Applied Mathematical Modelling最新文献

{"title":"Event-triggered prescribed-time distributed formation control of marine surface vessels with prescribed performance","authors":"Shasha Wang ,&nbsp;Dongchen Dai ,&nbsp;Lili Li ,&nbsp;Shuang Gao ,&nbsp;Zhouhua Peng ,&nbsp;Yulong Tuo","doi":"10.1016/j.apm.2025.116117","DOIUrl":"10.1016/j.apm.2025.116117","url":null,"abstract":"<div><div>In this paper, an event-triggered prescribed-time distributed formation control method is designed for marine surface vessels with prescribed-time prescribed performance subject to compound uncertainties. Firstly, we introduce variable substitutions to simplify the mathematical model of marine surface vessels. Then, a prescribed-time extended state observer is constructed to estimate unmeasured velocities and compound uncertainties at a prescribed-time. Meanwhile, a novel prescribed-time performance function with an error transformation is designed to impose constraints on formation errors. Subsequently, we design an event-triggered control mechanism taking account of error constraints, which reduces the operating frequency of actuators without weakening system transient performance. Based on the designed extended state observer, performance function and event-triggered control mechanism, a prescribed-time distributed formation control law is developed for marine surface vessels with distinguished convergence performance, good transient performance, and low actuator losses. At last, simulations are conducted to illustrate the advantages and application prospects of the designed approach. The proposed method has several notable characteristics compared with most existing strategies: 1) it guarantees the prescribed-time convergence of the formation errors; 2) it achieves prescribed-time error constraints by using the designed performance function; 3) it actualizes the quantitative balance between error constraints and the operating frequency of actuators via the proposed event-triggered control mechanism, which can avoid the excessive wear on actuators.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116117"},"PeriodicalIF":4.4,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An alternative minimization method for TV-image deblurring in tensor space","authors":"Haonan Tao ,&nbsp;Zhibao Li","doi":"10.1016/j.apm.2025.116102","DOIUrl":"10.1016/j.apm.2025.116102","url":null,"abstract":"<div><div>The total variation (TV) model is a straightforward yet effective approach for noise reduction and blurring suppression in image processing. It necessitates converting the image matrix into a vector for problem-solving, which may compromise the preservation of the original image structure, especially in color images. In this paper, we propose a third-order tensor TV model for image deblurring in fractional-order differential form (t-FTV), based on the tensor t-product. We then develop a customized alternating minimization (AM) method to solve the tensor TV optimization problem. Next, we derive the optimality conditions for the t-FTV optimization problem and establish the convergence results of the proposed AM algorithm. Additionally, we compare the numerical performance of the proposed model against other methods for grayscale, color, and multispectral image deblurring. The results demonstrate that the proposed tensor TV model outperforms existing models.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116102"},"PeriodicalIF":4.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New analytical laws and applications of interaction potentials with a focus on van der Waals attraction","authors":"A. Borković ,&nbsp;M.H. Gfrerer ,&nbsp;R.A. Sauer","doi":"10.1016/j.apm.2025.116100","DOIUrl":"10.1016/j.apm.2025.116100","url":null,"abstract":"<div><div>The paper aims to improve the efficiency of modeling interactions between slender deformable bodies that resemble the shape of fibers. Interaction potentials are modeled as inverse-power laws with respect to the point-pair distance, and the complete body-body potential is obtained by pairwise summation (integration). To speed-up integration, we consider the analytical pre-integration of potentials between specific geometries such as disks, cylinders, rectangles, and rectangular prisms. Several exact new interaction laws are obtained, such as disk-infinite half-space and (in-plane) rectangle-rectangle for an arbitrary exponent, and disk-disk and rectangle-rectangle for van der Waals attraction. To balance efficiency and accuracy, approximate laws are proposed for disk-disk, point-cylinder, and disk-cylinder interactions. Additionally, we have developed a novel formulation for the interaction between a spatial beam and an infinite half-space. The application of the pre-integrated interaction potentials within the finite element method is illustrated via two examples.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116100"},"PeriodicalIF":4.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiphysics simulation of slag melting in an induction furnace for sustainable silicon production","authors":"A. Bermúdez ,&nbsp;O. Crego ,&nbsp;J.L. Ferrín ,&nbsp;B. García ,&nbsp;D. Gómez ,&nbsp;I. Martínez ,&nbsp;L.J. Pérez-Pérez ,&nbsp;P. Salgado","doi":"10.1016/j.apm.2025.116107","DOIUrl":"10.1016/j.apm.2025.116107","url":null,"abstract":"<div><div>This work presents a multiphysics mathematical modelling and numerical simulation of the slag melting process in an induction furnace, with a focus on the production of sustainable silicon through the EU SisAl Pilot project. The mathematical model incorporates electromagnetic, thermal and hydrodynamic phenomena in a coupled axisymmetric framework to simulate the melting of a CaO-SiO₂ slag, a key component in the aluminothermic reduction process for silicon production. The model addresses the challenge of heating the poorly electrically conductive slag using a graphite crucible and it also accounts for buoyancy-driven convection in the molten slag. The numerical simulations are validated against experimental data from pilot scale trials at Elkem's plant in Norway. In addition, sensitivity analyses are carried out considering both the progressive filling of the furnace and the inclusion of surface-to-surface radiation models.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116107"},"PeriodicalIF":4.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A coupled δ+-SPH-NOSB-PD method: Towards fluid-structure interaction problems involving violent free-surface flows and isotropic structural linear elastic deformations and failures","authors":"Guang-Qi Liang ,&nbsp;Peng-Nan Sun ,&nbsp;Hong-Guan Lyu ,&nbsp;Gui-Yong Zhang","doi":"10.1016/j.apm.2025.116104","DOIUrl":"10.1016/j.apm.2025.116104","url":null,"abstract":"<div><div>In this paper, a robust integrated particle model is developed by coupling smoothed particle hydrodynamics (SPH) and peridynamics (PD) to deal with the fluid-structure interaction (FSI) problems involving violent free-surface flows and isotropic structural linear elastic deformations and failures. The partitioned approach is conducted in between a stable and accurate <span><math><msup><mrow><mi>δ</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-SPH fluid model and a non-ordinary state-based PD (NOSB-PD) structure model based on the idea of non-local interactions. The SPH fluid model is strengthened with a set of previously advanced numerical techniques, hence, the developed coupled scheme is referred to as an enhancement of the traditional SPH-PD. Crack initiation and propagation in structural responses under fluid dynamics are considered, which is relatively rare in previous FSI simulations. The information between the boundaries is transferred via the acceleration-based way and pressure integration method, which helps to ensure numerical stability and accuracy. In addition, a modified sequential staggered (MSS) algorithm is adopted to improve the efficiency when the time step of the structure significantly differs from that of the fluid. Firstly, the performance of the PD-based structure model is verified by three benchmarks, namely a free oscillating cantilever plate, stress distribution inside an isotropic plate with a circular opening and the Kalthoff-Winkler impact test. Then, several challenging FSI problems are simulated to validate the accuracy and robustness of the present FSI solver in predicting the fluid fields and the elastic response and fracture of the structure. The results achieved are in good agreement with the references, verifying the scheme's feasibility in this work.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116104"},"PeriodicalIF":4.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The construction method of chaotic system model based on state variables and uncertain variables and its application in image encryption","authors":"Jingfeng Jie ,&nbsp;Yang Yang ,&nbsp;Ping Zhang","doi":"10.1016/j.apm.2025.116097","DOIUrl":"10.1016/j.apm.2025.116097","url":null,"abstract":"<div><div>This paper focuses on the construction of nonlinear dynamic models, specifically targeting continuous chaotic systems. It introduces an innovative approach to integrating state variables and uncertain variables to construct continuous chaotic systems. Initially, a unified construction method is proposed, combining state variables with a determinable amplitude matrix. The feasibility of this method is verified through the definition of the Lyapunov index. Using a three-dimensional chaotic system with a single nonlinear structure as an example, numerical parameters are screened based on the Lyapunov index. Additionally, permutation entropy is utilized to explore changes in the system's chaotic behavior induced by random natural values and mathematical functions in random amplitudes. The model is then extended to a four-dimensional state, demonstrating the complex characteristics of the system in this higher dimension through various complexities, thus highlighting the universal applicability of the construction method. Finally, the constructed three-dimensional and four-dimensional continuous systems are applied to a DNA-based color image encryption system. Comparative analyses of robustness and security show that the proposed method offers significant advantages in practical applications. The results indicate that this method is not only theoretically innovative in constructing chaotic systems but also holds high practical value.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"144 ","pages":"Article 116097"},"PeriodicalIF":4.4,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Torque tracking position control of DLR-HIT II robotic hand using a real-time physics-informed neural network","authors":"Ali Al-Shahrabi ,&nbsp;Masoud J. Javid ,&nbsp;Ashraf A. Fahmy ,&nbsp;Christian A. Griffiths ,&nbsp;Chunxu Li","doi":"10.1016/j.apm.2025.116110","DOIUrl":"10.1016/j.apm.2025.116110","url":null,"abstract":"<div><div>This paper presents a novel approach for controlling the DLR-HIT II robotic hand by leveraging physics-informed neural networks (PINNs) for torque and position control. This method eliminates the need for additional control inputs or external controllers, achieving high precision and simplified dynamics, which is validated through extensive simulations that closely replicate experimental conditions, demonstrating the system's ability to handle external disturbances and maintain accurate trajectory tracking. The strategy only requires time and joint position data as inputs, allowing the network to compute velocity and acceleration internally. Time normalization enhances the model's ability to generalize across different time scales and ensures stable training. The method demonstrates strong generalization from a limited training set and successfully performs across diverse trajectory types. This simplification significantly reduces computational complexity and facilitates real-time control in advanced robotic applications.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"145 ","pages":"Article 116110"},"PeriodicalIF":4.4,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cooperative-transportation dynamics and oscillation control of two helicopters transporting a rigid load","authors":"Guanfu Li,&nbsp;Jie Huang,&nbsp;Jiajun Chen","doi":"10.1016/j.apm.2025.116111","DOIUrl":"10.1016/j.apm.2025.116111","url":null,"abstract":"<div><div>The twin helicopter slung system can be effectively utilized for handling rigid loads. Nevertheless, the intense oscillations caused by the coupling dynamics of two helicopters, cables, and slung loads complicate the transportation system, reduce transportation efficiency, and bring pilot challenges. While considerable research has been conducted on twin or multiple helicopters suspending a load, fewer studies have addressed the coupling characteristics among multi-helicopter attitudes, multi-cable swing, and cable-suspended loads pitch. This paper established an analytical dynamic model of twin helicopters carrying a rigid load in the horizontal position undergoing planar motions. The model accurately describes the effects of load size on the dynamics of horizontal lifting motions and the differences in the coupled oscillations between the two helicopters and two cables. Additionally, a hybrid control architecture, integrating a dual-feedback model-tracking controller with two cascaded discontinuous piecewise smoothers, was designed to simultaneously reject external disturbances and minimize oscillations. The simulation results verified the dynamics of transportation system, and quantitatively prove the effectiveness of the proposed controller in comparison to a prior controller.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"144 ","pages":"Article 116111"},"PeriodicalIF":4.4,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trampoline metamaterial coupled with Helmholtz resonator for enhanced acoustic piezoelectric energy harvesting","authors":"Tian Deng ,&nbsp;Luke Zhao ,&nbsp;Feng Jin","doi":"10.1016/j.apm.2025.116109","DOIUrl":"10.1016/j.apm.2025.116109","url":null,"abstract":"<div><div>To enhance acoustic piezoelectric energy harvesting at lower frequencies, this study proposes a coupled structure comprising a trampoline metamaterial and a Helmholtz resonator. The trampoline metamaterial incorporates periodically arranged composite resonant pillars embedded in a perforated thin plate. By designing a point defect in the metamaterial, vibro-acoustic energy can be intentionally confined to the defect location at the defect band frequency. Considering the amplified acoustic pressure in the Helmholtz resonator, the incorporation of the trampoline metamaterial into a Helmholtz resonant cavity enables enhanced energy localization. Initially, a mathematical model for calculating the first resonant band gap is established. The band gap and corresponding defect band frequency are then validated by comparing numerical simulation with experimental results. Subsequently, numerical simulations are conducted to investigate the influences of hole radius and coupled structure on piezoelectric energy harvesting performance. These simulations revealed that an increase in the hole radius significantly enhances vibro-acoustic localization and piezoelectric conversion efficiency of the trampoline metamaterial. Furthermore, the synergistic interaction of the coupled structure between the defect state in the trampoline metamaterial and the acoustic pressure amplification in the Helmholtz resonator further enhances the energy harvesting performance. At an acoustic incident amplitude of 2 Pa and a defect band frequency of 1068.5 Hz, the coupled structure attains a maximum output voltage of 5.94 V and power of 39.10 μW. These values demonstrate enhancements of 2.65 times and 2.80 times, respectively, compared to the uncoupled trampoline metamaterial with a hole radius of <em>r</em>₀=1.5 mm. Such findings offer guidance for designing piezoelectric energy harvester in applications such as self-powered sensors and small electrical devices.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"144 ","pages":"Article 116109"},"PeriodicalIF":4.4,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entropy consistent and hyperbolic formulations for compressible single- and two-phase flows modeling in both rigid and elastically deformable pipes: Application to Euler, Kapila and Baer-Nunziato equations","authors":"F. Daude ,&nbsp;R.A. Berry ,&nbsp;F. Crouzet ,&nbsp;P. Galon","doi":"10.1016/j.apm.2025.116096","DOIUrl":"10.1016/j.apm.2025.116096","url":null,"abstract":"<div><div>The mathematical modeling of compressible flows in both rigid and elastic pipes is discussed here. Both single- and two-phase flow modeling are considered in the present paper. First, the derivation of the models through the integration of the 3-D equations over the radially deformable inner pipe cross-section is described. Then, the Coleman-Noll procedure is used in order to formulate constitutive/closure laws consistent with the second law of thermodynamics leading to entropy consistent models. For elastically deformable pipes, an additional closure law relating the elastic variation of the cross-section area with the internal fluid pressure is also considered. The derivation of this closure law, classically referred to as the tube law, is also discussed here. This effective averaging procedure leads to non-conservative terms in the one-dimensional models linked to the pressure effects due to the spatial and temporal cross-section variations. The mathematical properties of the obtained system of partial differential equations, i.e. hyperbolicity, the structure of the waves, the expression of the Riemann invariants and the existence of a mathematical entropy, are then examined. In addition, the consequences of the definition of shock-waves for these models are also discussed. The Euler equations are first considered and analyzed in this context. Then, the approach is extended to more advanced compressible two-phase flow modeling. The two examples considered in the present paper are the Kapila five-equation and the Baer-Nunziato seven-equation models involving non-conservative terms due to the change of volume fraction in the balance equations which are for the first time investigated in this context. The corresponding models are shown to be hyperbolic and the characteristic fields are analyzed. Finally, some shock-tube problems in both rigid or elastic pipes are examined showing agreement with the present mathematical analysis.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"144 ","pages":"Article 116096"},"PeriodicalIF":4.4,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}