Avalanches

In a sandpile at rest with a slope less than the angle of repose, static friction produces solid-like behavior: the material remains at rest even though gravitational forces create macroscopic stresses on its surface. If the pile is tilted several degrees above the angle of repose, grains start to flow, like in a fluid. However, this flow is clearly not that of an ordinary fluid because it only exists in a boundary layer at the pile's surface. We might view this flow, or any granular flow, as that of a dense gas since gases, too, are made up of discrete particles with negligible cohesive forces between them.

In this picture, a pile of mustard seeds has been tilted just past the angle at which grains begin to flow. Only seeds within the top few layers participate in the flow, as indicated by the blurred streaks in this exposure. The image, originally a black and white photograph, was colorized to highlight the motion of the top layers against the deeper, stationary (and hence brighter) layers. This image appeared as cover photo of the April 1996 issue of Physics Today.

Avalanches in sandpiles have become a fruitful metaphor for describing many other, and often more microscopic, dissipative dynamical systems, such as the motion of flux lines (vortex avalanches) in a type-II superconductor. Other, related nonlinear dynamical phenomena include breakdown in semiconductors at high electric fields, superconducting Josephson junction arrays, stick-slip friction on a microscopic scale and earth-quake dynamics on a macroscopic scale. Find out more about these connections in the review articles listed here.

• H. M. Jaeger, C.-h. Liu, and S. Nagel, "Relaxation at the Angle of Repose, Physical Review Letters, 62, 40 (1988).
• L. P. Kadanoff, S. R. Nagel, L. Wu, and S.-m. Zhou, "Scaling and Universality in Avalanches," Physical Review A, 39, 6527 (1989).
• H. M. Jaeger, C.-h. Liu, S. R. Nagel, and T. A. Witten, "Flow in Granular Materials: Self-Organized Non-Critical Behavior," in Relaxation and Related Topics in Complex Systems, I. A. Campbell and C. Giovannella, Eds. London: Plenum Press, 235 (1990).
• H. M. Jaeger, C.-h. Liu, S. R. Nagel, and T. A. Witten, "Friction in Granular Flows", Europhysics Letters, 11, 619 (1990).
• C.-h. Liu, H. M. Jaeger, and S. R. Nagel, "Finite Size Effects in a Sandpile", Physical Review A, 43, 7091 (1991).
• S. R. Nagel, "Instabilities in a Sandpile," Rev. Mod. Phys., 64, 321 (1992).

• R. J. Zieve, T. F. Rosenbaum, H. M. Jaeger, G. T. Seidler, G. W. Crabtree, and U. Welp, "Vortex Avalanches at One-Thousandth the Superconducting Transition Temperature", Physical Review B, 53, 11849 (1996).
• E. R. Nowak, O. W. Taylor, L. Liu, and H. M. Jaeger, "Magnetic Flux Instabilities in Superconducting Niobium Rings: Tuning the Avalanche Behavior", Phys. Rev. B, 55, 11702 (1997).