论文标题
部分可观测时空混沌系统的无模型预测
Coherent Smith-Purcell $γ$-Ray Emission
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。
We investigate the Smith-Purcell emission produced by electron- or ion-beam-driven coherent excitation of nuclei arranged in periodic crystal lattices. The excitation and subsequent radiative decay of the nuclei can leave the target in the initial ground state after $γ$-ray emission, thus generating a coherent superposition of the far-field photon amplitude emanating from different nuclei that results in sharp angular patterns at spectrally narrow nuclear transition energies. We focus on Fe-57 as an example of two-level nuclear lossy system giving rise to Smith-Purcell emission at 14.4\,keV with a characteristic delay of 1.2\,ns relative to the excitation time. These properties enable a clean separation from faster and spectrally broader emission mechanisms, such as bremsstrahlung. Besides its fundamental interest, our study holds potential for the design of high-energy, narrow-band, highly-directive photon sources, as well as a means to store energy in the form of nuclear excitations.
