论文标题
部分可观测时空混沌系统的无模型预测
Ultimate speed of the supercurrent and its pairing mechanism
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。
Recently, the room-temperature superconductor (RTSC) was discovered as a two-dimensional (2D) square lattice made of a metal wherein positive charges, i.e. holes, were heavily concentrated. The experimental result for the critical magnetic field $H_{c}$ was fully consistent with the view on the RTSC that its lattice unit -- a metal island -- is filled with the Slater's atoms. Each Slater's atom has the expanded diameter of 14.5 nm in order to have perfect diamagnetism with the magnitude corresponding to a single flux quantum $ϕ_{0}$. Its expanded orbit is associated with the fine structure constant $α\approx \frac{1}{137}$. In this paper, another important critical value -- the critical current $I_{c}$ -- is reported. It was found that the supercurrent has achieved the ultimate speed of matter, i.e., the speed of light, $c$. Beginning with a warm-up exercise for the Bohr's atom, how the Slater's atom is formed and why the $c$ appears are shown. These considerations lead to a simple view on the pairing mechanism of superconductivity, which also gives an ample indication of the most mysterious physical number $α$. Finally, it is shown that the proposed pairing mechanism in terms of London's canonical momentum naturally generates the perfect diamagnetic $ϕ_{0}$ of the Slater's atom, and the superconducting energy gap $Δ$ is predicted.