Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg-Landau equation.
Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg-Landau equation.
复制标题
斜层对流时空混沌缺陷轨迹统计及复Ginzburg-Landau方程。
作者：
C. Huepe;Hermann Riecke;K. Daniels;E. Bodenschatz
对于复杂金兹堡-朗道方程（CGL）数值模拟和倾斜层对流（ILC）实验中观测到的时空混沌，我们报道了缺陷和缺陷环统计的数值和实验数据。这些回路由时空中的缺陷轨迹组成，它们通过成对湮灭或相关缺陷的产生相互连接。虽然大多数这样的环路很小，只包含一些缺陷，但环路分布函数只随着与环路大小相关的数量而缓慢衰减，符合幂律行为。对于CGL，在我们的计算精度范围内，发现三个幂律指数中的两个与先前对简单晶格模型的研究一致。在CGL和ILC的某些参数体系中，我们的单缺陷统计结果与先前报道的缺陷动力学与随机步行者的动力学一致的研究结果有显著的偏差，这些缺陷动力学与随机步行者的动力学一致，随机步行者以固定的概率产生并通过随机碰撞湮灭。
For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg-Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space-time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions.