Rough wall effect on micro-swimmers

Gérard-Varet, David; Giraldi, Laëtitia

doi:10.1051/cocv/2014046

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…Assuming only, in the second point of Hypothesis 1, that the equality holds for one point of M may seem a somehow useless mathematical refinement. Quite the reverse, the explicit computation of Lie ξ ∆ M in concrete cases is often very involved and can still be hardly carried out for one particular ξ (see for instance [3,5,7,9,12]). Definition 2.4 A swimmer satisfying Hypothesis 1 will be called controllable.…”

Section: Remark 22mentioning

confidence: 99%

Optimal strokes for driftless swimmers: A general geometric approach

2019

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Swimming consists by definition in propelling through a fluid by means of bodily movements. Thus, from a mathematical point of view, swimming turns into a control problem for which the controls are the deformations of the swimmer. The aim of this paper is to present a unified geometric approach for the optimization of the body deformations of so-called driftless swimmers. The class of driftless swimmers includes, among other, swimmers in a 3D Stokes flow (case of micro-swimmers in viscous fluids) or swimmers in a 2D or 3D potential flow. A general framework is introduced, allowing the complete analysis of five usual nonlinear optimization problems to be carried out. The results are illustrated with examples coming from the literature and with an in-depth study of a swimmer in a 2D potential flow. Numerical tests are also provided.

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Section: Remark 22mentioning

confidence: 99%

Optimal strokes for driftless swimmers: A general geometric approach

2019

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“…Despite the pioneer works modeling and analysing the motions of micro-swimmers (see for instance [29,19,18,25,11,28,27]), the swimming of micro-organisms has only been recently tackled as a control problem. A lot of controllability results for various swimmers has been obtained (see for instance [4,5,24,26,23] for axi-symmetric swimmers, [3,21] for general swimmers or [6,12] when the fluid domain is not the whole space R 3 ). Let us also point out that numerical strategy for axi-symmetric swimmers have already been presented in [2].…”

Section: Application To Time Optimal Micro-swimmersmentioning

confidence: 99%

15. Time-optimal control for a perturbed Brockett integrator

Lohéac¹,

Scheid²

2016

Variational Methods

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The aim of this work is to compute time optimal controls for a perturbation of a Brockett integrator with state constraints. Brockett integrator and its perturbations appears in many applications fields. One of them described in details in this note is the swimming of microorganisms. We present some key results for a fast and robust numerical method to compute time optimal controls for the perturbation of a Brockett integrator. This numerical method is based on explicit formulae of time optimal controls for the Brockett integrator. The methodology presented in this work is applied to the time optimal control of a micro-swimmer.

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“…This is a novelty compared to other controllability results, see for instance [3,24], where four elementary deformations are required to fully control the rigid position of the swimmer. Let us also point out the works [1,18] where less than four elementary deformations are required. Nevertheless, in these works, the fluid is only present on half of the space R 3 , and they enrich the reachable set using the boundary effects.…”

Section: Introductionmentioning

confidence: 99%

Controllability of low Reynolds numbers swimmers of ciliate type

Lohéac

Takahashi

2020

ESAIM: COCV

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We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.

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Rough wall effect on micro-swimmers

Cited by 8 publications

References 30 publications

Optimal strokes for driftless swimmers: A general geometric approach

Optimal strokes for driftless swimmers: A general geometric approach

15. Time-optimal control for a perturbed Brockett integrator

Controllability of low Reynolds numbers swimmers of ciliate type

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