α₂ Close to Jamming
Close to Jamming
Glassy behavior starts at \( \phi \approx 0.55 – 0.59 \)
Jamming is at \( \phi \approx 0.64 \)
What happens if we go really close to jamming?
Permanent Caging
Floaters
Floaters
Step Distributions
Close to Jamming: | Glassy: |
\( \Delta \phi = \phi_J - \phi = -10^{-4} \) | \( \phi = 0.59 \), \( \Delta \phi = -0.05 \) |
 |  |
Floaters
Close to Jamming: | Glassy: |
Step Distributions
Close to Jamming: | Glassy: |
| |
Peak at \( 10^{-2} \) : Tight Cages | Peak at \( 10^{-1} \) : Caged Floaters |
Peak at \( 10^{-1} \) : Caged Particles | Peak at \( 10^{0} \) : Rearrangements |
Step Distributions Close to Jamming
Solid: Backbone | Dashed: Floaters | Thin Dotted: Both |
Rearrangements
Hypothesis: Micro-rearrangements and rearrangements occur at different values of \( \Delta \phi\), with \( \Delta \phi \) dependent on system size.
Micro-Rearrangements
Back to Glassy Behavior
System Size Dependence of \( \alpha_2 \)
System Size Dependence of \( \alpha_2 \)
Does \(\phi^\star \) increase with \(N\)?