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Dynamical correlations near dislocation jamming

Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value $σ=σ_c$. Nevertheless the nature of this transition has not been ascertained. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to $σ_c$, by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first passage time distribution exhibits scaling, and a related peak {\it dynamical} susceptibility $χ_4^*$ diverges as $χ_4^* \sim (σ-σ_c)^{-α}$, with $α\approx 1.1$. We relate this scaling to an avalanche description of the dynamics. While the static structural correlations are found to be independent of the external stress, we identify a diverging dynamical correlation length $ξ_y$ in the direction perpendicular to the dislocation glide motion.