论文标题
部分可观测时空混沌系统的无模型预测
The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis
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。
This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom $f$ of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder-piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a mid year undergraduate student. We present simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and of the experimental data. We find $f(\textrm{He}) = 3.48 \pm 0.14$, $f(\textrm{N}_2) = 4.92 \pm 0.24$, $f(\textrm{Air}) = 4.96 \pm 0.25$, $f(\textrm{CO}_2) = 6.46 \pm 0.39$ at room temperature and atmospheric pressure. The results for CO$_2$ requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.
