9 research outputs found
Ordering and finite-size effects in the dynamics of one-dimensional transient patterns
We introduce and analyze a general one-dimensional model for the description
of transient patterns which occur in the evolution between two spatially
homogeneous states. This phenomenon occurs, for example, during the
Freedericksz transition in nematic liquid crystals.The dynamics leads to the
emergence of finite domains which are locally periodic and independent of each
other. This picture is substantiated by a finite-size scaling law for the
structure factor. The mechanism of evolution towards the final homogeneous
state is by local roll destruction and associated reduction of local
wavenumber. The scaling law breaks down for systems of size comparable to the
size of the locally periodic domains. For systems of this size or smaller, an
apparent nonlinear selection of a global wavelength holds, giving rise to long
lived periodic configurations which do not occur for large systems. We also
make explicit the unsuitability of a description of transient pattern dynamics
in terms of a few Fourier mode amplitudes, even for small systems with a few
linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende
Numerical study of pattern formation following a convective instability in non-Boussinesq fluids
We present a numerical study of a model of pattern formation following a
convective instability in a non-Boussinesq fluid. It is shown that many of the
features observed in convection experiments conducted on gas can be
reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The
formation of hexagonal patterns, rolls and spirals is studied, as well as the
transitions and competition among them. We also study nucleation and growth of
hexagonal patterns and find that the front velocity in this two dimensional
model is consistent with the prediction of marginal stability theory for one
dimensional fronts.Comment: 9 pages, report FSU-SCRI-92-6
Dynamics of ordering processes in annealed dilute systems: Island formation, vacancies at domain boundaries, and compactification
Coarsening of solid-liquid mixtures in a random acceleration field
The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future