Multiscale Model. Simul.最新文献_第6页

How do degenerate mobilities determine singularity formation in Cahn-Hilliard equations? 简并迁移率如何决定Cahn-Hilliard方程中的奇点形成?

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1391249

Catalina Pesce, A. Münch

引用次数: 5

Quadrature by Parity Asymptotic eXpansions (QPAX) for scattering by high aspect ratio particles 高纵横比粒子散射的宇称渐近展开式正交

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21M1416801

C. Carvalho, A. Kim, L. Lewis, Zois Moitier

{"title":"Quadrature by Parity Asymptotic eXpansions (QPAX) for scattering by high aspect ratio particles","authors":"C. Carvalho, A. Kim, L. Lewis, Zois Moitier","doi":"10.1137/21M1416801","DOIUrl":"https://doi.org/10.1137/21M1416801","url":null,"abstract":"We study scattering by a high aspect ratio particle using boundary integral equation methods. This problem has important applications in nanophotonics problems, including sensing and plasmonic imaging. To illustrate the effect of parity and the need for adapted methods in presence of high aspect ratio particles, we consider the scattering in two dimensions by a sound-hard, high aspect ratio ellipse. This fundamental problem highlights the main challenge and provide valuable insights to tackle plasmonic problems and general high aspect ratio particles. For this problem, we find that the boundary integral operator is nearly singular due to the collapsing geometry from an ellipse to a line segment. We show that this nearly singular behavior leads to qualitatively different asymptotic behaviors for solutions with different parities. Without explicitly taking this nearly singular behavior and this parity into account, computed solutions incur a large error. To address these challenges, we introduce a new method called Quadrature by Parity Asymptotic eXpansions (QPAX) that effectively and efficiently addresses these issues. We first develop QPAX to solve the Dirichlet problem for Laplace's equation in a high aspect ratio ellipse. Then, we extend QPAX for scattering by a sound-hard, high aspect ratio ellipse. We demonstrate the effectiveness of QPAX through several numerical examples.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121567562","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: 0

Diffusive Limit of a Two-Dimensional Well-Balanced Scheme for the Free Klein-Kramers Equation 自由Klein-Kramers方程二维良好平衡格式的扩散极限

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/20M1337077

L. Gosse

引用次数: 3

Phase Transition and Asymptotic Behavior of Flocking Cucker-Smale Model 群集cucker - small模型的相变与渐近行为

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1399877

Xing-Bei Li

引用次数: 0

Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity 具有单调非线性的多尺度椭圆方程的迭代数值均匀化

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1389900

Xinliang Liu, Eric T. Chung, Lei Zhang

引用次数: 5

Metropolized Multiscale Forest Recombination for Redistricting 都市多尺度森林重划组合

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1406854

E. Autry, Daniel Carter, G. Herschlag, Zach Hunter, J. Mattingly

引用次数: 13

High-Frequency Homogenization for Electromagnetic Heating of Periodic Media 周期介质电磁加热的高频均匀化

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/20m1369415

J. M. Gaone, B. Tilley, V. Yakovlev

引用次数: 0

High Contrast Elliptic Operators in Honeycomb Structures 蜂窝结构中的高对比度椭圆算子

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1408968

M. Cassier, M. Weinstein

{"title":"High Contrast Elliptic Operators in Honeycomb Structures","authors":"M. Cassier, M. Weinstein","doi":"10.1137/21m1408968","DOIUrl":"https://doi.org/10.1137/21m1408968","url":null,"abstract":"We study the band structure of self-adjoint elliptic operators $mathbb{A}_g= -nabla cdot sigma_{g} nabla$, where $sigma_g$ has the symmetries of a honeycomb tiling of $mathbb{R}^2$. We focus on the case where $sigma_{g}$ is a real-valued scalar: $sigma_{g}=1$ within identical, disjoint\"inclusions\", centered at vertices of a honeycomb lattice, and $sigma_{g}=g gg1 $ (high contrast) in the complement of the inclusion set (bulk). Such operators govern, e.g. transverse electric (TE) modes in photonic crystal media consisting of high dielectric constant inclusions (semi-conductor pillars) within a homogeneous lower contrast bulk (air), a configuration used in many physical studies. Our approach, which is based on monotonicity properties of the associated energy form, extends to a class of high contrast elliptic operators that model heterogeneous and anisotropic honeycomb media. Our results concern the global behavior of dispersion surfaces, and the existence of conical crossings (Dirac points) occurring in the lowest two energy bands as well as in bands arbitrarily high in the spectrum. Dirac points are the source of important phenomena in fundamental and applied physics, e.g. graphene and its artificial analogues, and topological insulators. The key hypotheses are the non-vanishing of the Dirac (Fermi) velocity $v_D(g)$, verified numerically, and a spectral isolation condition, verified analytically in many configurations. Asymptotic expansions, to any order in $g^{-1}$, of Dirac point eigenpairs and $v_D(g)$ are derived with error bounds. Our study illuminates differences between the high contrast behavior of $mathbb{A}_g$ and the corresponding strong binding regime for Schroedinger operators.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121685276","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: 7

Estimation of the Koopman Generator by Newton's Extrapolation 用牛顿外推法估计库普曼发生器

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/20M1333006

R. Sechi, A. Sikorski, Marcus Weber

引用次数: 0

Finite Temperature Cauchy-Born Rule and Stability of Crystalline Solids with Point Defects 点状缺陷结晶固体的有限温度Cauchy-Born规则与稳定性

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/20m1341520

T. Luo, Yang Xiang, J. Yang

引用次数: 0