  We examine the behavior of the diffusion coefficient of the ST2 model of
water over a broad region of the phase diagram via molecular dynamics
simulations. The ST2 model has an accessible liquid-liquid transition between
low-density and high-density phases, making the model an ideal candidate to
explore the impacts of the liquid-liquid transition on dynamics. We locate
characteristic dynamical loci in the phase diagram and compare them with the
previously investigated thermodynamic loci. The low-density liquid phase shows
a crossover from non-Arrhenius to Arrhenius behavior, signaling the onset of a
crossover from fragile-to-strong behavior. We explain this crossover in terms
of the asymptotic approach of the low-density liquid to a random tetrahedral
network, and show that the temperature dependence of the diffusion coefficient
over a wide temperature range can be simply related to the concentration of
defects in the network. Our findings thus confirm that the low-density phase of
ST2 water is a well-defined metastable liquid.
