Partial Differential Equations in Applied Mathematics最新文献

英文中文

Predicting heat transfer Performance in transient flow of CNT nanomaterials with thermal radiation past a heated spinning sphere using an artificial neural network: A machine learning approach 利用人工神经网络预测带有热辐射的 CNT 纳米材料流经加热旋转球体时的瞬态传热性能：机器学习方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-22 DOI: 10.1016/j.padiff.2024.100936

An efficient heat transfer phenomenon using nanofluid have greater challenges in various industries, engineering application the recent trend. Keeping this in present scenario, this study aims to optimize the heat transmission rate in the magnetized flow of nanomaterials through a rotating, spinning sphere. The heat transfer phenomena in the time-dependent fluid are enhanced by the incorporation of nonlinear radiation and a variable heat source. Additionally, the free convective flow is influenced by the effects of thermal buoyancy and a transverse magnetic field. The proposed model along with several factors is standardized through adequate transformation rules. Further, shooting-based Runge-Kutta technique is adopted with the help of built-in MATLAB function bvp4c for the solution of the transformed system. The prime focus of the proposed work is the optimizing heat transfer rate combined with regression analysis using artificial neural network and then it uses Levenberg Marquardt algorithm with well-posed training, testing, and validation data. The error analysis also presented briefly and the variation of characterizing parameters is depicted via graphs. Further, the important outcomes are; the particle concentration of carbon nanotubes contributes to decelerating the velocity profiles, leading to an increase in boundary layer thickness. In contrast, increasing magnetization has the opposite effect. Both nonlinear radiative heat and an additional heat source enhance the heat transfer phenomenon.

利用纳米流体实现高效传热是各行各业面临的巨大挑战，也是工程应用的最新趋势。鉴于此，本研究旨在优化磁化纳米材料流经旋转球体时的热传导率。通过加入非线性辐射和可变热源，增强了随时间变化的流体中的传热现象。此外，自由对流还受到热浮力和横向磁场的影响。通过适当的转换规则，对所提出的模型和几个因素进行了标准化。此外，在 MATLAB 内置函数 bvp4c 的帮助下，采用了基于射击的 Runge-Kutta 技术来求解转换后的系统。建议工作的主要重点是利用人工神经网络结合回归分析来优化传热率，然后使用 Levenberg Marquardt 算法和精心设计的训练、测试和验证数据。还简要介绍了误差分析，并通过图表描述了特征参数的变化。此外，重要的结果是：碳纳米管的颗粒浓度会使速度曲线减速，导致边界层厚度增加。相反，增加磁化率则会产生相反的效果。非线性辐射热和附加热源都会增强热传递现象。

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引用次数: 0

Two-cluster synchronization in a fully coupled network of Mackey–Glass generators 完全耦合的麦基-玻璃发电机网络中的双簇同步

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-21 DOI: 10.1016/j.padiff.2024.100930

We study a fully connected network of Mackey–Glass generators, each described by the Mackey–Glass delay differential equation. This system can exhibit non-trivial behaviour over time. One interesting scenario of such behaviour is cluster synchronization—regimes in which all components are divided into several groups, each oscillating in the same mode. Cluster synchronization can appear in various systems, such as neural networks and biological systems. In this work, we investigate the case of two-cluster synchronization and prove the existence of such modes.

我们研究了一个完全连接的麦基-格拉斯发电机网络，每个发电机都由麦基-格拉斯延迟微分方程描述。随着时间的推移，该系统会表现出非同寻常的行为。这种行为的一种有趣情形是群同步--在这种情形下，所有元件被分成若干组，每组以相同的模式振荡。群同步可出现在各种系统中，如神经网络和生物系统。在这项工作中，我们研究了双簇同步的情况，并证明了这种模式的存在。

引用次数: 0

Polynomial dynamical systems associated with the KdV hierarchy 与 KdV 层次相关的多项式动力系统

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-21 DOI: 10.1016/j.padiff.2024.100928

In 1974, S.P. Novikov introduced the stationary

n

-equations of the Korteweg–de Vries hierarchy, namely the

n

-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial

2 n

integrals, in

ℂ^{3 n}

. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the

n

-Novikov equations. Thus, we solve the well-known problem of the relationship between the

n

-Novikov equations for different

n

1974 年，诺维科夫（S.P. Novikov）提出了科特维格-德-弗里斯层次的静态 n方程，即 n-诺维科夫方程。这些方程与ℂ3n 中可积分的多项式动力学系统相关，具有多项式 2n 积分。在本文中，我们构建了一个无穷维多项式动力系统，它对于 n-Novikov 方程对应的所有动力系统都是通用的。因此，我们解决了众所周知的不同 n 的 n-Novikov 方程之间的关系问题。

引用次数: 0

On the study of double dispersive equation in the Murnaghan’s rod: Dynamics of diversity wave structures 关于默纳汉杆中的双分散方程研究：多样性波结构动力学

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-20 DOI: 10.1016/j.padiff.2024.100916

This article secures the various wave structures of the fractional double dispersive equation, a significant nonlinear equation that describes the propagation of nonlinear waves within the elastic, uniform, and inhomogeneous Murnaghan’s rod. The model under discussion has a wide range of applications in science and engineering. Two recently developed analytical techniques known as the improved generalized Riccati equation mapping method and the multivariate generalized exponential rational integral function method have been applied to the proposed equation for the first time. A variety of solutions have been revealed such that dark, singular, bright-dark, bright, complex, and combined solitons. Furthermore, we include a diverse array of plots that illustrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. Within the context of the proposed model, these visualizations give a clear understanding of the behavior and characteristics of the solutions. This study’s results have the potential to enhance comprehension of the nonlinear dynamic characteristics exhibited by the specified system and validate the efficacy of the implemented techniques. The achieved results significantly enhance our understanding of nonlinear science and the nonlinear wave fields associated with more complex nonlinear models.

分式双色散方程是一个重要的非线性方程，用于描述非线性波在弹性、均匀和不均匀 Murnaghan 杆内的传播。该模型在科学和工程领域有着广泛的应用。最近开发的两种分析技术，即改进的广义里卡提方程映射法和多元广义指数有理积分函数法，首次被应用于所提出的方程。我们发现了多种解，如暗孤子、奇异孤子、亮暗孤子、亮孤子、复孤子和组合孤子。此外，我们还绘制了一系列不同的曲线图，说明所获得的解与一些重要参数的关系，从而突出分数导数的影响。在所提出模型的背景下，这些可视化图让我们清楚地了解解的行为和特征。这项研究的结果有可能加强对指定系统所表现出的非线性动态特性的理解，并验证所实施技术的有效性。所取得的成果极大地增强了我们对非线性科学以及与更复杂的非线性模型相关的非线性波场的理解。

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引用次数: 0

Diverse soliton wave profile analysis in ion-acoustic wave through an improved analytical approach 通过改进的分析方法分析离子声波中的多样性孤子波剖面

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-20 DOI: 10.1016/j.padiff.2024.100932

In engineering and applied sciences, several physical phenomena can be more precisely characterized by employing nonlinear fractional partial differential equations. The primary goal of this research is to examine the traveling wave solution in closed form for the nonlinear acoustic wave propagation model known as the time fractional simplified modified Camassa–Holm equation, which is used to explain the unidirectional propagation of shallow-water waves with non-hydrostatic pressure and explains the dispersion properties of numerous phenomena like fluid flow, control theory, liquid drop patterning in plasma, acoustics, fusion, and fission processes, etc. The utmost potential approach, namely the new auxiliary equation technique, is applied for analyzing the time nonlinear fractional simplified modified Camassa-Holm equation in the logic of the newest established truncated M-fractional derivative. The fractional partial differential equations have been transformed to the ordinary differential equation using the complex wave transformation in the sense of truncated M-fractional derivative. A variety of soliton solutions, including anti-kink, single soliton, anti-bell, bell, kink, multiple soliton, double soliton, singular-kink, compacton shape, periodic shape, and so many, are displayed in the diagram of 3D and contour plots by taking into account a number of various parameters. It is essential to point out that all derived outcomes are directly compared to the original solutions to certify their exactness. Results show that the used scheme is capable, simple, and straightforward and can be useful to a variety of complex phenomena. The acquired results are unique for the model equation and could be applied to the analysis of several nonlinear study fields.

在工程和应用科学领域，利用非线性分数偏微分方程可以更精确地描述一些物理现象。本研究的主要目标是研究非线性声波传播模型（即时间分数简化修正卡马萨-霍尔姆方程）的闭合形式行波解，该方程用于解释具有非静水压力的浅水波的单向传播，并解释流体流动、控制理论、等离子体中的液滴图案、声学、核聚变和裂变过程等众多现象的分散特性。在最新建立的截断 M 分导数逻辑中，应用了最大势方法，即新的辅助方程技术，来分析时间非线性分式简化修正卡马萨-霍姆方程。利用截断 M 分导数意义上的复波变换将分数偏微分方程转换为常微分方程。通过考虑各种参数，在三维图和等值线图中显示了各种孤子解，包括反孤子、单孤子、反钟、钟、孤子、多孤子、双孤子、奇异孤子、紧凑孤子形状、周期形状等。必须指出的是，所有得出的结果都直接与原始解进行了比较，以证明其精确性。结果表明，所使用的方案简单明了，适用于各种复杂现象。所获得的结果对于模型方程来说是独一无二的，可以应用于多个非线性研究领域的分析。

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引用次数: 0

Convective diffusive thermal flow over an inclined surface with viscous dissipation and aligned magnetic field applications 带有粘性耗散和对齐磁场应用的倾斜表面上的对流扩散热流

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-20 DOI: 10.1016/j.padiff.2024.100924

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

这项研究结合了多孔介质倾斜表面导致的粘性流体磁化混合对流的传热和传质波动。研究探讨了索雷特效应和粘性耗散设备的贡献。此外，还通过热辐射、热源和焦耳加热效应评估了传热改善情况。此外，还研究了浓缩现象的化学反应报名。基于新变量的影响，将问题对流到非二维框架中。采用扰动技术跟踪分析结果。研究了扰动参数影响下的物理可视化和结果解释。研究发现，热量和质量的传递会因索雷特数的增加而增强。化学反应的存在导致浓度曲线下降。上述结果可应用于传热和传质过程、化学反应、制造系统、化学工程、挤压过程等。

引用次数: 0

The nanoparticles aggregation aspects on the chemically reactive unsteady flow of alumina-water based nanofluid: A Keller box approach with applications of wavelet physics inspired neural networks 纳米颗粒聚集对氧化铝-水基纳米流体化学反应不稳定流的影响：应用小波物理学启发神经网络的凯勒盒方法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-19 DOI: 10.1016/j.padiff.2024.100931

The present study explores the unsteady flow of a nanoliquid past a stretching cylinder with the consequence of heat source/sink and chemical reaction. Additionally, the effect of nanoparticle aggregation, convective boundary conditions, and magnetic field on the liquid flow is taken into consideration. Utilizing similarity variables, the modeled equations are transformed into dimensionless ordinary differential equations (ODEs). Further, the obtained ODEs are numerically solved by using the Keller box method. Moreover, the physics-informed neural network (PINN) is applied to analyze the flow, heat, and mass transport features. Graphical illustrations are used to display the influence of various parameters on the velocity, concentration, and temperature profiles for aggregation and without aggregation cases. As the value of the magnetic parameter increases, the temperature and concentration profile upsurge, but the reverse trend can be seen in the velocity profile. The concentration and temperature profiles rise as the unsteadiness parameter increases, but the velocity profile declines. The concentration, velocity, and temperature profiles are strengthened by an improvement in the curvature parameter value. The intensification in the values of the chemical reaction parameter declines the concentration.

本研究探讨了纳米液体在热源/沉降和化学反应作用下流经拉伸圆柱体的非稳态流动。此外，还考虑了纳米粒子聚集、对流边界条件和磁场对液体流动的影响。利用相似变量，模型方程被转化为无量纲常微分方程（ODE）。然后，利用凯勒盒方法对得到的 ODE 进行数值求解。此外，还应用物理信息神经网络（PINN）分析流动、热量和质量传输特征。在有聚集和无聚集的情况下，采用图表说明了各种参数对速度、浓度和温度曲线的影响。随着磁性参数值的增加，温度和浓度曲线上升，但速度曲线的趋势相反。随着不稳定性参数的增加，浓度和温度曲线上升，但速度曲线下降。曲率参数值的增加会加强浓度、速度和温度曲线。化学反应参数值的增加会降低浓度。

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引用次数: 0

Optimal feedback stabilization of fractional output in semilinear distributed systems 半线性分布式系统中分数输出的最优反馈稳定

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-18 DOI: 10.1016/j.padiff.2024.100911

This study explores the stabilization of state–space fractional derivatives in semilinear distributed systems, using the Riemann–Liouville derivative of order $α$ , where $α$ lies within the interval $(0, 1)$ . The main objective is to develop effective feedback control strategies that ensure both strong and weak stabilization of fractional outputs. Additionally, we tackle a fractional minimization problem to enhance the system’s performance. A numerical simulation example is provided to demonstrate the practical significance of the proposed stabilization theorems.

本研究探讨了半线性分布式系统中状态空间分数导数的稳定问题，使用的是阶数为 α 的黎曼-刘维尔导数，其中 α 位于 0,1 的区间内。主要目标是开发有效的反馈控制策略，确保分数输出的强稳定和弱稳定。此外，我们还解决了分数最小化问题，以提高系统性能。我们提供了一个数值模拟示例，以证明所提出的稳定定理的实际意义。

引用次数: 0

Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations 乘法微积分中阿多米分解技术的修正及在非线性方程中的应用

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-18 DOI: 10.1016/j.padiff.2024.100902

Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.

乘法微积分是一种数学体系，是传统微积分的替代方案。它不像传统微积分那样使用加法和减法来衡量变化，而是使用乘法和除法。非线性方程的框架是一个非常强大的工具，在推动我们对各种应用科学现象的理解方面，它已被证明是无价之宝。这一框架使研究人员能够深入了解大量科学问题。利用乘法微积分对非线性方程的迭代方法进行物理解释，为求解此类方程提供了独特的视角，并为各个科学学科的应用提供了可能。乘法微积分与以指数增长或衰减为特征的过程天然吻合。在许多物理、生物和经济系统中，量的变化与其当前状态成正比。与传统的加法相比，乘法微积分能更准确地模拟这些过程。例如，人口增长、放射性衰变和复利都能更好地用乘法来描述。这项工作的主要目的是在乘法微积分框架内修改和实施阿多米分解法，并开发一类有效的乘法数值算法，以获得非线性方程解的最佳近似值。我们建立了乘法迭代法的收敛标准。为了证明这些新递推关系的应用和有效性，我们考虑了一些数值示例。我们将乘法迭代法与类似的现有普通方法进行了比较。我们还通过绘制残差对数提供了图形比较。构建新算法的目的是展示乘法微积分的实施和有效性。

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引用次数: 0

Vibrations of a vertical beam rotating with variable angular velocity 以可变角速度旋转的垂直横梁的振动

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-09-18 DOI: 10.1016/j.padiff.2024.100929

An Euler-Bernoulli beam in vertical position rotating about its symmetry axis along its length is considered. The angular velocity is assumed to have small fluctuations about a constant mean velocity. The partial differential equation of motion is derived first. The equation is cast into a non-dimensional form. The natural frequencies are calculated for the pinned-pinned case. Principle parametric resonances such that the fluctuation frequency being close to two times one of the natural frequencies are considered. By employment of the Method of Multiple Scales, an approximate perturbation solution is found. The frequency response diagrams are drawn and the bifurcation points for transition from the trivial solution to the non-trivial solution are calculated. The conditions for which such resonances occur are exploited in the numerical results.

我们考虑了一个垂直位置的欧拉-伯努利梁，该梁沿其长度方向绕对称轴旋转。假定角速度围绕恒定的平均速度小幅波动。首先推导运动偏微分方程。将该方程转化为非维度形式。计算销钉-销钉情况下的固有频率。考虑了原理参数共振，即波动频率接近自然频率的两倍。通过使用多尺度法，找到了近似扰动解。绘制了频率响应图，并计算了从微扰解向非微扰解过渡的分岔点。数值结果利用了发生这种共振的条件。

引用次数: 0

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