Multi-scale Cycle Tracking in Dynamic Planar Graphs
This work addresses the need to understand cycles in force networks for granular materials, which is crucial for mechanical and kinematic properties, but it appears incremental as it adapts existing concepts from merge trees.
The paper tackled the problem of analyzing cycles in 2D force networks within granular materials to understand their evolution under external loads, and the result was a nested tracking framework that demonstrated effectiveness on experimental data from photoelastic disks.
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.