Mathematics and Computers in Simulation最新文献

{"title":"Unconditionally energy stable time marching numerical schemes for the modified phase field crystal equation","authors":"Fan Zhang ,&nbsp;Hai-Wei Sun ,&nbsp;Tao Sun ,&nbsp;Tian-Yi Li","doi":"10.1016/j.matcom.2025.07.047","DOIUrl":"10.1016/j.matcom.2025.07.047","url":null,"abstract":"<div><div>The modified phase field crystal (MPFC) equation is a sixth-order nonlinear damped wave equation modeling a viscoelastic response to perturbations to the density field. In this study, we propose first- and second-order time marching numerical schemes to solve the MPFC equation under the periodic boundary conditions. Recently, the scalar auxiliary variable (SAV) method has received considerable attention in solving of the gradient flow equations due to its advantage of preserving the energy dissipation law in a discrete sense. The proposed numerical schemes in this work are based on the exponential SAV (ESAV) method. More specifically, the scalar variable in the ESAV method is an exponential form rather than the square root function typically employed in the SAV approach. By making this distinctive change, the ESAV schemes are able to solve only one linear system with constant coefficients at each time step. In this paper, we first propose the first-order ESAV scheme based on the backward Euler method, then we develop the second-order ESAV scheme by utilizing the leapfrog approach. Theoretically, we present the unique solvability, mass conservation and unconditional energy stability of our proposed schemes. Moreover, a rigorous error analysis is provided for the second-order ESAV scheme. A comprehensive set of numerical simulations and examples are provided to validate the effectiveness of these schemes.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 589-611"},"PeriodicalIF":4.4,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144758067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distributed robust anti-interference Nash equilibrium search for second-order multi-agent systems and its application","authors":"Yong Chen ,&nbsp;Bowen Hao ,&nbsp;Fuxi Niu ,&nbsp;Jiarui Li ,&nbsp;Xiaohong Nian ,&nbsp;Hailiang Hou","doi":"10.1016/j.matcom.2025.07.042","DOIUrl":"10.1016/j.matcom.2025.07.042","url":null,"abstract":"<div><div>This paper focuses on achieving a distributed Nash equilibrium while accounting for both matched and mismatched disturbances. It introduces an algorithm that relies on disturbance estimation and a distributed feedforward controller. The algorithm is mainly divided into two parts. The first part is to design effective disturbance observers for different types of disturbances, and the second part is to design distributed feedforward feedback control algorithm utilizing these disturbance observations. By employing this algorithm, the agents’ states ultimately converge to Nash equilibrium points. The convergence of the algorithm is proved by the input state stability criterion and Lyapunov stability analysis. Finally, a numerical simulation and experimental scenario were designed to verify the effectiveness of the algorithm.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 571-588"},"PeriodicalIF":4.4,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144758066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel time-dependent sampled-data control for fuzzy Markov jump systems with cyber-attacks and missing measurements","authors":"Visakamoorthi Balasubramani,&nbsp;Sung-ho Hur","doi":"10.1016/j.matcom.2025.07.038","DOIUrl":"10.1016/j.matcom.2025.07.038","url":null,"abstract":"<div><div>A time-dependent sampled-data controller (SDC) is designed to examine the stochastic stability and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance of a class of fuzzy Markov jump systems (FMJSs) subjected to limited external perturbations and time-variant mode-dependent delays. For the FMJS, first, a time-dependent SDC with randomly occurring cyber-attacks and missing data measurements that adhere to the Bernoulli distribution is developed. Subsequently, a new stochastic Lyapunov–Krasovskii functional (LKF) is developed in the mode-dependent augmented form to take full advantage of the variable properties of the actual sampling pattern. Furthermore, the principal Lyapunov term accounts for aperiodic sampling to varying degrees. To guarantee the stochastic stability of the closed-loop system, new delay-dependent criteria are established within the framework of linear matrix inequalities according to the proposed time-dependent control approach and LKF. Finally, two illustrative applications are presented to verify the mathematical findings with reduced conservatism, that is, by expanding the sampling period size and decreasing the number of decision variables.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 520-537"},"PeriodicalIF":4.4,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00321-0","DOIUrl":"10.1016/S0378-4754(25)00321-0","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"238 ","pages":"Page 637"},"PeriodicalIF":4.4,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144704298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability analysis and optimal intervention design for age-structured HIV/AIDS transmission model with protective consciousness","authors":"Yaping Wang,&nbsp;Lin Hu,&nbsp;Lin-Fei Nie","doi":"10.1016/j.matcom.2025.07.036","DOIUrl":"10.1016/j.matcom.2025.07.036","url":null,"abstract":"<div><div>In keeping with the age heterogeneity observed in HIV/AIDS transmission, a novel age-structured model incorporating protective consciousness is introduced. Our research delves into the existence and stability of steady states in relation to basic reproduction number <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> (or <span><math><msub><mrow><mover><mrow><mi>ℛ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span>). Specifically, we demonstrate that when the basic reproduction number is less than 1, a globally stable disease-free steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> exists, this implies that the disease will disappear. In scenarios where disease-induced death is absent, the endemic steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> becomes the sole existing steady state and exhibits local asymptotic stability for the basic reproduction number is more than 1, thereby perpetuating the disease. To further enhance the applicability of our model, we incorporate control functions such as physical distancing, educational campaigns, and treatment and then formulate an optimal control problem and rigorously prove the existence and uniqueness of optimal control solution. This approach provides a robust theoretical foundation for designing effective intervention strategies. Numerical simulations are conducted to illustrate the core findings of our study, indicating the critical role of age variability in the dissemination dynamics of HIV/AIDS. Notably, our results suggest that targeting educational interventions to achieve self-protection awareness toward younger populations yields significantly greater effectiveness compared to implementing uniform strategies across all age groups. This insight underscores the importance of age-specific approaches in optimizing resource allocation and maximizing public health impact.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 494-519"},"PeriodicalIF":4.4,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144720985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00322-2","DOIUrl":"10.1016/S0378-4754(25)00322-2","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"238 ","pages":"Page 638"},"PeriodicalIF":4.4,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144704299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mesh-based segmentation for automated margin line generation on incisors receiving crown treatment","authors":"Ammar Alsheghri ,&nbsp;Ying Zhang ,&nbsp;Farnoosh Ghadiri ,&nbsp;Julia Keren ,&nbsp;Farida Cheriet ,&nbsp;Francois Guibault","doi":"10.1016/j.matcom.2025.07.054","DOIUrl":"10.1016/j.matcom.2025.07.054","url":null,"abstract":"<div><div>Dental crowns are essential dental treatments for restoring damaged or missing teeth of patients. Recent design approaches of dental crowns are carried out using commercial dental design software. Once a scan of a preparation is uploaded to the software, a dental technician needs to manually define a precise margin line on the preparation surface which constitutes a nonrepeatable and inconsistent procedure. This work proposes a new framework to determine margin lines automatically and accurately using deep learning. A dataset of incisor teeth was provided by a collaborating dental laboratory to train a deep learning segmentation model. A mesh-based neural network was modified by changing its input channels and used to segment the prepared tooth in two regions such that the margin line is contained within the boundary faces separating the two regions. Next, k-fold cross-validation was used to train 5 models and a voting classifier technique was used to combine their results to enhance the segmentation. After that, boundary smoothening and optimization using the graph cut method was applied to refine the segmentation results. Then, boundary faces separating the two regions were selected to represent the margin line faces. A spline was approximated to best fit the centers of the boundary faces to predict the margin line. Our results show that an ensemble model combined with maximum probability predicted the highest number of successful test cases (7 out of 13) based on a maximum distance threshold of 200 μm (representing human error) between the predicted and ground truth point clouds. It was also demonstrated that the better the quality of the preparation, the smaller the divergence between the predicted and ground truth margin lines (Spearman’s rank correlation coefficient of −0.683). We provide the train and test datasets for the community.<span><span>¹</span></span></div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 716-728"},"PeriodicalIF":4.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144725004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Combinatorial potential of random equations with mixture models: Modeling and simulation","authors":"Wolfgang Hoegele","doi":"10.1016/j.matcom.2025.07.033","DOIUrl":"10.1016/j.matcom.2025.07.033","url":null,"abstract":"<div><div>The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters as random variables, have a long history and a broad range of applications. The specific novelty of this explorative study lies on the demonstration of the combinatorial complexity of these equations and their solutions with mixture model parameters. In a Bayesian argumentation framework, we derive a likelihood function and posterior density of approximate solutions while avoiding significant restrictions about the type of nonlinearity of the equation or mixture models, and demonstrate their numerically efficient implementation for the applied researcher. In the results section, we are specifically focusing on expressive example simulations showcasing the combinatorial potential of random linear equation systems and nonlinear systems of random conic section equations. Introductory applications to portfolio optimization, stochastic control and random matrix theory are provided in order to show the wide applicability of the presented methodology.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 696-715"},"PeriodicalIF":4.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advanced heuristic computing with Gudermannian neural networks for mathematical modeling of divorced dynamics in social networks","authors":"Sana Ullah Saqib ,&nbsp;Yin-Tzer Shih ,&nbsp;Muhammad Wajahat Anjum ,&nbsp;Muhammad Shoaib","doi":"10.1016/j.matcom.2025.07.048","DOIUrl":"10.1016/j.matcom.2025.07.048","url":null,"abstract":"<div><div>This study investigates the transmission dynamics of divorce within social networks through the innovative application of Gudermannian neural networks (GNNs), combined with a hybrid optimization framework that integrates heuristic genetic algorithms (HGAs) and sequential quadratic programming (SQP). The proposed methodology, referred to as HGA-SQP-GNN, is employed to analyze the intricacies of marital dissolution, encapsulated within the Married-Divorced-Separated (MDS) mathematical framework. This framework categorizes individuals into three distinct groups: Married (M), Divorced (D), and Separated (S). The findings show that about 80 % of marriages end in separation by the end of the observed period. This statistic highlights how divorced individuals can significantly influence the likelihood of separation among married couples, emphasizing the need for targeted interventions to address the rise of broken families. Furthermore, the study demonstrates the robustness and effectiveness of the proposed HGA-SQP-GNN algorithm, as shown by the optimal solutions achieved compared to the traditional Adam method. Our study highlights the urgent need for focused interventions to curb the proliferation of broken families. A hybrid technique, HGA-SQP-GNN, enables rapid convergence optimization by minimizing the mean square error (MSE), which acts as the fitness function for optimization. The robustness and efficacy of the proposed algorithm are confirmed by comparing the optimal solutions of the hybrid approach with the numerical results obtained from the Adam method. The precise measurements of absolute error findings, ranging from 10⁻² to 10⁻¹², demonstrate the value and effectiveness of the proposed algorithm. The reliability, stability, and convergence characteristics of the integrated techniques are further verified through statistical analyses, including mean absolute deviation, root mean square error, and Theil's inequality coefficient. Additionally, the lower values of minimum, median, and SIR, ranging from 10⁻⁵ to 10⁻¹², further validate the accuracy, robustness, and efficacy of the proposed solver.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 745-765"},"PeriodicalIF":4.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PID tuning strategies for boost converters. Optimal compromise between performance and noise amplification","authors":"Roberto Sanchis ,&nbsp;José María Martín","doi":"10.1016/j.matcom.2025.07.009","DOIUrl":"10.1016/j.matcom.2025.07.009","url":null,"abstract":"<div><div>This paper presents some PID tuning strategies for the control of boost converters, that exhibit non-minimum phase behavior. First, some simple model identification techniques based on the step response are presented. Then, a PID tuning technique based on the fixed robustness tuning line concept, developed by the authors, is revised and applied to the tuning of PID controllers for boost converters. The proposed techniques allow the user to freely select the desired robustness, defined as the maximum sensitivity (<span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>). They also permit to find an optimal compromise between measurement noise amplification and performance, in terms of disturbance rejection and reference tracking. Some direct tuning equations are also proposed to directly compute the controller parameters using some measurements from an open-loop step test. No previous proposals in literature about PID tuning of boost converters allow the free selection of robustness and compromise between performance and noise amplification, as the proposed approach. Experimental validation on two real boost converter prototypes, one overdamped and one underdamped, show the superiority of the proposed approaches, measured in terms of robustness, disturbance IAE, settling time and overshoot in the step response, compared to the use of a theoretical model of the converter based on the component values. The experiments demonstrate a reduction in the overshoot from 50% to less than 5%, and a 30% reduction in the settling time compared to theoretical model-based tuning. The results of this paper are intended for those practitioners who design boost converters and want a simple tool to tune the PID controller for the converter.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 381-402"},"PeriodicalIF":4.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}