Applied Mathematical Modelling最新文献_第7页

Mathematical modelling of chemical detection in porous substrates using sampling coatings 利用取样涂层在多孔基质中进行化学检测的数学建模

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-18 DOI: 10.1016/j.apm.2025.116694

Aoibheann Murray , Ellen Luckins , Yixuan Sun , Stuart Notman , Lesley Hetherington , Merlin Etzold

Sampling coatings are a developing technology for detection and quantification of contaminants in porous materials (PM). The sampling coating is a substance of high contaminant affinity that is applied onto the PM and left to absorb contaminant. Upon removal, it is analysed to determine the amount of contaminant absorbed. Whilst sampling coatings have been shown to recover more contaminant from PM than traditional methods, the role of transport kinetics has not been recognized, hindering the quantitative interpretation of the measurements. We present a mathematical modeling framework for sampling coatings, incorporating coupled vaporisation and transport within the PM and absorption into the coating. We show that, on practical time scales (hours to days), only a fraction of the contaminant present in the PM enters the sampling coating and chemical equilibrium is not reached. The sampling efficiency, which we define to be the fraction of the contaminant in the coating, thus depends on the sampling time. We find an analytical solution of the model, valid for feasible sampling times in the physical parameter regime, along with an explicit expression for the sampling efficiency as a function of time. Dependence on the physical system parameters is investigated numerically: the height, diffusivity, and structure of the PM, and the type of chemical contaminant, are identified as key factors affecting sampling efficiency. We further propose a method to quantify contamination in the field using sampling-coating measurements. Our model and results enable practitioners to determine important properties when designing coatings and will inform future experimental work.

取样涂层是一种用于检测和定量多孔材料中污染物的新兴技术。采样涂层是一种高污染物亲和力的物质，它被涂在PM上并留下吸收污染物。去除后，对其进行分析以确定污染物的吸收量。虽然取样涂层已被证明比传统方法从PM中回收更多的污染物，但尚未认识到运输动力学的作用，阻碍了测量结果的定量解释。我们提出了一个采样涂层的数学建模框架，将耦合汽化和PM内的运输以及吸收到涂层中。我们表明，在实际的时间尺度上（小时到天），PM中只有一小部分污染物进入采样涂层，化学平衡没有达到。采样效率，我们定义为涂层中污染物的比例，因此取决于采样时间。我们找到了该模型的解析解，该解对物理参数范围内可行的采样时间有效，并给出了采样效率作为时间函数的显式表达式。对物理系统参数的依赖性进行了数值研究：确定了PM的高度、扩散率和结构以及化学污染物的类型是影响采样效率的关键因素。我们进一步提出了一种方法来量化污染在现场使用采样涂层测量。我们的模型和结果使从业者能够在设计涂料时确定重要的性能，并将为未来的实验工作提供信息。

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引用次数: 0

Wave scattering at a rectangular junction of four waveguides 四波导矩形结处的波散射

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-18 DOI: 10.1016/j.apm.2025.116697

Afnan A. Aldosri , Michael H. Meylan , Ben Wilks

We consider the scattering of linear waves in two dimensions by a rectangular region at the junction of four waveguides: a geometry not previously studied in the literature. A solution to the frequency domain problem is obtained by exploiting reflective symmetry to reduce the full problem to sub-problems defined on one quadrant of the junction. These sub-problems are solved using the eigenfunction matching method. The solution to the problem in the full region is then recovered from the solutions to the sub-problems, and a scattering matrix for the junction is presented. Finally, the solution in the time domain is constructed as a superposition of the frequency domain solutions and visualised for a range of incident pulses and waveguide geometries.

我们考虑线性波在二维中的散射，在四个波导交界处的矩形区域：以前没有在文献中研究过的几何形状。利用反射对称，将整个问题简化为在结的一个象限上定义的子问题，得到了频域问题的解。这些子问题采用特征函数匹配法求解。然后从子问题的解中恢复到整个区域的问题解，并给出了结的散射矩阵。最后，时域的解被构造为频域解的叠加，并对一系列入射脉冲和波导几何形状进行可视化。

引用次数: 0

Debye screening in surface waves in microstructured semiconductors with Drude-modelled carrier transport: A Robin boundary generalization 微结构半导体表面波的德拜筛选与德鲁德模型载流子输运：罗宾边界推广

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-17 DOI: 10.1016/j.apm.2025.116702

Mahargha Biswas

This work develops a comprehensive theoretical model for Rayleigh-type surface waves in a semi-infinite n-type piezoelectric-flexoelectric semiconductor subjected to a static magnetic field. Two previously underexplored mechanisms are emphasized: Debye-Hückel electrostatic screening and Hall current-induced magnetoelectric anisotropy. The intrinsic inhomogeneity introduced by spatially non-uniform carrier distributions near the surface arising from doping effects is captured through a nontrivial Debye screening layer, which needs a shift from classical electrostatic boundary assumptions. Accordingly, generalized Robin-type boundary conditions are derived, synthesizing the limiting cases of the Dirichlet and Neumann formulations (corresponding to electrically short and open cases). The Hall effect is incorporated through a modified current continuity relation, based on the Drude model, wherein Lorentz-force-mediated charge carrier deflection introduces off-diagonal modifications drift-diffusion tensors. The governing system of Rayleigh wave is constructed from the fully coupled magneto-flexoelectro-elastic field equations, wherein flexoelectricity and strain-gradient elasticity introduce size-dependent electromechanical coupling. Dispersion relations are derived analytically in the long-wavelength limit and numerically solved for general cases, revealing a profound sensitivity of the Rayleigh wave phase velocity and attenuation to the interplay between the Debye screening scale, Hall mobility, and flexoelectric coefficients. The findings highlight the limitations of simplified boundary treatments in semiconductor acoustics and demonstrate multiple tunable wave effects resulting from multiscale interaction mechanisms. This framework provides a physically coherent and mathematically sound basis for designing and optimizing next-generation surface acoustic wave (SAW) devices.

本文建立了一个在静态磁场作用下半无限n型压电-柔性半导体中瑞利型表面波的综合理论模型。强调了两个以前未充分探索的机制：debye - h ckel静电筛选和霍尔电流诱导的磁电各向异性。由掺杂效应引起的表面附近空间非均匀载流子分布引入的本征不均匀性通过非平凡德拜屏蔽层捕获，这需要从经典静电边界假设中转变。因此，综合Dirichlet和Neumann公式的极限情况（对应于电短和开情况），导出了广义robin型边界条件。霍尔效应是通过基于德鲁德模型的修正电流连续性关系来实现的，其中洛伦兹力介导的载流子偏转引入了非对角线修正漂移扩散张量。瑞利波的控制系统是由完全耦合的磁-柔-电-弹场方程构成的，其中柔电和应变梯度弹性引入了尺寸相关的机电耦合。在长波长极限下解析推导了色散关系，并对一般情况进行了数值求解，揭示了瑞利波相速度和衰减对德拜筛分尺度、霍尔迁移率和挠曲电系数之间的相互作用具有深刻的敏感性。这些发现突出了半导体声学中简化边界处理的局限性，并展示了由多尺度相互作用机制产生的多重可调谐波效应。该框架为设计和优化下一代表面声波（SAW）器件提供了物理上连贯和数学上合理的基础。

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引用次数: 0

Global sliding mode compensation control for flexible servo systems with friction-induced excitation 摩擦激励柔性伺服系统的全局滑模补偿控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-17 DOI: 10.1016/j.apm.2025.116712

Haozhe Wang , Xiaopeng Li , Xing Fan , Yanqing Tie , Fanjie Li

Friction-induced excitations in gear meshing generate nonlinear disturbances that amplify tracking errors and degrade control performance in flexible servo systems. To address this issue, a novel global sliding mode control strategy incorporating a motor-side disturbance observer is proposed to improve control accuracy and system robustness. First, a dynamic model of the flexible servo system is established, accounting for flexible joints, friction-induced excitations, and the end mass. The LuGre model is employed to describe the gear friction torque, taking into account temperature rise, backlash, and bearing stiffness. Based on motor state feedback, a nonlinear disturbance observer is developed to estimate and compensate for friction-induced excitations, and a global sliding mode control strategy is designed. Moreover, a sigmoid function is embedded in the control law to suppress chattering and enhance control smoothness. Finally, simulation and experimental results demonstrate that the proposed method significantly improves control accuracy and motion performance. Error statistics indicate that the proposed strategy outperforms conventional PD control, reducing the mean absolute error and standard deviation by 83 % and 81.6 % for the rotation angle, and by 57.28 % and 58.28 % for the acceleration profile, respectively. These results confirm the effectiveness of the proposed strategy.

在柔性伺服系统中，齿轮啮合中的摩擦激励会产生非线性扰动，增大跟踪误差，降低控制性能。为了解决这一问题，提出了一种包含电机侧扰动观测器的全局滑模控制策略，以提高控制精度和系统鲁棒性。首先，建立了考虑柔性关节、摩擦激励和末端质量的柔性伺服系统动力学模型。采用LuGre模型来描述齿轮摩擦力矩，同时考虑了温升、间隙和轴承刚度。基于电机状态反馈，设计了非线性扰动观测器来估计和补偿摩擦诱导的扰动，并设计了全局滑模控制策略。在控制律中嵌入s型函数抑制抖振，提高控制平滑度。仿真和实验结果表明，该方法显著提高了控制精度和运动性能。误差统计表明，该策略优于传统的PD控制，旋转角度的平均绝对误差和标准差分别降低了83%和81.6%，加速度剖面的平均绝对误差和标准差分别降低了57.28%和58.28%。这些结果证实了所提出策略的有效性。

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引用次数: 0

Numerical modelling of nanometer-thickness liquid lubrication in point contacts with coating considering surface force effects 考虑表面力效应的涂层点接触纳米厚度液体润滑数值模拟

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-17 DOI: 10.1016/j.apm.2025.116703

Yanfei Fang , Yusong Chen , Hui Xuan , Xiangrong Li , Peiyan Cheng , Wanglong Zhan

In liquid lubrication systems, surface forces significantly influence the lubrication performance at the nanoscale liquid film thickness in coated point contacts. This study develops a numerical model to investigate macro-scale liquid lubrication behavior, incorporating surface force effects in point contacts with coating. The analysis focuses on the lubrication performance under the combined influence of the characteristics of coated surfaces, surface forces, and hydrodynamic effect. The results reveal that the interaction between surface forces (such as those due to hydration and electrical double layer) and hydrodynamic forces is essential for balancing the applied load. Additionally, the nanoscale film thickness significantly affects the repulsive forces generated by hydration. Enhancing the interfacial hydration can increase the load-carrying capacity of surface forces. Conversely, increasing the thickness of soft coating leads to a slight increase in the lubricated film thickness and an enhancement of the hydrodynamic pressure effect. Furthermore, the hydrodynamic effect improves as the velocity increases, while the influence of surface forces diminishes as the thin film thickness increases, leading to a reduction in the surface forces load-carrying capacity ratio.

在液体润滑系统中，表面作用力显著影响涂覆点接触中纳米级液膜厚度的润滑性能。本研究建立了一个数值模型来研究宏观尺度的液体润滑行为，并考虑了与涂层点接触时表面力的影响。重点分析了涂层表面特性、表面力和流体动力效应共同影响下的润滑性能。结果表明，表面力（如水化和电双层力）与水动力之间的相互作用对于平衡施加的载荷至关重要。此外，纳米级薄膜厚度对水化产生的排斥力有显著影响。增强界面水化作用可以提高表面力的承载能力。相反，增加软膜厚度会导致润滑膜厚度的轻微增加和动水压力效应的增强。水动力效应随着流速的增加而增强，而表面力的影响随着薄膜厚度的增加而减弱，导致表面力承载能力比减小。

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引用次数: 0

Dynamic information priority fractional discrete multivariate grey polynomial model for lithium-ion battery health monitoring 锂离子电池健康监测的动态信息优先分数离散多元灰色多项式模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-16 DOI: 10.1016/j.apm.2025.116707

Min Sun, Yang Cao, Qinqin Shen

Accurately assessing the state of health of lithium-ion batteries is crucial to guarantee the safe operation of energy storage systems. The adaptive variable fractional order multivariate grey model, with its strengths in modeling small-sample and multivariate systems and its ability to dynamically capture nonlinear features, has shown great potential in SOH monitoring. However, it still suffers from insufficient consideration of new information, incomplete monitoring, and presence of conversion errors. To address these limitations, a dynamic information priority fractional discrete multivariate grey polynomial model is proposed. Firstly, a dynamic new information priority fractional accumulation generating operator is introduced to differentially define and optimize the orders of all dependent and independent variables, thereby reflecting the information discrepancy and new information priority in the capacity degradation process. Secondly, the driving terms are incorporated into the model structure to fully capture the interactive relationships between SOH and health factors. Finally, the idea of discrete modeling is adopted to eliminate conversion errors. Some properties of the accumulation operators are analyzed. The methods for calculating model parameters as well as the optimal polynomial orders and accumulation orders are discussed. The proposed model is applied to several lithium-ion battery datasets from NASA and compared with some recently proposed multivariate grey models and deep learning models. The results indicate that the proposed model shows high accuracy and better stability in capacity degradation prediction and health factor monitoring.

准确评估锂离子电池的健康状态对于保证储能系统的安全运行至关重要。自适应变分数阶多变量灰色模型以其在小样本和多变量系统建模方面的优势和动态捕捉非线性特征的能力，在SOH监测中显示出巨大的潜力。然而，它仍然存在对新信息考虑不足、监测不完整和存在转换错误等问题。针对这些局限性，提出了一种动态信息优先级分数阶离散多元灰色多项式模型。首先，引入一个动态的新信息优先级分数积累生成算子，差分定义和优化所有因变量和自变量的顺序，从而反映容量退化过程中的信息差异和新信息优先级；其次，将驱动项纳入模型结构，充分捕捉SOH与健康因素之间的交互关系。最后，采用离散建模的思想消除了转换误差。分析了积累算子的一些性质。讨论了模型参数的计算方法以及最优多项式阶数和最优累积阶数。将提出的模型应用于NASA的几个锂离子电池数据集，并与最近提出的一些多元灰色模型和深度学习模型进行了比较。结果表明，该模型在容量退化预测和健康因素监测方面具有较高的准确性和稳定性。

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引用次数: 0

Efficient Hamel’s integrator for vehicle-manipulator systems 用于车辆操纵系统的高效Hamel积分器

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-16 DOI: 10.1016/j.apm.2025.116708

Benliang Wang , Donghua Shi , Zhipeng An

Vehicle-manipulator systems offer versatile manipulation and mobility in challenging environments. However, conventional dynamic modeling approaches often encounter singularities and may fail to capture underlying symmetries. In addition, they typically exhibit high computational complexity, which scales cubically with the total degrees of freedom of the vehicle and manipulator. This work proposes a singularity-free formulation for vehicle-manipulator systems built on Hamel’s formalism. This approach is particularly advantageous for nonholonomic systems, as applying the Lagrange–d’Alembert principle within this framework eliminates the unnecessary Lagrange multipliers associated with velocity constraints. Furthermore, we present an efficient variational integrator, augmented with a quasi-Newton algorithm, that solves the root-finding problem for the discrete Hamel’s equations with linear time complexity. We demonstrate the effectiveness of the variational integrator through numerical studies of a space manipulator and a nonholonomic mobile manipulator, and verify its linear-time complexity with a dedicated performance benchmark.

车辆操纵系统在具有挑战性的环境中提供多功能操纵和机动性。然而，传统的动态建模方法经常遇到奇点，可能无法捕获潜在的对称性。此外，它们通常表现出很高的计算复杂性，这与车辆和操纵器的总自由度成三次比例。这项工作提出了一个基于Hamel形式主义的车辆操纵系统的无奇点公式。这种方法对于非完整系统特别有利，因为在这个框架内应用拉格朗日-达朗贝尔原理消除了与速度约束相关的不必要的拉格朗日乘子。此外，我们提出了一个有效的变分积分器，用拟牛顿算法扩充，解决了具有线性时间复杂度的离散Hamel方程的寻根问题。通过对空间机械臂和非完整移动机械臂的数值研究，证明了变分积分器的有效性，并通过专门的性能基准验证了其线性时间复杂度。

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引用次数: 0

FASTer: A highly efficient part-scale thermal simulator for powder bed fusion 更快：粉末床熔合的高效部分规模热模拟器

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-16 DOI: 10.1016/j.apm.2025.116690

S.R. Cooke, C.W. Sinclair, D.M. Maijer

To overcome computational bottlenecks in the thermal simulation of large powder bed fusion builds, we introduce a physically grounded layer-truncation strategy in the context of a semi-analytical model. By treating only the most recent layers exactly and approximating the thermal contributions from layers far from the heat source using an analytical correction, we restore computational efficiency at minimal degradation in accuracy. Across various test cases, this approach showed maximum temperature errors under 7 ^∘C while delivering a more than tenfold speed-up in an 8 hr build. Even better computational efficiency would be attained for longer builds. We demonstrate the method on complex, multi-layer, part-scale thermal analyses that would be infeasible with conventional tools (e.g. finite element analysis). This paves the way for rapid thermal predictions in powder bed fusion, ready for integration with residual-stress, microstructure, and defect models to optimise build strategies at scale.

为了克服大型粉末床熔合热模拟中的计算瓶颈，我们在半解析模型的背景下引入了一种物理接地层截断策略。通过精确地处理最近的层，并使用解析校正近似远离热源的层的热贡献，我们以最小的精度退化恢复了计算效率。在各种测试用例中，这种方法显示出在7°C下的最大温度误差，同时在8小时的构建中提供了10倍以上的加速。对于更长的构建，甚至可以获得更好的计算效率。我们在复杂的、多层的、局部尺度的热分析上展示了这种方法，这是传统工具（例如有限元分析）无法实现的。这为粉末床熔合的快速热预测铺平了道路，可以与残余应力、微观结构和缺陷模型集成，以大规模优化构建策略。

引用次数: 0

A joint multi-contrast MRI reconstruction model based on minimax concave penalty 基于极大极小凹惩罚的联合多对比MRI重建模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-16 DOI: 10.1016/j.apm.2025.116687

Yiming Gao , Luying Gui

Multi-contrast magnetic resonance imaging (MRI) has attracted significant attention in medical imaging due to its ability to show distinct properties of the same region of interest, for instance, T₁- and T₂-weighted images. The standard approach to acquiring these multi-modality images is to treat them separately without considering their similarities during reconstruction. In this paper, we propose a nonconvex joint regularized model for multi-contrast MRI reconstruction in term of edge structures. The minimax concave penalty (MCP) is employed as a nonconvex regularizer to capture the shared edge feature, and we further reformulate the associated model as an equivalent biconvex problem via the concave conjugate. Then, an alternating minimization method is proposed to solve the optimization problem, and some weak convergence analysis for the biconvex model with a nonsmooth coupled term is presented. Finally, the numerical experiments show that the proposed nonconvex joint reconstruction method achieves better edge preservation than existing variational methods for piecewise constant images.

多对比磁共振成像（MRI）在医学成像中引起了极大的关注，因为它能够显示同一感兴趣区域的不同特性，例如T1和t2加权图像。获取这些多模态图像的标准方法是分别处理，而不考虑它们在重建过程中的相似性。本文提出了一种基于边缘结构的非凸关节正则化多对比MRI重建模型。采用极大极小凹惩罚（MCP）作为非凸正则化器捕获共享边特征，并通过凹共轭将相关模型重新表述为等效双凸问题。然后，提出了一种交替最小化方法来求解优化问题，并对具有非光滑耦合项的双凸模型进行了弱收敛性分析。最后，数值实验表明，对于分段常量图像，所提出的非凸联合重建方法比现有的变分方法具有更好的边缘保持效果。

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引用次数: 0

An innovative data-driven grey Bernoulli model for the port container throughput forecasting 基于数据驱动的港口集装箱吞吐量预测灰色伯努利模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-12-15 DOI: 10.1016/j.apm.2025.116709

Lin Yang , Pan Yang , Xuemei Li , Yuhu Cui , Guangxue Wan

With the increasing importance of container transport in global trade and marine supply chain, it is crucial to make precise predictions of its throughput. From a data-driven perspective, this study proposes a dynamic adaptive structural prediction framework designed to identify time series patterns characterized by rising, declining, fluctuating, and stationary trends. Firstly, this framework improves the conventional grey Bernoulli model by introducing adaptive multi-weight coefficients and structural segmentation approach. Specifically, adaptive multi-weight coefficients prioritize recent data through dynamic weighting, enhancing the timeliness to optimize initial values. Furthermore, the structural segmentation approach is employed to optimize the background value so as to effectively mitigating the influence of inherent data patterns. Besides, a nonlinear parameter optimization approach for the novel model based on the Particle Swarm Optimization algorithm is proposed, with robustness test through ablation experiment analysis, sensitivity analysis, comparative analysis with other algorithms and different division interval. We verify the proposed model’s superiority by applying it to the port container throughput forecasting with mean absolute percentage errors of 0.8637 %, 0.2312 %, 4.9046 %, 8.5412 %, and 1.4073 %, respectively. Results reveal that the novel model demonstrates superior accuracy, flexibility, and broad applicability. Consequently, the novel model is deployed for container throughput predictions in 2024–2030. This study delivers a valuable tool for port decision makers to rationally plan layout, optimize resource allocation, and improve operational efficiency.

随着集装箱运输在全球贸易和海洋供应链中的重要性日益提高，对其吞吐量进行准确预测至关重要。从数据驱动的角度出发，本研究提出了一个动态自适应结构预测框架，旨在识别以上升、下降、波动和平稳趋势为特征的时间序列模式。首先，该框架通过引入自适应多权系数和结构分割方法对传统的灰色伯努利模型进行改进；具体而言，自适应多权系数通过动态加权对近期数据进行优先排序，增强了优化初始值的时效性。此外，采用结构分割方法对背景值进行优化，有效减轻了固有数据模式的影响。此外，提出了一种基于粒子群优化算法的新模型非线性参数优化方法，并通过烧蚀实验分析、灵敏度分析、与其他算法的对比分析和不同除法区间进行鲁棒性检验。将该模型应用于港口集装箱吞吐量预测，平均绝对百分比误差分别为0.8637%、0.2312%、4.9046%、8.5412%和1.4073%，验证了该模型的优越性。结果表明，该模型具有较高的准确性、灵活性和广泛的适用性。因此，该新模型可用于2024-2030年的集装箱吞吐量预测。本研究为港口决策者合理规划布局、优化资源配置、提高运营效率提供了有价值的工具。

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引用次数: 0