论文标题

部分可观测时空混沌系统的无模型预测

Physical and chemical vertical structure of magnetostatic accretion disks of young stars

论文作者

Khaibrakhmanov, Sergey A., Dudorov, Alexander E., Vasyunin, Anton I., Kiskin, Mikhail Yu.

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。

The vertical structure of the accretion disks of young stars with fossil large-scale magnetic field is studied. The equations of magnetostatic equilibrium of the disk are solved taking into account the stellar gravity, gas and magnetic pressure, turbulent heating, and heating by stellar radiation. The modelled physical structure of the disk is used to simulate its chemical structure, in particular, to study the spatial distribution of CN molecules. The disk of the typical T Tauri star is considered. Simulations show that the temperature within the disk in the region $r<50$ au decreases with height and density profiles are steeper than in the isothermal case. Outside the `dead' zone, vertical profiles of the azimuthal component of the magnetic field are nonmonotonic, and the magnetic field strength maximum is reached within the disk. The magnetic pressure gradient can cause an increase in the disk thickness in comparison with the hydrostatic one. The CN molecule concentration is maximum near the photosphere and in the disk atmosphere where the magnetic field strength at chosen parameters is $\sim 0.01$ G. Measurements of the Zeeman splitting of CN lines in the submm range can be used to determine the magnetic field strength in these regions of accretion disks.

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