界面网络中的受挫结
Frustrated junctions in interfacial networks
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中文总结 AI 辅助
本文揭示三维界面网络中四重节点处Herring条件虽各自满足但相互不兼容，导致无局部平衡几何，并给出半各向同性极限下的四面体边长约束，适用于泡沫、多晶、组织等。
中文摘要 AI 辅助
材料与生命系统中的界面网络通过界面和结点的运动与重排而演化。结点处的局部平衡要求界面力平衡。我们证明，在三维空间中，经典的三重线Herring条件是必要但不充分的：在四重节点处相交的四条三重线可能各自满足Herring平衡，但四个条件却相互不兼容。这样的受挫结点不存在可容许的局部平衡几何。在半各向同性极限下，六个界面能必须构成一个非退化四面体的边长，其可构造性由Cayley-Menger行列式决定。这一隐藏的相容性约束源于三维几何，并广泛适用于泡沫、多晶体、组织及其他界面网络。
英文摘要
Networks of interfaces in materials and living systems evolve through motion and rearrangement of interfaces and junctions. Local equilibrium at a junction requires interfacial force balance. We show that in three dimensions the classical Herring condition for triple lines is necessary but insufficient: four triple lines meeting at a quadruple node may each satisfy Herring equilibrium, while the four conditions remain mutually incompatible. Such a frustrated node has no admissible local equilibrium geometry. In the semi-isotropic limit, the six interfacial energies must form the edge lengths of a non-degenerate tetrahedron, with constructibility determined by the Cayley-Menger determinant. This hidden compatibility constraint arises from three-dimensional geometry and applies broadly to foams, polycrystals, tissues and other interfacial networks.
发表机构
- Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
- Integrated Dynamic Electron Solutions, Inc.（集成动态电子解决方案有限公司）
- Division of Solid Mechanics, Lund University（隆德大学固体力学系）
机构由 AI 辅助整理，请以论文原文为准。
