  We study flow-induced enhancement of the speed of pulsating traveling fronts
for reaction-diffusion equations, and quenching of reaction by fluid flows. We
prove, for periodic flows in two dimensions and any combustion-type reaction,
that the front speed is proportional to the square root of the (homogenized)
effective diffusivity of the flow. We show that this result does not hold in
three and more dimensions. We also prove conjectures from [1,3,11] for cellular
flows, concerning the rate of speed-up of fronts and the minimal flow amplitude
necessary to quench solutions with initial data of a fixed (large) size
