SIAM Journal on Applied Mathematics最新文献

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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 Q2 Mathematics

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 Q2 Mathematics

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 Q2 Mathematics

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 Q2 Mathematics

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 Q2 Mathematics

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 Q2 Mathematics

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

A Multifaceted Study of Nematic Order Reconstruction in Microfluidic Channels 微流控通道中向列有序重构的多方面研究

IF 1.9 4区数学 Q2 Mathematics

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-27 DOI: 10.1137/22m1490909

James Dalby, Yucen Han, Apala Majumdar, Lidia Mrad

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2284-2309, December 2023.
Abstract. We study order reconstruction (OR) solutions in the Beris–Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of physical interest. We show that OR solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. We prove the existence of unique, symmetric, and nonsingular nematic profiles for boundary conditions that do not allow for OR solutions. We compute asymptotic expansions for OR-type solutions for passive flows with nonconstant velocity and pressure, and active flows, which shed light on the internal structure of domain walls. The asymptotics are complemented by numerical studies that demonstrate the universality of OR-type structures in static and dynamic scenarios.

SIAM应用数学学报，83卷，第6期，2284-2309页，2023年12月。摘要。我们在Beris-Edwards框架下研究了微流控通道中被动和主动向列流的有序重建(OR)解。OR解决方案展示了多域和域壁，因此具有物理意义。我们证明了对于恒速恒压被动流动存在OR解，但仅适用于特定的边界条件。在不允许或解的边界条件下，证明了唯一、对称和非奇异向列型轮廓的存在性。我们计算了非恒定速度和压力的被动流动和主动流动的or型解的渐近展开式，从而揭示了区域壁面的内部结构。数值研究补充了渐近性，证明了or型结构在静态和动态情况下的普遍性。

引用次数: 1

Prevalence of Multistationarity and Absolute Concentration Robustness in Reaction Networks 反应网络中多平稳性和绝对浓度鲁棒性的普遍性

IF 1.9 4区数学 Q2 Mathematics

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-20 DOI: 10.1137/23m1549316

Badal Joshi, Nidhi Kaihnsa, Tung D. Nguyen, Anne Shiu

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2260-2283, December 2023.
Abstract. For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks and prove edge-probability thresholds at which, with high probability, multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero and the other “lifting” multistationarity from small networks to larger ones.

SIAM应用数学杂志，83卷，第6期，2260-2283页，2023年12月。摘要。对于系统生物学中产生的反应网络，具有两个或多个稳定状态的能力，即多平稳性，是生化开关的重要特性。另一个最近受到广泛关注的性质是绝对浓度鲁棒性(ACR)，这意味着某些物种的浓度在所有正稳态下都是相同的。在这项工作中，我们调查了每个属性的普遍性，同时密切关注这些属性何时一起出现。具体来说，我们考虑了一个随机块框架来生成随机网络，并证明了边缘概率阈值，在该阈值下，多平稳性在高概率下出现，并且ACR变得罕见。我们还表明，两种性质同时出现的小窗口只出现在有许多物种的网络中。综上所述，我们的结果证实，在随机可逆网络中，ACR和多平稳性一起，甚至单独的ACR，都是非典型的。我们的证明依赖于两个先前的结果，一个与缺乏性为零的网络的普遍性有关，另一个将多平稳性从小型网络“提升”到大型网络。

{"title":"Prevalence of Multistationarity and Absolute Concentration Robustness in Reaction Networks","authors":"Badal Joshi, Nidhi Kaihnsa, Tung D. Nguyen, Anne Shiu","doi":"10.1137/23m1549316","DOIUrl":"https://doi.org/10.1137/23m1549316","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2260-2283, December 2023. Abstract. For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks and prove edge-probability thresholds at which, with high probability, multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero and the other “lifting” multistationarity from small networks to larger ones.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2

Power-Engine-Load Form for Dynamic Absolute Concentration Robustness 动力-发动机负载形式的动态绝对集中稳健性

IF 1.9 4区数学 Q2 Mathematics

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-20 DOI: 10.1137/22m1535450

Badal Joshi, Gheorghe Craciun

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2237-2259, December 2023.
Abstract. In a reaction network, the concentration of a species with the property of dynamic absolute concentration robustness (dynamic ACR) converges to the same value independent of the overall initial values. This property endows a biochemical network with output robustness and therefore is essential for its functioning in a highly variable environment. It is important to identify the structure of the dynamical system as well as the constraints required for dynamic ACR. We propose a power-engine-load form of dynamic ACR and obtain results regarding convergence to the ACR value based on this form.

SIAM应用数学学报，83卷，第6期，2237-2259页，2023年12月。摘要。在反应网络中，具有动态绝对浓度鲁棒性(dynamic绝对浓度鲁棒性，动态ACR)的物种的浓度收敛到与整体初始值无关的同一值。这一特性赋予生化网络输出鲁棒性，因此对其在高度可变的环境中发挥作用至关重要。确定动力系统的结构以及动态ACR所需的约束条件是很重要的。提出了一种动力-发动机-负荷形式的动态ACR，并在此基础上得到了ACR值收敛性的结果。

引用次数: 0

Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations 具有反应扩散和移动边界的细胞极性和运动:严格的模型分析和鲁棒模拟

IF 1.9 4区数学 Q2 Mathematics

SIAM Journal on Applied Mathematics

Pub Date : 2023-11-16 DOI: 10.1137/22m1506766

Shuang Liu, Li-Tien Cheng, Bo Li

SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of a moving cell boundary. Such a moving boundary is often simulated by a phase-field model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimuli and capture both the linear and the circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.

SIAM应用数学杂志，出版前。摘要。细胞极性和运动是许多生物功能的基础。实验和理论研究表明，某些蛋白质的相互作用导致细胞极化，并在控制细胞运动中起着关键作用。我们研究细胞极性和运动基于一类生物物理模型，包括不同蛋白质的反应-扩散方程和移动细胞边界的动力学。这种移动边界通常用相场模型来模拟。我们首先应用匹配渐近分析从相场模型推导出细胞边界的锐界面模型。然后，我们开发了一种鲁棒的数值方法，该方法结合了水平集方法来跟踪移动细胞的尖锐边界和精确的离散化技术来求解移动细胞区域上的反应扩散方程。我们广泛的数值模拟预测了各种刺激下的细胞极化，并捕获了长时间运动细胞的线性和圆形轨迹。特别是，我们已经确定了一些控制不同细胞轨迹的关键参数，这些参数通过简化模型预测的准确性较低。我们的工作将不同的模型联系起来，并开发了能够适应具有挑战性的三维模拟的工具。

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引用次数: 0

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