论文标题
部分可观测时空混沌系统的无模型预测
Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas
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。
In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental formula; while for relativistic particles, a general scattering theory was used which calculates S matrix. In this paper, Lippmann-Schwinger equation is applied uniformly to both low-momentum and relativistic particles. The cross sections are valuated to the first order of Born approximation. One-body time-independent Green's functions for relativistic free particles are given. Compared to the general scattering theory, the fundamental theory has a clearer physical picture and the approximations made are more explicit.
