Studies in Applied Mathematics最新文献_第9页

Global Dynamics of a Partially Degenerate Nonlocal Model for Mosquito-Borne Disease Transmission 蚊媒疾病传播部分退化非局部模型的全局动力学

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-22 DOI: 10.1111/sapm.70101

Mengjie Han, Zhenguo Bai, Yijun Lou

Host mobility and environmental heterogeneity in vector populations are critical determinants of spatial patterns in mosquito-borne disease transmission. To investigate the impact of spatial heterogeneity and host dispersal on transmission dynamics, this manuscript proposes a partially degenerate nonlocal dispersal Ross–Macdonald model. The basic reproduction number $� � �_{R � 0 �} � �$ is identified as a critical threshold that determines the global dynamics of the model. The analytical challenge of noncompact solution map of this partially degenerate nonlocal model is addressed using comparison arguments for the phase space of Lebesgue measurable and bounded functions. Furthermore, we characterize the asymptotic behavior of $� � �_{R � 0 �} � �$ under small and large diffusion regimes, linking dispersal rates to transmission potential. Numerical simulations reveal how host mobility and spatially varying environment modulate disease persistence and transmission risks. Simulations also indicate that the model assuming local dispersal may underestimate transmission risks, and the epidemic size does not monotonically increase with $� � �_{R � 0 �} � �$ .

媒介种群的宿主移动性和环境异质性是蚊媒疾病传播空间格局的关键决定因素。为了研究空间异质性和寄主扩散对传播动力学的影响，本文提出了一个部分简并的非局部扩散Ross-Macdonald模型。基本复制数R 0$ mathcal {R}_0$被确定为决定模型全局动态的临界阈值。利用Lebesgue可测函数和有界函数相空间的比较论证，解决了这种部分退化非局部模型的非紧解映射的解析难题。此外，我们描述了r0 $mathcal {R}_0$在小扩散和大扩散状态下的渐近行为，将扩散速率与传播势联系起来。数值模拟揭示了宿主的移动性和空间变化的环境如何调节疾病的持久性和传播风险。模拟还表明，假设局部扩散的模型可能低估了传播风险，并且流行病规模并不随着R 0$ mathcal {R}_0$单调增加。

{"title":"Global Dynamics of a Partially Degenerate Nonlocal Model for Mosquito-Borne Disease Transmission","authors":"Mengjie Han, Zhenguo Bai, Yijun Lou","doi":"10.1111/sapm.70101","DOIUrl":"https://doi.org/10.1111/sapm.70101","url":null,"abstract":"<div>\u0000 \u0000 Host mobility and environmental heterogeneity in vector populations are critical determinants of spatial patterns in mosquito-borne disease transmission. To investigate the impact of spatial heterogeneity and host dispersal on transmission dynamics, this manuscript proposes a partially degenerate nonlocal dispersal Ross–Macdonald model. The basic reproduction number <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math> is identified as a critical threshold that determines the global dynamics of the model. The analytical challenge of noncompact solution map of this partially degenerate nonlocal model is addressed using comparison arguments for the phase space of Lebesgue measurable and bounded functions. Furthermore, we characterize the asymptotic behavior of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math> under small and large diffusion regimes, linking dispersal rates to transmission potential. Numerical simulations reveal how host mobility and spatially varying environment modulate disease persistence and transmission risks. Simulations also indicate that the model assuming local dispersal may underestimate transmission risks, and the epidemic size does not monotonically increase with <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math>.</div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891661","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}

引用次数: 0

Finite-Dimensional Reductions and Finite-Gap-Type Solutions of Multicomponent Integrable PDEs 多分量可积偏微分方程的有限维约简和有限间隙型解

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-21 DOI: 10.1111/sapm.70100

Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup–Boussinesq equations. We suggest a methodology for constructing a series of solutions for all systems in the family. The crux of the approach lies in reducing this system to a dispersionless integrable system which is a special case of linearly degenerate quasilinear systems actively explored since the 1990s and recently studied in the framework of Nijenhuis geometry. These infinite-dimensional integrable systems are closely connected to certain explicit finite-dimensional integrable systems. We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.

本文的主要对象是最近发现的一类多分量可积偏微分方程组，其特殊情况包括许多著名的方程，如Korteweg-de Vries、耦合KdV、Harry Dym、耦合Harry Dym、Camassa-Holm、多分量Camassa-Holm、dullin - gottwwald - holm和kap - boussinesq方程。我们建议一种方法来构建一系列解决方案的所有系统在家庭。该方法的关键在于将该系统简化为无色散可积系统，该系统是线性退化拟线性系统的一种特殊情况，自20世纪90年代以来一直在积极探索，最近在Nijenhuis几何框架下进行了研究。这些无限维可积系统与某些显式有限维可积系统密切相关。我们提供了我们的多分量PDE系统的解与这个有限维系统的解之间的联系，并用它来构造多分量孤子解和余弦解的模拟动画。

{"title":"Finite-Dimensional Reductions and Finite-Gap-Type Solutions of Multicomponent Integrable PDEs","authors":"Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev","doi":"10.1111/sapm.70100","DOIUrl":"https://doi.org/10.1111/sapm.70100","url":null,"abstract":"The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup–Boussinesq equations. We suggest a methodology for constructing a series of solutions for all systems in the family. The crux of the approach lies in reducing this system to a dispersionless integrable system which is a special case of linearly degenerate quasilinear systems actively explored since the 1990s and recently studied in the framework of Nijenhuis geometry. These infinite-dimensional integrable systems are closely connected to certain explicit finite-dimensional integrable systems. We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144881460","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}

引用次数: 0

A New Transformation for the Subcritical Fast Diffusion Equation With Source and Applications 亚临界快速扩散方程的一种新变换及其应用

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-20 DOI: 10.1111/sapm.70098

Razvan Gabriel Iagar, Ariel Sánchez

<div> A new transformation for radially symmetric solutions to the subcritical fast diffusion equation with spatially inhomogeneous source <div><math> <semantics> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>u</mi> <mo>=</mo> <mi>Δ</mi> <msup> <mi>u</mi> <mi>m</mi> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> <mi>σ</mi> </msup> <msup> <mi>u</mi> <mi>p</mi> </msup> </mrow> <annotation>$$begin{equation*} partial _tu=Delta u^m+|x|^{sigma }u^p end{equation*}$$</annotation> </semantics></math></div>posed for <math> <semantics> <mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>∈</mo> <msup> <mi>R</mi> <mi>N</mi> </msup> <mo>×</mo> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo>)</mo> </mrow> </mrow> <annotation>$(x,t)in mathbb {R}^Ntimes (0,infty)$</annotation> </semantics></math> and with dimension and exponents <div><math> <semantics> <mrow> <mi>N</mi> <mo>≥</mo> <mn>3</mn> <mo>,</mo> <mspace></mspace> <mn>0</mn> <mo><</mo> <mi>m</mi> <mo><</mo> <msub> <mi>m</mi> <mi>c</mi> </msub> <mo>:</mo> <mo>=</mo>

空间非齐次源∂t u = Δ u m的亚临界快速扩散方程径向对称解的新变换+ | x | σ u p $$begin{equation*} partial _tu=Delta u^m+|x|^{sigma }u^p end{equation*}$$（x, t）∈rn × (0，∞)$(x,t)in mathbb {R}^Ntimes (0,infty)$且维数和指数N≥3，0 ＆lt; m ＆lt; m= n−2 n，引入σ∈(−2,∞)$$begin{equation*} Nge 3, quad 0<m<m_c:=frac{N-2}{N}, quad sigma in (-2,infty) end{equation*}$$。它对临界指数m s = N - 2起着一种对称的作用N + 2，p L (σ) = 1 + σ (1−m) 2；p s (σ) = m (N+ 2 σ + 2) n−2。$$begin{equation*} m_s=frac{N-2}{N+2}, quad p_L(sigma)=1+frac{sigma (1-m)}{2}, quad p_s(sigma)=frac{m(N+2sigma +2)}{N-2}. end{equation*}$$然后应用该变换对有源的亚临界快速扩散方程的有或没有有限时间爆破的自相似解进行分类，{当p ＆gt； max为1时，p L (σ)}$p>max lbrace 1,p_L(sigma)rbrace$，以作者以前的结果为起点。

{"title":"A New Transformation for the Subcritical Fast Diffusion Equation With Source and Applications","authors":"Razvan Gabriel Iagar, Ariel Sánchez","doi":"10.1111/sapm.70098","DOIUrl":"https://doi.org/10.1111/sapm.70098","url":null,"abstract":"<div>\u0000 \u0000 A new transformation for radially symmetric solutions to the subcritical fast diffusion equation with spatially inhomogeneous source\u0000\u0000 <div><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>∂</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>Δ</mi>\u0000 <msup>\u0000 <mi>u</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>x</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <mi>σ</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>u</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$begin{equation*} partial _tu=Delta u^m+|x|^{sigma }u^p end{equation*}$$</annotation>\u0000 </semantics></math></div>posed for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$(x,t)in mathbb {R}^Ntimes (0,infty)$</annotation>\u0000 </semantics></math> and with dimension and exponents \u0000 <div><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mn>0</mn>\u0000 <mo><</mo>\u0000 <mi>m</mi>\u0000 <mo><</mo>\u0000 <msub>\u0000 <mi>m</mi>\u0000 <mi>c</mi>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <mo>=</mo>\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869804","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}

引用次数: 0

Thermal Convection in a Sixth-Order Generalized Navier–Stokes Fluid 六阶广义Navier-Stokes流体中的热对流

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-20 DOI: 10.1111/sapm.70099

Giulia Giantesio, Alberto Girelli, Chiara Lonati, Alfredo Marzocchi, Alessandro Musesti, Brian Straughan

In this work, we deal with a problem of thermal convection for a fluid satisfying Navier–Stokes equation containing the spatial derivatives of the velocity field of sixth order, with the introduction of a tri-Laplacian term. It was pointed out by several authors, for example, Fried and Gurtin, that contributions of higher order take into account microlength effects; these phenomena are relevant in microfluidic flows. In particular, we follow the isothermal model of Musesti, using a Boussinesq approximation, so that the density in the body force term depends on the temperature to consider buoyancy effects that occur when the fluid is heated and it expands. We discuss different meaningful boundary conditions that have a key role to understand the effects of higher-order derivatives in microfluidic scenarios with convection. We carry out the complete study of linear and nonlinear stability for the flow. In addition, we complete the treatment with the analysis of critical wavenumbers and Rayleigh numbers for convection in the fluid.

在这项工作中，我们处理了一个流体的热对流问题，该问题满足包含六阶速度场空间导数的Navier-Stokes方程，并引入了三拉普拉斯项。一些作者指出，例如Fried和Gurtin，高阶的贡献考虑了微长效应；这些现象与微流体流动有关。特别地，我们采用了Musesti的等温模型，使用了Boussinesq近似，因此，体力项中的密度取决于温度，以考虑流体受热膨胀时发生的浮力效应。我们讨论了不同的有意义的边界条件，这些边界条件对于理解高阶导数在对流微流体场景中的影响具有关键作用。我们对流动的线性和非线性稳定性进行了全面的研究。此外，我们还通过分析流体对流的临界波数和瑞利数来完成处理。

{"title":"Thermal Convection in a Sixth-Order Generalized Navier–Stokes Fluid","authors":"Giulia Giantesio, Alberto Girelli, Chiara Lonati, Alfredo Marzocchi, Alessandro Musesti, Brian Straughan","doi":"10.1111/sapm.70099","DOIUrl":"https://doi.org/10.1111/sapm.70099","url":null,"abstract":"In this work, we deal with a problem of thermal convection for a fluid satisfying Navier–Stokes equation containing the spatial derivatives of the velocity field of sixth order, with the introduction of a tri-Laplacian term. It was pointed out by several authors, for example, Fried and Gurtin, that contributions of higher order take into account microlength effects; these phenomena are relevant in microfluidic flows. In particular, we follow the isothermal model of Musesti, using a Boussinesq approximation, so that the density in the body force term depends on the temperature to consider buoyancy effects that occur when the fluid is heated and it expands. We discuss different meaningful boundary conditions that have a key role to understand the effects of higher-order derivatives in microfluidic scenarios with convection. We carry out the complete study of linear and nonlinear stability for the flow. In addition, we complete the treatment with the analysis of critical wavenumbers and Rayleigh numbers for convection in the fluid.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70099","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869803","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}

引用次数: 0

Elastic Curves With Variable Bending Stiffness 变弯曲刚度弹性曲线

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-20 DOI: 10.1111/sapm.70097

Oliver Gross, Ulrich Pinkall, Moritz Wahl

We study stationary points of the bending energy of curves $� � � γ � : � � [� a �, � b �] � � \to � �^{R � n �} � � �$ subject to constraints on the arc length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the arc length of the curve. Physically, this can be understood as a model for an elastic wire with isotropic cross section of varying thickness. We derive the corresponding Euler–Lagrange equations for variations that are compactly supported away from the endpoints thus obtaining characterizations for elastic curves with variable bending stiffness. Moreover, we provide a collection of alternative characterizations, for example, in terms of the curvature function. Adding to numerous known results relating elastic curves to dynamics, we explore connections between elastic curves with variable bending stiffness, variable length pendulums, and the flow of vortex filaments with finite thickness.

我们研究了曲线γ弯曲能的平稳点：[a]b]→R n $gamma: [a,b]rightarrow mathbb {R}^n$受弧长和曲线完整度的约束，同时允许沿曲线弧长可变的弯曲刚度。从物理上讲，这可以理解为具有不同厚度的各向同性截面的弹性线的模型。我们为远离端点的紧支承弹性曲线导出了相应的欧拉-拉格朗日方程，从而获得了变弯曲刚度弹性曲线的特征。此外，我们还提供了一系列可选择的表征，例如，根据曲率函数。除了众多已知的弹性曲线与动力学相关的结果外，我们还探讨了可变弯曲刚度弹性曲线、变长摆和有限厚度涡旋细丝流动之间的联系。

{"title":"Elastic Curves With Variable Bending Stiffness","authors":"Oliver Gross, Ulrich Pinkall, Moritz Wahl","doi":"10.1111/sapm.70097","DOIUrl":"https://doi.org/10.1111/sapm.70097","url":null,"abstract":"We study stationary points of the bending energy of curves <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>:</mo>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>b</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$gamma: [a,b]rightarrow mathbb {R}^n$</annotation>\u0000 </semantics></math> subject to constraints on the arc length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the arc length of the curve. Physically, this can be understood as a model for an elastic wire with isotropic cross section of varying thickness. We derive the corresponding Euler–Lagrange equations for variations that are compactly supported away from the endpoints thus obtaining characterizations for elastic curves with variable bending stiffness. Moreover, we provide a collection of alternative characterizations, for example, in terms of the curvature function. Adding to numerous known results relating elastic curves to dynamics, we explore connections between elastic curves with variable bending stiffness, variable length pendulums, and the flow of vortex filaments with finite thickness.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144869802","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}

引用次数: 0

Lattice Energy Minimization for the Difference of Theta and Epstein Zeta Functions Theta和Epstein Zeta函数差分的晶格能量最小化

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-13 DOI: 10.1111/sapm.70092

Jingxuan Sun, Zhen Song, Wenming Zou

Let $� � � z � \in � H � ≔ � {� z � = � x � + � i � y � \in � C � : � y � > � 0 �} � � �$ , and $� � � L � ≔ � Z � \oplus � z � Z � � �$ be the lattice in $� � �^{R � 2 �} � �$ . Let $� � � θ � � (� α �; � z �) � � ≔ � �_{\sum � � P � \in � L � ∖ � {� 0 �} �, � � | � L � | � = � 1 � �} � �^{e � � - � �^{� α � π � ∥ � P � ∥ � � 2 �} � �} � �$

由广泛使用的白金汉势V (r) = a 1 e−α π r驱动−a 2 1 r 6 $ V(r)=a_1e^{-alphapi r}-a_2frac{1}{r^6}$在物理学中，在本文中，我们探讨了minz∈H (ζ (6；Z)−b θ (α；z)) $min_{zinmathbb{H}}(zeta(6;z)-btheta(alpha;z))$对于任意b∈R $binmathbb{R}$。这项工作的一个关键发现是系数α $alpha$显著影响最优晶格构型，当b $ b$从−∞$ -infty$到+∞$ +infty$变化时，导致三种不同的相变模式：对于α = 1 $ alpha = 1$，最优晶格经过六边形→$rightarrow$宽菱形→$rightarrow$方形→$rightarrow$矩形的过渡。对于α ＆gt；α∗= 2.39⋯$ alpha > alpha ^* = 2.39cdots$，跃迁遵循六边形→$rightarrow$窄菱形。对于1 ＆lt；α≤α * $ 1 < alpha le alpha ^*$，则出现一个扩展的过渡序列：六边形→$rightarrow$宽菱形→$rightarrow$方形→$rightarrow$矩形→$rightarrow$窄菱形。值得注意的是，我们发现了一个以前被忽视的结晶现象：窄菱形晶格，这是一种特殊类型的菱形结构，与Luo和Wei以及b<s:1> termin报道的结构不同。我们的结果为猜想和开放性问题提供了部分答案。此外，我们还建立了由两个完全不同的函数之差形成的势的完全极小化结果。我们还导出了最小化的一个必要条件，即F s， α (z)=0$ F_{s,alpha}(z)=0$（见（1.1）），它对非完全单调函数有更广泛的适用性。

{"title":"Lattice Energy Minimization for the Difference of Theta and Epstein Zeta Functions","authors":"Jingxuan Sun, Zhen Song, Wenming Zou","doi":"10.1111/sapm.70092","DOIUrl":"https://doi.org/10.1111/sapm.70092","url":null,"abstract":"<div>\u0000 \u0000 Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>z</mi>\u0000 <mo>∈</mo>\u0000 <mi>H</mi>\u0000 <mo>≔</mo>\u0000 <mo>{</mo>\u0000 <mi>z</mi>\u0000 <mo>=</mo>\u0000 <mi>x</mi>\u0000 <mo>+</mo>\u0000 <mi>i</mi>\u0000 <mi>y</mi>\u0000 <mo>∈</mo>\u0000 <mi>C</mi>\u0000 <mo>:</mo>\u0000 <mi>y</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$zin mathbb {H}coloneqq lbrace z=x+iyin mathbb {C}:y>0rbrace$</annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>≔</mo>\u0000 <mi>Z</mi>\u0000 <mi>⊕</mi>\u0000 <mi>z</mi>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$Lcoloneqq mathbb {Z} oplus z mathbb {Z}$</annotation>\u0000 </semantics></math> be the lattice in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math>. Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>α</mi>\u0000 <mo>;</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>≔</mo>\u0000 <msub>\u0000 <mo>∑</mo>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>∈</mo>\u0000 <mi>L</mi>\u0000 <mo>∖</mo>\u0000 <mo>{</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mo>|</mo>\u0000 <mi>L</mi>\u0000 <mo>|</mo>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mi>π</mi>\u0000 <mo>∥</mo>\u0000 <mi>P</mi>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$theta","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832596","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}

引用次数: 0

Heterogeneously Structured Compartmental Models of Epidemiological Systems: From Individual-Level Processes to Population-Scale Dynamics 流行病学系统的异质结构分区模型：从个体水平的过程到种群尺度的动态

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-12 DOI: 10.1111/sapm.70091

Emanuele Bernardi, Tommaso Lorenzi, Mattia Sensi, Andrea Tosin

We develop a general modeling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based model that describes the dynamics of single individuals in terms of stochastic processes. Then, we formally derive: (i) the mesoscopic counterpart of this model, which is formulated as a system of integrodifferential equations for the distributions of individuals over the structuring-variable domains of the different compartments; (ii) the corresponding macroscopic model, which takes the form of a system of ordinary differential equations for the fractions of individuals in the different compartments and the mean levels of expression of the traits represented by the structuring variables. We employ a reduced version of the macroscopic model to obtain a general formula for the basic reproduction number,

� � �_{R � 0 �} � �

, in terms of key parameters and functions of the underlying microscopic model, so as to illustrate how such a modeling framework makes it possible to draw connections between fundamental individual-level processes and population-scale dynamics. Finally, we apply the modeling framework to case studies based on classical compartmental epidemiological systems, for each of which we report on Monte Carlo simulations of the individual-based model as well as on analytical results and numerical solutions of the macroscopic model.

我们开发了一个由连续变量构成的区隔流行病学系统的通用建模框架，这些变量与区隔特定特征的表达水平有关。我们首先制定了一个基于个体的模型，该模型描述了随机过程中单个个体的动态。然后，我们正式推导出：(i)该模型的介观对应，它被表述为个体在不同隔间的结构变量域上分布的积分微分方程系统；（ii）相应的宏观模型，该模型采用常微分方程系统的形式，用于不同隔间中的个体分数和结构变量所代表的特征的平均表达水平。我们采用了宏观模型的简化版本，得到了微观模型关键参数和函数的基本再现数R 0$ mathcal {R}_0$的一般公式。为了说明这样一个建模框架是如何使在基本的个人层面的过程和人口规模的动态之间建立联系成为可能的。最后，我们将建模框架应用于基于经典隔间流行病学系统的案例研究，并对每个案例报告了基于个体的模型的蒙特卡罗模拟以及宏观模型的分析结果和数值解。

{"title":"Heterogeneously Structured Compartmental Models of Epidemiological Systems: From Individual-Level Processes to Population-Scale Dynamics","authors":"Emanuele Bernardi, Tommaso Lorenzi, Mattia Sensi, Andrea Tosin","doi":"10.1111/sapm.70091","DOIUrl":"https://doi.org/10.1111/sapm.70091","url":null,"abstract":"We develop a general modeling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based model that describes the dynamics of single individuals in terms of stochastic processes. Then, we formally derive: (i) the mesoscopic counterpart of this model, which is formulated as a system of integrodifferential equations for the distributions of individuals over the structuring-variable domains of the different compartments; (ii) the corresponding macroscopic model, which takes the form of a system of ordinary differential equations for the fractions of individuals in the different compartments and the mean levels of expression of the traits represented by the structuring variables. We employ a reduced version of the macroscopic model to obtain a general formula for the basic reproduction number, <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math>, in terms of key parameters and functions of the underlying microscopic model, so as to illustrate how such a modeling framework makes it possible to draw connections between fundamental individual-level processes and population-scale dynamics. Finally, we apply the modeling framework to case studies based on classical compartmental epidemiological systems, for each of which we report on Monte Carlo simulations of the individual-based model as well as on analytical results and numerical solutions of the macroscopic model.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70091","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814646","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}

引用次数: 0

Structural and Microthermal Effects on the Exponential Stabilization of Poroelastic Systems 孔隙弹性体系指数稳定性的结构和微热效应

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-06 DOI: 10.1111/sapm.70089

Marcel Lucas Picanço Nascimento, Anderson de Jesus Araújo Ramos, Mirelson Martins Freitas, Carlos Alberto da Silva Nonato

In this work, we study the well-posedness and the asymptotic behavior of the solutions of a poroelastic system under the effects of viscoporosity, viscoelasticity, and microtemperature. We present the surprising fact of the exponential stabilization of the system, even under the condition $� � � Σ � : � = � γ � τ � - � �^{ε � 2 �} � = � 0 � � �$ , which reduces the internal energy dissipation of the system. This finding contrasts with recent results in the literature, where it is shown that $� � � Σ � = � 0 � � �$ destroys the exponential stability of the thermal system. Furthermore, we prove that the microthermal effect is not sufficient to guarantee the analyticity of the solutions.

本文研究了粘弹性、粘弹性和微温度作用下多孔弹性系统解的适定性和渐近性。我们给出了系统的指数稳定的惊人事实，即使在Σ条件下：= γ τ−ε 2 = 0 $Sigma:= gamma tau - varepsilon ^{2} = 0$，减小了系统的内部能量耗散。这一发现与最近文献中的结果形成对比，其中表明Σ = 0 $Sigma = 0$破坏了热系统的指数稳定性。进一步证明了微热效应不足以保证解的解析性。

{"title":"Structural and Microthermal Effects on the Exponential Stabilization of Poroelastic Systems","authors":"Marcel Lucas Picanço Nascimento, Anderson de Jesus Araújo Ramos, Mirelson Martins Freitas, Carlos Alberto da Silva Nonato","doi":"10.1111/sapm.70089","DOIUrl":"https://doi.org/10.1111/sapm.70089","url":null,"abstract":"In this work, we study the well-posedness and the asymptotic behavior of the solutions of a poroelastic system under the effects of viscoporosity, viscoelasticity, and microtemperature. We present the surprising fact of the exponential stabilization of the system, even under the condition <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>:</mo>\u0000 <mo>=</mo>\u0000 <mi>γ</mi>\u0000 <mi>τ</mi>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mi>ε</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$Sigma:= gamma tau - varepsilon ^{2} = 0$</annotation>\u0000 </semantics></math>, which reduces the internal energy dissipation of the system. This finding contrasts with recent results in the literature, where it is shown that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Σ</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$Sigma = 0$</annotation>\u0000 </semantics></math> destroys the exponential stability of the thermal system. Furthermore, we prove that the microthermal effect is not sufficient to guarantee the analyticity of the solutions.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70089","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782636","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}

引用次数: 0

Emergence of Coupled Korteweg–de-Vries Equations in m $m$ Fields m$ m$场中耦合Korteweg-de-Vries方程的出现

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-06 DOI: 10.1111/sapm.70090

Sharath Jose, Manas Kulkarni, Vishal Vasan

The Korteweg–de-Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi-component systems relevant for multi-species fluids and cold atomic mixtures. We present a general framework in which a family of multi-component KdV (mcKdV) equations naturally arises from a broader mathematical structure under reasonable assumptions on the nature of the nonlinear couplings. In particular, we derive a universal form for such a system of $� � m � �$ coupled KdV-type equations that is parameterized by $� � m � �$ non-zero real numbers and two symmetric functions of those $� � m � �$ numbers. Second, we show that physically relevant setups such as $� � � N � \geq � m � + � 1 � � �$ multi-component nonlinear Schrödinger equations (mcNLS), under scaling and perturbative treatment, reduce to such a mcKdV equation for a specific choice of the symmetric functions. The reduction from mcNLS to mcKdV requires one to be in a suitable parameter regime where the associated sound speeds of mcNLS are repeated. Hence, we connect the assumptions made in the derivation of the mcKdV system to physically interpretable assumptions for the mcNLS equation. Lastly, our approach provides a systematic foundation for facilitating a natural emergence of multi-component partial differential equations starting from a general mathematical structure.

Korteweg-de-Vries （KdV）方程在广泛的学科中具有重要的基础意义，可以推广到与多组分流体和冷原子混合物相关的多组分系统。我们提出了一个一般框架，在该框架中，在对非线性耦合性质的合理假设下，一组多分量KdV （mcKdV）方程自然地从更广泛的数学结构中产生。特别地，我们导出了由m$ m$非零实数和这些m$ m$数的两个对称函数参数化的m$ m$耦合kdv型方程组的一般形式。其次，我们证明了物理上相关的设置，如N≥m+1$ Nge m+1$多分量非线性Schrödinger方程（mcNLS），在标度和微扰处理下，对于特定选择的对称函数，可以简化为这样的mcKdV方程。从mcNLS到mcKdV的降低需要一个合适的参数范围，其中mcNLS的相关声速是重复的。因此，我们将mcKdV系统推导中的假设与mcNLS方程的物理可解释假设联系起来。最后，我们的方法为促进从一般数学结构开始的多分量偏微分方程的自然出现提供了系统的基础。

{"title":"Emergence of Coupled Korteweg–de-Vries Equations in \u0000 \u0000 m\u0000 $m$\u0000 Fields","authors":"Sharath Jose, Manas Kulkarni, Vishal Vasan","doi":"10.1111/sapm.70090","DOIUrl":"https://doi.org/10.1111/sapm.70090","url":null,"abstract":"The Korteweg–de-Vries (KdV) equation is of fundamental importance in a wide range of subjects with generalization to multi-component systems relevant for multi-species fluids and cold atomic mixtures. We present a general framework in which a family of multi-component KdV (mcKdV) equations naturally arises from a broader mathematical structure under reasonable assumptions on the nature of the nonlinear couplings. In particular, we derive a universal form for such a system of <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> coupled KdV-type equations that is parameterized by <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> non-zero real numbers and two symmetric functions of those <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> numbers. Second, we show that physically relevant setups such as <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$Nge m+1$</annotation>\u0000 </semantics></math> multi-component nonlinear Schrödinger equations (mcNLS), under scaling and perturbative treatment, reduce to such a mcKdV equation for a specific choice of the symmetric functions. The reduction from mcNLS to mcKdV requires one to be in a suitable parameter regime where the associated sound speeds of mcNLS are repeated. Hence, we connect the assumptions made in the derivation of the mcKdV system to physically interpretable assumptions for the mcNLS equation. Lastly, our approach provides a systematic foundation for facilitating a natural emergence of multi-component partial differential equations starting from a general mathematical structure.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144782637","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}

引用次数: 0

Analysis of Flux-Ratio Bifurcation in Ionic Flows via Classical Poisson–Nernst–Planck Models 用经典泊松-能-普朗克模型分析离子流的通量比分岔

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-08-06 DOI: 10.1111/sapm.70087

Hamid Mofidi, Fazel Hadadifard, Mingji Zhang

The flux ratio serves as a valuable characteristic for assessing the influence of permanent charge on the fluxes of different ion species. Our work analyzes flux ratios and their bifurcations in ionic flows using Poisson–Nernst–Planck models. Unlike Ussing's and Hodgkin–Keynes's ratios, our flux-bifurcation analysis captures the emergence and disappearance of multiple flux-ratio solutions as boundary conditions and permanent charge vary. We identify bifurcation points for flux ratios and characterize their dependence on system parameters, such as boundary conditions and permanent charge. Specifically, we examine the qualitative behavior of fluxes and flux ratios with respect to current, boundary concentrations, and boundary electric potentials at bifurcation points. This study can contribute to a deeper understanding of the underlying mechanisms governing ionic flows and could offer valuable insights for the design and optimization of ion channels in practical applications.

通量比是评估永久电荷对不同离子通量影响的一个有价值的特征。我们的工作使用泊松-能-普朗克模型分析了离子流中的通量比及其分支。与Ussing和Hodgkin-Keynes的比率不同，我们的通量分岔分析捕捉了随着边界条件和永久电荷的变化，多个通量比解的出现和消失。我们确定了通量比的分岔点，并描述了它们对系统参数（如边界条件和永久电荷）的依赖。具体地说，我们研究了通量和通量比在分岔点上与电流、边界浓度和边界电势有关的定性行为。该研究有助于深入了解控制离子流动的潜在机制，并可为实际应用中离子通道的设计和优化提供有价值的见解。

引用次数: 0

首页上一页

3
4
5
6
7
8
9
10

下一页尾页