Multistep Methods Research Articles

Preparation of Highly Efficient and Stable All-Inorganic CsPbBr3 Perovskite Solar Cells Using Pre-Crystallization Multi-Step Spin-Coating Method

All-inorganic CsPbBr3 perovskite solar cells have garnered extensive attention in the photovoltaic domain due to their remarkable environmental stability. Nevertheless, CsPbBr3 prepared using the conventional sequential deposition method suffers from issues such as inferior crystallinity, low phase purity, and poor film morphology. Herein, we propose a pre-crystallization methodology by introducing a minute quantity of CsBr into the PbBr2 precursor solution to generate a small amount of CsPb2Br5 crystals within the PbBr2 film, leading to a porous PbBr2 film with enhanced crystallinity. Under the influence of more pores and CsPb2Br5 crystals as nucleation sites for inducing growth, a CsPbBr3 film with a larger crystal size, lower grain boundary density, stronger crystallinity, and higher phase purity is formed. Compared with untreated devices, photovoltaic devices prepared using the pre-crystallization method achieved a champion photovoltaic conversion efficiency (PCE) of 8.62%. Furthermore, pre-crystallized devices demonstrate higher stability than untreated ones and can still retain 94% of the original PCE after being exposed to air for 1000 h without encapsulating.

Supercooled large droplet size distribution effects on airfoil icing: A numerical investigation based on a new coupled Eulerian method

Supercooled large droplets (SLDs) under natural icing conditions have the characteristics of easy deformation in motion and easy splashing on impact, and a bimodal droplet size distribution that has received less attention. The modified form of the Rosin-Rammler function was improved to achieve a more accurate nonlinear fitting of the SLD distribution curve. The droplet size distribution was divided into non-equipartition continuous multiple components. The drag source term of each component was coupled with the overall droplet size distribution, and the Eulerian equations of each component of SLDs were solved simultaneously. A new coupled Eulerian method for non-equipartition continuous multi-size droplets was proposed to simulate the impact characteristics of SLDs, and the SLD collection coefficients were validated. Effects of the ratio between the number of large and small droplet components and the number of all components on the simulation results were investigated to select a better combination based on stable convergence calculation steps and the calculation time. This new method was added to the multi-step icing numerical method, and the accuracy and robustness of the method in icing shape prediction were verified based on the freezing drizzle, median volume diameter < 40 μm (FZDZ, MVD < 40 μm) icing condition. Airfoil icing characteristics based on the bimodal and monomodal distribution were compared, and the icing shapes at the leading edge were similar. Still, the upper and lower limits of the icing shapes with the bimodal distribution were nearer to the trailing edge and the ice layer was thicker there.

Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study

A potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the man-made groundwater reservoir is modeled as a coupled poroviscoelastic–viscoelastic medium, and the underlying wave propagation problem is solved using a three-dimensional discontinuous Galerkin method coupled with an Adams–Bashforth time stepping scheme. The wave problem solver is used to generate databases for the neural network-based machine learning model to estimate the water volume. In the numerical examples, we investigate a deconvolution-based approach to normalize the effect from the source wavelet in addition to the network's tolerance for noise levels. We also apply the SHapley Additive exPlanations method to obtain greater insight into which part of the input data contributes the most to the water volume estimation. The numerical results demonstrate the capacity of the fully connected neural network to estimate the amount of water stored in the porous storage reservoir.

Enhancing Water Pollution Management Through a Comprehensive Fractional Modeling Framework and Optimal Control Techniques

Water pollution poses a significant threat to public health, particularly in developing nations. This study aims to enhance our understanding of water pollution transmission dynamics by introducing a novel mathematical model within a general fractional framework. The model offers a comprehensive analysis, including assessing solution feasibility and the stability of equilibrium points. To effectively implement this model, we develop an efficient numerical scheme based on the trapezoidal method. Furthermore, we conduct a thorough error discussion and convergence analysis. Notably, we devise and evaluate a new strategy to effectively tackle the associated fractional optimal control problem concerning water pollutant transmission. Applying this approach to a real case demonstrates its substantial impact, notably in reducing non-soluble contaminants within the water transmission system.

Direct Zeptomole Detection of RNA Biomarkers by Ultrabright Fluorescent Nanoparticles on Magnetic Beads.

Nucleic acids are important biomarkers in cancer and viral diseases. However, their ultralow concentration in biological/clinical samples makes direct target detection challenging, because it leads to slow hybridization kinetics with the probe and its insufficient signal-to-noise ratio. Therefore, RNA target detection is done by molecular (target) amplification, notably by RT-PCR, which is a tedious multistep method that includes nucleic acid extraction and reverse transcription. Here, a direct method based on ultrabright dye-loaded polymeric nanoparticles in a sandwich-like hybridization assay with magnetic beads is reported. The ultrabright DNA-functionalized nanoparticle, equivalent to ≈10 000 strongly emissive rhodamine dyes, is hybridized with the magnetic bead to the RNA target, providing the signal amplification for the detection. This concept (magneto-fluorescent sandwich) enables high-throughput detection of DNA and RNA sequences of varied lengths from 48 to 1362nt with the limit of detection down to 0.3 fm using a plate reader (15 zeptomoles), among the best reported for optical sandwich assays. Moreover, it allows semi-quantitative detection of SARS-CoV-2 viral RNA directly in clinical samples without a dedicated RNA extraction step. The developed technology, combining ultrabright nanoparticles with magnetic beads, addresses fundamental challenges in RNA detection; it is expected to accelerate molecular diagnostics of diseases.

Multistep Iterative Methods for Solving Equations in Banach Space

The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, the uniqueness of the required solution that can be computed under ω-continuity, and conditions on the first derivative, which is on the method. But, earlier studies used high-order derivatives, even though those derivatives do not appear in the body structure of the proposed method. In addition to this, they did not propose computable estimates and semi-local convergence. We checked the applicability of our study to three real-life problems for semi-local convergence and two problems chosen for local convergence. Based on the obtained results, we conclude that our approach improves its applicability and makes it suitable for challenges in applied science.

Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results

In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, the same derivative than in the previous step. Initially, we develop a quad-parametric class with a first-order convergence rate. Subsequently, by restricting one of its parameters, we accelerate the convergence to achieve a third-order uni-parametric family. We thoroughly investigate the convergence properties of this final class of iterative methods, assess its stability through dynamical tools, and evaluate its performance on a set of test problems. We conclude that there exists one optimal fourth-order member of this class, in the sense of Kung–Traub’s conjecture. Our analysis includes stability surfaces and dynamical planes, revealing the intricate nature of this family. Notably, our exploration of stability surfaces enables the identification of specific family members suitable for scalar functions with a challenging convergence behavior, as they may exhibit periodical orbits and fixed points with attracting behavior in their corresponding dynamical planes. Furthermore, our dynamical study finds members of the family of iterative methods with exceptional stability. This property allows us to converge to the solution of practical problem-solving applications even from initial estimations very far from the solution. We confirm our findings with various numerical tests, demonstrating the efficiency and reliability of the presented family of iterative methods.

A Fuzzy Optimal Base Stock System for Tolerant Clients

Base stock is an amount of stock that a company requires to maintain in order to handle an unexpected huge demand. To lerant clients are the clients who are tolerant to the company’s delayed supply, who come back to the same company even if their demands are not met within their expected time. This implies that the clients are solely relied on that company. Marketing manager requires to maintain on hand to satisfy such tolerant clients’ demands with some delay, no longer than expected by that tolerant client.This paper diagnosis the performance measures of optimal base stock system for tolerant clients in fuzzy environment. The fuzzy numbers can be modified to crisp number with the help of fuzzy ranking methods. Here the used fuzzy ranking method is prominent for de-fuzzification. The famous Triangular fuzzy number and Trapezoidal fuzzy number methods are played a major role for de-fuzzification. At last, the optimization of base stock is verified with numerical examples in fuzzy environment.

Raspberry ketone loaded self nanoemulsifying system of cardamom oil: Assessment of phase behavior, dissolution rate and anti-hyperlipidemic activity

Raspberry ketone (RK), a polyphenolic antioxidant, possesses free radical scavenging against oxidative species and has potential of anti-inflammatory, anti-proliferative and anti-aging activities. Major pharmaceutical restriction associated with RK is its poor dissolution characteristic owing to its hydrophobic nature. Present investigation is an attempt to improve dissolution behavior of RK using cardamom oil (CO) based self nanoemulsifying system (SNE) design and preclinical assessed for anti-hyperlipidemic activity. Demarcation of phase boundaries to exactly locate nanoemulsion areas were explored using ternary plots drawn between CO as oil phase, Tween 80/PEG 600 as Smix at 1:1; 1:2; 2:1 and 3:1 ratios. Previously ternary components were selected on the basis of solubility of RK and aqueous dispersibility of CO. Nanoemulsion areas developed under ternary phase region were quantified using trapezoidal method and found in the order 1:1 > 1:2 > 3:1 > 2:1 of Smix. Aqueous dilutibility of SNEs followed the pattern of dilutions lines drawn across the ternary phase and its interference. Optimized SNE produced 97.1 % transmittance with average droplet size 101 nm, zeta potential −2.27 mV and 0.186 mS/cm conductivity. In-vitro RK release was examined in HCl buffer at pH 1.2 and phosphate buffer at pH 6.8 showed a significant difference in the RK dissolved (p < 0.01) compared to RK suspension (control F6). Optimized formulation (F3) at two doses level (RK loading of 80 and 160 mg/kg) vs. RK suspension (160 mg/kg) was pre-clinically administered for four weeks to assess anti-hyperlipidemic activity. Lipid profile markers (levels of VLDL, HDL, LDL, total triglyceride and total cholesterol) were significantly reduced from nanoemulsion formulation as compared to its suspension. SNE formulations were stable with no appreciable loss in quality and performance for six month storage at 30 ± 2 °C; 65 ± 5 % RH conditions. CO based SNE design significantly extended the ternary area for nanoemulsion development as well as RK solubility; which in turn improved dissolution rate of RK and showed anti-hyperlipidemic activity.

Development of Neurospecific Assessment Scale for Nomophobics – An Observational Study

Abstract Background: Nomophobia is a condition where people feel anxious or tense when they need to disconnect from their phone or other Internet-connected devices. Because of this elevated level of dependence on modern gadgets to offload the cognitive demands of life, anxiety develops when they are expected to be detached from it. The role of neurospecific domains such as cognitive flexibility, memory, attention, information processing, inhibitory control, and reward perception has previously been studied in nomophobics. However, there is no tool developed yet that quantifies the affection of these neurospecific domains in nomophobics. Objective: The objective of this study was to develop a scale for the assessment of “Neurospecific Domains” (in terms of memory, attention, cognitive flexibility, inhibitory control, information processing, and reward perception) among nomophobics. Methods: The neurospecific assessment scale for nomophobics (NSASN) was developed using a multistep method which included conceptualization and item generation followed by one round of expert validation of the item and of the scale. The content validity index was used to validate the various domains in the scale. Results: The computed content validity final score for Round 1 of the scale was found to be 0.79. Conclusion: The NSASN was developed to assess neurospecific domains among nomophobics and achieved a statistically satisfactory content validity.

Numerical approximation of a generalized time fractional partial integro-differential equation of Volterra type based on a meshless method

The moving least squares (MLS) approximation is used in this study to solve time-fractional partial integro-differential equations (TFPIDE). In our approach, we approximate the time Caputo fractional derivative term and the integral term by using a finite difference scheme and trapezoidal method, respectively, which yields an order of accuracy of O(τ+τ2−α), where 0<α<1. We thoroughly investigate the applicability and validity of the proposed method and provide an error estimate for its performance. Additionally, we solve various numerical problems to demonstrate the accuracy and computational efficiency of our approach, confirming the theoretical findings.

Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model

The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.

Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model

The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.

Numerical Simulation Model of the Infectious Diseases by Comparing Backward Euler Method and Adams-Bash forth 2-Step Method

In this work, the Backward Euler technique and the Adams-Bashforth 2-step method—two numerical approaches for solving the SIR model of epidemiology are compared for performance. An essential resource for comprehending the transmission of infectious illnesses like COVID-19 in the SIR model. While the explicit Adams-Bash forth 2-step approach is well known for its computing efficiency, the implicit Backward Euler method is noted for its stability. The study evaluates the accuracy, strength, and computing cost of the two approaches to determine which approach is best for simulating the spread of infectious illnesses. The SIR Model was easily solved using the Adams Bashforth 2-step analysis and the Backward Euler method. The approaches' solutions are close to the exact requirements. There are important distinctions between the two-step Adams Bashforth and backward Euler procedures. The running time of the Adams Bashforth 2-step backward Euler method is shorter than that of the backward Euler method.

Fifth-order A(α)-stable block hybrid adams-moulton method for solutions of predator-prey and Lorenz Systems

Problems associated with nonlinearity in predator-prey and chaotic nature embedded in Lorenz system place a significant challenge on numerical methods for their solutions. Some numerical methods may become unstable as step size increases. In this study, a fifth-order A(alpha )-stable (alpha = 89.90 ) k-step block hybrid Adams-Moulton method (BHAMM) was derived incorporating 16/9 as an off-step interpolation point using multistep collocation and matrix inversion technique. Choice of the off-step point of the BHAMM was in the upper part of interval of interpolation points. It was shown that the derived block method was consistent and zero-stable hence a convergent block method. Numerical simulations of predator-prey and Lorenz systems with the newly derived k=3 BHAMM indicated that it was adequate and compared well with Matlab ode23s.

On the Influence of Fractional-Order Resonant Capacitors on Zero-Voltage-Switching Quasi-Resonant Converters

This paper focuses on the influence of the fractional-order (FO) resonant capacitor on the zero-voltage-switching quasi-resonant converter (ZVS QRC). The FO impedance model of the capacitor is introduced to the circuit model of the ZVS QRC; hence, a piecewise smooth FO model is developed for the converter. Numerical solutions of the converter are obtained by using both the fractional Adams–Bashforth–Moulton (F-ABM) method and Oustaloup’s rational approximation method. In addition, the analytical solution of the converter is obtained by the Grünwald–Letnikov (GL) definition, which reveals the influence of the FO resonant capacitor on the zero-crossing point (ZCP) and resonant state of the converter. An experimental platform was built to verify the results of the theoretical analysis and numerical calculation.

A Multistep Method for Integration of Perturbed and Damped Second-Order ODE Systems

Based on the Ψ-functions series method, a new numerical integration method for perturbed and damped second-order systems of differential equations is presented. This multistep method is defined for variable step and variable order (VSVO) and maintains the good properties of the Ψ-functions series method. In addition, it incorporates a recurring algebraic procedure to calculate the algorithm’s coefficients, which facilitates its implementation on the computer. The construction of Ψ-functions and the Ψ-functions series method are presented to address the construction of both explicit and implicit multistep methods and a predictor–corrector method. Three problems analogous to those solved by the Ψ-functions series method are analyzed, contrasting the results obtained with the exact solution of the problem or with its first integral. The first example is the integration of a quasi-periodic orbit. The second example is a Structural Dynamics problem associated with an earthquake, and the third example studies an equatorial satellite with perturbation J2. This allows us to compare the good behavior of the new code with other prestige codes.

CO2 Electroreduction by Engineering the Cu2O/RGO Interphase

In the present investigation, Cu2O-based composites were successfully prepared through a multistep method where cubic Cu2O nanoparticles (CU Cu2O) have been grown on Reduced Graphene Oxide (RGO) nanosheets. The structural and morphological properties of the materials have been studied through a comprehensive characterization, confirming the coexistence of crystalline Cu2O and RGO. Microscopical imaging revealed the intimate contact between the two materials, affecting the size and the distribution of Cu2O nanoparticles on the support. The features of the improved morphology strongly affected the electrochemical behavior of the composites, increasing the activity and the faradaic efficiencies towards the electrochemical CO2 reduction reaction process. CU Cu2O/RGO 2:1 composite displayed selective CO formation over H2, with higher currents compared to pristine Cu2O (−0.34 mA/cm2 for Cu2O and −0.64 mA/cm2 for CU Cu2O/RGO 2:1 at the voltage of −0.8 vs. RHE and in a CO2 atmosphere) and a faradaic efficiency of 50% at −0.9 V vs. RHE. This composition exhibited significantly higher CO production compared to the pristine materials, indicating a favorable *CO intermediate pathway even at lower voltages. The systematic investigation on the effects of nanostructuration on composition, morphology and catalytic behavior is a valuable solution for the formation of effective interphases for the promotion of catalytic properties providing crucial insights for future catalysts design and applications.

United States Marine Corps Recruit Training Demands Associated With Performance Outcomes.

United States Marine Corps' (USMC) recruit training is a 13-week program designed to maximize physical and mental performance adaptations. The purpose of this study was to evaluate the training demands and characteristics that are associated with performance outcomes during USMC recruit training. A total of 196 recruits (M = 97 and W = 99) were monitored and tested throughout training. Laboratory-based performance testing occurred at the start of weeks 2 and 11 and consisted of body mass assessments, countermovement vertical jump, and isometric mid-thigh pull. Military-specific performance testing occurred twice within the first 8 weeks of training and included the physical fitness test (PFT) and combat fitness test (CFT) implemented by the USMC. Resilience data were collected at week 2 using the Connor-Davidson Resilience Scale. Workload, sleep, and stress responses were monitored at weeks 2, 7, and 11. Recruits were provided with a wearable tracking device which utilized heart rate and accelerometry-based technology to determine energy expenditure (EE), distances (DIS), and sleep metrics. Data were averaged over a 3-day period. Salivary cortisol testing occurred at the start of each monitoring week. Change scores were calculated for performance tests, and body mass was calculated from data obtained at week 2 to week 11. Area under the curve was calculated for the workload, sleep metrics, and cortisol responses using the trapezoidal method. Pearson product-moment correlations (r) were used to assess the relationships between training demands and performance. An α level of 0.05 was used to establish significance. A moderate positive correlation was found between changes in body mass and peak power (P < .001; r = 0.43). Weak positive correlations were found between changes in body mass and peak force (P = .002; r = 0.28), as well as body mass and resilience (P = .03; r = 0.19). A moderate negative correlation was observed between changes in body mass and PFT (P < .001; r = -0.49). A weak negative correlation was found between changes in body mass and EE (P = .003; r = -0.24). A weak negative correlation was found between changes in peak power and EE (P = .001; r = -0.29). A weak positive correlation was found between changes in peak power and changes in CFT (P = .05; r = 0.19) A weak negative correlation was found between changes in sleep continuity and CFT (P = .02; r = -0.20). A weak negative correlation was found between cortisol and changes in PFT (P = .05; r = -0.20). A weak negative correlation was found between cortisol and both EE (P = .001; r = -0.27) and DIS (P = .045; r = -0.16). A weak negative correlation was found between EE and sleep continuity (P < .001; r = -0.34). Weak negative correlations were found between sleep duration and both DIS (P = .01; r = -0.18) and steps (P = .003; r = -0.21). Increases in body mass throughout training were positively associated with strength and power changes, but negatively related to PFT scores. Changes in peak power related to improvements in CFT scores; however, higher workloads (i.e., EE) were negatively associated with peak power. The identification of the USMC physical and physiological training demands that are associated with performance outcomes may be a valuable resource to guide conditioning efforts to boost military readiness.

Power and Mittag–Leffler laws for examining the dynamics of fractional unemployment model: A comparative analysis

Unemployment is a major problem worldwide and is one of the key factors determining a nation’s economic status. The issue of unemployment is made more difficult globally by the ongoing rise in labor force participation and the scarcity of job positions. In this work, we study the unemployment model with two distinct fractional-order derivatives: the Caputo operator and the Atangana–Baleanu operator in the sense of Caputo (ABC). These derivatives under consideration are the operators widely utilized in modeling real-world phenomena in fractional dynamics. The existence and uniqueness of the solutions to the fractional model under consideration are ascertained using the fixed-point theory. The Hyers-Ulam analysis is employed to determine stability. For the numerical results, we present an Adams-type predictor–corrector (PC) technique for Caputo derivative and an extended Adams Bashforth (ABM) method for Atangana–Baleanu derivative. The outcomes achieved with the Atangana–Baleanu–Caputo and Caputo derivatives are identical to those of the regular case when fractional order ν=1.00. However, the results obtained change slightly as fractional order assumes values smaller than one, and this variation becomes most noticeable when the fractional order ν<0.72. This is because of the fractional derivative definitions’ underlying kernel. It is shown that the Mittag–Leffler kernel derivative provides better results for smaller fractional orders.