Multi-scale Cycle Tracking in Dynamic Planar Graphs

TL;DR

This paper introduces a nested tracking framework for analyzing multi-scale cycles in 2D force networks of granular materials, revealing their evolution and role in system properties.

Contribution

It develops a novel cycle hierarchy computation method using domain partitioning and duality concepts, applied to granular force networks.

Findings

Effective cycle hierarchy extraction demonstrated on experimental data

Revealed multi-scale cycle evolution under external loads

Enhanced understanding of force network mechanics

Abstract

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.