作为一级跃迁的发电机起始：磁流体动力学壳模型的教训
Dynamo Onset as a First-Order Transition: Lessons from a Shell Model for Magnetohydrodynamics
摘要：
本文对磁流体动力学（MHD）湍流壳模型中的发电机作用在磁普朗特数$Pr_{\rm M}$和磁雷诺数$Re_{\rm M}$的宽范围内进行了系统的、高分辨率的研究。我们的研究表明，这是很自然的发电机开始认为是一个非平衡，一阶相变之间的两个不同的湍流，但统计稳定的状态。磁能和动能之比是这种转变的一个方便的序参量。利用这个序参量，我们得到了$(Pr^{-1}_{\rm M}, Re_{\rm M})$平面内MHD壳模型中发电机形成的稳定性图（或非平衡相图）。发电机边界，发电机和非发电机区域分开，似乎有分形特征。我们得到的滞后行为的序参量跨越这个边界和建议的成核型现象。
英文摘要：
We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number $Pr_{\rm M}$ and the magnetic Reynolds number $Re_{\rm M}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $(Pr^{-1}_{\rm M}, Re_{\rm M})$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
