Characterize the transition to overdamped modes

Characterize completely the transition to overdamped vibrational modes in damped jammed packings as the dimensionless grain-contact damping parameter becomes large.

Background

The paper analyzes damped vibrational modes in jammed packings primarily in the low-damping regime, where the modal structure remains broadly similar to that of weakly damped systems. The authors observe that increasing the dimensionless damping parameter shifts low-frequency and scattering modes and causes many scattering modes to become overdamped.

A complete description of how the mode spectrum changes through this transition is not provided, making the large-damping regime an explicitly identified unresolved problem.

References

Many of the scattering modes become overdamped (i.e., $\hat\omega_i=0$) as $\hat\gamma$ is increased further. We leave a complete characterization of the transition to overdamped modes for future study.

— Proximity to Jamming Governs Acoustic Attenuation in Damped Packings  (2608.28157 - Kawamura et al., 28 Aug 2026) in Section 3, paragraph following Fig. 3 (discussion of Fig. 3)

While we have characterized the modal structure of damped packings across a range of $\hat\gamma$ and $P$, a complete theoretical understanding of the scattering regime remains open. In particular, the residual pressure dependence of compression waves in both the viscous damping regime ($\hat{\alpha} \propto \hat{\gamma}\hat{\omega}2 \hat{P}{1/4}$) and scattering-dominated region ($\hat{\alpha} \propto \hat\gammab\hat{\omega} \hat{P}{1/4}$), as shown in Fig.~\ref{fig:compAttenuation}, and the transition to overdamped modes at large $\hat\gamma$ all warrant further investigation.

— Proximity to Jamming Governs Acoustic Attenuation in Damped Packings  (2608.28157 - Kawamura et al., 28 Aug 2026) in Section 4, final discussion paragraph