The Influence of Network Topology on Sound Propagation in Granular Materials

TL;DR

This study explores how the topology of force networks in granular materials influences sound propagation, revealing that different network diagnostics correlate with various phases of wave transmission and can identify key structural scales.

Contribution

The paper introduces the use of spatially-embedded network measures to analyze sound propagation in granular media, highlighting the role of meso-scale structures and phase-dependent network diagnostics.

Findings

Network diagnostics can probe structures at multiple scales.

Meso-scale community structure correlates with scattering phase.

Global efficiency relates to the injection phase of sound.

Abstract

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.