is hindered by several limitations associated with conventional organic liquid electrolytes. In this study, we report the synthesis of a novel sodium polyeugenol borate (Na-PEB) salt, which offers low cost and environmental sustainability, synthesized via a cationic polymerization method. Na-PEB was then combined with poly(ethylene glycol) (PEG) 4000 to form the Na-PEB-PEG composite electrolyte. Na-PEB-PEG has perfect thermal stability with an initial decomposition temperature of 376 degrees C, a satisfactory ionic conductivity of up to 1.5 x 10-5 S/cm at room temperature, a wide electrochemical window as high as 2.3 V, and a high sodium-ion transference number of >0.96 at 30 degrees C. It also shows the diffusivity constant in the order of 10-6 m2/s and ionic mobility in the order of 10-8 m2 v-1s-1 at 30 degrees C. The electrolyte matrix shows a low energy requirement of ionic transport, i.e., 0.266 eV. On behalf of these findings, Na-PEB-PEG-based semisolid polymer electrolyte confirms its potential for application in sodium-ion-based energy storage systems.

Polymer-based solar cells have emerged as a promising class of next-generation photovoltaic devices due to their lightweight nature, mechanical flexibility, tunable optoelectronic properties, and potential for low-cost, large-area fabrication. This tutorial review provides a comprehensive overview of the fundamental and applied aspects of polymer having solar cells. It encompassing their operational principles based on exciton generation, dissociation, charge transport, and collection. Key photovoltaic parameters are discussed alongside the influence of materials and device architecture on performance. Additionally, it outlines the principal characterization techniques for establishing correlations between nanoscale structures and macroscopic performance. Various architectures, including single-junction, tandem, and inverted configurations, are detailed, along with the role of donor–acceptor polymers, non-fullerene acceptors, and conjugated systems in enhancing light absorption, charge separation, and transport. Principles for polymer selection are addressed with a focus on bandgap engineering, chemical stability, and morphological control to achieve high-efficiency and operational stability. Processing techniques are explored as scalable approaches to improve device performance and reproducibility. Strategies for photovoltaic properties enhancement, including molecular engineering, additive incorporation, controlled annealing, and encapsulation, are highlighted. This study aims to serve as an educational resource and a technical reference for researchers, guiding the rational design, fabrication, and optimization of polymer having solar cells toward high-efficiency, stable, and commercially viable technologies.

We report experimental and theoretical investigations on the quaternary Heusler alloy CoRuTiGe, synthesized using the arc melting technique. Crystal structure analysis reveals a tetragonal structure at room temperature. Magnetization measurements as a function of temperature and magnetic field indicate a ferromagnetic nature with a saturation magnetization of similar to 0.681 & micro;B/f.u. at 5 K. The temperature dependence of electrical resistivity shows a nearly linear decrease in the high-temperature range, indicating the spin gapless semiconductor (SGS) like behavior of the material. This SGS nature is further supported by the weak temperature-dependent carrier concentration and mobility. Hall effect analysis reveals that the anomalous Hall effect in CoRuTiGe arises from both intrinsic and extrinsic mechanisms. Additionally, a well-defined symmetric negative magnetoresistance is observed at low temperatures. These results offer insights that could aid in designing new spin gapless semiconductors with enhanced Curie temperatures for spintronic applications.

In this article, we develop a compact finite difference scheme to solve the convection-diffusion-wave equation incorporating the fractional derivative viewed as the Caputo derivative. The numerical discretization of the fractional derivative of order α ( 1<α <2 ) is performed with new coefficients (i+1/2)^2-α-(i-1/2)^2-α instead of (i+1)^2-α-i^2-α and the space derivatives are substituted with a compact difference scheme of fourth order. The method is proven unconditionally stable. Furthermore, we have shown that the proposed scheme converges with order O(τ ^3-α+h^4) . The scheme’s efficiency is demonstrated through numerical results and plots that authenticate the theoretical results.

In this study, pristine and strontium-doped neodymium manganite perovskites (Nd1_ xSrxMnO3) were synthesized via the combustion method. Structural and morphological characterizations were carried out using X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and Xray photoelectron spectroscopy (XPS). The electrical transport properties were systematically investigated through resistivity measurements under varying temperatures and magnetic fields, alongside a detailed analysis of magnetoresistance behavior. Pristine NdMnO3 exhibits insulating behavior, while a metal-insulator transition emerges at 175 K with minimal Sr doping, becoming more pronounced under a 5 T magnetic field. However, at higher doping concentrations, the system reverts to an insulating state. Notably, Nd0.7Sr0.3MnO3 demonstrates a more gradual decline in magnetoresistance compared to its undoped counterpart. These findings provide critical insights into the role of strontium doping in modulating electrical transport and magnetoresistive properties, highlighting its potential for advanced sensor applications.

The current experimental investigation emphases on the synthetization and characterizations of pure and Fe3+ Cu2+ co-doped [Ni0.5Fe0.02Cu0.06Ox, Ni0.5Fe0.04Cu0.04Ox, and Ni0.5Fe0.06Cu0.02Ox] NiO nanoparticles (NPs) prepared through the hydrothermal method for improved supercapacitor performance. The synthesized NiO NPs were subjected to annealing at 800 °C and subsequently examined using a range of characterization methods.The XRD analysis verified the existence of a face-centered cubic (FCC) structure.The FESEM-EDAX confirmed successful dopant incorporation, revealing changes in surface morphology and particle size. An enhancementin the optical bandgap from 3.15 to 3.45 eV was found by the UV–Vis-DRS study, indicating the possibility of quantum confinement effects. The XPS provided insights into the surface chemistry, confirming the presence and concentrations of Ni2+, Fe3+ and Cu2+ ions in their respective chemical states. BET analysis indicated a reduction in the specific surface areafrom 18.59 m2/g (pure NiO) to 11.04 m2/g (co-doped NiO), but an increase in pore diameter facilitates ion diffusion. Electrochemical analysis showed that [Ni0.5Fe0.06Cu0.02Ox] achieved a highest specific capacitance of 546 F g−1, at 10 mVs−1exhibiting significantly superior performance than pure NiO NPs.This study highlighted the potential of Fe3+ and Cu2+ co-doped NiO NPs in enhancing the electrochemical performance of supercapacitors through improved charge storage capacity and conductivity.Furthermore, cyclic stability testing revealed that the co-doped sample retained approximately 92.12

The development of Fe 3 GeTe 2 and other recently introduced cleavable ferromagnets provides a foundation for constructing magnetically active 2D van der Waals heterostructures. While these architectures are primarily designed to explore their potential applications and functionalities, fundamental physical properties are important for understanding their charge and spin transport behavior. Herein, good quality single crystals of Fe 3 GeTe 2 are grown by two distinct methods, self‐flux and chemical vapor transport, and their structural and transport properties are compared. The two crystals have slight variation in stoichiometry and exhibit distinct defect density, carrier mobility, Curie temperature ( T C ), and magnetoresistance behavior. Both the crystals show anomalous Hall resistivity caused by skew scattering in the particular temperature range.

Iron-based metal matrix composites have shown promising potential as bearing materials for various tribological applications, and hence attained the interest of the researchers. Therefore, an attempt has been made to examine the outcome of certain process variables upon the frictional properties of Fe-ZrO 2 metal matrix composite (MMC) developed via powder metallurgy (PM). The experimental design for the applicable wear tests was carried out according to a face-centred central composite design (FCCD) utilizing response surface methodology (RSM). The tribological performance was assessed under various operating parameters of applied load (5–10 N), sliding speed (0.75–1.25 m/s) and sliding distance (200–600 m) using a pin-on-disc tribometer. The significance of the process variables upon the responses (coefficient of friction and wear rate) was investigated using analysis of variance technique. The regression equations were generated, and confirmatory experiments were executed using new parametric conditions to ensure the sufficiency of the developed models. Surface and contour plots depict the increment in coefficient of friction initially, and then decrement, while the wear rate is seen to be increasing at all levels of process variables. Moreover, the microstructures of the composite and worn surface morphology were investigated using various microstructural characterization techniques.

In agriculture, nitrogen (N) plays a crucial role, and its application invites significant environmental challenges with the pressing need to increase the efficiency of N fertilization in the context of improving the efficiency, productivity, economic, and environmental aspects of the crop production system, the present research aimed at developing enhanced N fertilizers to limit the frequency of application of N to the soil ecosystem while achieving high yields of good quality. In this perspective, synthesized various grades of ureapolyacrylamide (UPAM) as a slow-release N-fertilizer and studied its application potential for two and three-split applications on yield and yield attributes and N-use efficiency (N-UE) on rice and maize which are N- exhaustive crops. Results demonstrated that UPAM-2 significantly enhanced both economic and biological yield and N-UE. In maize (61.28 qha- 1), two split applications of UPAM-2 were the most effective, while three split applications optimized results in rice (59.64 qha- 1). Results from N-UE, the highest agronomic use efficiency (AGRN; 26.55 & 23.75 kgkg- 1), apparent N recovery (ANRN; 64.51 & 54.79 %), and partial factor productivity (PFPN; 51.06 & 40.63 kgkg- 1) were found in two and three split applications of UPAM-2 in maize and rice crops. Results from economic analysis of highest net returns (98936 & 99,990 Indian Rupee ha- 1) and benefit:cost ratio (1.68 & 1.60) were also found in two and three split applications of UPAM-2 grade treated plots in both crops. Understanding these outcomes involves various contributors working at different scales under diverse agroecological conditions.

This paper proposes a uniformly convergent numerical method for a class of singularly perturbed turning point problems with a time-lag defined on a rectangular domain. We consider an interior repulsive turning point with odd multiplicity ⩾ 1 . Twin boundary layers arise in the proximity of endpoints of the spatial domain due to the presence of the perturbation parameter. Preliminary results such as minimum principle, stability estimate, and solution derivative bounds for the continuous problem applicable in the convergence analysis are presented. First, we employ the Crank–Nicolson scheme to semi-discretize the continuous problem in the time direction, and then the cubic ℬ -spline functions on an appropriate Shishkin mesh are used to get a full discretization. The convergence analysis uses the maximum norm to obtain parameter-uniform error estimates. Three test problems are solved numerically to validate the theoretical results and confirm the scheme’s effectiveness.

Tellurium (Te) is predicted to host topological phases of matter and the growth of Te single crystals with controlled carrier concentration is important for harnessing this elemental semiconductor for device applications. Here we present an open-ended chemical vapor transport method for the growth of Te single crystals. With this fast growth method, crystals of a few micrometers to millimeters in size with different carrier concentrations and defect densities can be grown. At 500 degrees C growth temperature and 100 sccm Ar + H2 flow rate, Te crystals start to form. The crystal thickness and hole carrier concentration (n) increase on increasing the growth temperature, the crystal size increases with increasing dwell time, and the typical crystal width decreases on increasing the flow rate. Te crystals with n <= 4.2 x 1017 cm-3 exhibit a resistivity upturn at low temperatures indicating the charge freeze-out effect while the crystals with higher carrier concertation exhibit a typical metallike behavior.

This paper is focused on computing an approximate numerical solution of the strongly nonlinear multi-order fractional version (SNMOFV) of a BVP that appears in the theory of chemical reactors. The fractional derivative is defined by using Caputo’s methodology. This research article present a numerical method based upon collocation method with Laguerre polynomials (LPs) and Vieta–Lukas polynomials (VLPs) for the considered problem. This method’s key benefit is the excellent precision and user-friendly approach that are obtained from a limited number of Laguerre and Vieta–Lukas polynomials. Basically, in this article, we offer the numerical solution of the considered fraction model by using the Laguerre collocation technique (LCT) and the Vieta–Lukas collocation technique (VLCT). Also, we present a comparison of the collocation technique with the generalized differential transform method (GDTM). Error analysis of LCT and VLCT is also presented in this paper.

We explored the in situ and real-time monitoring of the electric dipolar relaxation during the interaction of ammonia (NH3) gas, a crucial phenomenon in the gas sensing mechanism of conducting polymers, with dodecyl-benzene-sulfonic acid (DBSA)-doped polyaniline (PANI) nanocomposite polymer thin films. Dielectric spectroscopy from 20 Hz to 100 MHz was performed to analyze the dynamical behavior of the interaction process of DBSA-doped PANI nanocomposite polymer thin film with NH3 molecules. Initially, with no NH3 gas, the dielectric measurement showed a negative relative dielectric constant (about -6500 at 20 Hz) at low frequencies, indicating the conducting nature of unadorned DBSA-doped PANI nano-composite thin film (PANI-DBSA). On exposing PANI-DBSA film to NH3, the low frequency dipolar relaxation process was observed in the dielectric spectra. A shift toward the high frequency as a function of NH3 exposure time was observed, elucidating a continuous increase in dielectric strength and density of dipoles in the composite film with increasing exposure time which allows the gas a deeper penetration into the film and hence the increase in the density of dipoles. Removal of NH3 gas from PANI-DBSA allowed the system to retain its previous state,which is significant for sensing applications.

The development of Fe3GeTe2 and other recently introduced cleavable ferromagnets provides a foundation for constructing magnetically active 2D van der Waals heterostructures. While these architectures are primarily designed to explore their potential applications and functionalities, fundamental physical properties are important for understanding their charge and spin transport behavior. Herein, good quality single crystals of Fe3GeTe2 are grown by two distinct methods, self-flux and chemical vapor transport, and their structural and transport properties are compared. The two crystals have slight variation in stoichiometry and exhibit distinct defect density, carrier mobility, Curie temperature (T C), and magnetoresistance behavior. Both the crystals show anomalous Hall resistivity caused by skew scattering in the particular temperature range.

Identification and understanding of charge conduction mechanisms for functional oxide based devices become necessary to implement any potential applications in spintronics. In this context, present communication deals with the phenomenological percolation model that governs the charge transport properties of chemically grown LaFeO3/La0.7Ca0.3MnO3/SrTiO3 (LFO/LCMO/STO) structure. Various structural aspects have been explored through X-ray diffraction (XRD) measurements. Temperature dependent resistivity behaviors [recorded under current in plane (CIP) mode and current perpendicular to plane (CPP) modes] under different applied magnetic fields have been understood using phenomenological percolation model. In this, phase separation scenario and disordered interface between LFO and LCMO layers have been identified to play effectively their interesting roles. Intrinsic and extrinsic contributions of MR have been identified for both the measurement geometries across LCMO thin film and LFO/LCMO interface. Isothermal magnetoresistance (MR) behaviors have been explained on the basis of universal model for MR isotherms which strongly support the role of electronic phase fluctuations and disordered LFO/LCMO interface. Present research findings demonstrate a practical approach to tune the resistive state of functional oxides by precisely controlling the interface between them. This also serves a better way to control the resistive state of functional oxide thin films by applying external magnetic field and to understand related charge conduction processes.

The approximate numerical approach for the system of coupled nonlinear ordinary differential equations (ODEs) of a biochemical reaction model is very important for biochemists and scientist working in the field of biochemistry and related issues.Within this article, two computational algorithms for numerically solving a biochemical reaction model with timefractional derivatives are examined and compared.The first technique depends on the collocation method along with the shifted Jacobi operational matrix for fractional derivative defined in the Caputo sense, and using this technique, we created a system of algebraic equations from the given fractional model.Another approach is centered on the basic theorem of fractional calculus and the characteristics of Newton's polynomial interpolation (NPI).We use these two methods to compute solution for the fractional biochemical reaction model.The model's computational outcomes are compared by using the recommended techniques in this work.Graphical and tabular forms are used to confirm the reliability and effectiveness of both techniques and an excellent match is discovered.