Postdoc: Extensive Spatiotemporal Chaos in Extended Nonequillibrium Systems

9503963波登恰兹这个提议的目的是研究描述某些实验系统的微观方程的数值和分析。本研究将沿着三个方向进行，将对模拟实验进行定量比较，研究实验系统中的长度、尺度和有序参数，以及考察拓扑缺陷的出现和作用。这项提议的一个具体目标是利用强大的并行计算设施来探索由Boussinesq方程描述的新的物理制度。虽然以前已经对这些方程进行了模拟，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。通过比较使用谱方法的代码和基于迭代方法(如多重网格或类共轭梯度方法)的代码，我们将开发一个针对并行计算机进行优化的通用可伸缩Boussinesq求解器，该求解器将允许对长宽比大于100的大系统进行长时间积分，并且在所有方向上具有可调的分辨率。下一代对流程序将允许这项研究对扩展对流系统中的时空混沌进行详尽的探索，希望这些探索将构成向类似平衡热力学的形式迈出的重要一步。

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.