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Vector Field Flow Measurements in Singular Fields Review

Learn about measuring flow of vector fields with singularities along and across closed curves, coping with singularities in a gradient field. Covers examples and scenarios when encountering singularities.

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Vector Field Flow Measurements in Singular Fields Review

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  1. VC.06 Flow Measurements in Fields with Singularities (Day 2)

  2. Review: The Flow of A Vector Field ALONG a Closed Curve: • Let C be a closed curve parameterized counterclockwise. Let Field(x,y) be a vector field with no singularities on the interior region R of C. Then: • This measures the net flow of the vector field ALONG the closed curve.

  3. Review: The Flow of A Vector Field ACROSS a Closed Curve: • Let C be a closed curve parameterized counterclockwise. Let Field(x,y) be a vector field with no singularities on the interior region R of C. Then: • This measures the net flow of the vector field ACROSS the closed curve.

  4. Summary: The Flow of a Gradient Field Along a Closed Curve

  5. Much Ado About Singularities All of our calculations yesterday were for curves that did not contain any singularities. Today, we will talk about how to cope with vectors fields that have singularities!

  6. Example 1: A Flow Along Measurement With a Singularity

  7. Example 1: A Flow Along Measurement With a Singularity

  8. Example 2: A Flow Along With Multiple Singularities? No Problem!

  9. Example 2: A Flow Along With Multiple Singularities? No Problem!

  10. Summary: Flow Along When rotField(x,y)=0

  11. Summary: Flow Along When divField(x,y)=0

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