论文标题
部分可观测时空混沌系统的无模型预测
Analytic Solutions of Brans-Dicke Cosmology: Early Inflation and Late Time Accelerated Expansion
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 most general exact solutions of Brans-Dicke cosmology by choosing the scale factor "a" as the new independent variable. It is shown that a set of three field equations can be reduced to a constraint equation and a first order linear differential equation. Thus this new set of equations is solvable when one supplies one of the following pairs of functions: (Φ(a), \r{ho}(a)), (Φ(a), V(a)) or (Φ(a), H(a)). A universe with a single component energy-matter density is studied. It is seen that when there is no constant energy density, the Hubble function still contains a constant term which causes exponential expansion. This constant is expressed in terms of the initial values of the universe. An early universe and the present universe with dark energy are studied. In addition late time accelerated expansion is also explained with cosmic domain walls. If we take Brans-Dicke parameter w>4*10^4 formulas of the Hubble function reduce to solutions of ΛCDM cosmology. Therefore comparison of our results with recent observations of type Ia supernovae indicates that eighty-nine percent of present universe may consist of domain walls while rest is matter.
