Patterns often spontaneously appear in systems containing an energy source and a sink. Some examples are the convection rolls that appear when fluid is heated from below or the stripes seen in clouds on a windy day. We study the patterns that form on the surface of a vertically oscillated layer of grains. Here, the energy source is the moving container and the sink is the dissipative collisions between the grains.

We explore the pheonomena using a container of uniform spherical particles of different materials including steel, brass, and lead. The layer is vibrated using an electromechanical shaker. Patterns are visualized by shining light on the surface at an angle. Thus peaks will appear light and valleys dark.

Figure 1 Experimental setup.	Figure 2 Pattern illumination by LED ring.

We also have developed a molecular dynamics simulation to study shaken granular material. This code was originally developed to reproduce the surface wave patterns seen in experiment, but has since been used to investigate many qualities of granular media. The code solves Newton's equations with gravity to calculate the trajectories of the particles. The dynamics of the collisions are modeled using the collision operator proposed by O.R. Walton in Particulate Two-Phase Flow. The particles in the simulation are frictional spheres that rotate.

Typical patterns seen in the experiments and simulations can be seen below. The shape of the pattern depends on the non-dimensional shaking acceleration, Γ, and the non-dimensional frequency, f*. The amplitude of the patterns depend on the shaking acceleration. If the container is shaken vigorously enough, chaotic patterns emerge. The phase diagram for the conditions at which the different patterns appear is also shown below.

Figure 3 Surface wave patterns in experiment and simulation	Figure 4 Phase diagram for granular surface wave patterns. Letters correspond to those in Figure 3.

1. P. B. Umbanhowar, F. Melo, and H. L. Swinney
"Periodic, aperiodic, and transient patterns in vibrated granular layers"
Physica A 249, 1-9 (1998).
[Journal URL], [pdf]

2. C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney
"Patterns in 3D vertically oscillated granular layers: simulation and experiment"
Phys. Rev. Lett. 80, 57-60 (1998).
[Journal URL], [pdf]

3. Daniel I. Goldman, M. D Shattuck, H. L. Swinney, and G. H. Gunaratne
"Emergence of Order in an Oscillating Granular Layer"
Physica A 306, 180-188 (2002).
[Journal URL], [pdf]

4. Sung Joon Moon, M. D. Shattuck, C. Bizon, D. I. Goldman, J. B. Swift, and H. L. Swinney
"Phase Bubbles and Spatiotemporal Chaos in Granular Patterns"
Phys. Rev. E 65, 011301, 1-10 (2002).
[Journal URL], [pdf], [ps]

5. Daniel I. Goldman, J. B. Swift, Harry L. Swinney
"Noise, coherent fluctuations, and the onset of order in an oscillated granular fluid"
Phys. Rev. Lett. 92, 174302, 1-4 (2004).
preprint at cond-mat/0308028, [Journal URL], [pdf], [ps]

6. Sung Joon Moon, J. B. Swift, and H. L. Swinney
"Role of friction in pattern formation in oscillated granular layers"
Phys. Rev. E 69, 31301, 1-6 (2004).
preprint at cond-mat/0308541, [Journal URL], [pdf], [ps]

7. J. Bougie, J. Kreft, J. B. Swift, Harry L. Swinney
"Onset of Patterns in an Oscillated Granular Layer: Continuum and Molecular Dynamics Simulations"
Phys. Rev. E 71, 21301, 1-9 (2005).
[Journal URL], [pdf], [ps]

These are just a sample of the publications from CNLD on pattern formation in grains. More are listed on the group's publication site.