NONLINEAR DYNAMICS IN PERIODICALLY REPEATED SETS OF DIRECTIONAL SOLIDIFICATION CELLS

Numerical simulations of two-dimensional, spatially periodic cellular structures in directional solidification of a binary alloy show the existence of multiple steady-state, traveling-wave, and spatiotemporally chaotic structures in samples that admit up to eight cells. This variety of dynamics is observed within a small range of dimensionless growth rate P above the critical value P(c) and transitions occur on long time scales; both phenomena are linked to the shallow neutral stability curve, which controls the initial formation of cells. Traveling-wave states bifurcate supercritically from stationary cellular patterns and have lateral wave speeds that increase proportional to P-P(c), in agreement with the theory for traveling waves introduced by parity-breaking bifurcations.