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Collocation Method for the Numerical Solution of Multi-Order Fractional Differential Equations 多阶分数阶微分方程数值解的配点法
Pub Date : 2023-06-04 DOI: 10.46481/jnsps.2023.1075
G. Aji̇leye, A. James
This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in the Caputo sense. The problem was transformed from its integral form into a system of linear algebraic equations. Using matrix inversion, the algebraic equations are solved and their solutions are substituted into the approximate equation to give the numerical results. The effectiveness and precision of the method were illustrated with the use of numerical examples.
本文提出了一种卡普托意义上具有初始条件的多阶分数阶微分方程数值积分的配位方法。这个问题由积分形式转化为线性代数方程组。采用矩阵反演的方法,对代数方程进行求解,并将其解代入近似方程,得到数值结果。通过算例说明了该方法的有效性和精度。
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引用次数: 0
Numerical Analysis of Fractional-Order Dynamic Dengue Disease Epidemic in Sudan 苏丹分数阶登革热动态流行的数值分析
Pub Date : 2023-05-28 DOI: 10.46481/jnsps.2023.1464
Fathelrhman EL Guma, O. Badawy, Mohammed Berir, Mohamed A. Abdoon
The main idea of this work is numerical simulation and stability analysis for the fractional-order dynamics of the dengue disease outbreak in Sudan. This research uses a computer technique based on the Adams-Bashforth approach to numerically resolve a fractional-order dengue epidemic in Sudan. Analyses of numerical and dynamic stability show that the fractional-order dengue fever model is sensitive to initial conditions for those parameters. Therefore, the parameters’ values are critical in establishing how many individuals will get better from their sickness and how many will become ill. The proposed method is effective in providing an illustration of the solution’s dynamics over a very long horizon of time, which is crucial for making accurate predictions about the spread of dengue in Sudan. In addition, this method can be utilized to assess the efficacy of various intervention strategies and inform public health policies aimed at reducing the burden of dengue fever in Sudan. It can also assist in identifying areas most susceptible to dengue infestations and prioritizing disease control resources.
本工作的主要思想是对苏丹登革热疫情的分数阶动力学进行数值模拟和稳定性分析。本研究使用基于Adams-Bashforth方法的计算机技术,对苏丹的分数阶登革热流行进行数值解析。数值稳定性和动态稳定性分析表明,分数阶登革热模型对这些参数的初始条件很敏感。因此,这些参数的值对于确定有多少人会从疾病中恢复,有多少人会生病至关重要。所提出的方法有效地说明了在很长一段时间内解决方案的动态,这对于准确预测登革热在苏丹的传播至关重要。此外,该方法可用于评估各种干预战略的效力,并为旨在减轻苏丹登革热负担的公共卫生政策提供信息。它还可以帮助确定最易受登革热侵扰的地区,并确定疾病控制资源的优先次序。
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引用次数: 1
Non-Intrusive Load Monitoring (NILM), Interests and Applications 非侵入式负载监测(NILM),兴趣和应用
Pub Date : 2023-05-27 DOI: 10.46481/jnsps.2023.1208
Leonce W. Tokam, S. Ouro-Djobo
In developing effective energy management mechanisms, new concepts have been developed to provide new approaches. Non-intrusive load monitoring (NILM) is an approach that was originally developed to allow the occupants of a room to identify the contribution of each appliance to the total electricity consumption of the room through a single point measurement device. The aim is to provide customers with information that will enable them to act as ``  `  consum'actors", i.e., people who undertake to change their electricity consumption habits for an objective cause. The progress of artificial intelligence in its various forms (machine learning, big data, internet of things) have greatly contributed to increase the interest of NILM among researchers in different fields. Indeed, some of them are adapting this concept to research areas such as water, transport, health, the environment and agriculture. In this context, applications in these fields have been developed to show the potential and benefits of using this approach. In addition to presenting non-intrusive load monitoring (NILM) in its general framework, this article presents the interests and applications of this approach in various fields.
在发展有效的能源管理机制方面,已经发展了新的概念,提供了新的方法。非侵入式负载监测(NILM)是一种最初开发的方法,允许房间的居住者通过单点测量设备确定每个设备对房间总耗电量的贡献。其目的是向客户提供信息,使他们能够成为“消费者行为者”,即承诺为客观原因改变其用电习惯的人。各种形式的人工智能(机器学习、大数据、物联网)的进步极大地促进了不同领域研究人员对NILM的兴趣。事实上,他们中的一些人正在将这一概念应用于水、交通、卫生、环境和农业等研究领域。在这种情况下,已经开发了这些领域的应用程序,以显示使用这种方法的潜力和好处。除了介绍非侵入式负载监测(NILM)的一般框架外,本文还介绍了该方法在各个领域的兴趣和应用。
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引用次数: 0
Approximate solution of space fractional order diffusion equations by Gegenbauer collocation and compact finite difference scheme 空间分数阶扩散方程的Gegenbauer配置和紧致有限差分格式近似解
Pub Date : 2023-05-22 DOI: 10.46481/jnsps.2023.1368
K. Issa, Steven Ademola Olorunnisola, T. Aliu, Adeshola Adeniran Dauda
In this paper, approximation of space fractional order diffusion equation are considered using compact finite difference technique to discretize the time derivative, which was then approximated via shifted Gegenbauer polynomials using zeros of (N - 1) degree shifted Gegenbauer polynomial as collocation points. The important feature in this approach is that it reduces the problems to algebraic linear system of equations together with the boundary conditions gives (N + 1) linear equations. Some theorems are given to establish the convergence and the stability of the proposed method. To validate the efficiency and the accuracy of the method, obtained results are compared with the existing results in the literature. The graphical representation are also displayed for various values of beta Gegenbauer polynomials. It can be observe in the tables of the results and figures that the proposed method performs better than the existing one in the literature.
利用紧致有限差分技术对空间分数阶扩散方程的时间导数进行离散化,并以移位的(N - 1)次移位的Gegenbauer多项式的零点为配点,利用移位的Gegenbauer多项式对时间导数进行逼近。该方法的重要特点是将问题简化为代数线性方程组,并结合边界条件给出(N + 1)个线性方程组。给出了一些定理,证明了该方法的收敛性和稳定性。为了验证该方法的有效性和准确性,将所得结果与文献中已有的结果进行了比较。图形表示也显示了各种值的 β Gegenbauer多项式。从结果表和图中可以看出,本文提出的方法优于现有文献中的方法。
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引用次数: 0
Pre-functions and Extended pre-functions of Complex Variables 复变量的预函数与扩展预函数
Pub Date : 2023-05-21 DOI: 10.46481/jnsps.2023.1427
Thirumalai A, Muthunagai K, R. Agarwal
Pre-functions are functions that possess a sequence ${f_{n}(z,beta)}$ which tends to one of the elementary functions as $n$ tends to infinity and $beta$ tends to 0. The main objective of this paper is to broaden the scope of pre-functions from functions of a real variable to functions of a complex variable by introducing pre-functions of a complex variable. We have analyzed the pre-functions of a complex variable for their properties. The pre-Laguerre, pre-Bessel and pre-Legendre polynomials of a complex variable have been obtained as special cases. Graphs have been used to visualize complex pre-functions.
预函数是具有序列${f_{n}(z,beta)}$的函数,该序列趋于一个初等函数,如$n$趋于无穷,$beta$趋于0。本文的主要目的是通过引入复变量的预函数,将预函数的范围从实变量的函数扩大到复变量的函数。我们分析了一个复变量的前函数的性质。作为特殊情况,得到了复变量的pre-Laguerre、pre-Bessel和pre-Legendre多项式。图形已用于可视化复杂的预函数。
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引用次数: 0
Evaluation of ANFIS Predictive Ability Using Computed Sediment from Gullies and Dam 利用沟坝泥沙计算评价ANFIS预测能力
Pub Date : 2023-05-21 DOI: 10.46481/jnsps.2023.1028
S. O. Oladosu, Alfred S. Alademomi, James Bolarinwa Olaleye, Joseph Olalekan Olusina, Tosin J. Salami
The study proposed an Adaptive Neuro-Fuzzy Inference Systems (ANFIS) model capable of predicting sediment deposited in a dam and sediment loss-in-transit (SLIT) using the potential of a formulated mathematical relation. The input parameters consist of five members viz: the rainfall, the slope, the particle size, the velocity, and the computed total volume of sediment exited from two prominent gullies for 2017, 2018, and 2019. The outputs are the total volume of sediment deposited at the adjoining Ikpoba dam for 2017, 2018, and 2019, respectively. The Ordinary Least Square (OLS) regression model on sediment volume retained all covariates with p<0.05, explaining 93.8% of the variability in the dataset. The multicollinearity effect on the dataset was assessed using the Variance Inflation Factor (VIF) which was found not to pose a problem for (VIF<5). The model was validated using the (MSE), the (MAE), and the correlation coefficient (r). The best prediction was obtained as: (RMSE = 0.0423; R2 = 0.947). The predicted volume of sediment was 842,895.8547m3 with an error of -0.3295344% and the predicted volume of SLIT was 57,787.98m3 which is an indication that ANFIS performs satisfactorily in predicting sediment volume for the gullies and the dam respectively
该研究提出了一个自适应神经模糊推理系统(ANFIS)模型,该模型能够利用公式数学关系的势来预测大坝的泥沙淤积和输沙损失(SLIT)。输入参数包括五个成员,即2017年、2018年和2019年的降雨量、坡度、粒径、流速和计算的两个主要沟道的泥沙总量。输出分别为2017年、2018年和2019年邻近Ikpoba大坝沉积的沉积物总量。泥沙体积的普通最小二乘(OLS)回归模型保留了所有协变量,p<0.05,解释了数据集中93.8%的变异。使用方差膨胀因子(VIF)评估数据集的多重共线性效应,发现对(VIF<5)不构成问题。利用(MSE)、(MAE)和相关系数(r)对模型进行验证,得到的最佳预测结果为:(RMSE = 0.0423;R2 = 0.947)。预测泥沙体积为842,895.8547m3,误差为-0.3295344%;狭缝预测泥沙体积为57,787.98m3,表明ANFIS对沟渠和坝体的泥沙体积预测效果较好
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引用次数: 0
Generation of Electricity From a Hydraulic Turbine in the Djonou River (Benin) Djonou河水轮机发电(贝宁)
Pub Date : 2023-05-21 DOI: 10.46481/jnsps.2023.1263
Mahouton Justine Carine Adjassa, G. Koto N’Gobi, H. Donnou, C. Kouchadé, B. Kounouhewa
The shortage of electricity in rural areas despite the hydraulic potential they possess is becoming a challenge for Benin. To date, nearly 140,000 people spread over the 42 lakeside villages of this country live in energy inaccessibility, insecurity and poverty. To overcome this situation, the present study is therefore interested in the production of electrical energy on an experimental basis in low water periods thanks to an Archimedean screw turbine which operates at low flow rates and height of fall on the river. Djonou located in southern Benin a few kilometers from the University of Abomey-Calavi. The geometrical and hydraulic parameters of the screw were therefore determined and the device was modeled using Autocard software. A prototype was then made with local recycled materials and tested on the river. The screw specifications indicate an inside and outside radius of 0.072 m and 0.135 m. The length of the screw was set at 0.46 m for a blade radius estimated at 0.137 m. The number of screw blades is equal to 2 with a flow rate of 0.049 $ m^{3}/s $. The inclination angle of the screw is $25^{circ}$. The device on the experimental site produces a voltage of 16 V and provides a current of about 0.12 A which can power a 2 W lamp. This performance of the prototype made on a small scale is a reliable indicator of the optimal use of this technology in the national hydraulic network of Benin to supply populations with electrical energy.
尽管农村地区具有水力潜力,但电力短缺正成为贝宁面临的挑战。迄今为止,分布在这个国家42个湖边村庄的近14万人生活在能源匮乏、不安全和贫困之中。为了克服这种情况,本研究因此对在低水期的实验基础上生产电能感兴趣,这要感谢阿基米德螺杆式涡轮机,该涡轮机在低流量和河上的落差高度下运行。约努位于贝宁南部,距离阿博米-卡拉维大学仅几公里。因此,确定了螺杆的几何和水力参数,并使用Autocard软件对该装置进行了建模。然后用当地的回收材料制作了一个原型,并在河上进行了测试。螺钉规格内半径为0.072 m,外半径为0.135 m。螺杆长度设定为0.46 m,叶片半径估计为0.137 m。螺旋叶片数为2,流速为0.049 $ m^{3}/s $。螺杆倾角为$25^{circ}$。实验现场的装置产生16v的电压,提供约0.12 a的电流,可以为2w的灯供电。小规模生产的原型机的这种性能是贝宁国家水力网络最佳利用这项技术向人口提供电能的可靠指标。
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引用次数: 0
Theoretical Study on 10C Elastic Scattering Cross Sections Using Different Cluster Density Distributions and Different Potentials 不同簇密度分布和不同电位下10C弹性散射截面的理论研究
Pub Date : 2023-05-21 DOI: 10.46481/jnsps.2023.1392
S. Olorunfunmi, A. Bahini, A. Olatinwo
Elastic scattering cross sections are a fundamental aspect of nuclear physics research, and studying the cross sections of various nuclei can provide important insights into the behavior of nuclei. In this study, the elastic scattering cross sections of 10C projectile by 27Al, 58Ni, and 208Pb target nuclei are analyzed. The aim of this study is to investigate the cluster structure of 10C and the sensitivity of the elastic scattering cross sections to different potentials. To achieve this objective, the double folding optical model and a simple cluster approach are used to analyze the cross sections. The real part of the optical potential is obtained by folding two different effective interactions, Michigan-3-Yukawa (M3Y) and JeukenneLejeune-Mahaux (JLM), with four different cluster density distributions of the 10C nucleus: 6Be + alpha, 9B + p, 8Be + p + p, and alpha + alpha + p + p. The imaginary part is taken to be a Woods-Saxon phenomenological form. The sensitivity of the elastic scattering cross sections to different potentials is assessed by comparing the results obtained using different potentials. The cluster structure of 10C is validated by comparing the theoretical results with experimental data. The results show that the cross sections are sensitive to the choice of potential used and that the cluster structure of 10C is validated. The theoretical results show reasonable agreement with the experimental data.
弹性散射截面是核物理研究的一个基本方面,研究各种核的截面可以为了解核的行为提供重要的见解。本研究分析了10C弹在27Al、58Ni和208Pb靶核作用下的弹性散射截面。本研究的目的是研究10C的团簇结构及其弹性散射截面对不同电位的敏感性。为了实现这一目标,使用双折叠光学模型和简单的聚类方法来分析截面。光势的实部通过折叠两个不同的有效相互作用,Michigan-3-Yukawa (M3Y)和JeukenneLejeune-Mahaux (JLM),得到10C核的四种不同的团束密度分布:6Be + α, 9B + p, 8Be + p + p和 α + α + p + p。虚部采用Woods-Saxon现象学形式。通过比较不同电位下得到的结果,评价了弹性散射截面对不同电位的灵敏度。通过理论结果与实验数据的对比,验证了10C的聚类结构。结果表明,截面对电势的选择很敏感,证明了10C的簇状结构是正确的。理论计算结果与实验数据吻合较好。
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引用次数: 0
Thermal instability of rotating Jeffrey nanofluids in porous media with variable gravity 变重力多孔介质中旋转Jeffrey纳米流体的热不稳定性
Pub Date : 2023-05-20 DOI: 10.46481/jnsps.2023.1366
Pushap Lata Sharma, Deepak Bains, Pankaj Thakur
It is investigated how changes in gravity affect the thermal instability rotating Jeffrey nanofluids in porous media. Along with the Galerkin method and normal mode approach, the Darcy model is used. The distinct variable gravity parameters taken in this paper are: h(z)=z2-2z, h(z)=-z2, h(z)=-z and h(z)=z and their effects on the Jeffrey parameter, Taylor number, moderated diffusivity ratio, porosity of porous media, Lewis number and nanoparticle Rayleigh number on stationary convection have been scrutinized and graphically shown. Our finding demonstrates that varying gravity parameter h(z)=z2-2z has more stabilising impact on stationary convection. We have also discovered the necessary condition for overstability in the instance of oscillatory convection for this problem.
研究了重力变化对多孔介质中旋转杰弗里纳米流体热不稳定性的影响。在伽辽金法和正态法的基础上,采用了达西模型。本文研究了h(z)=z2-2z、h(z)=-z2、h(z)=-z、h(z)=-z和h(z)=z等不同的重力参数对静止对流中Jeffrey参数、Taylor数、缓和扩散率比、多孔介质孔隙度、Lewis数和纳米颗粒瑞利数的影响,并用图形表示。我们的发现表明,改变重力参数h(z)=z2-2z对静止对流有更大的稳定作用。我们还发现了该问题在振荡对流情况下出现过稳定的必要条件。
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引用次数: 1
Study of the passivation of defects in the perovskite cell: application to Sahelian climate conditions 钙钛矿电池中缺陷钝化的研究:在萨赫勒气候条件下的应用
Pub Date : 2023-05-14 DOI: 10.46481/jnsps.2023.1250
Essodossomondom Anate, N. Kata, H. Samah, A. S. Maiga
This article is devoted to the study of the performance of the photovoltaic cell based on perovskite (MAPbI3) in real conditions of sub-Saharan Africa. A model of this cell has been made taking into account the integration of defects at the interfaces. After a study of the sensitivity of these defects, a passivation layer was introduced at the interface to improve the performance of the cell. The influence of temperature and irradiance on the performance of perovskite cells was studied on the one hand with defects at the interfaces and on the other hand with the integration of a passivation layer of defects. The results show a decrease of the performance ratio for the non-passivated cell due to the defects present at the interfaces of the said cell. The models developed under SCAPS-1D were validated by applying it to a real module found in the literature under the same conditions. The performance calculation shows a satisfactory qualitative and quantitative agreement. The results relative to the performance ratios obtained for the simulated models show that perovskite is on the right track for a potential future candidacy to the most suitable technologies for sub-Saharan Africa.
本文致力于研究基于钙钛矿(MAPbI3)的光伏电池在撒哈拉以南非洲实际条件下的性能。考虑了界面缺陷的集成,建立了该单元的模型。在研究了这些缺陷的灵敏度后,在界面处引入了钝化层以提高电池的性能。研究了温度和辐照度对钙钛矿电池性能的影响,一方面研究了界面缺陷,另一方面研究了缺陷钝化层的集成。结果表明,由于所述电池的界面存在缺陷,未钝化电池的性能比降低。在SCAPS-1D下开发的模型通过将其应用于文献中在相同条件下发现的真实模块来验证。性能计算结果表明,其定性和定量结果一致。相对于模拟模型获得的性能比率的结果表明,钙钛矿在未来可能成为撒哈拉以南非洲最合适的技术候选物的正确轨道上。
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引用次数: 0
期刊
Journal of the Nigerian Society of Physical Sciences
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