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Issue 13, 2010
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Super-diffusion around the rigidity transition: Lévy and the Lilliputians

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Abstract

By analyzing the displacement statistics of an assembly of horizontally vibrated bi-disperse frictional grains in the vicinity of the jamming transition experimentally studied before (F. Lechenault, O. Dauchot, G. Biroli and J.-P. Bouchard, Europhys. Lett., 2008, 83, 46003), we establish that their superdiffusive motion is a genuine Lévy flight, but with a ‘jump’ size that is very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.

Graphical abstract: Super-diffusion around the rigidity transition: Lévy and the Lilliputians

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Article information


Submitted
12 Jan 2010
Accepted
25 Mar 2010
First published
26 May 2010

Soft Matter, 2010,6, 3059-3064
Article type
Paper

Super-diffusion around the rigidity transition: Lévy and the Lilliputians

F. Lechenault, R. Candelier, O. Dauchot, J.-P. Bouchaud and G. Biroli, Soft Matter, 2010, 6, 3059
DOI: 10.1039/C000802H

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