论文标题

部分可观测时空混沌系统的无模型预测

Order and density fluctuations near the boundary in sheared dense suspensions

论文作者

Miller, Joia M., Blair, Daniel L., Urbach, Jeffrey S.

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。

We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension, observing modest shear-induced ordering and a nearly linear flow profile. At high concentration ($ϕ= 0.55$) and applied stress just below shear thickening, we report ordering fluctuations with high temporal resolution, and directly measure a decrease in order with distance from the suspension's bottom boundary as well as a direct correlation between order and particle concentration. Higher applied stress produces shear thickening with large fluctuations in boundary stress which we find are accompanied by dramatic fluctuations in suspension flow speeds. The peak flow rates are independent of distance from the suspension boundary, indicating that they likely arise from transient jamming that creates solid-like aggregates of particles moving together, but only briefly because the high speed fluctuations are interspersed with regions flowing much more slowly, suggesting that shear thickening suspensions possess complex internal structural dynamics, even in relatively simple geometries.

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