首页 > 最新文献

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

英文 中文
Surface impedance and topologically protected interface modes in one-dimensional phononic crystals 一维声子晶体中的表面阻抗和拓扑保护界面模式
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-24 DOI: 10.1098/rspa.2023.0533
A. Coutant, B. Lombard
When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings.
当半无限声子晶体(PC)接触时,它们的边界可能存在局部模式。核心问题通常是预测它们的存在并确定其稳定性。随着拓扑绝缘体领域的迅速发展,人们开发出了强大的工具来解决这些问题。特别是,当应用于具有镜像对称性的一维系统时,体-界对应关系声称界面模式的存在是由 PC 的体特性计算出的拓扑不变量给出的,这确保了强大的稳定性。这种一维体-边界对应关系已在各种研究中得到证实。最近的尝试利用了表面阻抗的概念,依赖于传递矩阵的分析计算。在本研究中,我们证明了所有具有镜像对称性的一维 PC 的表面阻抗随频率的单调演化。这一结果使我们建立了更强版本的体界对应关系,不仅保证了拓扑保护界面态的存在性,而且保证了其唯一性。这一对应关系被扩展到包括不完美界面、谐振器阵列或色散介质在内的更大一类一维模型。我们提出了数值模拟来说明理论发现。
{"title":"Surface impedance and topologically protected interface modes in one-dimensional phononic crystals","authors":"A. Coutant, B. Lombard","doi":"10.1098/rspa.2023.0533","DOIUrl":"https://doi.org/10.1098/rspa.2023.0533","url":null,"abstract":"When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry, the bulk-boundary correspondence claims that the existence of interface modes is given by a topological invariant computed from the bulk properties of the PC, which ensures strong stability properties. This one-dimensional bulk-boundary correspondence has been proven in various works. Recent attempts have exploited the notion of surface impedance, relying on analytical calculations of the transfer matrix. In the present work, the monotonic evolution of surface impedance with frequency is proven for all one-dimensional PCs with mirror symmetry. This result allows us to establish a stronger version of the bulk-boundary correspondence that guarantees not only the existence but also the uniqueness of a topologically protected interface state. This correspondence is extended to a larger class of one-dimensional models that include imperfect interfaces, array of resonators, or dispersive media. Numerical simulations are proposed to illustrate the theoretical findings.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pushing coarse-grained models beyond the continuum limit using equation learning 利用方程学习将粗粒度模型推向连续极限
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-10 DOI: 10.1098/rspa.2023.0619
Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson
Mathematical modelling of biological population dynamics often involves proposing high-fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an approximate coarse-grained differential equation that captures population-level features only. These coarse-grained models are only accurate in certain asymptotic parameter regimes, such as enforcing that the time scale of individual motility far exceeds the time scale of birth/death processes. When these coarse-grained models are accurate, the discrete model still abides by conservation laws at the microscopic level, which implies that there is some macroscopic conservation law that can describe the macroscopic dynamics. In this work, we introduce an equation learning framework to find accurate coarse-grained models when standard continuum limit approaches are inaccurate. We demonstrate our approach using a discrete mechanical model of epithelial tissues, considering a series of four case studies that consider problems with and without free boundaries, and with and without proliferation, illustrating how we can learn macroscopic equations describing mechanical relaxation, cell proliferation, and the equation governing the dynamics of the free boundary of the tissue. While our presentation focuses on this biological application, our approach is more broadly applicable across a range of scenarios where discrete models are approximated by approximate continuum-limit descriptions.
建立生物种群动态数学模型通常需要提出基于离散代理的高保真模型,以捕捉随机性和个体水平的过程。这些模型通常与仅捕捉种群水平特征的近似粗粒度微分方程一起考虑。这些粗粒度模型只有在某些渐近参数情况下才是准确的,例如强制要求个体运动的时间尺度远远超过出生/死亡过程的时间尺度。当这些粗粒度模型准确时,离散模型在微观层面仍遵守守恒定律,这意味着存在某种宏观守恒定律可以描述宏观动力学。在这项工作中,我们引入了一个方程学习框架,以便在标准连续极限方法不准确时找到准确的粗粒度模型。我们使用上皮组织的离散机械模型来演示我们的方法,考虑了一系列四个案例研究,包括有自由边界和无自由边界的问题,以及有增殖和无增殖的问题,说明我们如何学习描述机械弛豫、细胞增殖的宏观方程,以及支配组织自由边界动态的方程。虽然我们的演讲侧重于这一生物应用,但我们的方法更广泛地适用于一系列离散模型近似连续极限描述的场景。
{"title":"Pushing coarse-grained models beyond the continuum limit using equation learning","authors":"Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson","doi":"10.1098/rspa.2023.0619","DOIUrl":"https://doi.org/10.1098/rspa.2023.0619","url":null,"abstract":"Mathematical modelling of biological population dynamics often involves proposing high-fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an approximate coarse-grained differential equation that captures population-level features only. These coarse-grained models are only accurate in certain asymptotic parameter regimes, such as enforcing that the time scale of individual motility far exceeds the time scale of birth/death processes. When these coarse-grained models are accurate, the discrete model still abides by conservation laws at the microscopic level, which implies that there is some macroscopic conservation law that can describe the macroscopic dynamics. In this work, we introduce an equation learning framework to find accurate coarse-grained models when standard continuum limit approaches are inaccurate. We demonstrate our approach using a discrete mechanical model of epithelial tissues, considering a series of four case studies that consider problems with and without free boundaries, and with and without proliferation, illustrating how we can learn macroscopic equations describing mechanical relaxation, cell proliferation, and the equation governing the dynamics of the free boundary of the tissue. While our presentation focuses on this biological application, our approach is more broadly applicable across a range of scenarios where discrete models are approximated by approximate continuum-limit descriptions.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media 抑制双列维指数分数克尔介质中的孤子坍缩、调制不稳定性和流氓波激发
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0765
Ming Zhong, Yong Chen, Zhenya Yan, B. Malomed
We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1   α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.
我们为激光系统中光脉冲的传播引入了一个广义分数非线性薛定谔方程(FNLS),该方程包含两个分数色散/衍射项(由其莱维指数 α 1 α 2 ∈ ( 1 , 2 ] 量化),以及自聚焦或散焦克尔非线性。 以及自聚焦或失焦的克尔非线性。通过变分近似得到了一些基本孤子,并与数值结果进行了比较验证。我们发现,在只有一个莱维指数(LI)α = 1 的一维立方 FNLS 方程中出现的孤子坍缩现象,在双莱维指数 FNLS 系统中可以被抑制。此外,还探讨了孤子在与高斯脉冲碰撞和系统参数绝热变化时的稳定性。在双 LI 系统中还研究了连续波的调制不稳定性(MI)。特别是,当两个衍射系数的符号相反时,在散焦非线性情况下可能会出现调制不稳定性。利用 MI 的结果,我们在连续波的顶部产生了一阶和二阶流氓波,对于克尔非线性的两种符号都是如此。
{"title":"Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media","authors":"Ming Zhong, Yong Chen, Zhenya Yan, B. Malomed","doi":"10.1098/rspa.2023.0765","DOIUrl":"https://doi.org/10.1098/rspa.2023.0765","url":null,"abstract":"\u0000 We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices,\u0000 \u0000 \u0000 \u0000 α\u0000 \u0000 1\u0000 \u0000 \u0000  \u0000 \u0000 α\u0000 \u0000 2\u0000 \u0000 \u0000 ∈\u0000 (\u0000 1\u0000 ,\u0000 2\u0000 ]\u0000 \u0000 \u0000 , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI)\u0000 \u0000 \u0000 α\u0000 =\u0000 1\u0000 \u0000 \u0000 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.\u0000","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139638861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explorations of the holonomy of a rolling sphere 滚动球体的整体性探索
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0684
Theresa E. Honein, Oliver M. O’Reilly
Consider a rigid body rolling with one point in contact with a fixed surface. Now suppose that the instantaneous point of contact traces out a closed path. As a demonstration of a phenomenon known as holonomy, the body will typically not return to its original orientation. The simplest demonstration of this phenomenon in rigid body dynamics occurs in the motion of a rolling sphere and finds application to path planning and reorientation of spherical robots. Motivated by earlier works of Bryant and Johnson, we establish expressions for the change in orientation of a rolling sphere after completing a rectangular path. We use numerical methods to show that all possible changes in orientation are possible using a single rectangular path. Based on the Euler angle parameterization of a rotation, we develop a more intuitive method to achieve a desired orientation using three rectangular paths. With regards to applications, the paths we discuss can be employed to achieve any desired reorientation of a spherical robot.
考虑一个刚体在滚动时有一点与固定表面接触。现在假设瞬时接触点划出了一条封闭路径。为了证明一种被称为整体性的现象,刚体通常不会回到原来的方向。这种现象在刚体动力学中最简单的演示就是滚动球体的运动,并可应用于球形机器人的路径规划和重新定向。受布赖恩特和约翰逊早期研究的启发,我们建立了滚动球体完成矩形路径后方向变化的表达式。我们使用数值方法证明,使用单一矩形路径可以实现所有可能的方向变化。基于旋转的欧拉角参数化,我们开发了一种更直观的方法,利用三条矩形路径实现所需的方向。在应用方面,我们讨论的路径可用于实现球形机器人的任何所需的方向调整。
{"title":"Explorations of the holonomy of a rolling sphere","authors":"Theresa E. Honein, Oliver M. O’Reilly","doi":"10.1098/rspa.2023.0684","DOIUrl":"https://doi.org/10.1098/rspa.2023.0684","url":null,"abstract":"Consider a rigid body rolling with one point in contact with a fixed surface. Now suppose that the instantaneous point of contact traces out a closed path. As a demonstration of a phenomenon known as holonomy, the body will typically not return to its original orientation. The simplest demonstration of this phenomenon in rigid body dynamics occurs in the motion of a rolling sphere and finds application to path planning and reorientation of spherical robots. Motivated by earlier works of Bryant and Johnson, we establish expressions for the change in orientation of a rolling sphere after completing a rectangular path. We use numerical methods to show that all possible changes in orientation are possible using a single rectangular path. Based on the Euler angle parameterization of a rotation, we develop a more intuitive method to achieve a desired orientation using three rectangular paths. With regards to applications, the paths we discuss can be employed to achieve any desired reorientation of a spherical robot.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139640083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns 结合可展开和不可展开图案的混合折纸组件的几何力学原理
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0716
Kevin T. Liu, G. H. Paulino
Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.
折纸提供了一种将平面转化为复杂三维几何图形的方法,可应用于可部署结构、元材料、机器人等领域。三浦织和蛋盒是两种基本的平面折纸图案。人们对这两种图案进行了深入研究,它们已成为许多工程应用和衍生折纸图案的基础。在这里,我们研究了由三浦织纹和蛋盒图案的单元格组合而成的混合结构。我们找到了形成混合结构所需的相容性约束,并推导出其运动学特性,如自锁和泊松比。然后,我们将三浦-蛋盒混合结构的上述特性与三浦织纹和蛋盒纹的另一种概括--变形纹的特性进行比较。此外,我们还研究了将 Miura-ori、蛋盒和 morph 的所有三个单元格结合在一起所形成的结构。我们的研究结果表明,这种图案具有可调的自锁状态和泊松比,超出了其组成成分。由不同折纸图案组合而成的混合图案是一种从简单成分中衍生出更多工程应用功能的途径。
{"title":"Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns","authors":"Kevin T. Liu, G. H. Paulino","doi":"10.1098/rspa.2023.0716","DOIUrl":"https://doi.org/10.1098/rspa.2023.0716","url":null,"abstract":"Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study the hybrid structure formed by combining unit cells of the Miura-ori and eggbox patterns. We find the compatibility constraints required to form the hybrid structure and derive properties of its kinematics such as self-locking and Poisson’s ratio. We then compare the aforementioned properties of the Miura-eggbox hybrid with those of the morph pattern, another generalization of the Miura-ori and eggbox patterns. In addition, we study the structure formed by combining all three unit cells of the Miura-ori, eggbox and morph. Our results show that such patterns have tunable self-locking states and Poisson’s ratio beyond their constituent components. Hybrid patterns formed by combining different origami patterns are an avenue to derive more functionality from simple constituents for engineering applications.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139631592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scattering kernel of an array of floating ice floes: application to water wave transport in the marginal ice zone 浮冰阵列的散射核:应用于边缘冰区的水波传输
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2024-01-01 DOI: 10.1098/rspa.2023.0633
F. Montiel, M. H. Meylan, S. C. Hawkins
A radiative transfer model of water wave scattering in the marginal ice zone is considered. In this context, wave energy redistribution across the directional components of the spectrum as a result of scattering by the constituent ice floes is typically modelled via a scattering kernel describing the far-field directionality of the scattered wave field produced by a single floe in isolation. Recognizing the potential importance of the floe size distribution (FSD) on wave scattering, we propose an enhanced scattering kernel constructed from the far-field scattering pattern of a circular array of floes. This is achieved by solving the self-consistent multiple scattering of a time-harmonic plane wave by a large array of floating circular floes with radii sampled from a prescribed FSD. A fast multipole method is implemented to accelerate the numerical estimation of the solution. Simulations are then conducted to characterize the properties of the scattering kernel for a range of configurations. It is found that the scattering kernel obtained for a wide array has a large, narrow transmission peak in the forward direction, while it uniformizes low-amplitude scattered waves in other directions. An idealized application to radiative transfer theory is also considered.
研究考虑了边缘冰区水波散射的辐射传递模型。在这种情况下,由于组成浮冰的散射,波能在频谱的方向分量上重新分配,通常是通过描述单个浮冰产生的散射波场远场方向性的散射核来模拟的。由于认识到浮冰大小分布(FSD)对波散射的潜在重要性,我们提出了一种根据浮冰圆形阵列远场散射模式构建的增强型散射核。这是通过求解大型圆形浮体阵列对时谐平面波的自洽多重散射来实现的,浮体的半径从规定的 FSD 中采样。采用了快速多极法来加速解的数值估算。然后进行模拟,以确定一系列配置的散射核的特性。结果发现,在宽阵列中获得的散射核在正向有一个大而窄的传输峰值,而在其他方向则均匀分布着低振幅散射波。还考虑了辐射传递理论的理想化应用。
{"title":"Scattering kernel of an array of floating ice floes: application to water wave transport in the marginal ice zone","authors":"F. Montiel, M. H. Meylan, S. C. Hawkins","doi":"10.1098/rspa.2023.0633","DOIUrl":"https://doi.org/10.1098/rspa.2023.0633","url":null,"abstract":"A radiative transfer model of water wave scattering in the marginal ice zone is considered. In this context, wave energy redistribution across the directional components of the spectrum as a result of scattering by the constituent ice floes is typically modelled via a scattering kernel describing the far-field directionality of the scattered wave field produced by a single floe in isolation. Recognizing the potential importance of the floe size distribution (FSD) on wave scattering, we propose an enhanced scattering kernel constructed from the far-field scattering pattern of a circular array of floes. This is achieved by solving the self-consistent multiple scattering of a time-harmonic plane wave by a large array of floating circular floes with radii sampled from a prescribed FSD. A fast multipole method is implemented to accelerate the numerical estimation of the solution. Simulations are then conducted to characterize the properties of the scattering kernel for a range of configurations. It is found that the scattering kernel obtained for a wide array has a large, narrow transmission peak in the forward direction, while it uniformizes low-amplitude scattered waves in other directions. An idealized application to radiative transfer theory is also considered.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139634343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths 绕弯:波导拐角和迷宫对长波的反射和传输
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0635
P. A. Martin
Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission coefficients, correct to first order in the ratio of the waveguide width to the wavelength. Detailed results are given for sharp bends of arbitrary angle, including right-angled bends and hairpin bends. Applications to multiple scattering by labyrinthine structures are also made.
针对沿刚性管道的二维声波建立了长波渐近近似。声波受到障碍物、收缩、隆起和/或弯曲的散射。使用匹配渐近展开,需要计算阻塞系数,而阻塞系数是根据相关势流问题的解法定义的。重点是估算反射和透射系数,正确率为波导宽度与波长之比的一阶。详细结果适用于任意角度的急弯,包括直角弯和发夹弯。此外,还介绍了迷宫结构多重散射的应用。
{"title":"Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths","authors":"P. A. Martin","doi":"10.1098/rspa.2023.0635","DOIUrl":"https://doi.org/10.1098/rspa.2023.0635","url":null,"abstract":"Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission coefficients, correct to first order in the ratio of the waveguide width to the wavelength. Detailed results are given for sharp bends of arbitrary angle, including right-angled bends and hairpin bends. Applications to multiple scattering by labyrinthine structures are also made.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral wear modelling of rubber friction on a hard substrate with large surface roughness 橡胶在表面粗糙度较大的硬质基体上摩擦的光谱磨损模型
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0587
H. Tanaka, S. Yanagihara, K. Shiomi, T. Kuroda, Y. Oku
Soft-hard matter friction is a long-standing tribology problem that remains unclarified, requiring engineers to empirically predict the wear life. To clarify this issue, this study examines the transient running-in regime of rubber friction on a hard rough substrate and models the temporal wear progression using the spectrum curves of surface roughness for both materials. Performing a series of friction tests and three-dimensional surface-height measurements, the time-dependent behaviours of the power spectral densities (PSDs) are divided into two phases, namely the initial non-steady and long-term steady phases. The detailed spectral analyses of worn rubber surfaces in the initial phase lead to a blended PSD function between self-affine and K -correlation surface models, consisting of one variable (the Hurst exponent) that is saturated by the substrate self-affinity. Supported by the Greenwood–Williamson theory concerning rough contact mechanics, the volumetric estimate with the blended PSD function is used to assess the volume rate of wear debris in the steady phase, which is validated experimentally. These findings not only improve the wear predictions of soft materials from the initial measurements of worn surfaces but also help clarify the constrained multiscale mechanism of wear.
软硬物质摩擦是一个长期存在的摩擦学问题,至今仍未得到澄清,需要工程师根据经验预测磨损寿命。为了澄清这一问题,本研究探讨了橡胶在硬质粗糙基体上的瞬态磨合机制,并利用两种材料的表面粗糙度频谱曲线建立了时间磨损进展模型。通过一系列摩擦试验和三维表面高度测量,功率谱密度(PSD)随时间变化的行为分为两个阶段,即初始非稳定阶段和长期稳定阶段。通过对初始阶段磨损橡胶表面的详细光谱分析,得出了介于自亲和表面模型和 K - 相关表面模型之间的混合 PSD 函数,该函数由一个变量(赫斯特指数)组成,该变量因基底自亲和而饱和。在格林伍德-威廉姆森粗糙接触力学理论的支持下,混合 PSD 函数的体积估计值被用于评估稳定阶段磨损碎片的体积率,并得到了实验验证。这些发现不仅改进了根据磨损表面的初始测量结果对软材料磨损的预测,还有助于阐明磨损的多尺度约束机制。
{"title":"Spectral wear modelling of rubber friction on a hard substrate with large surface roughness","authors":"H. Tanaka, S. Yanagihara, K. Shiomi, T. Kuroda, Y. Oku","doi":"10.1098/rspa.2023.0587","DOIUrl":"https://doi.org/10.1098/rspa.2023.0587","url":null,"abstract":"Soft-hard matter friction is a long-standing tribology problem that remains unclarified, requiring engineers to empirically predict the wear life. To clarify this issue, this study examines the transient running-in regime of rubber friction on a hard rough substrate and models the temporal wear progression using the spectrum curves of surface roughness for both materials. Performing a series of friction tests and three-dimensional surface-height measurements, the time-dependent behaviours of the power spectral densities (PSDs) are divided into two phases, namely the initial non-steady and long-term steady phases. The detailed spectral analyses of worn rubber surfaces in the initial phase lead to a blended PSD function between self-affine and <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> </jats:inline-formula> -correlation surface models, consisting of one variable (the Hurst exponent) that is saturated by the substrate self-affinity. Supported by the Greenwood–Williamson theory concerning rough contact mechanics, the volumetric estimate with the blended PSD function is used to assess the volume rate of wear debris in the steady phase, which is validated experimentally. These findings not only improve the wear predictions of soft materials from the initial measurements of worn surfaces but also help clarify the constrained multiscale mechanism of wear.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electrosteric, van der Waals and elastic interaction of polyelectrolyte hydrogels 聚电解质水凝胶的静电、范德华和弹性相互作用
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0541
Reghan J. Hill
The electrosteric interaction energy for a charged hydrogel and hard plane, and between two charged hydrogels is derived in the Debye–Hückel approximation. This is combined with a van der Waals potential that explicitly addresses the Hamaker constant for the solvent-mediated hydrogel interactions. Then, in the Derjaguin approximation, DLVO-type interaction potentials are provided for hydrogel and hard/rigid spheres, accounting for elastic deformation that accompanies adhesion. As examples, this furnishes the energy for cohesion of soft polyelectrolyte microspheres, and provides a quantitative interpretation for the adhesion of rigid latex spheres to a soft deformable hydrogel, as reported by Sato et al. (Sato et al. 2017 Sci. Rep. 7 , 1–10 ( doi:10.1038/s41598-017-06257-1 )). The theory demonstrates that weak van der Waals attraction of hydrogels is readily balanced by electrosteric interactions, e.g. making colloidal hydrogel dispersions less stable than their rigid-particulate counterparts.
根据 Debye-Hückel 近似法推导出了带电水凝胶与硬平面以及两个带电水凝胶之间的静电相互作用能。这与范德华势结合在一起,范德华势明确解决了溶剂介导的水凝胶相互作用的哈马克常数问题。然后,在德雅金近似中,为水凝胶和硬/刚性球提供了 DLVO 型相互作用势,并考虑到了伴随粘附而来的弹性变形。例如,这提供了软聚电解质微球的内聚能,并为硬质乳胶球粘附到软质可变形水凝胶提供了定量解释,如 Sato 等人的报告(Sato et al.该理论表明,水凝胶的弱范德华吸引力很容易被静电相互作用所平衡,例如,使胶体水凝胶分散体的稳定性低于其刚性颗粒对应物。
{"title":"Electrosteric, van der Waals and elastic interaction of polyelectrolyte hydrogels","authors":"Reghan J. Hill","doi":"10.1098/rspa.2023.0541","DOIUrl":"https://doi.org/10.1098/rspa.2023.0541","url":null,"abstract":"The electrosteric interaction energy for a charged hydrogel and hard plane, and between two charged hydrogels is derived in the Debye–Hückel approximation. This is combined with a van der Waals potential that explicitly addresses the Hamaker constant for the solvent-mediated hydrogel interactions. Then, in the Derjaguin approximation, DLVO-type interaction potentials are provided for hydrogel and hard/rigid spheres, accounting for elastic deformation that accompanies adhesion. As examples, this furnishes the energy for cohesion of soft polyelectrolyte microspheres, and provides a quantitative interpretation for the adhesion of rigid latex spheres to a soft deformable hydrogel, as reported by Sato <jats:italic>et al.</jats:italic> (Sato <jats:italic>et al.</jats:italic> 2017 <jats:italic>Sci. Rep.</jats:italic> <jats:bold>7</jats:bold> , 1–10 ( <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" ext-link-type=\"uri\" xlink:href=\"http://dx.doi.org/doi:10.1038/s41598-017-06257-1\">doi:10.1038/s41598-017-06257-1</jats:ext-link> )). The theory demonstrates that weak van der Waals attraction of hydrogels is readily balanced by electrosteric interactions, e.g. making colloidal hydrogel dispersions less stable than their rigid-particulate counterparts.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix factorizations and pentagon maps 矩阵因式分解和五边形映射
IF 3.5 3区 综合性期刊 Q1 Mathematics Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0276
Pavlos Kassotakis
We propose a specific class of matrices that participate in factorization problems that turn out to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang–Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order N = 2 matrices of this specific class are equivalent to the homogeneous normalization map . From order N = 3 matrices, we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang–Baxter maps.
我们提出了一类特殊的矩阵,它们参与的因式分解问题等价于恒定和缠绕(非恒定)五边形、反五边形或杨-巴克斯特映射,用非交换变量表示。具体而言,我们证明了这一特定类别的 N = 2 阶矩阵的因式分解等价于同质归一化映射。从 N = 3 阶矩阵中,我们得到了同质归一化映射的扩展,以及新颖的缠绕五边形、反五边形和杨-巴克斯特映射。
{"title":"Matrix factorizations and pentagon maps","authors":"Pavlos Kassotakis","doi":"10.1098/rspa.2023.0276","DOIUrl":"https://doi.org/10.1098/rspa.2023.0276","url":null,"abstract":"We propose a specific class of matrices that participate in factorization problems that turn out to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang–Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> </jats:inline-formula> matrices of this specific class are equivalent to the <jats:italic>homogeneous normalization map</jats:italic> . From order <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:math> </jats:inline-formula> matrices, we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang–Baxter maps.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140026508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
期刊
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1