发表机构
Einstein Institute of Mathematics, Hebrew University of Jerusalem; IST Austria（希伯来大学耶路撒冷分校爱因斯坦数学研究所; 奥地利科学技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对含向错、位错拓扑缺陷的薄弹性片，基于完全非线性三维模型推导能量标度律，获有限厚度模型的首批严格界，为相关物理猜想提供数学支撑。
AI 中文摘要
针对含拓扑缺陷（向错和位错）的薄弹性片，基于完全非线性三维模型推导能量标度律。对于向错，其标度律在厚度参数上是紧的，相比以往结果的改进在于同时适用于正负向错（e-锥），且明确给出缺陷参数的依赖关系；不过该依赖关系仍非紧的。对于含位错的薄体，据所知，这是有限厚度模型的首批严格界，当伯格斯矢量相对于厚度不大时是紧的，且与物理学文献中关于标度的著名猜想相关。主要工具是在非欧弹性框架中将这类体建模为无旋预应变的体，无旋性使我们能得到下界的几何刚性估计。
英文摘要
We derive energy scaling laws for thin elastic sheets with topological defects --- disclinations and dislocations --- for a fully nonlinear 3D model. For disclinations, the scaling laws are tight in the thickness parameter, and improve upon previous results by applying simultaneously to positive and negative disclinations (e-cones) and by giving an explicit dependence on the defect parameter; this latter dependence is, however, still not tight. For thin bodies with dislocations, these are, to the best of our knowledge, the first rigorous bounds for models of finite thickness, are tight when the Burgers vector is not large with respect to the thickness, and relate to a well-known conjecture from the physics literature about the scaling. A main tool is modeling these bodies in the framework of non-Euclidean elasticity, as bodies with a curl-free pre-strain; the curl-freeness allows us to obtain geometric rigidity estimates for the lower bounds.
Commentsvr. 2: Minor changes in the proofs of some lemmas
