Direct Measurement of Dendritic Array Stability

Stability of a uniformly spaced dendritic array against a spatial period doubling instability was studied through UV thermal perturbations of every other dendrite tip. We observed that above a critical pulling speed the array is stable against these perturbations and we measured decreasing decay rates of the perturbed mode as we approached the critical speed. In the linear regime, our measurements are qualitatively consistent with the Warren-Langer linear stability analysis for a dendritic array [J. A. Warren and J. S. Langer, Phys. Rev. A 42, 3518 (1990); Phys. Rev. E 47, 2702 (1993)], while in the nonlinear regime fitting to a third order amplitude equation shows that the transition is subcritical.