ORDERING AND FINITE-SIZE EFFECTS IN THE DYNAMICS OF ONE-DIMENSIONAL TRANSIENT PATTERNS

We introduce and analyze a general one-dimensional model for the descr iption of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, dur ing the Freedericksz transition in nematic liquid crystals. The dynami cs leads to the emergence of finite domains that are locally periodic and independent of each other. This picture is substantiated by a fini te-size scaling law for the structure factor. The mechanism of evoluti on towards the final homogeneous state is by local roll destruction an d associated reduction of local wave number. The scaling law breaks do wn for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear se lection of a global wavelength holds, giving rise to long-lived period ic configurations which do not occur for large systems. We also make e xplicit the unsuitability of a description of transient pattern dynami cs in terms of a few Fourier mode amplitudes, even for small systems w ith a few linearly unstable modes.