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Mathematical Models and Methods in Applied Sciences最新文献

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Development of boundary layers in Euler fluids that on “activation” respond like Navier–Stokes fluids 欧拉流体中边界层的发展，其 "激活 "反应类似于纳维-斯托克斯流体
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-25 DOI: 10.1142/s021820252450012x
P. A. Gazca-Orozco, J. Málek, K. R. Rajagopal
{"title":"Development of boundary layers in Euler fluids that on “activation” respond like Navier–Stokes fluids","authors":"P. A. Gazca-Orozco, J. Málek, K. R. Rajagopal","doi":"10.1142/s021820252450012x","DOIUrl":"https://doi.org/10.1142/s021820252450012x","url":null,"abstract":"<p>We consider the flow of a fluid whose response characteristics change due the value of the norm of the symmetric part of the velocity gradient, behaving as an Euler fluid below a critical value and as a Navier–Stokes fluid at and above the critical value, the norm being determined by the external stimuli. We show that such a fluid, while flowing past a bluff body, develops boundary layers which are practically identical to those that one encounters within the context of the classical boundary layer theory propounded by Prandtl. Unlike the classical boundary layer theory that arises as an approximation within the context of the Navier–Stokes theory, here the development of boundary layers is due to a change in the response characteristics of the constitutive relation. We study the flow of such a fluid past an airfoil and compare the same against the solution of the Navier–Stokes equations. We find that the results are in excellent agreement with regard to the velocity and vorticity fields for the two cases.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140209773","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
Epidemics and Society - A Multiscale Vision from the Small World to the Globally Interconnected World 流行病与社会--从 "小世界 "到 "全球互联世界 "的多尺度视角
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-21 DOI: 10.1142/s0218202524500295
D. Burini, Damian A. Knopoff
{"title":"Epidemics and Society - A Multiscale Vision from the Small World to the Globally Interconnected World","authors":"D. Burini, Damian A. Knopoff","doi":"10.1142/s0218202524500295","DOIUrl":"https://doi.org/10.1142/s0218202524500295","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"77 s329","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140223217","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 dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model 神经母细胞瘤及其治疗数学模型的动力学和优化控制：数学模型的启示
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-16 DOI: 10.1142/s0218202524500210
José García Otero, Mariusz Bodzioch, Juan Belmonte-Beitia
{"title":"On the dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model","authors":"José García Otero, Mariusz Bodzioch, Juan Belmonte-Beitia","doi":"10.1142/s0218202524500210","DOIUrl":"https://doi.org/10.1142/s0218202524500210","url":null,"abstract":"<p>Celyvir is an advanced therapy medicine, consisting of mesenchymal stem cells (MSCs) containing the oncolytic virus ICOVIR 5. This paper sets out a dynamic system which attempts to capture the fundamental relationships between cancer, the immune system and adenoviruses. Two forms of treatment were studied: continuous and periodic, the second being closer to the real situation. In the analysis of the first model, in addition to identifying the critical points, their properties and bifurcation points, a number of numerical simulations were carried out. It has thus been shown that there are bistability regimes in which Celyvir can produce an equilibrium of tumor progression, or even freedom from tumor. A sensitivity analysis was also performed to determine which parameters are most important in the system. Subsequently, an optimal control problem with nonlinear objective functional has been formulated, where the therapeutic goal is not only to minimize the size of the tumor cell population and the total cost of treatment, but also to prevent the tumor from reaching a critical size. It has been shown that the optimal control is bang–bang. With the second model, a threshold value of viral load has been identified at which the success of the treatment could be ensured. It is clear in both models that a low viral load would lead to relapse of the disease. Finally, it is shown that a periodic bang–bang regime should be used to optimize treatment with Celyvir.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140145907","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
Macroscopic modeling of social crowds 社会人群的宏观建模
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-15 DOI: 10.1142/s0218202524400098
Livio Gibelli, Damián A. Knopoff, Jie Liao, Wenbin Yan
{"title":"Macroscopic modeling of social crowds","authors":"Livio Gibelli, Damián A. Knopoff, Jie Liao, Wenbin Yan","doi":"10.1142/s0218202524400098","DOIUrl":"https://doi.org/10.1142/s0218202524400098","url":null,"abstract":"<p>Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a “social crowd”. This paper introduces a novel approach by explicitly incorporating an “activity” variable into the modeling framework, which represents the evolving psychological states of pedestrians and is linked to crowd dynamics. To demonstrate the role of activity, we model pedestrian egress when this variable captures stress and awareness of contagion. In addition, to highlight the importance of dynamic changes in activity, we examine a scenario in which an unexpected incident necessitates alternative exits. These case studies demonstrate that activity plays a pivotal role in shaping crowd behavior. The proposed modeling approach thus opens avenues for more realistic macroscopic crowd descriptions with practical implications for crowd management.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"159 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139406","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
Pedestrian models with congestion effects 具有拥堵效应的行人模型
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-15 DOI: 10.1142/s0218202524400050
Pedro Aceves-Sánchez, Rafael Bailo, Pierre Degond, Zoé Mercier
{"title":"Pedestrian models with congestion effects","authors":"Pedro Aceves-Sánchez, Rafael Bailo, Pierre Degond, Zoé Mercier","doi":"10.1142/s0218202524400050","DOIUrl":"https://doi.org/10.1142/s0218202524400050","url":null,"abstract":"<p>We study the validity of the dissipative Aw–Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a steering behavior. Furthermore, we introduce a semi-implicit, structure-preserving, and asymptotic-preserving numerical scheme which can handle the numerical solution of the model efficiently. We perform the first numerical simulations of the dissipative Aw–Rascle system in one and two dimensions. We demonstrate the efficiency of the scheme in solving an array of numerical experiments, and we validate the model, ultimately showing that it correctly captures the fundamental diagram of pedestrian flow.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"364 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139391","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
Active particle methods towards a mathematics of living systems 主动粒子法走向生命系统数学
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-13 DOI: 10.1142/s0218202524020020
Nicola Bellomo, Franco Brezzi
{"title":"Active particle methods towards a mathematics of living systems","authors":"Nicola Bellomo, Franco Brezzi","doi":"10.1142/s0218202524020020","DOIUrl":"https://doi.org/10.1142/s0218202524020020","url":null,"abstract":"<p>This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward to research. Perspectives with emphasis on the interaction of multiple social dynamics.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139469","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
Moment methods for kinetic traffic flow and a class of macroscopic traffic models 动力学交通流的矩方法和一类宏观交通模型
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-06 DOI: 10.1142/s0218202524400074
Raul Borsche, Axel Klar
{"title":"Moment methods for kinetic traffic flow and a class of macroscopic traffic models","authors":"Raul Borsche, Axel Klar","doi":"10.1142/s0218202524400074","DOIUrl":"https://doi.org/10.1142/s0218202524400074","url":null,"abstract":"<p>Starting from a nonlocal version of a classical kinetic traffic model, we derive a class of second-order macroscopic traffic flow models using appropriate moment closure approaches. Under mild assumptions on the closure, we prove that the resulting macroscopic equations fulfill a set of conditions including hyperbolicity, physically reasonable invariant domains and physically reasonable bounds on the speed with which the waves propagate. Finally, numerical results for various situations are presented, illustrating the analytical findings and comparing kinetic and macroscopic solutions.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"159 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139419","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
Time-discrete momentum consensus-based optimization algorithm and its application to Lyapunov function approximation 基于时间离散动量共识的优化算法及其在 Lyapunov 函数近似中的应用
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-05 DOI: 10.1142/s0218202524400104
Seung-Yeal Ha, Gyuyoung Hwang, Sungyoon Kim
{"title":"Time-discrete momentum consensus-based optimization algorithm and its application to Lyapunov function approximation","authors":"Seung-Yeal Ha, Gyuyoung Hwang, Sungyoon Kim","doi":"10.1142/s0218202524400104","DOIUrl":"https://doi.org/10.1142/s0218202524400104","url":null,"abstract":"<p>In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, <i>Math. Models Methods Appl. Sci.</i><b>30</b> (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139530","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
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs Gevrey 类隐含映射定理在半线性椭圆 PDE 的 UQ 中的应用
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-03-05 DOI: 10.1142/s0218202524500179
Helmut Harbrecht, Marc Schmidlin, Christoph Schwab
{"title":"The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs","authors":"Helmut Harbrecht, Marc Schmidlin, Christoph Schwab","doi":"10.1142/s0218202524500179","DOIUrl":"https://doi.org/10.1142/s0218202524500179","url":null,"abstract":"<p>This paper is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly defined by a residual equation. Under <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>s</mi></math></span><span></span>-Gevrey assumptions on the residual equation, we establish <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>s</mi></math></span><span></span>-Gevrey bounds on the Fréchet derivatives of the locally defined data-to-solution mapping. This abstract framework is illustrated in a proof of regularity bounds for a semilinear elliptic partial differential equation with parametric and random field input.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140139521","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
Prediction-correction pedestrian flow by means of minimum flow problem 通过最小流量问题预测和修正人流量
Mathematical Models and Methods in Applied Sciences Pub Date : 2024-02-29 DOI: 10.1142/s0218202524500052
Hamza Ennaji, Noureddine Igbida, Ghadir Jradi
{"title":"Prediction-correction pedestrian flow by means of minimum flow problem","authors":"Hamza Ennaji, Noureddine Igbida, Ghadir Jradi","doi":"10.1142/s0218202524500052","DOIUrl":"https://doi.org/10.1142/s0218202524500052","url":null,"abstract":"<p>We study a new variant of mathematical prediction-correction model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via an eikonal equation <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo>∥</mo><mo>∇</mo><mi>φ</mi><mo>∥</mo><mo>=</mo><mi>f</mi></math></span><span></span>, with a positive continuous function <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi></math></span><span></span> connected to the speed of the spontaneous travel. The correction phase is handled by a new version of the minimum flow problem. This model is flexible and can take into account different types of interactions between the agents, from gradient flow in Wassersetin space to granular type dynamics like in sandpile. Furthermore, different boundary conditions can be used, such as non-homogeneous Dirichlet (e.g. outings with different exit-cost penalty) and Neumann boundary conditions (e.g. entrances with different rates). Combining finite volume method for the transport equation and Chambolle–Pock’s primal dual algorithm for the eikonal equation and minimum flow problem, we present numerical simulations to demonstrate the behavior in different scenarios.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203470","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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