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Preparation, structure and spectral characteristics of Zinc tellurite glasses system doped with different concentrations of Tm3+ 掺杂不同浓度 Tm3+ 的锌碲玻璃体系的制备、结构和光谱特性
Pub Date : 2024-05-22 DOI: 10.1142/s0217984924503822
Yan Fang, Chongjun He, Fangzhou Chen, Yiyang He, Yuangang Lu, Lijuan Liu, Mingjun Xia, Chenguang Deng, Qian Li, Huiting Chen
Gallium-tellurite glass is a new optical material with good transmittance in the infrared region up to 6.5[Formula: see text][Formula: see text]. Three different tellurate glasses were prepared: TeO2–ZnO–Ga2O3(TZG), TeO2–ZnO–La2O3(TZL) and TeO2–ZnO–B2O3(TZB). X-ray diffraction indicates that no crystal precipitates in the three glass systems, which maintain a stable glass state. Raman scattering experiments and fluorescence emission spectroscopy measurements were carried out on the tellulate glasses doped with the same concentration of Tm[Formula: see text]. It was found that the phonon energy of TZG(TeO2–ZnO–Ga2O3)-doped thulium glass is the lowest, and the emission light at 1380[Formula: see text]nm is the strongest with [Formula: see text][Formula: see text]nm fluorescence FWHM. These results show that Tm-doped TZG glass is a good luminescent material. Refractive indices were measured by the minimum deviation method. Sellmeier dispersion equation is obtained, which can be used to calculate the refractive index within visible and near-infrared spectral range. Furthermore, different Tm[Formula: see text] concentrations (0.4%, 0.8%, 1.2% and 2%) TZG glasses were prepared, the emission spectra and fluorescence lifetime were measured, and the emitted light was strongest when the thulium ion doping concentration is 1.2%. All the results suggest that these newly developed ternary tellurite glass systems are promising candidates for near/mid-infrared laser glass fibers, fiber amplifiers, or lasers.
镓碲玻璃是一种新型光学材料,在红外区域具有良好的透射率,最高可达 6.5[式:见正文][式:见正文]。我们制备了三种不同的碲玻璃:TeO2-ZnO-Ga2O3(TZG)、TeO2-ZnO-La2O3(TZL)和 TeO2-ZnO-B2O3(TZB)。X 射线衍射表明,这三种玻璃体系中没有晶体析出,保持了稳定的玻璃状态。对掺杂了相同浓度 Tm[式:见正文]的 Tellulate 玻璃进行了拉曼散射实验和荧光发射光谱测量。结果发现,掺杂 TZG(TeO2-ZnO-Ga2O3)的铥玻璃的声子能量最低,1380[式:见正文]nm 处的发射光最强,荧光 FWHM 为[式:见正文][式:见正文]nm。这些结果表明,掺 Tm 的高瞻基玻璃是一种良好的发光材料。用最小偏差法测量了折射率。得到的 Sellmeier 色散方程可用于计算可见光和近红外光谱范围内的折射率。此外,还制备了不同铥离子浓度(0.4%、0.8%、1.2% 和 2%)的高致密度玻璃,并测量了其发射光谱和荧光寿命。所有结果表明,这些新开发的三元碲玻璃系统有望成为近/中红外激光玻璃纤维、光纤放大器或激光器的候选材料。
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引用次数: 0
Joule heating effects on triple diffusive free convective MHD flow over a convective surface: A Lie-group transformation analysis 对流表面上三重扩散自由对流 MHD 流的焦耳加热效应:李群变换分析
Pub Date : 2024-05-22 DOI: 10.1142/s0217984924504128
Ammara Islam, Zafar Mahmood, Umar Khan, Bilal Ali, Md Irfanul Haque Siddiqui
This work integrates the Boussinesq approximation and magnetohydrodynamic effects to investigate the dynamics of incompressible triple diffusive fluid flow along a linearly stretched surface. Novel insights are revealed by contrasting instances with opposing and helpful flows. The partial differential equations are symmetrically reduced using Lie-group transformations, which make the Runge–Kutta shooting technique easier to solve. The effects of concentration buoyancy ratio, magnetic parameter, concentration parameter, and Lewis number on temperature, velocity, and concentration profiles are explained through graphical displays. Our results show that in both flow situations, the velocity distribution is decelerated by the magnetic parameter, and the salt concentration distributions are similarly affected by buoyancy ratio factors. Additionally, a higher Lewis number is associated with lower mass and heat transfer rates in the opposing and assisting fluid.
这项研究综合了布西内斯克近似和磁流体动力学效应,研究了不可压缩的三重扩散流体沿线性拉伸表面流动的动力学。通过对比对流和助流的实例,揭示了新的见解。偏微分方程利用李群变换进行对称还原,这使得 Runge-Kutta 射频技术更容易求解。浓度浮力比、磁参数、浓度参数和路易斯数对温度、速度和浓度剖面的影响通过图形显示进行了解释。我们的结果表明,在这两种流动情况下,速度分布受磁参数的影响而减速,盐浓度分布同样受浮力比因素的影响。此外,路易斯数越高,对流体和辅助流体的传质和传热速率越低。
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引用次数: 0
Viscous dissipation and Joule heating in case of variable electrical conductivity Carreau–Yasuda nanofluid flow in a complex wavy asymmetric channel through porous media 导电率可变的 Carreau-Yasuda 纳米流体在穿过多孔介质的复杂波浪形非对称通道中流动时的粘性耗散和焦耳热
Pub Date : 2024-05-21 DOI: 10.1142/s021798492450369x
Sameh E. Ahmed, A. Arafa, Sameh A. Hussein
This paper focuses on flow structures and thermal fields of the Carreau–Yasuda (CY) nanofluid model through a two-dimensional, wavy, complicated vertical asymmetrical conduit filled with porous elements. Formulations of the viscous dissipation in the case of CY nanofluids are derived and nonlinear radiation flux as well as joule heating are examined. Buongiorno’s nanofluid approach, which involves Brownian motion and thermophoresis aspects is considered. The electrical conductivity of the suspension is considered as a variable where it depends upon the ambient temperature and concentration distributions and the Joule heating impacts are not neglected. The approach of solving the problem is contingent upon converting the system to dimensionless form then the lubrication approach with low magnetic Reynold numbers is applied. Numerical solutions are found for the resultant system, and wide ranges are considered for Weissenberg number We, non-Newtonian parameter n and Darcy number [Formula: see text], namely, [Formula: see text], [Formula: see text] and [Formula: see text], respectively. The major results indicated that gradients of the pressure are higher in case of shear thickening [Formula: see text] comparing to in the instance of shear thinning [Formula: see text]. Also, the velocity is enhanced, close to the channel’s lowest portion, as the Weissenberg number is growing. The variable electrical conductivity gives a higher mass transfer rate compared to the constant property.
本文重点研究了 Carreau-Yasuda (CY) 纳米流体模型在充满多孔元素的二维波浪形复杂垂直不对称导管中的流动结构和热场。推导了 CY 纳米流体的粘性耗散公式,并研究了非线性辐射通量和焦耳热。考虑了 Buongiorno 的纳米流体方法,其中涉及布朗运动和热泳方面。悬浮液的导电率被视为一个变量,它取决于环境温度和浓度分布,焦耳热的影响也没有被忽略。解决问题的方法取决于将系统转换为无量纲形式,然后应用低磁雷诺数的润滑方法。对结果系统进行了数值求解,并考虑了魏森伯格数 We、非牛顿参数 n 和达西数[公式:见正文]的宽范围,即分别为[公式:见正文]、[公式:见正文]和[公式:见正文]。主要结果表明,与剪切变稀[式:见正文]的情况相比,剪切变稠[式:见正文]的情况下压力梯度更大。此外,随着魏森伯格数的增加,靠近通道最低部分的速度也会增加。与恒定电导率相比,可变电导率的传质速率更高。
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引用次数: 0
Delay volterra integrodifferential models of fractional orders and exponential kernels: Well-posedness theoretical results and Legendre–Galerkin shifted approximations 分数阶和指数核的延迟伏特拉积分微分模型:问题解决的理论结果和 Legendre-Galerkin 移位近似法
Pub Date : 2024-05-21 DOI: 10.1142/s0217984924503792
Hind Sweis, N. Shawagfeh, O. A. Arqub
The utilized research work studies the well-posedness theoretical results and Galerkin-shifted approximations of delay Volterra integrodifferential models of fractional orders and exponential kernels in linear and nonlinear types in the Caputo–Fabrizio sense. Schauder’s and Arzela–Ascoli’s theorems are employed to prove a local existence theorem. After that, the Laplace continuous transform is employed to establish and confirm the global well-posedness theoretical results for the presented delay model. For numerical solutions, the Legendre–Galerkin shifted approximations’ algorithm has been used by the dependence on the orthogonal Legendre shifted polynomials to find out the required approximations. Utilizing this scheme, the considered delay model is reduced to an algebraic system with initial constraints. The algorithm precision, error behavior, and convergence are studied. Several numerical experiments together with several tables and figures are included to present the performance and validation of the algorithm presented. At last, some consequences and notes according to the given consequences were offered in the final section with several suggestions to guide future action.
本研究工作研究了卡普托-法布里齐奥意义上的线性和非线性类型的分数阶和指数核的延迟伏特拉微分方程模型的拟合优度理论结果和伽勒金移位近似。利用 Schauder 和 Arzela-Ascoli 定理证明了局部存在定理。之后,利用拉普拉斯连续变换建立并确认了所提出延迟模型的全局拟合理论结果。在数值求解方面,采用了 Legendre-Galerkin 移位近似算法,通过依赖正交 Legendre 移位多项式找出所需的近似值。利用这一方案,所考虑的延迟模型被简化为一个具有初始约束条件的代数系统。对算法精度、误差行为和收敛性进行了研究。其中包括几个数值实验以及一些表格和数字,以展示所介绍算法的性能和验证。最后,在最后一节中,根据给出的结果提出了一些后果和说明,并提出了一些指导未来行动的建议。
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引用次数: 0
Stability analysis and retrieval of new solitary waves of (2+1)- and (3+1)-dimensional potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations using auxiliary equation technique 利用辅助方程技术对 (2+1)- 和 (3+1)- 维势能卡多姆采夫-彼得维亚什维利方程和 B 型卡多姆采夫-彼得维亚什维利方程的新孤波进行稳定性分析和检索
Pub Date : 2024-05-21 DOI: 10.1142/s021798492450413x
Fatma Nur Kaya Sağlam, Shabir Ahmad
The Kadomtsev–Petviashvili (KP) equations are nonlinear partial differential equations which are widely used for the modeling of wave propagation in hydrodynamic and plasma systems. This study aims to make a valuable contribution to the literature by providing new solitary waves to the (2+1)- and (3+1)-dimensional potential Kadomtsev–Petviashvili (pKP)-B-type Kadomtsev–Petviashvili (BKP) equations. For this, the auxiliary equation method associated with Bernoulli equation is used and new solutions for the considered equations are obtained. The stability of obtained solutions is demonstrated using nonlinear analysis. It is shown that this method for the considered pKP–BKP equations is an important step forward in an overall mathematical framework for similar equations.
卡多姆采夫-彼得维亚什维利(KP)方程是一种非线性偏微分方程,被广泛用于流体力学和等离子体系统中波传播的建模。本研究旨在为 (2+1)- 和 (3+1)- 维势能 Kadomtsev-Petviashvili (pKP)-B 型 Kadomtsev-Petviashvili (BKP) 方程提供新的孤波,从而为文献做出有价值的贡献。为此,使用了与伯努利方程相关的辅助方程方法,并获得了所考虑方程的新解。利用非线性分析证明了所求解的稳定性。结果表明,针对所考虑的 pKP-BKP 方程的这种方法是在类似方程的整体数学框架中向前迈出的重要一步。
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引用次数: 0
Impacts of activation energy and electroosmosis on peristaltic motion of micropolar Newtonian nanofluid inside a microchannel 活化能和电渗对微通道内微波牛顿纳米流体蠕动的影响
Pub Date : 2024-05-21 DOI: 10.1142/s0217984924504074
N. Eldabe, M. Y. Abouzeid, M. Abdelmoneim, M. Ouaf
This study investigates the impact of electroosmosis on the peristaltic flow of unsteady micropolar nanofluid with heat transfer. The findings could enhance the design of peristaltic pumps, potentially improving drug delivery systems, simulations of blood flow in medical devices, and cancer treatments. The fluid under investigation adheres to a micropolar model and flows through a microchannel that exhibits peristalsis along its walls. Moreover, the system is subjected to various external effects, including a uniform magnetic field, the electroosmotic phenomenon, heat absorption, and a chemical reaction with activation energy. Consequently, the problem is mathematically modulated by a system of nonlinear partial differential equations governing the velocity, temperature, and nanoparticle concentration. By employing wave transformation, these governing equations are reduced to ordinary differential equations (ODEs). The reduced equations were solved both analytically, using the homotopy perturbation method, and numerically, using the Runge–Kutta–Merson method. A comparison was made between the solutions, which were found to be closely aligned. Furthermore, a series of figures were employed to provide visual representation and discussion of the implications of the physical properties. The calculations reveal that the electroosmotic flow (EOF) enhances the axial flow of the micropolar fluid along the direction of the applied electric field. It is also observed that the increase in the activation energy (which indicates a low reaction rate) increases the concentration profile whereas the increase in the reaction rate parameter reduces the concentration profile. Additionally, the spin velocity of the particles is diminished by either an increase in the magnetic parameter or the coupling parameter.
这项研究探讨了电渗对带有热传导的非稳定微波纳米流体蠕动流动的影响。研究结果可改进蠕动泵的设计,从而改善药物输送系统、医疗设备中的血流模拟以及癌症治疗。所研究的流体附着在微极模型上,流经微通道,沿通道壁发生蠕动。此外,系统还受到各种外部效应的影响,包括均匀磁场、电渗现象、吸热以及具有活化能的化学反应。因此,该问题在数学上是由一个非线性偏微分方程系统来调节速度、温度和纳米粒子浓度的。通过波变换,这些控制方程被简化为常微分方程(ODE)。利用同调扰动法对简化方程进行了分析求解,并利用 Runge-Kutta-Merson 方法对其进行了数值求解。比较后发现,这些解法非常接近。此外,还采用了一系列图表来直观地表示和讨论物理特性的含义。计算结果表明,电渗流(EOF)增强了微极流体沿外加电场方向的轴向流动。计算还发现,活化能的增加(表明反应速率较低)会增加浓度分布,而反应速率参数的增加则会降低浓度分布。此外,磁参数或耦合参数的增加都会降低粒子的自旋速度。
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引用次数: 0
Constructing the soliton wave structure to the nonlinear fractional Kairat-X dynamical equation under computational approach 在计算方法下构建非线性分数凯拉特-X 动力方程的孤子波结构
Pub Date : 2024-05-18 DOI: 10.1142/s0217984924503962
M. Iqbal, Dianchen Lu, A. Seadawy, F. A. Alomari, Zhanar Umurzakhova, R. Myrzakulov
In this paper, the nonlinear fractional Kairat-X equation is investigated on the basis of computational simulation. The nonlinear fractional Kairat-X equation is an integrable equation and is used to explain the differential geometry of curves and equivalence aspects. Several kinds of solitary wave structures of the nonlinear fractional Kairat-X equation are established successfully via the implantation of the extended simple equation method. Here, we explore the interesting, novel and general solutions in trigonometric, exponential, and rational types, which represent periodic wave solitons, mixed solitons in the shape of bright–dark solutions, kink wave solitons, peakon bright and dark solitons, anti-kink wave solutions, bright solitons, dark solitons, and solitary wave structure. The physical structures of secured results, aided by numerical simulation, have numerous applications in applied sciences such as optical fiber, geophysics, laser optics, mathematical physics, nonlinear optics, nonlinear dynamics, communication system, and engineering. This study explores the physical behavior of models through the visualization of solutions in contour, 2D and 3D plots by revealing that these solutions yield profitable results in the field of mathematical physics. The study demonstrates that the proposed technique is more reliable, efficient, and powerful in analyzing nonlinear evolution equations in various domains of science.
本文在计算模拟的基础上研究了非线性分数 Kairat-X 方程。非线性分数 Kairat-X 方程是一个可积分方程,用于解释曲线的微分几何和等价方面。通过植入扩展简单方程方法,成功建立了非线性分数 Kairat-X 方程的几种孤波结构。在此,我们探索了有趣的、新颖的和一般的三角、指数和有理类型的解,它们代表了周期波孤子、明暗混合孤子、扭结波孤子、峰值明暗孤子、反扭结波解、明孤子、暗孤子和孤波结构。在数值模拟的辅助下,获得结果的物理结构在光纤、地球物理、激光光学、数学物理、非线性光学、非线性动力学、通信系统和工程等应用科学领域有着广泛的应用。本研究通过对等高线、二维和三维图解的可视化来探索模型的物理行为,揭示了这些解在数学物理领域产生的有利结果。研究表明,在分析各个科学领域的非线性演化方程时,所提出的技术更加可靠、高效和强大。
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引用次数: 0
Effects of promoter and dedoping process on electrorheological response of polyaniline-graft-chitosan copolymer 促进剂和掺杂工艺对聚苯胺-接枝壳聚糖共聚物电流变响应的影响
Pub Date : 2024-05-18 DOI: 10.1142/s0217984924420077
M. Cabuk, Mustafa Yavuz, H. Unal
In this study, electrorheological (ER) properties of biodegradable and conducting polyaniline-graft-chitosan (PAni-g-CS) copolymer particles were investigated. For this purpose, PAni and PAni-g-CS particles were synthesized by using in situ oxidative radicalic polymerization method. At first, PAni and PAni-g-CS/silicone oil (SO) ER suspensions (15% V/V) were subjected to external electric field and they exhibited low ER activity. When the external electric field strengths ([Formula: see text] were increased, both the suspensions showed electrical breakdown. Therefore, virgin PAni and PAni-g-CS were first subjected to dedoping process by treating with 1.0 M NaOH(aq) and non-ionic surfactant Triton X-100 (T-X) surfactant to enhance the expected ER activity and prevent the electrical breakdown. But we observed that the addition of T-X as promoter had no significant effect on the ER activity. On the other hand, electric filed-induced viscosities of both the suspensions were observed to enhance after the dedoping (DD) process and electrical breakdown prohibited. After the DD process, DD PAni-g-CS/SO ER system exhibited the highest electric field-induced viscosity by reaching 400[Formula: see text]Pa[Formula: see text]⋅[Formula: see text]s at [Formula: see text][Formula: see text]kV/mm. The highest ER efficiency was also obtained for DD PAni-g-CS/SO system at 15% (V/V) as 79. Additionally, typical shear thinning non-Newtonian viscoelastic behavior was observed under externally applied E. The conduction model of DD PAni-g-CS/SO system was determined to well fit the conduction model by showing a slope of [Formula: see text] calculated from the E vb. yield stress graph. In conclusion, conducting and biodegradable-dedoped PAni-g-CS particles would be a good candidate for potential ER applications as dry-based ER materials having high colloidal stability of 76%.
本研究调查了可生物降解的导电聚苯胺-接枝壳聚糖(PAni-g-CS)共聚物颗粒的电流变(ER)特性。为此,采用原位氧化自由基聚合法合成了 PAni 和 PAni-g-CS 颗粒。首先,将 PAni 和 PAni-g-CS/ 硅油(SO)ER 悬浮液(15% V/V)置于外电场中,它们表现出较低的ER活性。当外电场强度([公式:见正文])增加时,两种悬浮液都出现了电击穿。因此,我们首先用 1.0 M NaOH(aq)和非离子表面活性剂 Triton X-100(T-X)对原始 PAni 和 PAnii-g-CS 进行了掺杂处理,以提高预期的ER活性并防止电击穿。但我们观察到,添加 T-X 作为促进剂对 ER 活性没有显著影响。另一方面,我们观察到两种悬浮液的电锉诱导粘度在掺杂(DD)过程后都有所提高,电击穿现象也被禁止。经过 DD 处理后,DD PAni-g-CS/SO ER 系统的电场诱导粘度最高,在[式:见正文][式:见正文][式:见正文]kV/mm 时达到 400[式:见正文]Pa[式:见正文]⋅[式:见正文]s。DD PAni-g-CS/SO 系统在 15%(V/V)作为 79 时也获得了最高的 ER 效率。此外,在外部施加 E 的情况下,观察到了典型的剪切稀化非牛顿粘弹性行为。根据 E vb. 屈服应力图计算得出的斜率为[式:见正文],因此确定 DD PAni-g-CS/SO 系统的传导模型非常适合传导模型。总之,导电且可生物降解的掺杂 PAni-g-CS 颗粒将成为潜在 ER 应用的良好候选材料,作为干基 ER 材料,其胶体稳定性高达 76%。
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引用次数: 0
Impact of the Stefan gusting on a bioconvective nanofluid with the various slips over a rotating disc and a substance-responsive species 斯特凡阵风对生物对流纳米流体的影响,该流体在旋转圆盘和物质响应物种上有不同的滑动方式
Pub Date : 2024-05-18 DOI: 10.1142/s0217984924504062
K. Gangadhar, M. Rao, M. A. Kumari, A. Wakif
This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.
本文对浸没在含有微生物的水基纳米流体中的旋转圆盘上的稳定强制对流进行了深入的计算和理论分析。它深入研究了粘性纳米流体的边界层流动特性,考虑了斯特凡吹气效应和受磁场影响的多重滑移条件。值得注意的是,该研究考虑到了热辐射以及建设性和破坏性化学反应等新的方面。根据热泳和微观行为阐明了纳米粒子的运动,而体积分数的变化不会影响纳米流体的热物理性质。为了解决已改变的非线性微分方程组,采用了一种有效的数值方法,即 Keller-Box 方法,以获得临界和高效的解决方案。我们定义并应用了这些适当的变换。与吹吸法相比,它能更好地提高传热、传质和微生物的速率。一些主要的观察结果表明,随着磁场强度的增加,径向和切向的壁面摩擦力会减小。对热边界层厚度和温度的评估表明辐射参数 (Rd) 有所改善。本分析可应用于电磁微泵和纳米力学。至于在科学和工程领域的应用,基于微机电系统的微流体设备和微流体相关技术等技术将被接受。
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引用次数: 0
A novel design of layered recurrent neural networks for fractional order Caputo–Fabrizio stiff electric circuit models 针对分数阶卡普托-法布里齐奥僵硬电路模型的分层递归神经网络新设计
Pub Date : 2024-05-18 DOI: 10.1142/s0217984924503937
Aneela Kausar, Chuan-Yu Chang, Muhammad Asif Zahoor Raja, Muhammad Shoaib
Electrical engineering models often rely on complex circuit configurations that facilitate the dynamic flow of electrically charged particles within a closed conductive network. These circuits serve as essential tools for simulating and analyzing diverse electrical systems and components. This paper introduces a study on nonlinear fractional circuits modeling through the development of a stochastic neuro-computational artificial intelligent-based solver to address mathematical models governing the Fractional order Caputo–Fabrizio stiff electric circuit model (FO-CFSECM) by manipulating the knacks of layered recurrent neural networks (LRNNs) trained with Gradient-based local search algorithm (GLA). In fractional calculus, the Caputo–Fabrizio (CF) fractional order derivative (FOD) emerges as a powerful instrument, binding its capabilities to deliver remarkably accurate solutions for fractional stiff systems. The objective of this work is to exploit the numerical treatment comprehensively for the dynamics of fractal Resistor–Capacitor (RC) and fractal Resistor–Inductor (RL) circuit models by introducing the CF fractional operator. Through the application of artificial intelligence-based soft computing and advanced back-propagative deep neural networks, a deeper understanding of the behavior and distinctive characteristics inherent in these models is sought. The Levenberg–Marquardt optimizer serves as an efficient training GLA tool for learning of LRNNs weights of fractal RL/RC circuit models. The comparative studies on variants of FO-CFSECM demonstrate that LRNNs achieve an impressive mean square error (MSE) ranging from 10[Formula: see text] to 10[Formula: see text] and absolute error (AE) within 10[Formula: see text] to 10[Formula: see text]. The accuracy, reliability, and efficiency of LRNNs for solving the FO-CFSECM were further validated through MSE, AE, controlling parameters of state transitions, error histograms, and correlation measures.
电气工程模型通常依赖于复杂的电路配置,以促进带电粒子在封闭导电网络中的动态流动。这些电路是模拟和分析各种电气系统和组件的重要工具。本文通过开发一种基于随机神经计算的人工智能求解器,介绍了非线性分数电路建模研究,该求解器通过操纵使用基于梯度的局部搜索算法(GLA)训练的分层递归神经网络(LRNNs)的诀窍,来处理管理分数阶卡普托-法布里齐奥僵硬电路模型(FO-CFSECM)的数学模型。在分数微积分中,卡普托-法布里齐奥(Caputo-Fabrizio,CF)分数阶导数(FOD)是一种强大的工具,它能为分数刚性系统提供非常精确的解决方案。这项工作的目的是通过引入 CF 分数算子,对分形电阻器-电容器 (RC) 和分形电阻器-电感器 (RL) 电路模型的动力学进行全面的数值处理。通过应用基于人工智能的软计算和先进的反向传播深度神经网络,深入理解了这些模型的内在行为和显著特征。Levenberg-Marquardt 优化器是学习分形 RL/RC 电路模型的 LRNNs 权重的高效训练 GLA 工具。对 FO-CFSECM 变体的比较研究表明,LRNNs 的均方误差(MSE)在 10[公式:见正文]到 10[公式:见正文]之间,绝对误差(AE)在 10[公式:见正文]到 10[公式:见正文]之内,令人印象深刻。通过 MSE、AE、状态转换的控制参数、误差直方图和相关测量,进一步验证了 LRNNs 解决 FO-CFSECM 的准确性、可靠性和效率。
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Modern Physics Letters B
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