Studies in Applied Mathematics最新文献

{"title":"Complex Band Structure for Subwavelength Evanescent Waves","authors":"Yannick De Bruijn,&nbsp;Erik Orvehed Hiltunen","doi":"10.1111/sapm.70022","DOIUrl":"https://doi.org/10.1111/sapm.70022","url":null,"abstract":"<div>\u0000 \u0000 <p>We present the mathematical and numerical theory for evanescent waves in subwavelength bandgap materials. We begin in the one-dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance matrix, are available. As an example, we show that the gap functions can be used to accurately predict the decay rate of the interface mode of a photonic analogue of the Su–Schrieffer–Heeger model. In two dimensions, we derive the bandgap Green's function and characterize the subwavelength gap functions via layer potential techniques. By generalizing existing lattice-summation techniques, we illustrate our results numerically by computing the complex band structure in a variety of settings.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143248817","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":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70023","DOIUrl":"https://doi.org/10.1111/sapm.70023","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Role of Medical Supply Shortages on an Age-Structured Epidemic Model","authors":"Miao Zhou,&nbsp;Junyuan Yang,&nbsp;Jiaxu Li,&nbsp;Guiquan Sun","doi":"10.1111/sapm.70019","DOIUrl":"https://doi.org/10.1111/sapm.70019","url":null,"abstract":"<div>\u0000 \u0000 <p>A shortage of medical resources can arise when a multitude of patients rapidly emerge during the initial phases of an emerging infectious disease, due to limited availability of healthcare resources. Chronological age plays a pivotal role in both foreseeing and preventing infection patterns. In this investigation, we present an Susceptible-Infected-Recovered (SIR) model that integrates an age-structured and a saturated treatment function, and demonstrate its well-posedness. Our analysis reveals intricate patterns in the system, characterized by a steady-state bifurcation involving a backward bifurcation and a stable bifurcation representing a Hopf bifurcation. Notably, numerical simulations demonstrate that when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {R}_0&lt;1$</annotation>\u0000 </semantics></math>, the system exemplifies a novel phenomenon wherein a disease-free equilibrium coexists harmoniously with an enduring Hopf bifurcation. We conduct a real application for model calibration and suggest that enhancing medical facilities and minimizing treatment delays may prove to be of paramount importance in curtailing the spread of the disease.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143248816","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 Multiparameter Singular Perturbation Analysis of the Robertson Model","authors":"Lukas Baumgartner,&nbsp;Peter Szmolyan","doi":"10.1111/sapm.70020","DOIUrl":"https://doi.org/10.1111/sapm.70020","url":null,"abstract":"&lt;p&gt;The Robertson model describing a chemical reaction involving three reactants is one of the classical examples of stiffness in ODEs. The stiffness is caused by the occurrence of three reaction rates &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${k}_{1},{k}_{2},$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${k}_{3},$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with largely differing orders of magnitude, acting as parameters. The model has been widely used as a numerical test problem. Surprisingly, no asymptotic analysis of this multiscale problem seems to exist. In this paper, we provide a full asymptotic analysis of the Robertson model under the assumption &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;≪&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$k_1, k_3 ll k_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We rewrite the equations as a two-parameter singular perturbation problem in the rescaled small parameters &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143248818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dissipative Gradient Nonlinearities Prevent \u0000 \u0000 δ\u0000 $delta$\u0000 -Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models","authors":"Tongxing Li,&nbsp;Daniel Acosta-Soba,&nbsp;Alessandro Columbu,&nbsp;Giuseppe Viglialoro","doi":"10.1111/sapm.70018","DOIUrl":"https://doi.org/10.1111/sapm.70018","url":null,"abstract":"<p>We study a class of zero-flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density <span></span><math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math>, the chemosensitivities and the production rates of the chemoattractant <span></span><math>\u0000 <semantics>\u0000 <mi>v</mi>\u0000 <annotation>$v$</annotation>\u0000 </semantics></math> and the chemorepellent <span></span><math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math>. In addition, a source involving also the gradient of <span></span><math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math> is incorporated. Our overall study touches on different aspects: we address questions connected to local well-posedness, we derive sufficient conditions to ensure boundedness of solutions, and finally, we develop numerical simulations giving insights into the evolution of the system.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143111624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equivalence to the Classical Heat Equation Through Reciprocal Transformations","authors":"S. V. Meleshko,&nbsp;P. Siriwat,&nbsp;S. R. Svirshchevskii","doi":"10.1111/sapm.70010","DOIUrl":"https://doi.org/10.1111/sapm.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the equivalence of parabolic partial differential equations to the classical one-dimensional heat equation using reciprocal transformations. The equations are assumed to be autonomous, and the methodology applied is similar to S. Lie's approach to solving the linearization problem of second-order ordinary differential equations. The research is structured in two main parts. In the first part, necessary constraints on the class of parabolic partial differential equations with two independent variables, which are equivalent to the classical heat equation under a reciprocal transformation, are identified. In the second part, the remaining conditions are examined, and sufficient conditions are derived. The corresponding differential equations are then obtained. All possible cases that arise are thoroughly analyzed, and the theory is illustrated with several examples.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119707","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":"Spatial Movement With Explicit Memory and Nonlocal Pregnancy Delay","authors":"Xiaoxi Ding,&nbsp;Hao Shen,&nbsp;Yongli Song","doi":"10.1111/sapm.70011","DOIUrl":"https://doi.org/10.1111/sapm.70011","url":null,"abstract":"<div>\u0000 \u0000 <p>In depicting animal movement, besides considering spatial memory, the pregnancy period of the animals themselves should also be taken into account. This article proposes a novel single-population model with discrete memory delay and nonlocal spatiotemporal gestation delay. Assuming the positive equilibrium is locally stable without spatiotemporal delay, the study investigates two types of directional movements using memory delay and gestation delay as control parameters. The research shows that for the positive memory-based diffusion coefficient, the system destabilizes through homogeneous/nonhomogeneous Hopf bifurcations, but for the negative memory diffusion coefficient, the system not only undergo Hopf bifurcations but also becomes unstable through Turing bifurcations, and may even exhibit Turing–Hopf bifurcation. Finally, we use a diffusive logistic model with predation behavior as an example to numerically simulate the theoretical results and also discover stability switch phenomena.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119025","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":"Symmetry Analysis of the Two-Dimensional Stationary Magnetogasdynamics Equations With Coriolis Force in Lagrangian Coordinates","authors":"E. I. Kaptsov,&nbsp;S. V. Meleshko","doi":"10.1111/sapm.70015","DOIUrl":"https://doi.org/10.1111/sapm.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper focuses on symmetry analysis of the two-dimensional stationary magnetogasdynamics equations with Coriolis force in Lagrangian coordinates. This involves the identification of equivalence transformations and the Lie algebra admitted by the equations, and its extensions for various forms of magnetic fields and Coriolis parameter, as well as the construction of group foliations. A considerable part of the work is devoted to group foliations of the magnetogasdynamics equations, extending to the nonstationary isentropic case. The group foliations' approach is typically applied to equations admitting infinite-dimensional groups of transformations, thereby facilitating the simplification of their subsequent analysis. The results obtained in this study generalize previously known findings for the two-dimensional shallow water equations and stationary gas dynamics equations in Lagrangian coordinates. Utilizing the constructed group foliations, invariant solutions are derived for particular forms of the entropy, illustrating the potential for further investigation in this area.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119027","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":"Chebotarov Continua, Jenkins–Strebel Differentials and Related Problems: A Numerical Approach","authors":"M. Bertola","doi":"10.1111/sapm.70016","DOIUrl":"https://doi.org/10.1111/sapm.70016","url":null,"abstract":"<p>We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in special cases, provide solutions of (generalized) Chebotarov problem as well as being instances of Jenkins–Strebel differentials. The algorithm allows to construct Boutroux differentials with prescribed polar part, thus being useful in the theory of weighted capacity and random matrices.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Static States for Rotating Two-Component Bose–Einstein Condensates","authors":"Hichem Hajaiej,&nbsp;Xiao Luo,&nbsp;Tao Yang","doi":"10.1111/sapm.70013","DOIUrl":"https://doi.org/10.1111/sapm.70013","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study static states for rotating two-component Bose–Einstein condensates (BECs) in two and three dimensions. This leads to analyze normalized solutions for a coupled Schrödinger system with rotation. In dimension two, it corresponds to a mass-critical problem, for which we obtain some existence and nonexistence results. In the three-dimensional case, the problem becomes mass-supercritical, where we prove a multiplicity result along with an accurately asymptotical analysis. Furthermore, a stability result is also established in both cases. We not only extend the main results in Ardila and Hajaiej (<i>Journal of Dynamics and Differential Equations</i> 35 (2023), 1643–1665), Arbunich et al. (<i>Letters in Mathematical Physics</i> 109 (2019), 1415–1432), and Luo and Yang (<i>Journal of Differential Equations</i> 304 (2021), 326–347) from the rotating one-component BEC to rotating two-component BECs, but we also partially extend the results of Guo et al. (Discrete and Continuous Dynamical Systems 37 (2017), 3749–3786; <i>Journal of Differential Equations</i> 264 (2018), 1411–1441) from nonrotating two-component BECs to rotating two-component BECs.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119024","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}