GLOSSARY

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Given velocity vector 

LaTeX Math Inline
body{\vec {u}}=(u_x,u_y,u_z)
 the pathlines is a bunch of curves 
LaTeX Math Inline
body{\vec {r}}_s = \big( \, x_s, \, y_s, \, z_s \, \big) \in \mathbb{R}^3
, parametrized by real number the stem points
LaTeX Math Inline
bodys{\vec {r}}_{s0}
, and solving the following equation:

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