article · 26/05/2010
Super-diffusion around the rigidity transition: Levy and the Lilliputians
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Résumé
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 Levy 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.
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Lechenault, F., Candelier, R., Dauchot, O., Bouchaud, J.-P., & Biroli, G. (2010). Super-diffusion around the rigidity transition: Levy and the Lilliputians. Soft Matter, 6(13). https://doi.org/10.1039/c000802h@article{Lechenault2010_12,
author = {Lechenault, Frederic and Candelier, Raphael and Dauchot, Olivier and Bouchaud, Jean-Philippe and Biroli, Giolio},
year = {2010},
month = {5},
title = {Super-diffusion around the rigidity transition: Levy and the Lilliputians},
journal = {Soft Matter},
publisher = {ROYAL SOC CHEMISTRY},
volume = {6},
number = {13},
address = {THOMAS GRAHAM HOUSE, SCIENCE PARK, MILTON RD, CAMBRIDGE CB4 0WF, CAMBS, ENGLAND},
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 Levy 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.},
url = {http://www.dx.doi.org/10.1039/c000802h},
doi = {10.1039/c000802h},
issn = {1744-683X},
}TY - JOUR
AU - Lechenault, Frederic
AU - Candelier, Raphael
AU - Dauchot, Olivier
AU - Bouchaud, Jean-Philippe
AU - Biroli, Giolio
PY - 2010
DA - 2010/05/26
TI - Super-diffusion around the rigidity transition: Levy and the Lilliputians
JO - Soft Matter
VL - 6
IS - 13
PB - ROYAL SOC CHEMISTRY
SN - 1744-683X
AB - 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 Levy 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.
DO - 10.1039/c000802h
UR - http://www.dx.doi.org/10.1039/c000802h
ER -