The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal (PFC) model. In the model, dislocations are naturally created, without any textit{ad hoc} creation rules, by applying a shearing force to the perf
ectly periodic ground state. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. By data collapsing the event energy probability density function for different shearing rates, a connection to interface depinning dynamics is confirmed. The relevant critical exponents agree with mean field theory predictions.
A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as
those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match well the measured shapes near the vent at the top of observed travertine domes. Closer to the base of the dome, the solutions deviate from observations, and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane, and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.
