Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献_第7页

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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-01-24 DOI: 10.1098/rspa.2023.0533

A. Coutant, B. Lombard

{"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":"48 1","pages":""},"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

Improved estimates for the number of non-negative integer matrices with given row and column sums 给定行和列和的非负整数矩阵数的改进估计值

IF 3.5 3区综合性期刊

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-01-24 DOI: 10.1098/rspa.2023.0470

Maximilian Jerdee, Alec Kirkley, M. E. J. Newman

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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-01-10 DOI: 10.1098/rspa.2023.0619

Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson

{"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":"22 1","pages":""},"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

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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0635

P. A. Martin

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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0587

H. Tanaka, S. Yanagihara, K. Shiomi, T. Kuroda, Y. Oku

{"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 <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>K</mml:mi> </mml:math> -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":"47 1","pages":""},"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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0541

Reghan J. Hill

{"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 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.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"23 1","pages":""},"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

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-12-13 DOI: 10.1098/rspa.2023.0276

Pavlos Kassotakis

引用次数: 0

Prediction of general high-order lump solutions in the Davey–Stewartson II equation Davey-Stewartson II方程中一般高阶块解的预测

IF 3.5 3区综合性期刊

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-12-06 DOI: 10.1098/rspa.2023.0455

Xue-Wei Yan, Haie Long, Yong Chen

{"title":"Prediction of general high-order lump solutions in the Davey–Stewartson II equation","authors":"Xue-Wei Yan, Haie Long, Yong Chen","doi":"10.1098/rspa.2023.0455","DOIUrl":"https://doi.org/10.1098/rspa.2023.0455","url":null,"abstract":"Under investigation in this work is the Davey–Stewartson (DS) II equation. Based on the Kadomtsev–Petviashvili (KP) reduction method and Schur polynomial theory, we construct the general high-order lump solutions. The prediction solutions consisting of fundamental lumps and their positions are derived by extracting leading-order asymptotics of the Schur polynomials of true solutions. When indexes of the solutions are chosen as different positive integer combinations, the prediction solutions at large time reflect two classes of lump patterns of the true solutions. The first class of lump pattern with triangle shape is analytically described by root structure of the Yablonskii–Vorob’ev polynomial. When time <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>t</mml:mi> </mml:math> evolves from large negative to large positive, the triangle lump reverses itself along the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>y</mml:mi> </mml:math> -direction. The second class of lump pattern consists of non-triangle in outer region, which is analytically described by non-zero root structure of the Wronskian–Hermit polynomial, together with possible triangle in the inner region, which is analytically described by root structure of the Yablonskii–Vorob’ev polynomial. In addition, the non-triangle lump pattern in outer regions rotates at an angle while the possible triangle lump pattern in the inner region reverses itself along the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>y</mml:mi> </mml:math> -direction when time <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>t</mml:mi> </mml:math> evolves from large negative to large positive. The obtained results improve our understanding of time evolution mechanisms of high-order lumps.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"263 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025145","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

Effective statistical control strategies for complex turbulent dynamical systems 复杂湍流动力系统的有效统计控制策略

3区综合性期刊

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0546

Jeffrey Covington, Di Qi, Nan Chen

{"title":"Effective statistical control strategies for complex turbulent dynamical systems","authors":"Jeffrey Covington, Di Qi, Nan Chen","doi":"10.1098/rspa.2023.0546","DOIUrl":"https://doi.org/10.1098/rspa.2023.0546","url":null,"abstract":"Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling the statistical features of a turbulent system offers a more robust and efficient approach. Crude first-order linear response approximations were typically employed in previous works for statistical control with small initial perturbations. This paper aims to develop two new statistical control strategies for scenarios with more significant initial perturbations and stronger nonlinear responses, allowing the statistical control framework to be applied to a much wider range of problems. First, higher-order methods, incorporating the second-order terms, are developed to resolve the full control-forcing relation. The corresponding changes to recovering the forcing perturbation effectively improve the performance of the statistical control strategy. Second, a mean closure model for the mean response is developed, which is based on the explicit mean dynamics given by the underlying turbulent dynamical system. The dependence of the mean dynamics on higher-order moments is closed using linear response theory but for the response of the second-order moments to the forcing perturbation rather than the mean response directly. The performance of these methods is evaluated extensively on prototype nonlinear test models, which exhibit crucial turbulent features, including non-Gaussian statistics and regime switching with large initial perturbations. The numerical results illustrate the feasibility of different approaches due to their physical and statistical structures and provide detailed guidelines for choosing the most suitable method based on the model properties.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"67 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515145","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: 1

Equivalent in-plane elastic moduli of honeycomb materials under hypergravity conditions 超重力条件下蜂窝材料的等效面内弹性模量

3区综合性期刊

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-11-01 DOI: 10.1098/rspa.2023.0638

Lei Wang, Guannan Wang, Chaofeng Lü

{"title":"Equivalent in-plane elastic moduli of honeycomb materials under hypergravity conditions","authors":"Lei Wang, Guannan Wang, Chaofeng Lü","doi":"10.1098/rspa.2023.0638","DOIUrl":"https://doi.org/10.1098/rspa.2023.0638","url":null,"abstract":"Honeycomb materials frequently encounter hypergravity conditions in both aerospace and biological contexts during phases such as launch, reentry or under centrifugal motion. The significant body force engendered by hypergravity induces alterations in the microstructure of honeycomb materials, which in turn, influences their macroscopic mechanical behaviour. Leveraging the stiffness of the beam element as a pivotal variable, we successfully derived the equivalent moduli of the honeycomb material under hypergravity conditions. We further proposed the concept of a ‘hypergravity factor’, elucidating that the density of the base material, the dimensions of honeycomb cells and the magnitude of the hypergravity contribute to amplifying hypergravity effects. The results, numerically validated through finite-element simulations, could be reduced to the case that neglects body force. The critical buckling load of the honeycomb material under hypergravity can be assessed by setting the derived moduli to zero. In the presence of hypergravity, a honeycomb material undergoes a transition into a gradient material along the hypergravity direction, thereby exacerbating anisotropy. This phenomenon is theoretically expected to occur in virtually all porous materials. The analytical framework adopted, which employs beam stiffness as an intermediary variable, facilitates the extension of these results to honeycomb materials which encompass beam elements with functional gradients or varying cross-sectional morphologies.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"39 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764574","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