论文标题
部分可观测时空混沌系统的无模型预测
Coulombic Surface-Ion Interactions Induce Nonlinear and Chemistry-Specific Charging Kinetics
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。
While important for many industrial applications, chemical reactions responsible for charging of solids in water are often poorly understood. We theoretically investigate the charging kinetics of solid-liquid interfaces, and find that the time-dependent equilibration of surface charge contains key information not only on the reaction mechanism, but also on the valency of the reacting ions. We construct a non-linear differential equation describing surface charging by combining chemical Langmuir kinetics and electrostatic Poisson-Boltzmann theory. Our results reveal a clear distinction between late-time (near-equilibrium) and short-time (far-from-equilibrium) relaxation rates, the ratio of which contains information on the charge valency and ad- or desorption mechanism of the charging process. Similarly, we find that single-ion reactions can be distinguished from two-ion reactions as the latter show an inflection point during equilibration. Interestingly, such inflection points are characteristic of autocatalytic reactions, and we conclude that the Coulombic ion-surface interaction is an autocatalytic feedback mechanism.
