Studies in Applied Mathematics最新文献

英文中文

Mathematical Theory on Multi-Layered High-Contrast Acoustic Subwavelength Resonators 多层高对比声学亚波长谐振器的数学理论

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-12 DOI: 10.1111/sapm.70145

Youjun Deng, Lingzheng Kong, Hongjie Li, Hongyu Liu, Liyan Zhu

Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layered resonator has prompted the exploration of multi-layered metamaterials as an effective alternative, which consist of alternating nests of high-contrast materials, called “resonators”, and a background media. In this paper, we develop a general mathematical framework for studying acoustics within multi-layered high-contrast structures. First, by using layer potential techniques, we establish the representation formula in terms of a matrix type operator with a block tridiagonal form for multi-layered structures within general geometry. Then, we prove the existence of subwavelength resonances via the Gohberg–Sigal theory, which generalizes the celebrated Minnaert resonances in single-layered structures. Intriguingly, we find that the primary contribution to mode splitting lies in the fact that as the number of nested resonators increases, the degree of the corresponding characteristic polynomial also increases, while the type of resonance (consists solely of monopolar resonances) remains unchanged. Furthermore, we derive original formulas for the subwavelength resonance frequencies of concentric dual-resonator. Numerical results for different nested resonators are presented to corroborate the theoretical findings.

亚波长共振是对比介质中重要的声学现象。单层谐振器的窄带隙宽度促使探索多层超材料作为一种有效的替代方案，它由高对比度材料的交替巢组成，称为“谐振器”，以及背景介质。在本文中，我们开发了一个通用的数学框架来研究多层高对比度结构中的声学。首先，利用层势技术，建立了一般几何中多层结构的块三对角线形式的矩阵型算子的表示公式。然后，我们通过gohberg -信号理论证明了亚波长共振的存在，该理论推广了单层结构中著名的Minnaert共振。有趣的是，我们发现模式分裂的主要贡献在于，随着嵌套谐振子数量的增加，相应的特征多项式的程度也增加，而共振的类型（仅由单极共振组成）保持不变。进一步推导了同心双谐振器亚波长共振频率的原始公式。给出了不同嵌套谐振器的数值结果来证实理论结果。

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引用次数: 0

Muskat–Leverett Two-Phase Flow in Thin Cylindric Porous Media: Asymptotic Approach 薄圆柱形多孔介质中的Muskat-Leverett两相流：渐近方法

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-11 DOI: 10.1111/sapm.70137

Taras Mel'nyk, Christian Rohde

A reduced-dimensional asymptotic modeling approach is presented for the analysis of two-phase flow in a thin cylinder with an aperture of order <math> <semantics> <mrow> <mi>O</mi> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <annotation>$mathcal {O}(varepsilon)$</annotation> </semantics></math>, where <math> <semantics> <mi>ε</mi> <annotation>$varepsilon$</annotation> </semantics></math> is a small positive parameter. We consider a nonlinear Muskat–Leverett two-phase flow model expressed in terms of a fractional flow formulation and Darcy's law, with saturation and reduced pressure as unknown. The given flow seeps through the lateral surface of the cylinder. This exchange process leads to a nonhomogeneous Neumann boundary condition with an intensity factor <math> <semantics> <msup> <mi>ε</mi> <mi>α</mi> </msup> <annotation>$varepsilon ^alpha$</annotation> </semantics></math> <math> <semantics> <mrow> <mo>(</mo> <mi>α</mi> <mo>≥</mo> <mn>1</mn> <mo>)</mo> </mrow> <annotation>$(alpha ge 1)$</annotation> </semantics></math> that controls mass transport. Furthermore, the absolute permeability tensor comprises the intensity coefficient <math> <semantics> <msup> <mi>ε</mi> <mi>β</mi> </msup> <annotation>$varepsilon ^beta$</annotation> </semantics></math>, <math> <semantics> <mrow> <mi>β</mi> <mo>∈</mo> <mi>R</mi> </mrow> <annotation>$beta in mathbb {R}$</annotation> </semantics></math>, in the transverse direction. The asymptotic behavior of the solution is studied as <math> <semantics> <mrow> <mi>ε</mi> <mo>→</mo> <mn>0</mn> </mrow> <annotation>$varepsilon rightarrow 0$</annotation> </semantics></math>, that is, when the thin cylinder shrinks into an interval. Two qualitatively distinct cases were discovered in the asymptotic behavior of the solution: <math> <semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1<

提出了一种降维渐近建模方法，用于分析孔径为O (ε) $mathcal {O}(varepsilon)$阶的细圆柱内的两相流动，其中ε $varepsilon$是一个小的正参数。我们考虑一个非线性的马斯喀特-莱弗里特两相流模型，用分数流动公式和达西定律表示，饱和度和减压为未知。给定的流体渗过圆柱体的侧面。这种交换过程导致具有控制质量输运的强度因子ε α $varepsilon ^alpha$ (α≥1)$(alpha ge 1)$的非齐次诺伊曼边界条件。绝对渗透率张量在横向上包括强度系数ε β $varepsilon ^beta$, β∈R $beta in mathbb {R}$。研究了当ε→0 $varepsilon rightarrow 0$时，即当薄圆柱收缩成区间时，解的渐近性态。在解的渐近行为中发现了两种定性不同的情况：α = 1和β ＆lt； 2 $alpha =1 text{and} beta <2$，α ＆gt； β - 1和α ＆gt； 1 $alpha > beta -1 text{and} alpha >1$。在每一种情况下，两项渐近近似被构造为降低的压力和饱和度，伴随着严格的渐近估计。然后用这些近似值推导出各相压力和流速的近似值。根据参数α $alpha$和β $beta$的值（每个模型都是由两个微分方程组成的非线性椭圆-抛物方程组），导出了对应于两相马斯喀特-莱弗里特流的两个一维模型。

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引用次数: 0

Asymptotic Expansions for Solutions of Differential Equations Having Coalescing Turning Points, With an Application to Legendre Functions 具有合并拐点的微分方程解的渐近展开式，及其在Legendre函数中的应用

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-11 DOI: 10.1111/sapm.70138

T. M. Dunster

<div> Linear second-order ordinary differential equations of the form <math> <semantics> <mrow> <msup> <mi>d</mi> <mn>2</mn> </msup> <mi>w</mi> <mo>/</mo> <mi>d</mi> <msup> <mi>z</mi> <mn>2</mn> </msup> <mrow> <mo>=</mo> <mo>{</mo> </mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mi>f</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <annotation>$d^{2}w/dz^{2}=lbrace u^{2}f(a,z)$</annotation> </semantics></math> <math> <semantics> <mrow> <mo>+</mo> <mi>g</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> <mo>}</mo> <mi>w</mi> </mrow> <annotation>$+g(z)rbrace w$</annotation> </semantics></math> are studied for large values of the real parameter <math> <semantics> <mi>u</mi> <annotation>$u$</annotation> </semantics></math>, where <math> <semantics> <mi>z</mi> <annotation>$z$</annotation> </semantics></math> ranges over a bounded or unbounded complex domain <math> <semantics> <mi>Z</mi> <annotation>$Z$</annotation> </semantics></math>, and <math> <semantics> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>≤</mo> <mi>a</mi> <mo>≤</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo><</mo> <mi>∞</mi> </mrow> <annotation>$a_{0} le a le a_{1} < infty$</annotation> </semantics></math>. The functions <math> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <annotation>$f(a,z)$</annotation> </semantics></math> and <math> <semantics>

形式为d2w / dz2 = {u2f的线性二阶常微分方程(a)；Z)$d^{2}w/dz^{2}=lbrace u^{2}f(a,z)$ + g (Z) }w$+g(z)rbrace w$对于较大的实参数u $u$进行了研究；其中z $z$范围在有界或无界复域z $Z$上，且a 0≤a≤a 1 ＆lt；∞$a_{0} le a le a_{1} < infty$。函数f (a, z) $f(a,z)$和g (z) $g(z)$在z $Z$的内部是解析的。此外，f (a)z) $f(a,z)$在z $Z$中正好有两个简单的零对于连续依赖于a的a ＆gt； a 0 $a>a_{0}$$a$并合并成一个双零，即a→a 0 $a rightarrow a_{0}$。得到了抛物线柱面函数及其导数与慢变系数函数解的一致渐近展开式。该系数易于计算，并提供了明确的误差范围。然后将结果应用于推导出当ν $nu$和μ $mu$阶都很大时相关的Legendre函数的新的渐近展开式。

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引用次数: 0

Asymptotic Target Tracking in Discontinuous Dynamical Systems: Applications of Filippov's Inclusion Framework 不连续动力系统的渐近目标跟踪：Filippov包含框架的应用

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-11 DOI: 10.1111/sapm.70142

Woojoo Shim, Hyunjin Ahn

We propose two novel multiagent systems characterized by discontinuous vector fields, designed to track a given moving or stationary target while ensuring collision avoidance. Unlike traditional approaches that employ continuous vector fields, we adopt Filippov's differential inclusion framework to model the dynamics at discontinuity points. For each model, we present an admissible set of initial conditions, system parameters, kernel functions, and a target configuration that guarantees both qualitative and quantitative asymptotic tracking of a prescribed target while avoiding collisions.

我们提出了两种以不连续向量场为特征的新型多智能体系统，用于跟踪给定的运动或静止目标，同时确保避免碰撞。与使用连续向量场的传统方法不同，我们采用Filippov的微分包含框架来模拟不连续点的动力学。对于每个模型，我们提出了一组可接受的初始条件、系统参数、核函数和目标配置，以保证在避免碰撞的同时定性和定量地渐近跟踪指定目标。

引用次数: 0

The Kauffman Bracket Skein Module of Bonded Knots and Applications to Entangled Proteins 结合结的考夫曼支架绞丝模块及其在纠缠蛋白中的应用

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-07 DOI: 10.1111/sapm.70123

Boštjan Gabrovšek, Matic Simonič

We model proteins with intramolecular bonds, such as disulfide bridges, using the concept of bonded knots—closed loops in three-dimensional space equipped with additional bonds that connect different segments of the knot. We extend the Kauffman bracket polynomial (which is closely related to the Jones polynomial) to bonded knots through the introduction of the bonded version of the Kauffman bracket skein module. We show that this module is infinitely generated and torsion-free for both the rigid and topological case of bonded knots. In the rigid case, evaluating a bonded knot in the basis of this module yields an bonded knot invariant closely related to the APS bracket and the Simplified RNA polynomial.

我们利用键结的概念，用分子内键（如二硫桥）来模拟蛋白质。键结是三维空间中的闭合环，配备了连接结的不同部分的额外键。我们通过引入粘合版的考夫曼支架绞丝模块，将考夫曼支架多项式（与琼斯多项式密切相关）扩展到粘合结。我们证明了该模块在刚性和拓扑情况下都是无限生成和无扭转的。在刚性情况下，在此模块的基础上评估键结，得到与APS支架和简化RNA多项式密切相关的键结不变量。

引用次数: 0

Weak KAM Theory for Modified Korteweg-de Vries Equations 修正Korteweg-de Vries方程的弱KAM理论

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-07 DOI: 10.1111/sapm.70136

Xun Niu, Yong Li, Kaizhi Wang

We investigate the dynamics of the modified Korteweg-de Vries (mKdV) equation from the perspective of the weak Kolmogorov-Arnold-Moser (KAM) theory, and obtain that the associated Hamiltonian system admits a weak KAM solution. This solution satisfies the Hamilton–Jacobi equation in the sense of the minimal measure, which allows the system to be reduced to a class of integrable Hamiltonian systems. The minimal measure is closely related to the Aubry–Mather theory. Consequently, we establish the existence of a weak solution of the perturbed mKdV equation, despite the presence of system resonance. Finally, we extend this method to quasi-periodic perturbed mKdV equations and coupled mKdV equations, proving the existence of weak KAM solutions.

从弱Kolmogorov-Arnold-Moser （KAM）理论的角度研究了修正的Korteweg-de Vries （mKdV）方程的动力学性质，得到了相关的哈密顿系统允许一个弱KAM解。该解在极小测度意义上满足哈密顿-雅可比方程，使得系统可以简化为一类可积哈密顿系统。最小测度与奥布里-马瑟理论密切相关。因此，我们建立了扰动mKdV方程弱解的存在性，尽管存在系统共振。最后，将该方法推广到拟周期摄动mKdV方程和耦合mKdV方程，证明了弱KAM解的存在性。

引用次数: 0

On the Initial-Boundary Value Problem for the 2D Partially Dissipative Oldroyd-B Model: Global Well-Posedness and Large Time Stability 二维部分耗散oldyd - b模型的初边值问题：全局适定性和大时间稳定性

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-11-07 DOI: 10.1111/sapm.70139

Zhenrong Nong, Yinghui Wang, Huancheng Yao, Shihao Zhang

This work studies the global well-posedness of the Oldroyd-B model with anisotropic viscosity. While global existence and uniqueness of strong solutions for the fully dissipative Oldroyd-B model were established in Constantin–Kliegl [Archive for Rational Mechanics and Analysis, 206 (2012): 725–740], under $� � � �^{H � 2 �} � � (� �^{R � 2 �} �) � � � �$ initial data, the horizontally viscous counterpart—where dissipation of velocity acts only along the horizontal direction—remains unexplored. We establish the global existence and uniqueness of strong solutions to the initial-boundary value problem for the horizontally viscous Oldroyd-B model with arbitrary large initial data in the vertical strip domain $� � � [� 0 �, � 1 �] � \times � R � � �$ and the periodic channel $� � � [� 0 �, � 1 �] � \times � T � � �$ , where $� � T � �$ represents the one-dimensional torus. To the best of our knowledge, this work provides the first rigorous proof of global-in-time existence and uniqueness of strong solutions for the partially dissipative Oldroyd-B model. In addition, we investigate the long-time asymptotic behavior of solutions for small initial data in the periodic channel $� � � [� 0 �, � 1 �] � \times � T � � �$ . Our results extend the current analytical understanding of visco

本文研究了具有各向异性黏度的Oldroyd-B模型的全局适定性。在Constantin-Kliegl中建立了全耗散Oldroyd-B模型强解的整体存在唯一性[j] .力学与分析学报，206 (2012)：[725-740]，在H 2(R 2)$ H^2(mathbb {R}^2)$初始数据下，水平粘性对应部分（速度耗散仅沿水平方向起作用）仍未探索。本文建立了具有任意大初始数据的水平粘性Oldroyd-B模型初边值问题强解的全局存在唯一性[0]。1] × R $[0,1]乘以mathbb {R}$和周期通道[0,1]× T $[0,1]乘以mathcal {T}$，其中T $mathcal {T}$表示一维环面。据我们所知，这项工作首次提供了部分耗散的oldyd - b模型强解的全局时间存在性和唯一性的严格证明。此外，我们研究了周期通道[0,1]× T $[0,1]times mathcal {T}$中小初始数据解的长时间渐近行为。我们的结果扩展了目前对部分耗散约束下粘弹性流体动力学的分析理解。

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引用次数: 0

Global Solutions in the 2-D Case of a Degenerate Phase-Field Model for Spinodal Decomposition 退化相场模型的旋量分解的二维全局解

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-31 DOI: 10.1111/sapm.70132

Xingzhi Bian, Yangxin Tang, Lixian Zhao

We study an initial-boundary value problem for a novel phase-field model describing the evolution of spinodal decomposition, a typical example of solid-phase separation. The nonuniform, degenerate parabolic evolution equation in the model differs from the classical Cahn–Hilliard equation by a nonsmooth gradient term of the order parameter. The existing results are mostly limited to one-dimensional cases, and this paper aims to extend the results to two-dimensional spaces. We prove the global existence of weak solutions to this model and use the model to simulate the microstructural evolution of phase separation.

本文研究了描述固相分离过程中旋量分解演化的一种新型相场模型的初边值问题。模型中的非均匀退化抛物演化方程与经典Cahn-Hilliard方程的不同之处是阶参数的非光滑梯度项。现有的结果大多局限于一维情况，本文旨在将结果扩展到二维空间。我们证明了该模型的整体弱解的存在性，并利用该模型模拟了相分离过程的微观结构演化。

引用次数: 0

Issue Information-TOC 问题Information-TOC

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-31 DOI: 10.1111/sapm.70144

引用次数: 0

On the Evolution of Relativistic Dust in Schwarzschild–de Sitter and Schwarzschild–Anti-de Sitter Spacetimes. Part I: The Vanishing Mass Case 论相对论尘埃在史瓦西-德西特和反史瓦西特时空中的演化。第一部分：消失的质量案例

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-31 DOI: 10.1111/sapm.70134

Yifan Liu, Xianshu Qu, Yuzhu Wang, Changhua Wei

Given that relativistic density and velocity propagate at the same speed, the Cauchy problem with smooth and compactly supported initial data for relativistic dust in Schwarzschild–de Sitter (SdS) and Schwarzschild–anti-de Sitter (SAdS) spacetimes without black hole has been investigated using the characteristic method. Based on the explicit solution formulas under the spherically symmetric assumption, a precise classification of the initial data is provided, elucidating whether the classical solution for relativistic dust will persist globally or encounter a finite-time blowup. Moreover, the paper offers a further analysis of the exact blowup phenomenon, including detailed insights into the blowup rate related to the blowup time.

在相对论密度和速度以相同的速度传播的情况下，利用特征方法研究了在没有黑洞的Schwarzschild-de - Sitter （SdS）和Schwarzschild-anti-de - Sitter （SAdS）时空中相对论尘埃的光滑紧支持初始数据的Cauchy问题。基于球对称假设下的显式解公式，给出了初始数据的精确分类，阐明了相对论尘埃的经典解是全局持续存在还是遇到有限时间爆破。此外，本文还提供了对爆破现象的进一步分析，包括与爆破时间相关的爆破率的详细见解。

引用次数: 0

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