Multistep Methods Research Articles

Tailoring MnO2 nanowire defects with K-doping for enhanced electrochemical energy storage in aqueous supercapacitors

The fabrication of supercapacitors with outstanding performance is presented with a distinct defect-rich nanostructures. A one-pot, energy-efficient method for synthesizing defective manganese dioxide nanowires doped with potassium (K0.35MnO2) was developed. The introduction of potassium ions at 35 % birnessite resulted in a significant increase in lattice defects and an improvement in conductivity. Addition of KOH induces a phase transition from α-MnO2 to δ-MnO2. These imperfections result in a greater quantity of active sites, which are crucial for the process of energy storage. The K0.35MnO2 structure demonstrates a 405F/g increased capacity at a current density of 1 A/g. The asymmetric supercapacitor (K0.35MnO2/AC) that was manufactured exhibits a capacitance of 106.4F/g when operating at 1 A/g, while maintaining a maximum energy density of 71.5 Wh kg−1 and a power density of 672 W kg−1. Furthermore, 92.7 % of the initial capacitance of the device is retained even after 8,000 cycles at 20 A/g. This study presents novel insights into the production of defective materials for energy storage applications through the utilization of a one-pot process as opposed to the multi-step method. In order to produce high-performance supercapacitors for practical applications, the results indicate that defect engineering is a crucial factor.

Strong stability preserving second derivative multistep methods

Strong stability preserving second derivative multistep methods

Improved gene editing and fluorescent-protein tagging in Aspergillus nidulans using a Golden Gate-based CRISPR-Cas9 plasmid system

CRISPR-Cas9 systems can be used for precise genome editing in filamentous fungi, including Aspergillus nidulans. However, current CRISPR-Cas9 systems for A. nidulans rely on relatively complex or multi-step cloning methods to build a plasmid expressing both Cas9 and an sgRNA targeting a genomic locus. In this study we improve on existing plasmid-based CRISPR-Cas9 systems for Aspergilli by creating an extremely simple-to-use CRISPR-Cas9 system for A. nidulans genome editing. In our system, a plasmid containing both Cas9 and an sgRNA is assembled in a one-step Golden Gate reaction. We demonstrate precise, scarless genome editing with nucleotide-level DNA substitutions, and we demonstrate markerless gene tagging by fusing fluorescent-protein coding sequences to the endogenous coding sequences of several A. nidulans genes. We also describe A. nidulans codon-adjusted versions of multiple recent-generation fluorescent proteins, which will be useful to the wider Aspergillus community.

Development and validation of a questionnaire to evaluate attitude about menstruation among adolescent girls

Abstract: CONTEXT: Cultural influences promote secrecy, making it difficult for girls to openly discuss menstruation. This further impacts their attitude and emotional well-being. Showing adolescent girls the reality of menstruation would give them a clear understanding of menstruation. AIMS: The aim of this study was to develop and validate a questionnaire to evaluate attitude about menstruation among Adolescent girls. SETTINGS: Adolescent girls in Belagavi city. DESIGN: Exploratory study. SUBJECTS AND METHODS: The Adolescent Menstrual Attitude Inventory Questionnaire (AMAI-Q) was developed using a multistep method divided into two phases. Phase I: Concept elicitation, which includes identification of domains and item generation; and expert input, which includes content validation. Phase II: Pilot testing of 11 adolescent girls and reliability calculation using Cronbach’s alpha. STATISTICAL ANALYSIS USED: The content validity index of the questionnaire was calculated, and the reliability of the questionnaire was assessed using Cronbach’s alpha. RESULTS: The content validity of the questionnaire was tested using the content validity index, which was found to be 0.911. Reliability was assessed using Cronbach’s alpha and was found to be 0.818, indicating good reliability. CONCLUSIONS: The proposed questionnaire, AMAI-Q is well-validated, easy to administer, and has good reliability. AMAI-Q will be a suitable scale to evaluate attitude about menstruation among adolescent girls.

A besyian regularisation neural network approach for hepatitis B virus spread prediction and immune system therapy model

The primary aim of the article is to analyze the response of the human immune system when it encounters the hepatitis B virus. This is done using a mathematical system of differential equations. The differential equation system has six components, likely representing various aspects of the immune response or virus dynamics. A Bayesian regularization neural network has been presented in the process of training. These networks are employed to find solutions for different categories or scenarios related to hepatitis B infection. The Adams method is used to generate reference data sets. The back-propagated artificial neural network, based on Bayesian regularization, is trained and validated using the generated data. The data is divided into three sets: 90% for training and 5% each for testing and validation. The correctness and effectiveness of the proposed neural network model have been assessed using various evaluation metrics. The metrics have been used in this study are Mean Square Error (MSE), histogram errors, and regression plots. These measures provide support to the neural network to approximate the immune response to the hepatitis B virus.

About One Multistep Multiderivative Method of Predictor-Corrector Type Constructed for Solving İnitial-Value Problem for ODE of Second Order

Considering the wide application of the initial-value problem for Ordinary Differential Equations second-order with a special structure, here for solving this problem constructed the special Multistep Multiderivative Methods. Many scientists studied this problem , but the most distinguishing is the Ştörmer. To solve this problem here is proposed to use the Multistep Second derivative Method with a special structure. This method has been generalized by many authors, which is called as the linear Multistep Multiderivative Methods with the constant coefficients. Many authors shave shown that the Multistep Second derivative Method can be applied to solve the initial-value problem for ODEs of the first order. Euler himself using his famous method discovered that, in his method when moving from one point to another local truncation errors add up, the results of which reach a very large value. To solve this problem, he suggested using more accurate methods. For this aim, Euler proposed calculating the next term in the Taylor series of the solutions of the investigated problem. Developing this idea and papulation of the Multistep Multiderivative Methods here to solve the named problem it is suggested to use MultistepThriedderivative Methods, taking into account that methods of this type are more accurate. For the demonstration above, receiving results here have constructed some concrete methods. Also by using some of Dahlquist’s and Ibrahimov’s results for Multistep Methods with the maximum order of accuracy were compared. Proven that the MultistepThriedderivative Methods are more accurate than the others. By using model problems have illustrated some results received here.

Plasmonic semi shells derived from simultaneous in situ gold growth and anisotropic acid etching of ZIF-8 for photothermal ablation of metastatic breast tumor

Open nanoshells such as nanobowls or nanocups collectively described as ‘semi shells’ have unique plasmonic properties due to their lack of symmetry. So far, their fabrication was based on multistep and laborious methods such as solid state sputter coating or selective deposition/etching using sacrificial templates. In this work, we report a rapid one step colloidal synthetic protocol for PEGylated semi-shell (SS) fabrication by simultaneous facet specific anisotropic chemical etching of rhombic dodecahedral ZIF-8 and heterogenous nucleation & growth of gold. The SS possesses a strong localized surface plasmon resonance in the near-infrared region, which is retained after surface passivation with polyethylene glycol and subsequent cryopreservation for extended shelf-life. Freshly reconstituted PEGylated SS was found to be safe & non-toxic in healthy C57BL/6 mice post intravenous administration. The PEGylated SS displayed significant photothermal efficiency of ~37% with 808 nm laser irradiation. Preclinical assessment of intra-tumoral photothermal efficacy indicated complete remission of primary breast tumor mass with insignificant metastasis to vital organs in 4T1 FL2 tumor bearing CD1 nude mice. Further, PEGylated SS mediated photothermal therapy also yielded morbidity free survivael of 75% for up to 90 days, indicating their potential to significantly improve outcomes in advanced breast tumors.

Paradigm on Levenberg–Marquardt neural algorithm analysis of heat conduction optimization for ternary hybrid nanofluid with entropy generation

AbstractThe significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption (λ), magnetic strength (Tesla M), radiation parameter (Rd), Brownian motion (Br), and Eckert number (Ec). The findings have practical significance for optimizing material design in engineering and industrial applications.

An extended study of two multistep higher order convergent methods for solving nonlinear equations

The local analysis of convergence for two competing methods of order seven or eight is developed to solve Banach space‐valued equations. Previous studies have used the eighth or ninth derivative of the operator involved, which do not appear on the methods, to show the convergence of these methods on the finite‐dimensional Euclidean space. In addition, no computable error distances or isolation of the solution results are provided in this study. These problems limit the applicability of this method to solving equations with operators that are at least nine times differentiable. In the current study, only conditions on the first derivative, appearing in these methods, are employed to show the convergence of these methods. Moreover, computable error bounds depend on the distance in the world as well as the isolation of the solution. Results are provided based on generalized continuity conditions on the first derivative. Furthermore, the more interesting semi‐local analysis of convergence not given before these methods is presented using a majorizing sequence. Finally, a great deal of impressive numerical results has been shown on real‐world problems.

Inkjet assisted manufacturing of untethered magnetic devices: A comparison between three routes to pattern artificial water striders

AbstractUntethered devices controlled by an external magnetic field are becoming more and more widely used in a wealth of applicative fields: medicine, precise micromanipulation, and environment management. Their production strongly relies on the use of complex and time-consuming technologies typically borrowed from the microelectronic field. In an attempt to reduce costs and enhance manufacturing flexibility, additive manufacturing has been investigated as a relevant alternative for untethered microrobots production. Between the large number of additive manufacturing technologies, inkjet printing is relatively poorly investigated for the production of this kind of devices, and the present work aims at exploring its potential. The work establishes a comparison between different approaches for the inkjet manufacturing of magnetically guidable microdevices. In particular, it focuses on the manufacturing of fully inkjet-printed magnetic devices by proposing two methods of production. The first consists in the electroless metallization of non-magnetic devices printed with SU-8 resin, while the second is based on the inkjet printing of a dispersion of magnetic nanoparticles in SU-8 resin. As a result, inkjet-printed devices controllable by an external magnetic field can be obtained. Multi-step and one-step production methods are compared in terms of quality of the obtained elements, easiness of production, and mechanical properties. The morphology of the finished devices, their surface quality, and their magnetic actuability are analyzed and discussed.

Analysis of efficient discretization technique for nonlinear integral equations of Hammerstein type

Purpose This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, integrating past and present influences with nonlinear interactions. They are widely applied in control theory, population dynamics and physics. These equations are essential for solving complex real-world problems. Design/methodology/approach Demonstrating the solution’s existence and uniqueness in the equation is accomplished by using the Picard iterative method as a key technique. Using the trapezoidal discretization method is the chosen approach for numerically approximating the solution, yielding a nonlinear system of algebraic equations. The trapezoidal method (TM) exhibits quadratic convergence to the solution, supported by the application of a discrete Grönwall inequality. A novel Grönwall inequality is introduced to demonstrate the convergence of the considered method. This approach enables a detailed analysis of the equation’s behavior and facilitates the development of a robust solution method. Findings The numerical results conclusively show that the proposed method is highly efficacious in solving NVFHIEs, significantly reducing computational effort. Numerical examples and comparisons underscore the method’s practicality, effectiveness and reliability, confirming its outstanding performance compared to the referenced method. Originality/value Unlike existing approaches that rely on a combination of methods to tackle different aspects of the complex problems, especially nonlinear integral equations, the current approach presents a significant single-method solution, providing a comprehensive approach to solving the entire problem. Furthermore, the present work introduces the first numerical approaches for the considered integral equation, which has not been previously explored in the existing literature. To the best of the authors’ knowledge, the work is the first to address this equation, providing a foundational contribution for future research and applications. This innovative strategy not only simplifies the computational process but also offers a more comprehensive understanding of the problem’s dynamics.

Critical trigger of self-assembled bimetallic Fe/Mn-MOF with SnS2 heterojunctions by persulfate activation for efficient tetracyclines photodegradation

Developing advanced strategies, including exposing active site centers, regulating coordination environments, controlling crystallographic facets, optimizing electronic structures and constructing defects for enhancing photocatalytic performance is of great significance to improving the ecosystem. In this study, a novel self-assembled bimetallic Fe/Mn-MOF with SnS2 Z-scheme heterojunction photocatalyst was designed using a facile multistep solvothermal method. Benefiting from the interfacial heterojunction synergistic effect, the photocatalysts exhibited an outstanding catalytic performance. Nearly 91.4% efficiency of tetracyclines was degraded within 80 min through the assistance of a persulfate-based advanced oxidation process. DFT calculations utilizing the Fukui index identified the sites vulnerable to attack by the active species. As demonstrated by the trapping experiments and electron spin resonance (ESR), the involved oxygen-active species (•O2− and 1O2) facilitated the rapid degradation of tetracycline. The degradation pathways were further guided in the elucidation of the rationale mechanism and the toxicity of derived intermediates was revealed. This work opens a new strategy for the rational design of bimetallic photocatalysts, emphasizing interface-modulated heterojunctions for efficient solar energy conversion.

Fractional-ordered Adams–Bashforth–Moulton (FABM) method for [formula omitted] controllers’ numerical simulations for Direct Current (DC) motors in Electric Vehicles (EVs)

The model for the speed control in the Direct Current (DC) motors by developing different simulating models based upon Proportional Integral Derivative (PID) controllers with fractional-ordered Adams–Bashforth–Moulton (ABM) method has been developed. With the aim of more efficient insights, a general closed loop in PID type controllers have been constructed alongwith their implementation. PID control system consists of rule-set essential to monitor the different parameters of the environment. The control of mechanisms through Fractional-order controls (FOC) in real life applications require techniques that would build controllers; tune parameters for accurate and precise monitoring. It is known that PID controllers are sensitive to uncertainties which arise from imprecise knowledge of the kinematics and dynamics therefore an adaptive fractional PID (AFPID) controller has been proposed to use the robustness of fractional-ordered controller. In previous works, FPID controller parameters are constant during control process but in this study these parameters will be updated online with an adequate adaptation mechanism to have better results. Outcomes found to be consistent between represent a step towards understanding the relation between chaotic phenomena and fractional calculus. It has been observed that the PIηDλ control dynamics can boost the controllers’ performance by increase of tuning knobs. In addition, the initialization and execution time have decreased substantially from 2.64 to 0.87 secs and 0.5 to 0.15 secs.

Soil-structure interaction analysis of nuclear power plant structure using multi-step method in time-domain

Recently, several countries have experienced strong earthquakes, and there has been growing interest in the seismic design of structures. Particularly, consideration of soil-structure interaction (SSI) has become important when performing seismic response analysis for nuclear power plant (NPP) structures. A seismic analysis method that considers SSI in the time domain has been proposed in previous studies. This method is applicable to the seismic response of structures, because it can consider the influence of the SSI effect with the impedance function in the frequency domain and simultaneously considers the structural nonlinearity. However, it has only been applied to the structure comprising a single beam-stick. In this study, a modified method for applying it to more general structures is proposed, and its applicability is validated with an actual reactor containment building (RCB) structure comprising a three beam-sticks. Validation was performed by comparing the seismic responses with those of ACS SASSI. Using the proposed method, SSI analysis was performed with three soil profiles and the results were compared to investigate the effect of SSI on seismic responses, including the in-structure response spectrum (ISRS) and time history acceleration. For more realistic analysis, soil profile and earthquake input motion occurred in South Korea are adopted. Further, a multi-step method considering nonlinear behavior was also performed and compared with the linear case.

A low-complexity solution for LMIs of hardly constrained nonlinear MIMO tracking control systems

This research is dedicated to the discrete-time tracking control of nonlinear multi-input multi-output (MIMO) Newtonian mechanics systems with an equal number of inputs and outputs, in the presence of input saturation and high-order dynamics of the actuation system. Firstly, the continuous-time model of the plant and actuation system has been transformed into the discrete-time domain using Adams–Bashforth and Adams–Moulton discretization techniques. In the next step, considering saturation boundaries, the modified position and velocity references are derived using the discrete-time reaching law-based control approach. These modified references are obtained through an optimization algorithm that calculates the closest achievable position and velocity trajectories with respect to the desired reference trajectory. Modifying desired trajectories in MIMO systems results in the formation of a system of linear matrix inequalities (LMIs). Solving such systems of inequalities requires the use of complex methods, and this difficulty increases with the increase in the system’s degrees of freedom (DOFs). The proposed strategy offers a more straightforward approach to solving these inequalities. Once the modified references are calculated, the corresponding position and velocity control signals can be obtained using the mentioned reaching law strategies. The final step of the proposed algorithm is to combine the resulting position and velocity control signals using a Gaussian-weighted averaging method to form the main control signal. A desirable performance for the control system can be achieved by appropriately adjusting the standard deviations of the Gaussian weighing functions. To evaluate the performance characteristics of the proposed method, it has been applied in the tracking control procedure of a nonlinear 3-DOF mechanical system. The numerical simulation results demonstrate the effectiveness of the method.

Discretization methods and their extrapolations for two-dimensional nonlinear Volterra-Urysohn integral equations

In this paper, a class of nonlinear two-dimensional (2D) integral equations of Volterra type, i.e. Volterra-Urysohn integral equations, is studied. Following the ideas of [24], and assuming that the kernels of the integral equation are Lipschitz functions with respect to the dependent variable, the existence and uniqueness of a solution to the integral equation is shown by a technique based on the Picard iterative method. Then, the Euler and trapezoidal discretization methods are used to reduce the solution of the integral equation to the solution of a system of nonlinear algebraic equations. It is proved that the solution of the Euler method has first order convergence to the exact solution of the integral equation while the solution of the trapezoidal method has quadratic convergence. To prove the convergence of the trapezoidal method, a new Gronwall inequality is developed. Some numerical examples are given which confirm our theoretical results.

Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions

We propose a computation method for scattering poles of impedance obstacles. Boundary integral equations are used to formulate the problem. It is shown that the scattering poles are the eigenvalues of some integral operator. Then we employ the Nyström method to discretize the integral operator and obtain a nonlinear matrix eigenvalue problem. The eigenvalues are computed using a multistep parallel spectral indicator method. Numerical examples demonstrate the high accuracy of the proposed method and can serve as the benchmarks. Our study provides a practical approach and can be extended to other scattering problems. This paper continues our previous study on the computation method for scattering poles of sound-soft obstacles.

Heat transfer performance of regenerative cooling in the presence of supersonic combustion based on two-way decoupling method

As a promising active cooling method for aero engines, regenerative cooling with endothermic hydrocarbon fuel plays an important role in thermal protection systems. However, simply assuming the thermal boundary conditions for the numerical simulation of regenerative cooling as either Dirichlet or Neumann boundary conditions is often unsuitable, as the combustion process exhibits complex three-dimensional (3D) characteristics. We propose a novel multi-step iterative calculation method in this work to simulate the coupled flow and heat transfer between supersonic combustion in the combustor and regenerative cooling outside. The method captures the main features of the supersonic combustion including different shockwave structures, and generates a realistic 3D distribution of heat flux as the boundary condition for the regenerative cooling study. With improved simulation, the result shows that regenerative cooling significantly reduces the peak temperature of the combustor by 58.5% with a mass flow rate of 1 g/s. A local high-temperature region is observed on the coupled wall inside the combustor near the injector, where the flame is primarily concentrated. Increasing the mass flow rate by 100%, from 1 g/s to 2 g/s, leads to a reduction in the maximum wall temperature by up to 15.7%.

Honeycomb-like porous carbons derived from multistep pyrolysis of artificial humic acids as efficient sorbents for removing diethyl phthalate

The uprecycling of hydrothermal liquid waste-derived artificial humic acids into stable carbon materials is helpful for advancing the development of hydrothermal carbonization technology, but it has rarely been investigated. For the first time, a multistep pyrolysis method was designed to convert artificial humic acids into honeycomb-like porous carbons (PCs). The obtained PCs exhibited a high specific surface area, reaching 1728.55 m2/g, while nonactivation treatment still provided a high value of 1425.14 m2/g. The high-pyrolysis process yielded graphite-like structures and maintained surface functional groups. PCs have been applied as sorbents to remove the emerging plasticizer diethyl phthalate (DEP) in water environments and exhibit promising sorption capabilities (as high as 993.30 mg/g), which are much higher than those reported for other sorbents. The sorption rate was controlled by mass transfer and chemical-like sorption, whereas the sorption capability was controlled mainly by the adsorption process, especially pore filling. Partitioning, hydrogen bonding, pore filling and π–π stacking are possible sorption mechanisms. In addition to the specific surface area, the pore volume is a suitable parameter for assessing the sorption capability. Exogenous dissolved organic matter can affect the sorption of DEP onto PCs through cosorption and coverage of their surface, but its influence is limited. Excellent sorption performance can cover a wide range of pH conditions. The prepared PCs also showed notable reusability and practicality. In this study, an excellent method was proposed for recycling hydrothermal liquid waste and preparing PCs, and the prepared PCs exhibited great potential for environmental remediation.

FPGA Implementation of Sliding Mode Control and Proportional-Integral-Derivative Controllers for a DC–DC Buck Converter

DC–DC buck converters have been designed by incorporating different control stages to drive the switches. Among the most commonly used controllers, the sliding mode control (SMC) and proportional-integral-derivative (PID) controller have shown advantages in accomplishing fast slew rate, reducing settling time and mitigating overshoot. The proposed work introduces the implementation of both SMC and PID controllers by using the field-programmable gate array (FPGA) device. The FPGA is chosen to exploit its main advantage for fast verification and prototyping of the controllers. In this manner, a DC–DC buck converter is emulated on an FPGA by applying an explicit multi-step numerical method. The SMC controller is synthesized into the FPGA by using a signum function, and the PID is synthesized by applying the difference quotient method to approximate the derivative action, and the second-order Adams–Bashforth method to approximate the integral action. The FPGA synthesis of the converter and controllers is performed by designing digital blocks using computer arithmetic of 32 and 64 bits, in fixed-point format. The experimental results are shown on an oscilloscope by using a digital-to-analog converter to observe the voltage regulation generated by the SMC and PID controllers on the DC–DC buck converter.