DIRECTIONAL SOLIDIFICATION AT HIGH-SPEED .2. TRANSITION TO CHAOS

This paper continues our analysis of various aspects of interface dyna mics in rapid solidification. The description is based on a local cont inuum model, relevant to both liquid crystals and conventional materia ls. It was derived in a preceding paper, where we dealt with primary a nd secondary instabilities evolving from an initially flat interface w hen the control parameter, a renormalized temperature gradient, is dec reased. Here we focus on more complex dynamic states arising from the interaction of different oscillatory modes. We find quasiperiodic moti on to occur when one of the oscillators is a (parity-breaking) driftin g mode. Quasiperiodicity precedes a transition to chaos, the route to which we describe in some detail. The absence or manifestation of mode locking as well as other interesting dynamic states are discussed. A second quasiperiodic scenario, where the control parameter is the wave number of the pattern, provides evidence that the transition to chaos via intermediate quasiperiodic states is generic for systems that pos sess the drift instability. Both chaotic regimes are briefly character ized, and Lyapunov exponents are computed for a variety of states. We find that all chaotic states have two vanishing Lyapunov exponents, a feature that we explain as a consequence of translational invariance. An implication is that the Lyapunov dimension of chaotic attractors ex ceeds three. Moreover, we find attractors whose dimension is larger th an four. All the considered chaotic states are purely temporal. An out look is given on interesting and important questions related to the lo ng-time behavior of our model on large length scales, where spatiotemp oral chaos is to be expected.