Title: Disordered Contact Networks in Jammed Packings of Frictionless Disks

Author (Talk): Kabir Ramola, Brandeis University

Abstract:

We study contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the packing that partitions space into convex regions which are uniquely assigned to grains or voids. This allows us to characterize the local spatial structure of the packing near the transition using well-defined geometric objects. We study these networks using simulations of bidispersed disks interacting via a one-sided linear spring potential. We find that several underlying geometric distributions are reproducible and display self averaging properties. We find that the total grain area is a reliable real space parameter that can serve as a substitute for the packing fraction. For bidispersed disks with diameter ratio 1:1.4, the unjamming transition occurs at a fraction of occupied area $A_G^{*} = 0.446(1)$. We determine scaling exponents for the transition as the energy of the system approaches zero $E_G \to 0^+$, and the coordination number $Z$ approaches its isostatic value. We find $\Delta A_G \sim \Delta {E_G}^{0.28(2)}$ and $\Delta A_G \sim \Delta Z^{1.00(1)}$, representing new structural critical exponents.