论文标题
部分可观测时空混沌系统的无模型预测
Equation of State and Joule-Thomson Expansion for the FRW Universe in the Brane World Scenario
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 study the thermodynamic properties of the Friedmann-Robertson-Walker (FRW) universe in the brane world scenario, concentrating on the Randall-Sundrum II model. From the first law of thermodynamics for the FRW universe, we find that the work density W can be identified with the thermodynamic pressure P. We construct the equation of state P=P(V,T) for the FRW universe in the brane world scenario, which does not show P-V phase transition. We further study the Joule-Thomson expansion of the FRW universe, and derive the Joule-Thomson coefficient, which has an inversion point that is affected by the brane tension. These results could provide new ways to test the brane world scenario and extra dimension.
