Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T08:27:00.569Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of Sand

Published online by Cambridge University Press:  29 November 2013

Per Bak  and
Michael Creutz
Get access

Extract

“Sand” represents a “state of matter” to which not much attention has been paid. A sand pile can be formed into different shapes; it can exist in many stable states, almost all of which are not the flat lowest energy state. Thus, sand contains memory; one can write letters in sand. If a heap of sand is perturbed, for instance by adding more sand, by tilting the pile, or by shaking it, the system goes from one metastable state to another. In some sense, this happens by a diffusion process, but this process is very different from the process which relaxes a glass of water to equilibrium after shaking. The diffusion process in sand can stop at any of many states, and the process is a threshold process, where nothing happens before the perturbation reaches a minimum magnitude.

The threshold dynamics of sand is a paradigm of many processes in nature. Earthquakes occur only when the stress somewhere on the crust of the Earth exceeds a critical value, and the earthquake takes the crust from one stable state to another. Economie systems are driven by threshold processes: the individual agents change their behavior only when certain factors reach a certain level. Biological species emerge or die when specifie conditions in the ecology are fulfilled. Neurons in a network fire when the input reaches a threshold level, etc.

Type
Technical Features
Information
MRS Bulletin , Volume 16 , Issue 6 , June 1991 , pp. 17 - 21
Copyright
Copyright © Materials Research Society 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bak, P., Tang, C., and Wiesenfeld, K., Phys. Rev. Lett. 59 (1987) p. 381; Phys. Rev. A 38 (1988) p. 364; P. Bak and K. Chen, Sci. Am. 264 (1) (1991) p. 48.CrossRefGoogle Scholar
2.Dhar, D. and Ramaswamy, R., Phys. Rev. Lett. 63 (1989) p. 1659; D. Dhar, Phys. Rev. Lett. 64 (1990) p. 1613; D. Dhar and S. N. Majumdar, J. Phys. A 23 (1990) p. 4333.CrossRefGoogle Scholar
3.Mandelbrot, B., The Fractal Geometry of Nature (W.H. Freeman, San Francisco, 1982).Google Scholar
4.Bak, P. and Chen, K., Physica D 38 (1989) p. 5.Google Scholar
5.Creutz, M., Computers in Physics (1991), in press.Google Scholar
6.Held, G.A., Solina, D.H., Keane, D.T., Haag, W.J., Horn, P.M., and Grinstein, G., Phys. Ren Lett. 65 (1990) p. 1120.CrossRefGoogle Scholar
7.Jaeger, H.M., Liu, C., and Nagel, S.R., Phys. Rev. Lett. 69 (1989) p. 40.CrossRefGoogle Scholar
8.Kagan, Y.Y., “Seismic Moment Distribution,” preprint.Google Scholar
9.Bak, P. and Tang, C., J. Geophys. Res. B 94 (1989) p. 15,635; K. Ito and M. Matsuzaki, J. Geophys. Res. B 95 (1989) p. 6853; A. Sornette and D. Sornette, Europhys. Lett. 9 (1989) p. 192; K. Chen, P. Bak, and S.A. Obukhov, Phys. Rev. A 43 (1991) p. 625.CrossRefGoogle Scholar
10.Babcock, K.L. and Westervelt, R.M., Phys. Rev. Lett. 64 (1989) p. 2168.CrossRefGoogle Scholar
11.Che, X. and Suhl, H., Phys. Rev. Lett. 64 (1989) p. 1670.CrossRefGoogle Scholar
12.Bak, P., Chen, K., Scheinkman, J., and Woodford, M. (1991), preprint.Google Scholar
13.Kauffman, S. A. and Johnson, S., “Co-evolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Co-evolutionary Avalanches” (1991), preprint.Google Scholar
14.Bak, P., Chen, K., and Tang, C., Phys. Lett. 147 (1990) p. 297; L.P. Kadanoff, Phys. Today 44 (3) (1991) p. 9.CrossRefGoogle Scholar
15.Bobrov, W. S. and Lebyodkin, M., private communication.Google Scholar