## Title

**Vibrations in Jammed Solids: Beyond Linear Response**

## Speaker

**Corey O'Hern (Yale University)**

## Abstract

We propose a novel `phase diagram' for particulate systems
that interact via purely repulsive contact forces, such as granular
media and colloidal suspensions. We identify and characterize three
distinct classes of behavior as a function of the input kinetic
energy $T_0$ and packing fraction deviation from jamming onset $\Delta
\phi=\phi - \phi_J$ using molecular dynamics simulations of purely
repulsive frictionless disks. Iso-coordinated solids (ICS) can only
occur above jamming onset for $\Delta \phi > \Delta \phi_c(T_0)$; they
possess an average instantaneous coordination number that is greater
than the isostatic value required for mechanically stable packings.
ICS display harmonic vibrational response, where the density of
vibrational modes from the Fourier transform of the velocity
autocorrelation function is a set of $2N-2$ sharp peaks at the
eigenfrequencies associated with the dynamical matrix.
Hypo-coordinated solids (HCS) occur both above and below jamming
onset. For $\Delta \phi_c(T_0) > \Delta \phi > \Delta \phi_{cb}(T_0)$
(for $\Delta \phi >0$) and $|\Delta \phi| < \Delta \phi_{cb}(T_0)$
(for $\Delta \phi <0$), the network of interparticle contacts
fluctuates and the average coordination number is below the isostatic
value, but cage-breaking particle rearrangements do not occur. The
vibrational response of HCS is strongly nonharmonic. The density of
vibrational modes $D(\omega)$ for HCS is not a collection of sharp
peaks, and its precise form depends on the measurement method. For
$\Delta \phi < \Delta \phi_{cb}(T_0)$ ($\Delta \phi>0$) and $|\Delta
\phi| > \Delta \phi_{cb}(T_0)$ ($\Delta \phi<0$), particle
rearrangements occur, the structural relaxation time is finite, and
the density of vibrational modes resembles that for dense liquids with
nonzero intercept $D(0)$ and slope $D'(0) <0$ at zero frequency.
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