Multiscale Model. Simul.最新文献_第5页

Rigidity Percolation in Disordered 3D Rod Systems 无序三维杆系的刚性渗流

Multiscale Model. Simul. Pub Date : 2021-03-23 DOI: 10.1137/21m1401206

Samuel Heroy, D. Taylor, F. Shi, M. Forest, P. Mucha

{"title":"Rigidity Percolation in Disordered 3D Rod Systems","authors":"Samuel Heroy, D. Taylor, F. Shi, M. Forest, P. Mucha","doi":"10.1137/21m1401206","DOIUrl":"https://doi.org/10.1137/21m1401206","url":null,"abstract":"In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological or mechanical percolation) is well-known to occur in many composites at a critical density that exceeds the conductivity percolation threshold. Conductivity percolation occurs as a consequence of contact percolation, which refers to the conducting particles' formation of a connected component that spans the composite. Rheological percolation, however, has evaded a complete theoretical explanation and predictive description. A natural hypothesis is that rheological percolation arises due to rigidity percolation, whereby a rigid component of inclusions spans the composite. We model composites as random isotropic dispersions of soft-core rods, and study rigidity percolation in such systems. Building on previous results for two-dimensional systems, we develop an approximate algorithm that identifies spanning rigid components through iteratively identifying and compressing provably rigid motifs -- equivalently, decomposing giant rigid components into rigid assemblies of successively smaller rigid components. We apply this algorithm to random rod systems to estimate a rigidity percolation threshold and explore its dependence on rod aspect ratio. We show that this transition point, like the contact percolation transition point, scales inversely with the average (aspect ratio-dependent) rod excluded volume. However, the scaling of the rigidity percolation threshold, unlike the contact percolation scaling, is valid for relatively low aspect ratio. Moreover, the critical rod contact number is constant for aspect ratio above some relatively low value; and lies below the prediction from Maxwell's isostatic condition.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134012096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Online adaptive algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method 约束能量最小化广义多尺度间断伽辽金法的在线自适应算法

Multiscale Model. Simul. Pub Date : 2021-03-03 DOI: 10.1137/21m1402625

Sai-Mang Pun, Siu Wun Cheung

引用次数: 1

Statistical Learning of Nonlinear Stochastic Differential Equations from Nonstationary Time Series using Variational Clustering 基于变分聚类的非平稳时间序列非线性随机微分方程的统计学习

Multiscale Model. Simul. Pub Date : 2021-02-24 DOI: 10.1137/21m1403989

V. Boyko, S. Krumscheid, N. Vercauteren

引用次数: 4

Higher order phase averaging for highly oscillatory systems 高振荡系统的高阶相位平均

Multiscale Model. Simul. Pub Date : 2021-02-23 DOI: 10.1137/21m1430546

W. Bauer, C. Cotter, B. Wingate

{"title":"Higher order phase averaging for highly oscillatory systems","authors":"W. Bauer, C. Cotter, B. Wingate","doi":"10.1137/21m1430546","DOIUrl":"https://doi.org/10.1137/21m1430546","url":null,"abstract":"We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is useful for deriving reduced models that can be solved numerically with more efficiency, since larger timesteps can be taken. Recently, Haut and Wingate (2014) introduced the idea of computing finite window numerical phase averages in parallel as the basis for a coarse propagator for a parallel-in-time algorithm. In this contribution, we provide a framework for higher order phase averages that aims to better approximate the unaveraged system whilst still filtering fast motions. Whilst the basic phase average assumes that the solution independent of changes of phase, the higher order method expands the phase dependency in a basis which the equations are projected onto. In this new framework, the original numerical phase averaging formulation arises as the lowest order version of this expansion. Our new projection onto functions that are $k$th degree polynomials in the phase gives rise to higher order corrections to the phase averaging formulation. We illustrate the properties of this method on an ODE that describes the dynamics of a swinging spring due to Lynch (2002). Although idealized, this model shows an interesting analogy to geophysical flows as it exhibits a slow dynamics that arises through the resonance between fast oscillations. On this example, we show convergence to the non-averaged (exact) solution with increasing approximation order also for finite averaging windows. At zeroth order, our method coincides with a standard phase average, but at higher order it is more accurate in the sense that solutions of the phase averaged model track the solutions of the unaveraged equations more accurately.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124865586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Inverse Random Potential Scattering for Elastic Waves 弹性波的逆随机势散射

Multiscale Model. Simul. Pub Date : 2021-02-14 DOI: 10.1137/22m1497183

Jianliang Li, Peijun Li, Xu Wang

引用次数: 1

Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients 具有退化黏度系数的不可压缩轴对称欧拉方程的势奇异形成

Multiscale Model. Simul. Pub Date : 2021-02-12 DOI: 10.1137/22m1470906

T. Hou, D. Huang

引用次数: 1

High Order Numerical Homogenization for Dissipative Ordinary Differential Equations 耗散常微分方程的高阶数值均匀化

Multiscale Model. Simul. Pub Date : 2021-02-06 DOI: 10.1137/21m1397003

Zeyu Jin, Ruo Li