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- Scallop_theorem abstract "The Scallop theorem states that to achieve propulsion at low Reynolds number in Newtonian fluids a swimmer must deform in a way that is not invariant under time-reversal. Edward Mills Purcell stated this theorem in his 1977 paper Life at Low Reynolds Number explaining physical principles of aquatic locomotion. The theorem is named for the scallop, the only bivalve able to actively swim distances. However, its technique is not applicable to viscous fluids, thus the name of the theorem.Although the movement of animal cells is usually studied as they migrate, it seems likely that many motile cells can also swim. Thus, human granulocytes are able to migrate towards a source of a chemoattractant, the tripeptide FMLP, whilst suspended in a uniformly-dense (isodense) medium. They swim at the same speed as they would crawl on a solid surface. Likewise, Dictyostelium discoideum amoebae swim towards a chemical attractant, in this case cyclic AMP. The actual mechanism that these neutrophils or amoebae use to produce a thrust against the medium to propel themselves is uncertain; however, how they do so must be consistent with physical principles. To swim they must transmit a force against the viscous fluid in order to propel themselves forward. Different mechanisms by which they might do so were presented by Ed Purcell in a famous talk he gave celebrating the 80th birthday of his friend Viki Weisskopf.In this he developed his “scallop theorem”: a normal scallop moves by opening its shells slowly and shutting them quickly. In the latter step it quickly squeezes the fluid between the shells backwards and, using the momentum of the water, pushes itself forward. Purcell realised that a microorganism trying to do the same would simply move forwards on shutting its shells and move backwards to its original position on opening them. The set of movements is “reciprocal”: it appears the same if viewed forwards or backwards in time. He concluded that microorganisms cannot move by a reciprocal mechanism: to move, they must exert some thrust against the medium and do so in a non-reciprocal manner. He suggested various ways in which an organism could swim:They could do so with a flagellum, which rotates, pushing the medium backwards — and the cell forwards — in much the same way that a ship’s screw moves a ship. This is how some bacteria move; the flagellum is attached at one end to a complex rotating motor held rigidly in the bacterial cell surfaceThey could use a flexible arm: this could be done in many different ways. For example, mammalian sperm have a flagellum which, whip-like, wriggles at the end of the cell, pushing the cell forward. Cilia are quite similar structures to mammalian flagella; they can advance a cell like paramecium by a complex motion not dissimilar to breast stroke. A hypothetical toroidal cell could move by rotating its surface through the central hole, thereby creating a surface flow. The surface drag on the outer edges of the cell could provide the thrust against the medium needed to move the cell forward. This is related to the membrane flow model B of cell migration, except in that scheme the surface flow is achieved by removing surface from the rearward end of the cell and transporting it as vesicles through the cell interior to the cell's front.The manner in which cells swim, and therefore move, suggests that it is membrane flow which is the motor for movement.".
- Scallop_theorem wikiPageExternalLink Purcell_life_at_low_reynolds_number.pdf.
- Scallop_theorem wikiPageExternalLink reynolds.pdf.
- Scallop_theorem wikiPageExternalLink node3.html.
- Scallop_theorem wikiPageExternalLink watch?v=bSzHILX_vtY&feature=channel.
- Scallop_theorem wikiPageID "26259476".
- Scallop_theorem wikiPageLength "6185".
- Scallop_theorem wikiPageOutDegree "25".
- Scallop_theorem wikiPageRevisionID "633205290".
- Scallop_theorem wikiPageWikiLink Aquatic_locomotion.
- Scallop_theorem wikiPageWikiLink Bivalvia.
- Scallop_theorem wikiPageWikiLink Breaststroke.
- Scallop_theorem wikiPageWikiLink Category:Fluid_dynamics.
- Scallop_theorem wikiPageWikiLink Category:Physics_theorems.
- Scallop_theorem wikiPageWikiLink Cell_migration.
- Scallop_theorem wikiPageWikiLink Chemotaxis.
- Scallop_theorem wikiPageWikiLink Cilium.
- Scallop_theorem wikiPageWikiLink Cyclic_adenosine_monophosphate.
- Scallop_theorem wikiPageWikiLink Density.
- Scallop_theorem wikiPageWikiLink Dictyostelium_discoideum.
- Scallop_theorem wikiPageWikiLink Edward_Mills_Purcell.
- Scallop_theorem wikiPageWikiLink Flagellum.
- Scallop_theorem wikiPageWikiLink Granulocyte.
- Scallop_theorem wikiPageWikiLink Invariant_(physics).
- Scallop_theorem wikiPageWikiLink N-Formylmethionine-leucyl-phenylalanine.
- Scallop_theorem wikiPageWikiLink Newtonian_fluid.
- Scallop_theorem wikiPageWikiLink Paramecium.
- Scallop_theorem wikiPageWikiLink Reynolds_number.
- Scallop_theorem wikiPageWikiLink Scallop.
- Scallop_theorem wikiPageWikiLink Taxis.
- Scallop_theorem wikiPageWikiLink Victor_Weisskopf.
- Scallop_theorem wikiPageWikiLink Viscosity.
- Scallop_theorem wikiPageWikiLinkText "Scallop Theory".
- Scallop_theorem wikiPageWikiLinkText "Scallop theorem".
- Scallop_theorem date "April 2013".
- Scallop_theorem reason "This page is nearly an orphan, but should be linked from taxis as well as chemotaxis . Furthermore, the article itself is totally incoherent after the first paragraph.".
- Scallop_theorem wikiPageUsesTemplate Template:Cleanup.
- Scallop_theorem wikiPageUsesTemplate Template:Reflist.
- Scallop_theorem subject Category:Fluid_dynamics.
- Scallop_theorem subject Category:Physics_theorems.
- Scallop_theorem type Dynamic.
- Scallop_theorem type Law.
- Scallop_theorem type Mechanic.
- Scallop_theorem type Page.
- Scallop_theorem type Physic.
- Scallop_theorem type Theorem.
- Scallop_theorem comment "The Scallop theorem states that to achieve propulsion at low Reynolds number in Newtonian fluids a swimmer must deform in a way that is not invariant under time-reversal. Edward Mills Purcell stated this theorem in his 1977 paper Life at Low Reynolds Number explaining physical principles of aquatic locomotion. The theorem is named for the scallop, the only bivalve able to actively swim distances.".
- Scallop_theorem label "Scallop theorem".
- Scallop_theorem sameAs Q7429791.
- Scallop_theorem sameAs m.0b76ymn.
- Scallop_theorem sameAs Q7429791.
- Scallop_theorem wasDerivedFrom Scallop_theorem?oldid=633205290.
- Scallop_theorem isPrimaryTopicOf Scallop_theorem.