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John Drozd Colin Denniston Simulations of Collision Times In Gravity Driven Granular Flow bottom sieve particles at bottom go to top reflecting left and right walls periodic or reflecting front and back walls Snapshot of 2d simulation from paper: “Dynamics and stress in gravity-driven granular flow” Phys. Rev. E. Vol. 59, No. 3, March 1999 Colin Denniston and Hao Li 3d simulation

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Velocity q Collision rules for dry granular media as modelled by inelastic hard spheres As collisions become weaker (relative velocity v n small), they become more elastic.

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300 (free fall region) 250 (fluid region) 200 (glass region) 150

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300 (free fall region) 250 (fluid region) 200 (glass region) 150 Y Velocity Distribution Plug flow kink fracture Poiseuille flow

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Simulation of 16 by 16 system was performed by summer student Nehal Al Tarhuni Experiment by N. Menon and D. J. Durian, Science, 275, 1997. Simulation results Fluctuating and Flow Velocity v2v2 vfvf In Glassy Region !

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Simulation Experiment Quasi-1d Theory (Coppersmith, et al) (Longhi, Easwar) Impulse defined: Magnitude of momentum after collision minus momentum before collision. Related to Forces: Impulse Distribution Most frequent collisions contributing to smallest impulses

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Distribution of Impulses from "spheres in 2d" simulation fluid glass Exponent of 4

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Power Laws for Collision Times Similar power laws for 2d and 3d simulations! Collision time = time between collisions 1) spheres in 2d 2) 2d disks 3) 3d spheres

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Comparison With Experiment Figure from experimental paper: “Large Force Fluctuations in a Flowing Granular Medium” Phys. Rev. Lett. 89, 045501 (2002) E. Longhi, N. Easwar, N. Menon : experiment 1.5 vs. simulation 2.8 Discrepancy as a result of Experimental response time and sensitivity of detector. Experiment “Spheres in 2d”: 3d Simulation with front and back reflecting walls separated one diameter apart Pressure Transducer

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= 2.75 = 1.50 Probability Distribution for Impulses vs. Collision Times (log scale)

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random packing at early stage = 2.75 crystallization at later stage = 4.3 Is there any difference between this glass and a crystal? Answer: Look at Monodisperse grains Disorder has a universal effect on Collsion Time power law.

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Radius Polydispersity 2d disksSpheres in 2d 3d spheres 0 % (monodisperse) 4 4.3 3.4 15 % (polydisperse) 2.75 2.85 2.87 Summary of Power Laws

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Conclusions Power laws dependent on disorder. Using power laws can differentiate between granular fluid and glass. Can differentiate between granular glass and crystal! Is this universal?

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