# Packing loops into annular cavities

## TL;DR

This study investigates how a flexible rod packs into annular cavities, revealing a relationship between rod length and domain count, and uncovers new fluctuation phenomena and fractal characteristics in the packing process.

## Contribution

It introduces an exponential model for rod packing in annular cavities, analyzing initial conditions, dynamics, and limits, and links packing behavior to topological and fractal properties.

## Key findings

- Exponential model accurately describes packing data
- Discovered a new fluctuation phenomenon during packing
- Fractal dimension analysis offers novel insights

## Abstract

The continuous packing of a flexible rod in two-dimensional cavities yields a countable set of interacting domains that resembles non-equilibrium cellular systems and belongs to a new class of light-weight material. However, the link between the length of the rod and the number of domains requires investigation especially in the case of non-simply connected cavities, where the number of avoided regions emulates an effective topological temperature. In the present article we report the results of an experiment of injection of a single flexible rod into annular cavities in order to find the total length needed to insert a given number of loops (domains of one vertex). Using an exponential model to describe the experimental data we quite minutely analyze the initial conditions, the intermediary behavior, and the tight-packing limit. This method allows the observation of a new fluctuation phenomenon associated with instabilities in the dynamic evolution of the packing process. Furthermore, the fractal dimension of the global pattern enters the discussion under a novel point of view. A comparison with the classical problems of the random close packing of disks, and jammed disk packings is made.