论文标题
部分可观测时空混沌系统的无模型预测
New total transmission modes of the Kerr geometry with Schwarzschild limit frequencies at complex infinity
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 addition to the well-known quasinormal modes, the gravitational modes of the Kerr geometry also include sets of total-transmission modes. Each mode can be considered as an element of a sequence of modes parameterized by the angular momentum of the black hole. One family of gravitational total-transmission modes of Kerr have been known for some time. Modes in this family connect to a Schwarzschild limit where the mode frequency is finite and purely imaginary. Recently, what was thought to be an additional branch of this original family of modes was discovered. However, this new branch is actually a part of one of two entirely new families of total-transmission modes. Modes in these new families, surprisingly, connect to a Schwarzschild limit where the mode frequencies exist at complex infinity. We have numerically constructed full sets of sequences of gravitational total-transmission modes for harmonic indices $\ell=[2,8]$. Using these numerical sequences, we have been able to construct analytic asymptotic expansions for the mode frequencies and their associated separation constants. The asymptotic expansion for the separation constant used in constructing the total-transmission modes seems to be valid for general complex values of the oblateness parameter.
