SIAM Journal on Applied Mathematics最新文献

英文中文

Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries 球形几何中 PEC 电磁散射问题的组合纯场边界积分方程

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2024-01-12 DOI: 10.1137/23m1561865

Luiz Maltez-Faria, Carlos Pérez-Arancibia, Catalin Turc

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 19-38, February 2024.
Abstract. We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field [math] and (2) scalar quantity [math] are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green’s identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the field-only BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one—a property similar to second-kind integral equations.

SIAM 应用数学杂志》第 84 卷第 1 期第 19-38 页，2024 年 2 月。摘要。我们分析了完全导电球的频域电磁散射的某些纯场边界积分方程（BIE）的好求性。从（1）散射电场的三个分量[math]和（2）标量[math]是亥姆霍兹方程的辐射解这两个观察结果出发，我们发现，利用应用于上述量的格林等式和散射体表面的边界条件，可以推导出完全导电障碍物电磁散射的新边界积分方程公式。这些公式的未知量是散射电场三个分量的法向导数和散射体表面上散射电场的法向分量，因此这些公式被称为纯场边界积分方程。在本文中，我们在纯场 BIE 方法中使用了 Burton 和 Miller 的组合场方法，并推导出了新的边界积分公式，其特点是只有 Helmholtz 边界积分算子。根据亥姆霍兹边界积分算子在球形几何中的频谱特性，我们证明在球形几何情况下，组合的纯场边界积分算子是可对角的，并且其特征值在所有频率下都不为零。此外，我们还证明，对于球面几何，本文所考虑的其中一种纯场积分公式的特征值聚集在1处--这一性质类似于第二类积分方程。

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引用次数: 0

Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population 具有饱和发病函数的平流环境空间 SIS 流行病模型分析：I. 保持不变的总人口

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-12-08 DOI: 10.1137/22m1534699

Xiaodan Chen, Renhao Cui

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2522-2544, December 2023.
Abstract. This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number [math] was derived and the global dynamics of the system in terms of [math] was established: the disease-free equilibrium is unique and linearly stable if [math] and at least an endemic equilibrium exists if [math]. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.

SIAM 应用数学杂志》，第 83 卷第 6 期，第 2522-2544 页，2023 年 12 月。摘要本文对平流环境下受饱和感染机制控制的反应-扩散 SIS（易感-感染-易感）流行病模型进行定性分析。推导出了基本繁殖数[math]的变分表达式，并用[math]建立了系统的全局动力学：如果[math]，则无病平衡是唯一和线性稳定的；如果[math]，则至少存在一个流行平衡。更确切地说，我们探讨了基本繁殖数的定性特性，并研究了个体在扩散和平流方面的空间分布。我们发现，当平流较大时，会出现集中现象，而对于感染个体的小规模扩散，传染病将被根除。我们的理论结果可以为传染病预测和控制策略提供一些新的启示。

引用次数: 0

Modeling Acoustic Space-Coiled Metacrystals 声学空间卷曲元晶体建模

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-12-06 DOI: 10.1137/22m1527131

Joar Zhou Hagström, Kim Pham, Agnés Maurel

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2499-2521, December 2023.
Abstract. We present an effective model of “space-coiled metacrystals” composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry–Pérot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.

SIAM 应用数学杂志》，第 83 卷第 6 期，第 2499-2521 页，2023 年 12 月。摘要。我们提出了一种有效的 "空间卷曲元晶体 "模型，它由一个周期性的声刚性块阵列组成，其中的长槽被卷曲起来。块的周期性单元包含一个卷曲槽，其直线部分与波长尺度一致，这使得布拉格共振得以出现。这些共振会阻碍高传输，与整个槽的法布里-佩罗共振竞争，从而促进完美传输。这就导致了复杂的散射特性，而散射特性是由转折区域的特性驱动的，这些转折区域就像一维盘绕晶体中的原子。利用适当的缩放并结合二尺度均质化和匹配渐近技术，提出了这种元晶体的建模方法。通过与谐波和瞬态下的全波数值进行比较，验证了由此产生的模型。

引用次数: 0

Neuronal Resilience and Calcium Signaling Pathways in the Context of Synapse Loss and Calcium Leaks: A Computational MODELING Study and Implications for Alzheimer’s Disease 突触丢失和钙泄漏背景下的神经元弹性和钙信号通路:阿尔茨海默病的计算模型研究和意义

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-12-05 DOI: 10.1137/23m1557842

Piyush R. Borole, James M. Rosado, MeiRose Neal, Gillian Queisser

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2418-2442, December 2023.
Abstract. In this paper, a coupled electro-calcium model was developed and implemented to computationally explore the effects of neuronal synapse loss, in particular in the context of Alzheimer’s disease. Established parameters affected by Alzheimer’s disease, such as synapse loss, calcium leaks at deteriorating synaptic contacts, and downregulation of the calcium buffer calbindin, are subject to this study. Reconstructed neurons are used to define the computational domain for a system of PDEs and ODEs, discretized by finite differences and solved with a semi-implicit second-order time integrator. The results show neuronal resilience during synapse loss. When incorporating calcium leaks at affected synapses, neurons lose their ability to produce synapse-to-nucleus calcium signals, necessary for learning, plasticity, and neuronal survival. Downregulation of calbindin concentrations partially recovers the signaling pathway to the cell nucleus. These results could define future research pathways toward stabilizing the calcium signaling pathways during Alzheimer’s disease. The coupled electro-calcium model was implemented and solved using MATLAB https://github.com/NeuroBox3D/CalcSim.

SIAM应用数学学报，83卷，第6期，2418-2442页，2023年12月。摘要。本文开发并实现了一个耦合电钙模型，以计算探索神经元突触丢失的影响，特别是在阿尔茨海默病的背景下。受阿尔茨海默病影响的既定参数，如突触丢失、突触接触恶化时的钙泄漏以及钙缓冲物钙结合蛋白的下调，都是本研究的主题。重构神经元用于定义由偏微分方程和偏微分方程组成的系统的计算域，用有限差分离散，用半隐式二阶时间积分器求解。结果显示突触丢失时神经元的恢复能力。当受影响的突触发生钙泄漏时，神经元失去了产生突触到核钙信号的能力，这是学习、可塑性和神经元存活所必需的。下调钙结合蛋白浓度可部分恢复通往细胞核的信号通路。这些结果可以确定未来的研究途径，以稳定阿尔茨海默病期间的钙信号通路。利用MATLAB https://github.com/NeuroBox3D/CalcSim实现并求解了耦合电-钙模型。

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引用次数: 0

Design of Defected Non-hermitian Chains of Resonator Dimers for Spatial and Spatio-temporal Localizations 用于空间和时空定位的谐振器二聚体的缺陷非厄米链设计

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-12-05 DOI: 10.1137/23m1573896

Habib Ammari, Erik Orvehed Hiltunen, Thea Kosche

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2443-2468, December 2023.
Abstract. The aim of this article is to advance the field of metamaterials by proposing formulas for the design of high-contrast metamaterials with prescribed subwavelength defect mode eigenfrequencies. This is achieved in two settings: (i) design of non-Hermitian static materials and (ii) design of instantly changing non-Hermitian time-dependent materials. The design of static materials is achieved via characterizing equations for the defect mode eigenfrequencies in the setting of a defected dimer material. These characterizing equations are the basis for obtaining formulas for the material parameters of the defect which admit given defect mode eigenfrequencies. Explicit formulas are provided in the setting of one and two given defect mode eigenfrequencies in the setting of a defected chain of dimers. In the time-dependent case, we first analyze the influence of time boundaries on the subwavelength solutions. We find that subwavelength solutions are preserved if and only if the material parameters satisfy a temporal Snell’s law across the time boundary. The same result also identifies the change of the time frequencies uniquely. Combining this result with those on the design of static materials, we obtain an explicit formula for the material design of instantly changing defected dimer materials which admit subwavelength modes with prescribed time-dependent defect mode eigenfrequency. Finally, we use this formula to create materials which admit spatio-temporally localized defect modes.

应用数学学报，第83卷，第6期，第2443-2468页，2023年12月。摘要。本文的目的是通过提出具有指定亚波长缺陷模特征频率的高对比度超材料的设计公式来推动超材料领域的发展。这可以在两种情况下实现:(i)设计非厄米静态材料和(ii)设计瞬时变化的非厄米时变材料。静态材料的设计是通过描述缺陷二聚体材料中缺陷模特征频率的特征方程来实现的。这些表征方程是得到允许给定缺陷模态特征频率的缺陷材料参数公式的基础。在缺陷二聚体链的设置中，提供了一个和两个给定缺陷模式特征频率的设置的显式公式。在时间依赖的情况下，我们首先分析了时间边界对亚波长解的影响。我们发现当且仅当材料参数跨越时间边界满足时间斯涅尔定律时，亚波长解才被保留。同样的结果也唯一地标识了时间频率的变化。结合静态材料设计的结果，我们得到了瞬变缺陷二聚体材料设计的显式公式，该材料允许具有规定的时变缺陷模特征频率的亚波长模式。最后，我们使用这个公式来创建承认时空局域化缺陷模式的材料。

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引用次数: 0

Spectral Patterns of Elastic Transmission Eigenfunctions: Boundary Localization, Surface Resonance, and Stress Concentration 弹性传输特征函数的谱图:边界局部化、表面共振和应力集中

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-12-05 DOI: 10.1137/22m1538417

Yan Jiang, Hongyu Liu, Jiachuan Zhang, Kai Zhang

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2469-2498, December 2023.
Abstract. We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localization, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.

应用数学学报，第83卷，第6期，第2469-2498页，2023年12月。摘要。我们全面研究了弹性透射本征函数谱图的新发现，包括边界局部化、表面共振和应力集中。在这种情况下，区域是径向的，基本参数是恒定的，我们给出了严格的理由，并得出了对那些有趣的几何和物理模式的透彻理解。我们还给出了数值例子来验证相同的结果适用于一般的几何和参数设置。

引用次数: 1

Homogenization for a Variational Problem with a Slip Interface Condition 一类具有滑移界面条件的变分问题的均匀化

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-30 DOI: 10.1137/22m1506961

Miao-jung Yvonne Ou, Silvia Jiménez Bolaños

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2390-2417, December 2023.
Abstract. Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic materials, which are composites consisting of elastic frames whose pore space is filled with fluid. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip interface condition posed on the microscale. However, for certain pore fluids, the no-slip condition is known to be physically invalid. In the literature, slip boundary conditions have been considered for porous materials with rigid solid frames. For these rigid porous materials, the wave can only propagate in the pore fluid and hence the equations for the microscale are posed only in the pore space. Consequently, the slip on the interface involves only the fluid velocity and the fluid stress. In contrast, for poroelastic materials, the wave can propagate not only in the pore fluid but also in the solid frame; hence the slip conditions involve the velocities on both sides of the interface, rather than just the fluid side. With this slip condition, a variational boundary value problem governing the small vibrations of a periodic mixture of an elastic solid and a slightly viscous fluid is studied in this paper. The method of two-scale convergence is used to obtain the macroscopic behavior of the solution and to identify the role played by the slip interface condition.

应用数学学报，83卷，第6期，2390-2417页，2023年12月。摘要。受实际应用的启发，我们研究了界面滑移对孔隙弹性材料中有效波传播的影响。孔隙弹性材料是由弹性框架组成的，其孔隙空间充满流体。目前关于孔隙弹性波动方程均质化的文献都是基于微尺度上的无滑移界面条件。然而，对于某些孔隙流体，已知无滑移条件在物理上是无效的。在文献中，滑移边界条件已考虑与刚性实体框架多孔材料。对于这些刚性多孔材料，波只能在孔隙流体中传播，因此微尺度方程只能在孔隙空间中建立。因此，界面上的滑移只涉及流体速度和流体应力。相反，对于孔隙弹性材料，波不仅可以在孔隙流体中传播，而且可以在固体框架中传播;因此，滑移条件涉及界面两侧的速度，而不仅仅是流体一侧。在此滑移条件下，本文研究了弹性固体与微粘性流体周期性混合物的小振动变分边值问题。采用双尺度收敛的方法得到了解的宏观行为，并确定了滑移界面条件对解的影响。

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引用次数: 0

Multiscale Modeling and Analysis of Growth of Plant Tissues 植物组织生长的多尺度建模与分析

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-29 DOI: 10.1137/23m1553315

Arezki Boudaoud, Annamaria Kiss, Mariya Ptashnyk

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2354-2389, December 2023.
Abstract. How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue-scale model. Tissue-scale mechanical properties are computed from microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using the finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues.

应用数学学报，第83卷，第6期，2354-2389页，2023年12月。摘要。形态发生如何依赖于细胞性质是一个活跃的研究方向。在这里，我们专注于生长植物组织的力学模型，其中微观(亚)细胞结构被考虑在内。为了建立微观和宏观组织特性之间的联系，我们对生长植物组织的亚细胞分辨率模型进行了多尺度分析。我们使用均匀化严格推导出相应的宏观组织尺度模型。组织尺度的力学性能从微观结构和材料性能计算，考虑了生长场的变形。然后，我们考虑案例研究，并在数值上比较详细的微观模型和组织尺度模型，两者都使用有限元方法实现。我们发现宏观模型可以有效地对几种感兴趣的结构进行预测。我们的工作将有助于在生长组织的微观测量和宏观观察之间建立联系。

引用次数: 1

A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs 超图上意见动态有界置信度模型的密度描述

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-28 DOI: 10.1137/22m148608x

Weiqi Chu, Mason A. Porter

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2310-2328, December 2023.
Abstract. Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents comprise their opinions if they are close enough to each other. We study a density description of a Deffuant–Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM’s steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.

SIAM应用数学学报，83卷，第6期，2310-2328页，2023年12月。摘要。社会互动通常同时发生在三个或更多的主体之间。研究超图上的意见动态可以让人们研究这种多元互动对代理人意见的影响。在本文中，我们考虑了一个有界置信模型(BCM)，在该模型中，意见取连续值，如果相互作用的智能体彼此足够接近，则构成它们的意见。研究了超图上Deffuant-Weisbuch BCM的密度描述。当智能体的数量变得无限时，我们推导了平均场意见密度的速率方程，并证明了该速率方程产生了收敛到非相互作用意见聚类的概率密度。通过数值模拟，我们研究了基于密度的BCM稳态意见聚类的分叉，并证明了当智能体的数量变得无限时，基于智能体的BCM收敛于BCM的密度描述。

引用次数: 0

Hypernetworks: Cluster Synchronization Is a Higher-Order Effect 超级网络:集群同步是一种高阶效应

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-28 DOI: 10.1137/23m1561075

Sören von der Gracht, Eddie Nijholt, Bob Rink

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2329-2353, December 2023.
Abstract. Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.

应用数学学报，第83卷，第6期，2329-2353页，2023年12月。摘要。许多网络系统是由节点之间的非成对交互控制的。由此产生的高阶交互结构可以通过超网络进行编码。本文通过为每一个超网络定义一类可容许映射来考虑超网络上的动态系统。我们解释了如何通过寻找平衡分区来对超网络上的健壮集群同步模式进行分类，并将图纤化的概念推广到超网络上下文中。我们还证明了鲁棒同步模式只能完全由多项式允许的高阶映射确定。这意味着，与二元网络不同，超网络上的集群同步是一种高阶的，即非线性的效应。根据超网络的阶，我们给出了确定鲁棒同步模式的多项式允许映射的程度的一个公式。我们还通过调查一类例子证明了这个度是最优的。最后，我们证明了这种效应如何导致显著的同步中断分岔，发生在高多项式度。

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引用次数: 3

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