Dynamical heterogeneities

In the absence of an obvious structural order, the slowing down of the dynamics that occurs at the glass transition can be sought in the development of a spatial correlations in the dynamics of the system. It has therefore been proposed that the dynamics of density fluctuations, which controls the structural relaxation of the liquid, is heterogeneous in space. By defining an order parameter that characterizes the mean relaxation of the system, one can estimate the importance of these heterogeneities by analyzing the temporal fluctuations of this order parameter. We conducted this type of analysis during the thesis of Guillaume Marty in a two-dimensional granular system. We observed and characterized these fluctuations, but also directly visualized the dynamical heterogeneities. These heterogeneities are maximal for displacements of particles of the order of 10 ^ -1 diameter, which take place on times of the order of the liquid relaxation time.
Dauchot, O., Marty, G., & Biroli, G. (2005). Dynamical Heterogeneity Close to the Jamming Transition in a Sheared Granular Material. Prl, 95(26), 265701–4..
Subsequently, during the thesis of Raphael Candelier, we studied how the "jcage jumps » responsible for the relaxation of the liquid are organized in space and time. These are organized in compact clusters, which themselves avalanche over time to form the dynamical heterogeneities. This work is currently ongoing in collaboration with Giulio Biroli (CEA-Saclay), Andrea Liu (Penn U.) and François Landes.
Candelier, R., Dauchot, O., & Biroli, G. (2009). Building Blocks of Dynamical Heterogeneities in Dense Granular Media. Physical Review Letters, 102(8).
By investigating the dynamics at a higher surface fraction, near the surface fraction of jamming, during the thesis of Frederic Lechenault and Corentin Coulais, we were surprised to again observe heterogeneities of the dynamics, even on larger length-scales! However, these heterogeneities are of a different kind: they involve displacements of particles of the order of 10 ^ -3 diameter, which take place on the time scale of the vibrations. The presence of these heterogeneities, so deep in the glass phase, is linked to the existence of the Gardner’s phase.
Lechenault, F., Dauchot, O., Biroli, G., & Bouchaud, J.-P. (2008). Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass. EPL, 83, 46003
Coulais, C., Behringer, R. P., & Dauchot, O. (2012). Dynamics of the contacts reveals Widom lines for jamming. EPL (Europhysics Letters), 100(4), 44005.


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Mechanical Response of a Glass

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The Gardner’s phase

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