1. Granular Materials: A window to studying the Transition from a non-Newtonian Granular Fluid To A "Glassy" system: aka "The fluid-glass transition for hard spheres"
John Drozd and Dr. Colin Denniston

2. Velocity Savage and Jeffrey J. Fluid Mech. 130, 187, 1983. q
Collision rules for dry granular media as
modelled by inelastic hard spheres
As collisions become weaker
(relative velocity vn small),
they become more elastic.
C. Bizon et. al., PRL 80, 57, 1997.

3.  polydisperse monodisperse vy dvy/dt P y Polydispersity means
300 (free fall region)
Donev et al PRL96
"Do Binary Hard Disks
Exhibit an Ideal Glass
Transition?" 
polydisperse
monodisperse
250 (fluid region) vy
200 (glass region)
dvy/dt
150
P y
Polydispersity means
Normal distribution
of particle radii x z y
Donev et al PRE 71

4. The density in the glassy region is a constant.
In the interface between the fluid and the glass does the density approach the glass density exponentially?
0 = 0.9
0 = 0.95
0 = 0.99
Interface width seems to increase as 0  1  vy y
How does  depend on (1  0) ?

5. Density vs Height in Fluid-Glass Transition

6. Length Scale in Transition
"interface width diverges"
Slope =  0.007

7. Y Velocity Distribution Mono-disperse (crystallized) y only z x
300 (free fall region)
Poiseuille flow
250 (fluid region)
Plug flow
snapshot
200 (glass region)
Mono-disperse
(crystallized)
only
Mono
kink
fracture
150 y x z

8. Granular Temperature y x z 300 (free fall region) fluid
250 (fluid region)
235 (At Equilibrium
Temperature)
200 (glass region)
equilibrium
150 y
glass x z

9. Fluctuating and Flow Velocity
Experiment by
N. Menon and
D. J. Durian,
Science, 275, 1997.
16 x 16
32 x 32 v
Simulation results
In Glassy Region !
J.J. Drozd and
C. Denniston vf
Europhysics Letters, 76 (3), 360, 2006
"questionable" averaging over nonuniform regions gives 2/3

10.   1 in fluid glass transition
For 0 = 0.9,0.95,0.96,0.97,0.98,0.99
Subtracting of Tg and vc and not averaging over regions of different vx2
Down centre
Slope  =

11. "Particle Dynamics in
Sheared Granular Matter"
Physical Review Letters 85, Number 7, p. 1428
(2000)
Experiment:
(W. Losert, L. Bocquet,
T.C. Lubensky and
J.P. Gollub)

12. Velocity Fluctuations vs. Shear Rate
Slope =  0.018
Experiment
Slope = 0.4
From simulation
Must Subtract Tg !
Physical Review Letters 85, Number 7, (2000)

13. Conclusions
A gravity-driven hard sphere simulation was used to study the glass transition from a granular hard sphere fluid to a jammed glass.
We get the same 2/3 power law for velocity fluctuations vs. flow velocity as found in experiment, when each data point is averaged over a nonuniform region.
When we look at data points averaged from a uniform region we find a power law of 1 as expected.
We found a diverging length scale at this jamming (glass) to unjamming (granular fluid) transition. Silbert, Liu and Nagel (PRL 95, (2005)) also found diverging length scales near the unjamming transition for vibrations with jammed packings.
Finally, we compared our simulation to experiment on the connection between local velocity fluctuations and shear rate and found quantitative agreement.