Hyper-Objective Vortices
Hyper-Objective Vortices
复制标题
超客观漩涡
DOI：
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发表时间：
2020
影响因子：
5.2
通讯作者：
H. Theisel
中科院分区：
文献类型：
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作者：
Tobias Guenther;H. Theisel
矢量场的几乎所有属性，包括幅度、方向、<inline-formula><tex-math notation="LaTeX">$lambda _2$</tex-math><alternatives><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math><inline-graphic xlink:href="guenther-ieq1-2868760.gif"/></alternatives></inline-formula>和涡度，都会在观察者的任意运动下发生变化。这是不期望的，因为物理性质的测量理想地不应取决于（虚拟）测量设备移动的方式。有一些性质在某些类型的参考系变换下是不变的：伽利略不变性（在等速平移下的不变性）和客观性（在参考系的任何平滑旋转和平移下的不变性）。在本文中，我们引入了比客观性更难的条件：我们要求在任何光滑相似变换（旋转，平移和均匀尺度）下的不变性以及在参考系的任何光滑仿射变换下的不变性。我们表明，这些新的超客观的措施，允许提取的漩涡，改变它们的体积或变形。此外，我们提出了一个通用的方法，几乎任何涡措施转化为一个超客观的。我们将我们的方法应用于二维和三维矢量场的涡旋提取，并分析了伽利略不变量，目标和两个新的超目标方法的数值鲁棒性，提取时间和最小化残差。
Almost all properties of vector fields, including magnitude, direction, <inline-formula><tex-math notation="LaTeX">$lambda _2$</tex-math><alternatives><mml:math><mml:msub><mml:mi>λ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math><inline-graphic xlink:href="guenther-ieq1-2868760.gif"/></alternatives></inline-formula> and vorticity change under arbitrary movements of the observer. This is undesirable since measurements of physical properties should ideally not depend on the way the (virtual) measurement device moves. There are some properties that are invariant under certain types of reference frame transformations: Galilean invariance (invariance under equal-speed translation) and objectivity (invariance under any smooth rotation and translation of the reference frame). In this paper, we introduce even harder conditions than objectivity: we demand invariance under any smooth similarity transformation (rotation, translation and uniform scale) as well as invariance under any smooth affine transformation of the reference frame. We show that these new hyper-objective measures allow the extraction of vortices that change their volume or deform. Further, we present a generic approach that transforms almost any vortex measure into a hyper-objective one. We apply our methods to vortex extraction in 2D and 3D vector fields, and analyze the numerical robustness, extraction time and the minimization residuals for the Galilean invariant, objective, and the two new hyper-objective approaches.