Vibrational modes and spectrum of oscillators on a scale-free network

TL;DR

This paper investigates the vibrational modes and spectral properties of a model system of atoms connected by springs on a scale-free network, aiming to understand excitations in complex networked systems.

Contribution

It introduces a model of atoms and springs on a scale-free network to analyze vibrational modes and spectra, providing insights into excitations in such complex structures.

Findings

Characterization of vibrational spectra on scale-free networks

Identification of unique vibrational modes influenced by network topology

Insights into energy propagation in networked oscillator systems

Abstract

We study vibrational modes and spectrum of a model system of atoms and springs on a scale-free network in order to understand the nature of excitations with many degrees of freedom on the scale-free network. We assume that the atoms and springs are distributed as nodes and links of a scale-free network, assigning the mass $M_{i}$ and the specific oscillation frequency $\omega_{i}$ of the $i$-th atom and the spring constant $K_{ij}$ between the $i$-th and $j$-th atoms.