论文标题
纽顿后近似中的恒星结构模型
Stellar structure model in the post-Newtonian approximation
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 this work the influence of the post-Newtonian corrections to the equations of stellar structure is analysed. The post-Newtonian Lane-Emden equation follows from the corresponding momentum density balance equation. From a polytropic equation of state the solutions of the Lane-Endem equations in the Newtonian and post-Newtonian theories are determined and the physical quantities for the \textit{Sun}, for the white dwarf \textit{Sirius B} and for neutron stars with masses $M\simeq1.4M_\odot, 1.8M_\odot$ and $2.0M_\odot$ are calculated. It is shown that the post-Newtonian corrections to the fields of mass density, pressure and temperature are negligible for the \textit{Sun} and \textit{Sirius B}, but for stars with strong fields the differences become important. For the neutron stars analysed here the central pressure and the central temperature which follow from the post-Newtonian Lane-Emden equation are about fifty to sixty percent greater than those of the Newtonian theory and the central mass density is about three to four percent smaller.
