论文标题
部分可观测时空混沌系统的无模型预测
Local Hard-Sphere Poisson-Nernst-Planck Models for Ionic Channels with Permanent Charges
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 main goal of this work is to examine the qualitative effect of ion sizes via a steady-state boundary value problem. We study a one-dimensional version of a Poisson-Nernst-Planck system with a local hard-sphere potential model for ionic flow through a membrane channel with fixed boundary ion concentrations and electric potentials. A complete set of integrals for the inner system is illustrated that delivers information for boundary and internal layers. In addition, a group of simultaneous equations appears in the construction of singular orbits. The research aims to set up a simple formation defined by the profile of permanent charges with two mobile ion species, one positively charged, cation, and one negatively charged, anion. A local hard-sphere potential that depends pointwise on ion concentrations is included in the model to estimate ion-size impacts on the ionic flow. The analysis is built on the geometric singular perturbation theory, particularly on specific structures of this concrete model. For 1:1 ionic mixtures, we first conduct precise mathematical analysis and derive a matching system of nonlinear algebraic equations. We then extend the results by directing on a critical case where the current is zero. Treating the ion sizes as small parameters, we derive an approximation of zero-current fluxes for general values of permanent charge. We then focus on small values of permanent charge to obtain more concrete outputs. We will also examine ion size effects on the flow rate of matter for the zero-current case.
