Self-organized dendritic sidebranching in directional solidification: sidebranch coherence within uncorrelated bursts

We experimentally study the level of organization of dendritic sidebranching in directional solidification. For this, we extract successive interface positions at a fixed distance from the dendrite tips and we perform various correlation analyses. The sidebranching signals appear composed of randomly distributed bursts in which sidebranching coherence is surprisingly large and robust. This is attested by the large autocorrelation found in single bursts and the large cross-correlation found in any couple of bursts, even belonging to different sides of a dendrite or to different dendrites. However, the phase coherence of sidebranching breaks down at the transition between bursts. This restricts the coherence of extended sidebranching signals to a mean burst length and prevents the occurrence of large scale cross-correlation between them. This balanced view on sidebranching coherence stresses the capability of self-organization of dendrites in material science and sheds light on the nature of sidebranching on curved growing forms.