Cellular multiplets in directional solidification

We report the existence of new branches of steady state cellular structures in directional solidification. These structures consist of repeating cellular subunits, or multiplets, each containing a set of distinct cells separated by unequal grooves. A detailed numerical study of the symmetric model of directional solidification reveals that all multiplets bifurcate off the main singlet solution branch in two sets. Two points on the main branch, one corresponding to the onset of the Eckhaus instability at small cell spacing and the other to a fold of this branch at large spacing, are argued to be separate accumulation points for each set of multiplets. The set of structures bifurcating near the fold are morphologically similar to experimentally observed multiplets. In contrast, those bifurcating near the Eckhaus instability do not resemble experimental shapes. Furthermore, they are argued to be generically unstable. copyright 1997 The American Physical Society