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Mathematical Models and Methods in Applied Sciences最新文献

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Step-by-step solving virtual element schemes based on scalar auxiliary variable with relaxation for Allen-Cahn type gradient flows 基于标量辅助变量与松弛的逐步求解虚拟元素方案，用于 Allen-Cahn 型梯度流
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-07-26 DOI: 10.1142/s0218202524500453
Yanping Chen, Qiling Gu, Jian Huang
{"title":"Step-by-step solving virtual element schemes based on scalar auxiliary variable with relaxation for Allen-Cahn type gradient flows","authors":"Yanping Chen, Qiling Gu, Jian Huang","doi":"10.1142/s0218202524500453","DOIUrl":"https://doi.org/10.1142/s0218202524500453","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"30 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141800537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computational and Analytical Studies of a New Nonlocal Phase-Field Crystal Model in Two Dimensions 新型二维非局部相场晶体模型的计算与分析研究
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-07-21 DOI: 10.1142/s0218202524500441
Qiang Du, Kai Wang, Jianghui Yang
{"title":"Computational and Analytical Studies of a New Nonlocal Phase-Field Crystal Model in Two Dimensions","authors":"Qiang Du, Kai Wang, Jianghui Yang","doi":"10.1142/s0218202524500441","DOIUrl":"https://doi.org/10.1142/s0218202524500441","url":null,"abstract":"A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and phase transition. The NPFC incorporates a finite range of spatial nonlocal interactions that can account for both repulsive and attractive effects. The specific form is data-driven and determined by a fitting to the materials structure factor, which can be much more accurate than the LPFC and previously proposed fractional variant. In particular, it is able to match the experimental data of the structure factor up to the second peak, an achievement not possible with other PFC variants studied in the literature. Both LPFC and fractional PFC (FPFC) are also shown to be distinct scaling limits of the NPFC, which reflects the generality. The advantage of NPFC in retaining material properties suggests that it may be more suitable for characterizing liquid-solid transition systems. Moreover, we study numerical discretizations using Fourier spectral methods, which are shown to be convergent and asymptotically compatible, making them robust numerical discretizations across different parameter ranges. Numerical experiments are given in the two-dimensional case to demonstrate the effectiveness of the NPFC in simulating crystal structures and grain boundaries.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"88 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141818646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the continuum limit of epidemiological models on graphs: convergence and approximation results 论图上流行病学模型的连续极限：收敛和近似结果
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-04-30 DOI: 10.1142/s0218202524500271
Blanca Ayuso de Dios, Simone Dovetta, Laura V. Spinolo
{"title":"On the continuum limit of epidemiological models on graphs: convergence and approximation results","authors":"Blanca Ayuso de Dios, Simone Dovetta, Laura V. Spinolo","doi":"10.1142/s0218202524500271","DOIUrl":"https://doi.org/10.1142/s0218202524500271","url":null,"abstract":"<p>We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of <i>graphons</i> we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140814460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A nodally bound-preserving finite element method for reaction–convection–diffusion equations 反应-对流-扩散方程的节点保界有限元法
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-04-30 DOI: 10.1142/s0218202524500283
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
{"title":"A nodally bound-preserving finite element method for reaction–convection–diffusion equations","authors":"Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer","doi":"10.1142/s0218202524500283","DOIUrl":"https://doi.org/10.1142/s0218202524500283","url":null,"abstract":"<p>This paper introduces a novel approach to approximate a broad range of reaction–convection–diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the underlying differential equation. The main result of this work demonstrates that the numerical solution achieves an accuracy of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>O</mi><mo stretchy=\"false\">(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo stretchy=\"false\">)</mo></math></span><span></span> in the energy norm, where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span> represents the underlying polynomial degree. To validate the approach, a series of numerical experiments had been conducted for various problem instances. Comparisons with the linear continuous interior penalty stabilised method, and the algebraic flux-correction scheme (for the piecewise linear finite element case) have been carried out, where we can observe the favorable performance of the current approach.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140814759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings 以粘合剂弦为模型的阻尼动力系统轨迹向稳态的指数收敛
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-04-20 DOI: 10.1142/s021820252450026x
Giuseppe Maria Coclite, Nicola De Nitti, Francesco Maddalena, Gianluca Orlando, Enrique Zuazua
{"title":"Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings","authors":"Giuseppe Maria Coclite, Nicola De Nitti, Francesco Maddalena, Gianluca Orlando, Enrique Zuazua","doi":"10.1142/s021820252450026x","DOIUrl":"https://doi.org/10.1142/s021820252450026x","url":null,"abstract":"<p>We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140632361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Trends on the Systems Approach to Modeling SARS-CoV-2 Pandemics in a Globally Connected Planet 以系统方法模拟全球互联星球上的 SARS-CoV-2 大流行的新趋势
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-04-19 DOI: 10.1142/s0218202524500301
Giulia Bertaglia, Andrea Bondesan, Diletta Burini, Raluca Eftimie, Lorenzo Pareschi, Giuseppe Toscani
{"title":"New Trends on the Systems Approach to Modeling SARS-CoV-2 Pandemics in a Globally Connected Planet","authors":"Giulia Bertaglia, Andrea Bondesan, Diletta Burini, Raluca Eftimie, Lorenzo Pareschi, Giuseppe Toscani","doi":"10.1142/s0218202524500301","DOIUrl":"https://doi.org/10.1142/s0218202524500301","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":" 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140685479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic analysis of thin structures with point-dependent energy growth 随点能量增长的薄结构渐近分析
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-04-13 DOI: 10.1142/s0218202524500258
Michela Eleuteri, Francesca Prinari, Elvira Zappale
{"title":"Asymptotic analysis of thin structures with point-dependent energy growth","authors":"Michela Eleuteri, Francesca Prinari, Elvira Zappale","doi":"10.1142/s0218202524500258","DOIUrl":"https://doi.org/10.1142/s0218202524500258","url":null,"abstract":"<p>In this paper, 3D–2D-dimensional reduction for hyperelastic thin films modeled through energies with point-dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>-convergence. Integral representation results, with a more regular Lagrangian related to the original energy density, are provided for the lower dimensional limiting energy, in different contexts.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140553478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reaction–diffusion systems derived from kinetic theory for Multiple Sclerosis 多发性硬化症动力学理论衍生的反应-扩散系统
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-28 DOI: 10.1142/s0218202524500222
João Miguel Oliveira, Romina Travaglini
{"title":"Reaction–diffusion systems derived from kinetic theory for Multiple Sclerosis","authors":"João Miguel Oliveira, Romina Travaglini","doi":"10.1142/s0218202524500222","DOIUrl":"https://doi.org/10.1142/s0218202524500222","url":null,"abstract":"<p>In this paper, we present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic theory model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both interactions among different populations of human cells and the motion of immune cells, stimulated by cytokines. Moreover, we reproduce the consumption of myelin sheath due to anomalously activated lymphocytes and its restoration by oligodendrocytes. Successively, we fix a small time parameter and assume that the considered processes occur at different scales. This allows us to perform a formal limit, obtaining macroscopic reaction–diffusion equations for the number densities with a chemotaxis term. A natural step is then to study the system, inquiring about the formation of spatial patterns through a Turing instability analysis of the problem and basing the discussion on the microscopic parameters of the model. In particular, we get spatial patterns oscillating in time that may reproduce brain lesions characteristic of different phases of the pathology.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140310794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event 分析灾难事件中人类行为的时空平流扩散模型
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-26 DOI: 10.1142/s0218202524500234
Kamal Khalil, Valentina Lanza, David Manceau, M. A. Aziz-Alaoui, Damienne Provitolo
{"title":"Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event","authors":"Kamal Khalil, Valentina Lanza, David Manceau, M. A. Aziz-Alaoui, Damienne Provitolo","doi":"10.1142/s0218202524500234","DOIUrl":"https://doi.org/10.1142/s0218202524500234","url":null,"abstract":"<p>In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140310799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains 随时间变化的域中热传导可压缩自重力流的弱解
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-25 DOI: 10.1142/s0218202524500118
Kuntal Bhandari, Bingkang Huang, Šárka Nečasová
{"title":"Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains","authors":"Kuntal Bhandari, Bingkang Huang, Šárka Nečasová","doi":"10.1142/s0218202524500118","DOIUrl":"https://doi.org/10.1142/s0218202524500118","url":null,"abstract":"<p>In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of <i>ballistic energy</i> is utilized in this work.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"276 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140209727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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