Slide 1
Last time:
focused, nonlocal response from embedding singularities
Force propagation in a simple solid: two pictures
Why study solids like this?
packed hard particles: solidity without elasticity
Bead-by-bead packing makes minimal connectivity
Stress-balanced medium has ray-like force propagation
Simulation verifies stress balance condition
Simulation reveals wild heterogeneity
Simulation confirms ray-like propagation
Summary: forces in jammed solids
Vibrations:
another anomalous feature of jammed materials
Squeeze-jammed grains Þexcess slow vibrations
OÕHern simulation: isotropic hard particle pack
How many lowest modes in a solid of size L?
Marginally jammed particles are isostatic
Nearly isostatic packings have free modes
Energy ¨ dynamical matrix ¨ normal modes
Constructing slow modes of
Trial modes account for excess slow modes
Deformed free mode picture agrees with marginally jammed simulation
Further implications of deformed free modes
Properties of marginal modes
Frequency spacing probes vibrational coupling
Marginal modes without packing: randomized square network
randomized square lattice
reproduces properties of packed spheres vibrations
How do marginal modes transmit energy, momentum
energy current around a particle
Spatial distribution of energy current in randomized square lattice
Profile of energy current lacks correlation
Ray-like force propagation and isotropic packs
Randomized square lattice shows ray propagation
Conclusions
Slide 34
How compression dictates new contacts
Trial modes in real system
Slide 37