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Figure 1:
A “timeline” focussed on the topics covered in this review, including chemists, engineers, mathematicians, philosophers, and physicists who have contributed to the development of non-relativistic fluids, their relativistic counterparts, multi-fluid versions of both, and exotic phenomena such as superfluidity. |
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Figure 2:
A schematic illustration of two possible versions of parallel transport. In the first case (a) a vector is transported along great circles on the sphere locally maintaining the same angle with the path. If the contour is closed, the final orientation of the vector will differ from the original one. In case (b) the sphere is considered to be embedded in a three-dimensional Euclidean space, and the vector on the sphere results from projection. In this case, the vector returns to the original orientation for a closed contour. |
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Figure 3:
A schematic illustration of the Lie derivative. The coordinate system is dragged along with the flow, and one can imagine an observer “taking derivatives” as he/she moves with the flow (see the discussion in the text). |
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Figure 4:
The projections at point P of a vector ![]() ![]() ![]() |
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Figure 5:
An object with a characteristic size ![]() ![]() ![]() ![]() ![]() |
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Figure 6:
A local, geometrical view of the Euler equation as an integrability condition of the vorticity for a single-constituent perfect fluid. |
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Figure 7:
The push-forward from “fluid-particle” points in the three-dimensional matter space labelled by the coordinates ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 8:
The push-forward from a point in the ![]() ![]() ![]() |
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