Postdoc: Extensive Spatiotemporal Chaos in Extended Nonequillibrium Systems

9503963 Bodenchatz本提案的目的是研究数值和解析的微观方程描述某些实验系统。 本研究将从三个方面展开，即对模拟实验进行定量比较，研究实验系统中的长度尺度和序参量，以及考察拓扑缺陷的出现和作用。 这个建议的一个具体目标是使用强大的并行计算设施，探索新的物理制度所描述的Boussinesq方程。 虽然以前已经模拟过这些方程，但这些模拟仅限于小系统、短积分时间、有限的固定分辨率或特定的边界条件。 通过将使用谱方法的代码与基于迭代方法（例如多重网格或类似共轭梯度的方法）的代码进行比较，我们将开发一种针对并行计算机优化的通用可扩展Boussinesq求解器，该求解器将允许对纵横比大于100的大型系统进行长时间积分。并且在各个方向上的分辨率均可调。 下一代对流代码将允许这项研究在扩展对流系统中对时空混沌进行详尽的探索，并且希望这些探索将构成朝着类似于平衡热力学的形式主义迈出的重要一步。

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.