Kinematic Cartography and the Efficiency of Viscous Swimming

Hatton, Ross L.; Dear, Tony; Choset, Howie

doi:10.1109/tro.2017.2653810

Cited by 19 publications

(23 citation statements)

References 47 publications

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“…This numerical procedure limits the theoretical insight that can be developed from the technique but has been shown to improve significantly the results of the series expansion for two-dimensional Purcell-like low Reynolds number swimmers and some other two-dimensional non-low Reynolds number cases (Hatton & Choset 2011, 2013, 2015; Hatton et al. 2017; Ramasamy & Hatton 2017; Bittner et al. 2018; Ramasamy & Hatton 2019).…”

Section: Background: Geometric Swimming For Stokes Flowmentioning

confidence: 99%

“…A comparison of the accuracy between the embedded method and the small-stroke approximation in the minimal perturbation coordinates (Hatton & Choset 2011, 2013, 2015; Hatton et al. 2017; Ramasamy & Hatton 2017, 2019; Bittner et al. 2018) requires us therefore to consider the Purcell swimmer problem with arbitrary sized hinge angles.…”

Section: Treatment Of Non-commuting Variablesmentioning

confidence: 99%

“…2018). However, the same treatment is not generally possible for more complicated swimmers because of (i) non-commuting variables within the gauge field and (ii) difficulties visualising the configuration space (Hatton & Choset 2015; Hatton, Dear & Choset 2017; Ramasamy & Hatton 2017; Bittner, Hatton & Revzen 2018). Attempts to produce similar results often restrict the motion of the swimmer and the types of deformation.…”

Section: Introductionmentioning

confidence: 99%

“…For swimmers that travel in one dimension and only have two degrees of freedom, the geometrical techniques could be further simplified through the use of the Stokes theorem. This simplification allows the net displacement from any stroke to be visualised on a plane and thereby provides new insights into the propulsion mechanisms and how to design the swimmer's displacement (Shapere & Wilczek 1989b However, the same treatment is not generally possible for more complicated swimmers because of (i) non-commuting variables within the gauge field and (ii) difficulties visualising the configuration space (Hatton & Choset 2015;Hatton, Dear & Choset 2017;Ramasamy & Hatton 2017;Bittner, Hatton & Revzen 2018). Attempts to produce similar results often restrict the motion of the swimmer and the types of deformation.…”

Section: Introductionmentioning

confidence: 99%

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Geometric phase methods with Stokes theorem for a general viscous swimmer

Koens

Lauga

2021

J. Fluid Mech.

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Section: Background: Geometric Swimming For Stokes Flowmentioning

confidence: 99%

Section: Treatment Of Non-commuting Variablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Geometric phase methods with Stokes theorem for a general viscous swimmer

Koens

Lauga

2021

J. Fluid Mech.

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“…Hence these maps have been useful in applications of control theory and design optimisation [68][69][70].…”

Section: Net Displacement and Motility Mapsmentioning

confidence: 99%

The swimming of a deforming helix

et al. 2018

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Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induce movement by deforming a helical-shaped body.Recently, artificial devices have been created which also generate motion by deforming their helical body in a non-reciprocal way (Mourran et al. Adv. Mater. 29, 1604825, 2017). Inspired by these systems, we investigate the transport of a deforming helix within a viscous fluid. Specifically, we consider a swimmer that maintains a helical centreline and a single handedness while changing its helix radius, pitch and wavelength uniformly across the body. We first discuss how a deforming helix can create a non-reciprocal translational and rotational swimming stroke and identify its principle direction of motion. We then determine the leading-order physics for helices with small helix radius before considering the general behaviour for different configuration parameters and how these swimmers can be optimised. Finally, we explore how the presence of walls, gravity, and defects in the centreline allow the helical device to break symmetries, increase its speed, and generate transport in directions not available to helices in bulk fluids.

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