Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator.

When external stresses in a system--physical, social or virtual--are relieved through impulsive events, it is natural to focus on the attributes of these avalanches. However, during the quiescent periods between them, stresses may be relieved through competing processes, such as slowly flowing water between earthquakes or thermally activated dislocation flow between plastic bursts in crystals. Such smooth responses can in turn have marked effects on the avalanche properties.

Bending crystals: emergence of fractal dislocation structures.

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar structures strikingly similar to those seen experimentally-reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. Our model provides a framework for understanding emergent dislocation structures on the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modeling program, and a new example of self-similar structure formation in nonequilibrium systems.