9503963 Bodenchatz The objective of this proposal is to study numerical and analytically the microscopic equations describing certain experimental systems. This research will take three directions, it will make quantitative comparisons between simulations experiments, study lengthscale and order parameters in experimental systems, and examine the appearance and role of topological defects. A specific goal of this proposal is to use the powerful parallel computing facilities to explore new physical regimes which are described by the Boussinesq equations. Although the equations have been simulated before, the simulations have been limited to small systems, short integration times, limited fixed resolution, or particular boundary conditions. By comparing a code using spectral methods to one based on iterative methods, such as multigrid or conjugate-gradient-like methods, we will develop a general scalable Boussinesq solver optimized for parallel computers that will allow long integrations of large systems with aspect ratios greater than 100 and with adjustable resolution in all directions. This next generation convection code will allow this research to perform exhaustive explorations of spatiotemporal chaos in extended convection systems, and, hopefully, these explorations will constitute a significant step toward a formalism similar to equilibrium thermodynamics.
