Pub Date : 2023-04-13DOI: 10.1142/s0218202523500409
Jinchao Xu, Xiaofeng Xu
{"title":"Lack of Robustness and Accuracy of Most Numerical Schemes for Phase-Field Simulations","authors":"Jinchao Xu, Xiaofeng Xu","doi":"10.1142/s0218202523500409","DOIUrl":"https://doi.org/10.1142/s0218202523500409","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47291253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-24DOI: 10.1142/s021820252350032x
Dongnam Ko, Seung‐Yeal Ha, Euntaek Lee, Woojoo Shim
{"title":"Collective behaviors of stochastic agent-based models and applications to finance and optimization","authors":"Dongnam Ko, Seung‐Yeal Ha, Euntaek Lee, Woojoo Shim","doi":"10.1142/s021820252350032x","DOIUrl":"https://doi.org/10.1142/s021820252350032x","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47445289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-20DOI: 10.1142/s0218202523500458
D. Burini, N. Chouhad
This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in [9]. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. We refer to a selection of case studies, in detail: transport of virus models, social dynamics, and Keller-Segel in a fluid. The second part shows how an Hilbert type approach can be developed to derive models at the macroscale from the underlying description provided by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models corresponding to the selected case studies. Finally, a forward look into the future research perspectives is proposed.
{"title":"Cross diffusion models in complex frameworks From microscopic to macroscopic","authors":"D. Burini, N. Chouhad","doi":"10.1142/s0218202523500458","DOIUrl":"https://doi.org/10.1142/s0218202523500458","url":null,"abstract":"This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in [9]. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. We refer to a selection of case studies, in detail: transport of virus models, social dynamics, and Keller-Segel in a fluid. The second part shows how an Hilbert type approach can be developed to derive models at the macroscale from the underlying description provided by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models corresponding to the selected case studies. Finally, a forward look into the future research perspectives is proposed.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48453104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-03DOI: 10.1142/s0218202523500288
P. Edel, Y. Maday
In this work, the concept of dual natural-norm for parametrized linear equations is used to derive residual-based a posteriori error bounds characterized by a O (1) stability constant. We translate these error bounds into very effective practical a posteriori error estimators for reduced basis approximations and show how they can be efficiently computed following an offline/online strategy. We prove that our practical dual natural-norm error estimator out-performs the classical inf-sup based error estimators in the self-adjoint case. Our findings are illustrated on anisotropic Helmholtz equations showing resonant behavior. Numerical results suggest that the proposed error estimator is able to successfully catch the correct order of magnitude of the reduced basis approximation error, thus outperforming the classical inf-sup based error estimator even for non self-adjoint problems.
{"title":"Dual natural-norm a posteriori error estimators for reduced basis approximations to parameterized linear equations","authors":"P. Edel, Y. Maday","doi":"10.1142/s0218202523500288","DOIUrl":"https://doi.org/10.1142/s0218202523500288","url":null,"abstract":"In this work, the concept of dual natural-norm for parametrized linear equations is used to derive residual-based a posteriori error bounds characterized by a O (1) stability constant. We translate these error bounds into very effective practical a posteriori error estimators for reduced basis approximations and show how they can be efficiently computed following an offline/online strategy. We prove that our practical dual natural-norm error estimator out-performs the classical inf-sup based error estimators in the self-adjoint case. Our findings are illustrated on anisotropic Helmholtz equations showing resonant behavior. Numerical results suggest that the proposed error estimator is able to successfully catch the correct order of magnitude of the reduced basis approximation error, thus outperforming the classical inf-sup based error estimator even for non self-adjoint problems.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47085143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-03DOI: 10.1142/s021820252350029x
Xuehai Huang, Feng Wang
{"title":"Analysis of Divergence Free Conforming Virtual Elements for the Brinkman Problem","authors":"Xuehai Huang, Feng Wang","doi":"10.1142/s021820252350029x","DOIUrl":"https://doi.org/10.1142/s021820252350029x","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42428489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-03DOI: 10.1142/s0218202523500306
Bin Li, Li Xie
{"title":"Generalized solution and eventual smoothness in a logarithmic Keller-Segel system for criminal activities","authors":"Bin Li, Li Xie","doi":"10.1142/s0218202523500306","DOIUrl":"https://doi.org/10.1142/s0218202523500306","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47414741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-17DOI: 10.1142/s0218202523500239
Seung‐Yeal Ha, Jeongho Kim, Jinyeong Park
{"title":"Fast and slow clustering dynamics of Cucker-Smale ensemble with internal oscillatory phases","authors":"Seung‐Yeal Ha, Jeongho Kim, Jinyeong Park","doi":"10.1142/s0218202523500239","DOIUrl":"https://doi.org/10.1142/s0218202523500239","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42246082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-17DOI: 10.1142/s0218202523500240
J. Liao, Yi'ang Ren, Wenbin Yan
{"title":"Kinetic modeling of a leader-follower system in crowd evacuation with collective learning","authors":"J. Liao, Yi'ang Ren, Wenbin Yan","doi":"10.1142/s0218202523500240","DOIUrl":"https://doi.org/10.1142/s0218202523500240","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-17DOI: 10.1142/s0218202523400018
N. Bellomo, F. Brezzi
{"title":"Active Particle Models and Methods in Science and Society","authors":"N. Bellomo, F. Brezzi","doi":"10.1142/s0218202523400018","DOIUrl":"https://doi.org/10.1142/s0218202523400018","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47766093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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