Patterns in a vertically oscillated granular layer: (1) lattice dynamics and melting, (2) noise-driven hydrodynamic modes, (3) harvesting large particles – Experiments • Dan Goldman (now Berkeley) • Mark Shattuck (now City U. New York) Harry Swinney University of Texas at Austin – Simulations • Sung Jung Moon (now Prince • Jack Swift outhern Workshop on Granular Materials ucón, Chile 0-13 December 2003
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Experiments Dan Goldman (now Berkeley) Mark Shattuck ( now City U. New York )
Southern Workshop on Granular Materials Puc ón, Chile 10-13 December 2003. Patterns in a vertically oscillated granular layer: (1) lattice dynamics and melting, (2) noise-driven hydrodynamic modes, (3) harvesting large particles. Experiments Dan Goldman (now Berkeley) - PowerPoint PPT Presentation
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Patterns in a verticallyoscillated granular layer:
(1) lattice dynamics and melting, (2) noise-driven hydrodynamic modes,
(3) harvesting large particles
– Experiments• Dan Goldman (now Berkeley)
• Mark Shattuck (now City U. New York)
Harry SwinneyUniversity of Texas at Austin
– Simulations• Sung Jung Moon (now Princeton)
• Jack Swift
Southern Workshop on Granular MaterialsPucón, Chile 10-13 December 2003
Particles in a vertically oscillating container
light
f = frequency (10-200 Hz) = (acceleration amplitude)/g = 42f2/g (2-8)
Square pattern
f = 23 Hzacceleration = 2.6g
Particles:bronze, d=0.16 mm
layer depth = 3d
1000d
OSCILLONS
peak
crater
• localized• oscillatory: f /2• nonpropagating• stable
Umbanhowar, Melo,& Swinney, Nature (1996)
Oscillons:no
interactionat a
distance
Oscillons: building blocks for moleculeseach molecule is shown in its two opposite phases
dimer tetramer
polymerchain
Oscillons:building blocks of a granular lattice?
each oscillon consists of
100-1000 particles
Dynamics of a granular lattice
18 cm
Goldman, Shattuck, Moon, Swift, Swinney, Phys. Rev. Lett. 90 (2003)
= 2.90, f = 25 Hz, lattice oscillation 1.4 Hz
snapshot snapshot: close uptime evolution
Coarse-graining of granular lattice:
2 2
| sin( ) |lattice BZ
kaff
frequency at edgeof Brillouin zone
A lattice of balls connected by Hooke’s law springs?
Then the dispersion relation would be:
where k is wavenumber and a is lattice spacing
Compare measured dispersion relation with lattice model
lattice model
fLattice
(Hz)
= 2.75
kBrillouin Zone(for (1,1)T modes)
From space-time FFT I(kx,ky,fL)
Create defects: make lattice oscillations large
= 2.9
FFT FFT FFTapply FM 52 cycles later 235 cycles laterDEFECTS
( ) sin[2 sin(2 )]msmr
mr
fy t A ft f t
f
modulationrate = 2 Hz
32 Hz
containerposition:
Resonant modulation: FM at lattice frequency:
Frequency modulate the container, and
add graphite to reduce friction MELTING
= 2.9, f = 32 Hz, fmr(FM) = 2 Hz
add graphite by 175 cycles: melted56 cycles later
MD simulation: reduce friction to zerocrystal melts (without adding frequency modulation)