论文标题
部分可观测时空混沌系统的无模型预测
Isotopic Production Cross Sections in Proton-$^{12}$C Interactions for Energies from 10 MeV/N to 100 GeV/N
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。
Proton interactions with $^{12}$C nuclei are a frequent nuclear interaction leading to secondary radiation in tissues for space radiation and cancer therapy with protons or $^{12}$C beams. The fragmentation of $^{12}$C by protons produces a large number of heavy ion (A>4) target or projectile fragments often with high ionization density. Here we develop an analytical model of energy dependent proton-$^{12}$C cross sections for isotopic nuclei production. Using experimental data and a 2nd order optical model an accurate formula for the p-$^{12}$C absorption cross section from <10 MeV/n to >10 GeV/N is obtained. The energy dependence of the elemental and isotopic cross sections is modeled as multiplicities scaled to absorption cross section with average isotopic fractions estimated from experimental data. We show that this approach results in an accurate analytic formula model over the full energy range in Hadron therapy and space radiation protection studies.
