Frequency clustering and disaggregation in idealized fractal tree

TL;DR

This paper investigates how resonant frequency clusters form in idealized fractal trees using numerical modeling, revealing the influence of topology and symmetry on modal characteristics and robustness to structural perturbations.

Contribution

It demonstrates the relationship between frequency clustering, network topology, and symmetry in idealized fractal trees, highlighting robustness and percolation phenomena.

Findings

Larger frequency clusters correlate with Small World Network properties.

Topology and symmetry govern modal compartmentalization and robustness.

Perturbations above a threshold cause percolation of the largest cluster.

Abstract

The pattern of formation of resonant frequency clusters in idealized sympodial dichasium trees is revealed by numerical modeling and analysis. The larger cluster's cardinality correlates with that of a Small World Network, which share the same adjacency matrix. Topology and inherent symmetry of the structure dictate compartmentalization of the modal characteristics and robustness to perturbations to the limb geometry, and are not limited to a specific allometry. When the spatial symmetry of the limb geometry is perturbed above a certain level, we see percolation of the largest cluster.