论文标题

部分可观测时空混沌系统的无模型预测

Dynamic surface tension of the pure liquid-vapor interface subjected to the cyclic loads

论文作者

Yu, Zhiyong, Lv, Songtai, Zhang, Xin, Liang, Hongtao, Xie, Wei, Yang, Yang

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 demonstrate a methodology for computationally investigating the mechanical response of a pure molten lead surface system to the lateral mechanical cyclic loads and try to answer the question: how dose the dynamically driven liquid surface system follow the classical physics of the elastic-driven oscillation? The steady-state oscillation of the dynamic surface tension under cyclic load, including the excitation of high frequency vibration mode at different driving frequencies and amplitudes, was compared with the classical theory of single-body driven damped oscillator. Under the highest studied frequency (50 GHz) and amplitude (5%) of the load, the increase of the (mean value) dynamic surface tension could reach ~5%. The peak and trough values of the instantaneous dynamic surface tension could reach (up to) 40% increase and (up to) 20% decrease compared to the equilibrium surface tension, respectively. The extracted generalized natural frequencies and the generalized damping constants seem to be intimately related to the intrinsic timescales of the atomic temporal-spatial correlation functions of the liquids both in the bulk region and in the outermost surface layers. These insights uncovered could be helpful for quantitative manipulation of the liquid surface tension using ultrafast shockwaves or laser pulses.

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