论文标题
LIH分子中磁引起的电流密度中涡流的拓扑数据分析
Topological data analysis of vortices in the magnetically-induced current density in LiH molecule
论文作者
论文摘要
引入了一种新的在分子系统中磁引起的电流密度（MICD）中提取轴向（AV）和环形（TV）涡旋的新策略，并证明了其在LIH分子中的试验应用。它利用了AV和电视核心拓扑的差异，并涉及两个关键步骤：选择可以描述MICD中涡流核心及其后续拓扑分析的标量函数。选择的标量函数为$ω^{b_α} $，基于速度梯度$ω$方法在经典流量研究中已知。然后，使用拓扑数据分析（TDA）来分析$ω^{b_α} $标量场。特别是，TDA稳健地将该字段的不同拓扑特征分配给LIH：AV中的不同涡流类型，将最大值连接到域边界上的2个辅助，电视连接到输入数据的超级级别的1周期。两者都被提取为拓扑简化的$ω^{b_α} $标量字段的最多\ emph {持久性}特征。
A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-induced current density (MICD) in molecular systems is introduced, and its pilot application to LiH molecule is demonstrated. It exploits differences in the topologies of AV and TV cores and involves two key steps: selecting a scalar function that can describe vortex cores in MICD and its subsequent topological analysis. The scalar function of choice is $Ω^{B_α}$ based on the velocity-gradient $Ω$ method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the $Ω^{B_α}$ scalar field. In particular, TDA robustly assigns distinct topological features of this field to different vortex types in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles located on the domain's boundary, TV to a 1-cycle of the super-level sets of the input data. Both are extracted as the most \emph{persistent} features of the topologically-simplified $Ω^{B_α}$ scalar field.
