Fig. 1.

Vibrational modes in the model amorphous solid. Plots of $g(\omega )/{\omega }^{d-1}$ and of the $O^k$, $P^k$, $\delta E^{k\parallel }$, and $\delta E^{k\perp }$ of each mode $k$ as functions of $\omega$. (A) The 3D model system ($d=\mathrm{\hspace{0.17em}3}$). (B) The 2D model system ($d=\mathrm{\hspace{0.17em}2}$). The packing pressure is $p=\mathrm{\hspace{0.17em}5}\times {\mathrm{\hspace{0.17em}10}}^{-2}$. Inset in the third image from the top in A and B presents the plot of $O^k$ vs. $P^k$. For the 3D system in A, $g_{\text{ex}}(\omega )$, the vDOS of extended modes ($P^k>{\mathrm{\hspace{0.17em}10}}^{-2}$) and $g_{\text{loc}}(\omega )$, which is that of localized modes ($P^k<{\mathrm{\hspace{0.17em}10}}^{-2}$), are also presented in A in the top image and Inset of the second image from the top.