论文标题
部分可观测时空混沌系统的无模型预测
Design of acoustic diffraction plates for manipulating ultrasound in liquid Helium
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。
Many experiments in liquid Helium, such as the optical imaging of exploding electron bubbles, which enables research on individual particles under applied conditions, involve the usage of ultrasound generated by piezoelectric transducers. Previous studies either use planar transducers, which limits the maximum sound intensity and the spatial resolution, or curved transducers, which only allow observations at fixed foci and make it difficult to apply uniform electric fields. In this paper, we introduce the usage of acoustic diffraction plates in liquid Helium to amplify ultrasonic pressure oscillations at an arbitrary set of primary foci coupled with large counts of secondary foci, all of which can be freely moved around by changing the ultrasound frequency. The frequency dependence also allows us to generate controlled Faraday instabilities at the surface, which enables the generation of multi-electron bubbles with desired parameters.
