A Coordinate-Based Proof of the Scallop Theorem

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Ishimoto, Kenta ; Yamada, Michio (2012)
  • Publisher: Society for Industrial and Applied Mathematics
  • Journal: SIAM Journal on Applied Mathematics, volume 72, issue 5, pages 1,686-1,694 (issn: 0036-1399)
  • Subject: Stokes flow | microorganism | scallop theorem
    arxiv: Physics::Fluid Dynamics | Physics::Biological Physics | Quantitative Biology::Other | Quantitative Biology::Cell Behavior

We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a coordinate-based proof is first given to Purcell's scallop theorem including the body rotation.
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