论文标题
部分可观测时空混沌系统的无模型预测
Equilibrium thermodynamic properties of binary hard-sphere mixtures from integral equation theory
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。
The binary additive hard-sphere mixtures have been studied by the Ornstein-Zernike integral equation coupled with the Martynov-Sarkisov (MS) closure approximation. Virial equation of state is computed in the MS approximation. The excess chemical potential for the mixture is evaluated with a closed-form expression based on correlation functions. The excess Helmholtz free energy is obtained using the Euler relation of thermodynamics. Moreover, these thermodynamic quantities are obtained by the Boublík-Mansoori-Carnahan-Starling-Leland (BMCSL) formulas. Our findings for pressure and excess chemical potential for a number of binary sets of the mixtures from the MS approximation show good agreements with those obtained by the BMCSL formulas and available data in literature, having a maximum deviation of $5\%$ for a packing fraction up to 0.5. The maximum deviation of the excess free energy obtained for the mixtures is shown to be $\sim 16\%$ for a packing fraction of 0.5. To our knowledge, this work presents an initial calculation of an excess chemical potential of the system in the MS approximation.
