Nonlocal fractional Kardar-Parisi-Zhang dynamics of grain boundaries

The kinetic roughening of driven grain boundaries (GBs) is fundamentally mediated by the collective behavior of disconnections, whose long-range $1\mathrm{/}r$ elastic interactions distinguish them from conventional growing surfaces. Through large-scale molecular dynamics simulations and a nonlocal fractional Kardar-Parisi-Zhang (fKPZ) theory, we demonstrate that driven GBs undergo a sharp transition of morphology at the yield point, from the quenched Edwards-Wilkinson universality class ($H\approx 0.33$) to an anomalous fKPZ regime ($H\approx 0.8$), while the 1/r nonlocal elasticity manifests as the fractional relaxation of GB morphology. The results show that the avalanche noise arrests the gradient catastrophe induced by the KPZ nonlinearity. Governed by the nonlocal elastic kernels, the resulting morphology breaks the Gaussian self-affinity and parallels the universality class of dynamic fracture.