论文标题
部分可观测时空混沌系统的无模型预测
Ferrofluid drop impacts and Rosensweig peak formation in a non-uniform magnetic field
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Vertical drop impacts of ferrofluids onto glass slides in a non-uniform magnetic field have been studied using high-speed photography. Outcomes have been classified based on the motion of the fluid-surface contact lines, and formation of peaks (Rosensweig instabilities) which affect the height of the spreading drop. The largest peaks are nucleated at the edge of a spreading drop, similarly to crown-rim instabilities in drop impacts with conventional fluids, and remain there for an extended time. Impact Weber numbers ranged from 18.0 to 489, and the vertical component of the B-field was varied between 0 and 0.37 T at the surface by changing the vertical position of a simple disc magnet placed below the surface. The falling drop was aligned with the vertical cylindrical axis of the 25 mm diameter magnet, and the impacts produced Rosensweig instabilities without splashing. At high magnetic field strengths a stationary ring of ferrofluid forms approximately above the outer edge of the magnet.
