Pub Date : 2026-01-24DOI: 10.1016/j.apm.2026.116789
Agatha Joumaa , Paola Goatin , Giovanni De Nunzio
This study introduces a flexible macroscopic model for heterogeneous traffic flow on general road networks, allowing the presence of several vehicle classes with general speed functions and different maximal densities pertinent to urban environments. The model, applicable to shared road situations, is designed for describing both creeping phenomena and class-specific lane discipline. Extended to networks, the model addresses the dynamics at general m × n junctions by prescribing suitable coupling conditions. Using the passenger-car-equivalent representation, numerical experiments demonstrate the model’s effectiveness in handling different real-life traffic scenarios, each with their complexities. The study focuses on the assessment of total travel time and CO2 emissions in the network, highlighting influences from various factors and traffic management strategies such as route guidance and modal shift. Results show that the model can accurately describe scenarios of congested situations where cyclists navigate past queues of cars and cars overtake queues of trucks.
{"title":"A macroscopic framework for modeling heterogeneous traffic flows on urban networks","authors":"Agatha Joumaa , Paola Goatin , Giovanni De Nunzio","doi":"10.1016/j.apm.2026.116789","DOIUrl":"10.1016/j.apm.2026.116789","url":null,"abstract":"<div><div>This study introduces a flexible macroscopic model for heterogeneous traffic flow on general road networks, allowing the presence of several vehicle classes with general speed functions and different maximal densities pertinent to urban environments. The model, applicable to shared road situations, is designed for describing both creeping phenomena and class-specific lane discipline. Extended to networks, the model addresses the dynamics at general <em>m</em> × <em>n</em> junctions by prescribing suitable coupling conditions. Using the passenger-car-equivalent representation, numerical experiments demonstrate the model’s effectiveness in handling different real-life traffic scenarios, each with their complexities. The study focuses on the assessment of total travel time and CO<sub>2</sub> emissions in the network, highlighting influences from various factors and traffic management strategies such as route guidance and modal shift. Results show that the model can accurately describe scenarios of congested situations where cyclists navigate past queues of cars and cars overtake queues of trucks.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116789"},"PeriodicalIF":4.4,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047903","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}
Pub Date : 2026-01-23DOI: 10.1016/j.apm.2026.116772
M.R. Delfani, M. Yadollahi
The widespread application of nanowires in various industries, particularly in battery technology where they serve as electrode materials, has attracted considerable research attention. In this context, the present study aims at developing a cylindrical continuum model for such nanostructures and deriving analytical solutions for the elastic and plastic fields induced therein by solid-state ion diffusion and the presence of dislocations. Given the significance of size effects in nanoscale solid-mechanics problems, Helmholtz-type strain-gradient theory is employed to provide a size-dependent continuum framework for describing the relevant field quantities. The results obtained here indicate that dislocations contribute to a reduction in the overall stress levels within these structures. Additionally, it is shown that decreasing the cross-sectional radius of the nanowires leads to a further reduction in the diffusion-induced stress, even resulting in a transition from tensile to compressive stress states. This transition may facilitate crack closure, suggesting a hardening effect associated with structural miniaturization.
{"title":"Strain-gradient solution for solid-state ion diffusion induced stress in cylindrical nanowires with dislocation effects","authors":"M.R. Delfani, M. Yadollahi","doi":"10.1016/j.apm.2026.116772","DOIUrl":"10.1016/j.apm.2026.116772","url":null,"abstract":"<div><div>The widespread application of nanowires in various industries, particularly in battery technology where they serve as electrode materials, has attracted considerable research attention. In this context, the present study aims at developing a cylindrical continuum model for such nanostructures and deriving analytical solutions for the elastic and plastic fields induced therein by solid-state ion diffusion and the presence of dislocations. Given the significance of size effects in nanoscale solid-mechanics problems, Helmholtz-type strain-gradient theory is employed to provide a size-dependent continuum framework for describing the relevant field quantities. The results obtained here indicate that dislocations contribute to a reduction in the overall stress levels within these structures. Additionally, it is shown that decreasing the cross-sectional radius of the nanowires leads to a further reduction in the diffusion-induced stress, even resulting in a transition from tensile to compressive stress states. This transition may facilitate crack closure, suggesting a hardening effect associated with structural miniaturization.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116772"},"PeriodicalIF":4.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033521","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}
Pub Date : 2026-01-23DOI: 10.1016/j.apm.2026.116786
Changyu Wang , Liming Zhou
Smart devices based on functionally graded magneto-electro-elastic (FGMEE) materials often subject to complex multi-physics environments and exhibit anisotropic fracture behaviors. Past works usually examine the magneto-electro-mechanical coupling effects of MEE materials, ignoring the anisotropic behaviors. In this study, anisotropic phase-field models for brittle fracture in functionally graded magneto-electro-elastic (FGMEE) materials under hygrothermal environment are developed. To solve the problem, a multi-physics hybrid-staggered scheme in conjunction with an adaptive strategy is proposed. Systematic 2D and 3D simulations are organized to investigate the influences of multi-physics loadings. The present framework offers insights into multi-physics fracture in FGMEE devices and can be easily extended for other scenarios.
{"title":"On the phase-field modeling of anisotropic fracture in functionally graded magneto-electro-elastic materials under hygrothermal environment","authors":"Changyu Wang , Liming Zhou","doi":"10.1016/j.apm.2026.116786","DOIUrl":"10.1016/j.apm.2026.116786","url":null,"abstract":"<div><div>Smart devices based on functionally graded magneto-electro-elastic (FGMEE) materials often subject to complex multi-physics environments and exhibit anisotropic fracture behaviors. Past works usually examine the magneto-electro-mechanical coupling effects of MEE materials, ignoring the anisotropic behaviors. In this study, anisotropic phase-field models for brittle fracture in functionally graded magneto-electro-elastic (FGMEE) materials under hygrothermal environment are developed. To solve the problem, a multi-physics hybrid-staggered scheme in conjunction with an adaptive strategy is proposed. Systematic 2D and 3D simulations are organized to investigate the influences of multi-physics loadings. The present framework offers insights into multi-physics fracture in FGMEE devices and can be easily extended for other scenarios.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116786"},"PeriodicalIF":4.4,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033520","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}
Pub Date : 2026-01-22DOI: 10.1016/j.apm.2026.116781
Ke Liu, Biao Li, Siyuan Wang, Yazhi Li
{"title":"A thermo-chemo-mechanical damage model for predicting high-temperature oxidation and creep life of GH4169 superalloy","authors":"Ke Liu, Biao Li, Siyuan Wang, Yazhi Li","doi":"10.1016/j.apm.2026.116781","DOIUrl":"https://doi.org/10.1016/j.apm.2026.116781","url":null,"abstract":"","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"10 1","pages":""},"PeriodicalIF":5.0,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033534","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}
Pub Date : 2026-01-21DOI: 10.1016/j.apm.2026.116785
Jiaguo Zhou , Guoji Xu , Qi Tao , Yongle Li , Jinsheng Wang
In this study, an efficient parallelized adaptive learning framework is developed for estimating small failure probabilities. The method introduces a parallelized infilling criterion in which pseudo-learning functions, augmented by an influence factor, approximate the impact of newly selected samples on the learning-function values without requiring prior evaluations of the true performance function. An adaptive strategy is further employed to determine the optimal batch size in each iteration. Following the principle of maximizing uncertainty reduction in failure-probability estimation, an error-based learning-function allocation strategy is proposed to dynamically choose the most suitable function from a predefined library. For rare-failure scenarios, a Markov chain Monte Carlo-based importance sampling (MCMC-IS) scheme is adopted, in which a kernel density function is used to construct the IS density from the final failure population generated by MCMC. The effectiveness and robustness of the proposed framework are demonstrated through three numerical benchmarks and a suspension bridge subjected to wind and lane actions, with failure probabilities ranging from 10–5 to 10–9.
{"title":"An efficient parallelized adaptive learning framework for small failure probability analysis","authors":"Jiaguo Zhou , Guoji Xu , Qi Tao , Yongle Li , Jinsheng Wang","doi":"10.1016/j.apm.2026.116785","DOIUrl":"10.1016/j.apm.2026.116785","url":null,"abstract":"<div><div>In this study, an efficient parallelized adaptive learning framework is developed for estimating small failure probabilities. The method introduces a parallelized infilling criterion in which pseudo-learning functions, augmented by an influence factor, approximate the impact of newly selected samples on the learning-function values without requiring prior evaluations of the true performance function. An adaptive strategy is further employed to determine the optimal batch size in each iteration. Following the principle of maximizing uncertainty reduction in failure-probability estimation, an error-based learning-function allocation strategy is proposed to dynamically choose the most suitable function from a predefined library. For rare-failure scenarios, a Markov chain Monte Carlo-based importance sampling (MCMC-IS) scheme is adopted, in which a kernel density function is used to construct the IS density from the final failure population generated by MCMC. The effectiveness and robustness of the proposed framework are demonstrated through three numerical benchmarks and a suspension bridge subjected to wind and lane actions, with failure probabilities ranging from 10<sup>–5</sup> to 10<sup>–9</sup>.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116785"},"PeriodicalIF":4.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014793","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}
Pub Date : 2026-01-21DOI: 10.1016/j.apm.2026.116782
Xiaopeng Li , Shiyao Guo , Dan Zhang , Zhimin Lin
Self-overestimation is one of the main factors leading to asymmetric evaluations, which will profoundly affect the decision-making process. In this study, we propose a novel model of asymmetric comparisons from self-overestimation and systematically examine its implications for the evolution of cooperative behavior. Concretely speaking, when surrounded by a cooperative neighbor, the cooperative focal player will develop self-overestimation or overconfidence due to the favorable interaction environment, ultimately leading to additional self-overestimation β beyond actual payoffs. Furthermore, the cumulative self-overestimation is directly proportional to the number of cooperative neighbors. In other words, if the cooperative focal player has n cooperative neighbors, he will generate the total self-overestimation nβ. During strategy updating, the cooperative focal player compares his subjectively inflated fitness against the objectively realized payoffs of its opponents, thereby creating an asymmetrical comparison mechanism. Through systematic Monte Carlo simulations, we demonstrate that cooperative behavior can not only emerge but also be robustly maintained, even within the stringent constraints of the prisoner’s dilemma game on different types of populations. In particular, the dynamics of cooperation exhibits fascinating nonlinear changes as β increases. Additionally, for different network structures, strategy updating patterns, and types of social dilemmas, the proposed mechanism can still effectively promote the evolution of cooperation. Furthermore, we relax the constraint of self-overestimation and obtain more complex dynamics of the evolution of cooperation. We hope this study offers new perspectives and approaches for the deeper understanding of the evolution and dissemination of cooperation. What is particularly important is that we expect this findings to provide theoretical support for the social governance and the emergence of swarm intelligence.
{"title":"Asymmetric comparison from self-overestimation promotes cooperation in social dilemmas","authors":"Xiaopeng Li , Shiyao Guo , Dan Zhang , Zhimin Lin","doi":"10.1016/j.apm.2026.116782","DOIUrl":"10.1016/j.apm.2026.116782","url":null,"abstract":"<div><div>Self-overestimation is one of the main factors leading to asymmetric evaluations, which will profoundly affect the decision-making process. In this study, we propose a novel model of asymmetric comparisons from self-overestimation and systematically examine its implications for the evolution of cooperative behavior. Concretely speaking, when surrounded by a cooperative neighbor, the cooperative focal player will develop self-overestimation or overconfidence due to the favorable interaction environment, ultimately leading to additional self-overestimation <em>β</em> beyond actual payoffs. Furthermore, the cumulative self-overestimation is directly proportional to the number of cooperative neighbors. In other words, if the cooperative focal player has <em>n</em> cooperative neighbors, he will generate the total self-overestimation <em>nβ</em>. During strategy updating, the cooperative focal player compares his subjectively inflated fitness against the objectively realized payoffs of its opponents, thereby creating an asymmetrical comparison mechanism. Through systematic Monte Carlo simulations, we demonstrate that cooperative behavior can not only emerge but also be robustly maintained, even within the stringent constraints of the prisoner’s dilemma game on different types of populations. In particular, the dynamics of cooperation exhibits fascinating nonlinear changes as <em>β</em> increases. Additionally, for different network structures, strategy updating patterns, and types of social dilemmas, the proposed mechanism can still effectively promote the evolution of cooperation. Furthermore, we relax the constraint of self-overestimation and obtain more complex dynamics of the evolution of cooperation. We hope this study offers new perspectives and approaches for the deeper understanding of the evolution and dissemination of cooperation. What is particularly important is that we expect this findings to provide theoretical support for the social governance and the emergence of swarm intelligence.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116782"},"PeriodicalIF":4.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014471","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}
Pub Date : 2026-01-21DOI: 10.1016/j.apm.2026.116784
Hao Cheng
Missing data are commonly-seen in various regressions and applications. The paper investigates missing covariates imputation methods in smoothed composite quantile regression, and proposes a class of imputation algorithms under the framework of majorization-minimization. The convolution-type smoothing technique is applied to modify the check loss function, and the kernel smoother is used to approximate the general estimating equation containing missing covariates. Thus the paper proposes the first majorization-minimization imputation algorithm. Then the paper develops another new majorization-minimization imputation algorithm based on the estimating equation with inverse probability weighting adjustment. Extensive simulation studies are carried out to illustrate the performances of our proposed majorization-minimization imputation algorithms in smoothed composite quantile regression. Finally, both our proposed models and algorithms are applied to a real data example on the spatiotemporal evolution of new quality productive forces and the digital economy.
{"title":"Imputation algorithms based on the majorization-minimization framework for smoothed composite quantile regression and applications","authors":"Hao Cheng","doi":"10.1016/j.apm.2026.116784","DOIUrl":"10.1016/j.apm.2026.116784","url":null,"abstract":"<div><div>Missing data are commonly-seen in various regressions and applications. The paper investigates missing covariates imputation methods in smoothed composite quantile regression, and proposes a class of imputation algorithms under the framework of majorization-minimization. The convolution-type smoothing technique is applied to modify the check loss function, and the kernel smoother is used to approximate the general estimating equation containing missing covariates. Thus the paper proposes the first majorization-minimization imputation algorithm. Then the paper develops another new majorization-minimization imputation algorithm based on the estimating equation with inverse probability weighting adjustment. Extensive simulation studies are carried out to illustrate the performances of our proposed majorization-minimization imputation algorithms in smoothed composite quantile regression. Finally, both our proposed models and algorithms are applied to a real data example on the spatiotemporal evolution of new quality productive forces and the digital economy.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116784"},"PeriodicalIF":4.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033532","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}
Pub Date : 2026-01-21DOI: 10.1016/j.apm.2026.116778
Hasan Faik Kara , Metin Aydogdu
This study focuses on the steady-state dynamic behavior of a perfectly cylindrical tube made of a functionally graded material surrounded by an unbounded medium. In the two-dimensional mathematical model, the unbounded medium is excited by plane-harmonic SH-waves. The unbounded medium is assumed to be homogeneous, isotropic and linear elastic. The material of the tube is assumed to be linear elastic as well, but inhomogeneous, such that the shear modulus and the density of the material change linearly from inner surface to outer surface. Since this difference in the material properties also affects the governing equations, the problem is investigated in two distinct regions: the homogeneous unbounded region and the functionally graded region. Analytical solution for the homogeneous region is presented in terms of Fourier-Bessel series, similar to many existing studies in the literature. In the functionally graded region, analytical solution is obtained in terms of spherical Fourier-Bessel series by utilizing Finite Fourier Transform and successive variable transformations, which is new in literature. Complex coefficients of the solutions are determined from the boundary conditions at the inner and outer surface of the tube, which leads to the analytical exact solution. Parametric results are presented for various geometrical and material properties.
{"title":"Dynamical analysis of a functionally graded tube surrounded by a homogeneous infinite medium subjected to SH-waves","authors":"Hasan Faik Kara , Metin Aydogdu","doi":"10.1016/j.apm.2026.116778","DOIUrl":"10.1016/j.apm.2026.116778","url":null,"abstract":"<div><div>This study focuses on the steady-state dynamic behavior of a perfectly cylindrical tube made of a functionally graded material surrounded by an unbounded medium. In the two-dimensional mathematical model, the unbounded medium is excited by plane-harmonic SH-waves. The unbounded medium is assumed to be homogeneous, isotropic and linear elastic. The material of the tube is assumed to be linear elastic as well, but inhomogeneous, such that the shear modulus and the density of the material change linearly from inner surface to outer surface. Since this difference in the material properties also affects the governing equations, the problem is investigated in two distinct regions: the homogeneous unbounded region and the functionally graded region. Analytical solution for the homogeneous region is presented in terms of Fourier-Bessel series, similar to many existing studies in the literature. In the functionally graded region, analytical solution is obtained in terms of spherical Fourier-Bessel series by utilizing Finite Fourier Transform and successive variable transformations, which is new in literature. Complex coefficients of the solutions are determined from the boundary conditions at the inner and outer surface of the tube, which leads to the analytical exact solution. Parametric results are presented for various geometrical and material properties.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"156 ","pages":"Article 116778"},"PeriodicalIF":4.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033535","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}
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