通过双重映射追踪颗粒材料力网络中多尺度循环的演化
Multi-scale Cycle Tracking in Dynamic Planar Graphs
- 构建力网络循环的分层追踪框架，利用对偶性连接分区与环结构
- 在实验获取的光弹性盘力网络上验证，可捕捉多尺度循环动态变化
- 适合研究颗粒材料力学行为或拓扑分析的研究者
本文提出一种用于分析颗粒材料中二维力网络循环的嵌套追踪框架。这些材料由相互作用的颗粒组成，其相互作用由力网络描述。理解不同尺度下的循环及其在外力作用下的演化，对揭示系统的力学与运动学特性至关重要。本方法通过将二维区域划分为由力网络中的循环所围成的片段，构建循环层次结构。我们借鉴了原本用于合并树的嵌套追踪图概念，利用这种划分与循环之间的对偶关系。该方法在两个由光弹性盘实验获得的力网络上得到了验证。
原文摘要 · Abstract (English)
This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding the cycles within these networks at various scales and their evolution under external loads is crucial, as they significantly contribute to the mechanical and kinematic properties of the system. Our approach involves computing a cycle hierarchy by partitioning the 2D domain into segments bounded by cycles in the force network. We can adapt concepts from nested tracking graphs originally developed for merge trees by leveraging the duality between this partitioning and the cycles. We demonstrate the effectiveness of our method on two force networks derived from experiments with photoelastic disks.
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