Solitary waves in a chain of beads under Hertz contact

C. Coste, E. Falcon & S. Fauve

Laboratoire de Physique, École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France.

Reference:

Physical Review E, 56, 6104-6117 (1997)      An article within the collection: PRE Milestones DOI : http://journals.aps.org/pre/abstract/10.1103/PhysRevE.56.6104

Abstract:

We study experimentally the propagation of high-amplitude compressional waves in a chain of beads in contact, submitted or not to a small static force. In such a system, solitary waves have been theoretically predicted by Nesterenko [J. Appl. Mech. Tech. Phys. (USSR) 5, 733 (1984)]. We have built an impact generator in order to create high-amplitude waves in the chain. We observe the propagation of isolated nonlinear pulses, measure their velocity as a function of their maximum amplitude, for different applied static forces, and record their shape. In all experiments, we find good agreement between our observations and the theoretical predictions of the above reference, without using any adjustable parameter in the data analysis. We also show that the velocity measurements taken at three different nonzero applied static forces all lie on a single curve, when expressed in rescaled variables. The size of the pulses is typically one-tenth the total length of the chain. All the measurements support the identification of these isolated nonlinear pulses with the solitary waves predicted by Nesterenko.

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This article appears in the following collection:  PRE Milestones

Physical Review E published its 50,000th paper in September 2015. To celebrate this, the journal presents a series of milestone papers that were published since its inception in 1993. This is an eclectic collection of papers that made significant contributions to their field, chosen by the editors. A new milestone will be added each week.