Problems and progress in microswimming

DOI10.1007/BF02434055zbMath0867.76099OpenAlexW4231779336MaRDI QIDQ2365321

Richard Montgomery, Kurt M. Ehlers, Jair Koiller

Publication date: 22 January 1997

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02434055

zbMATH Keywords

parallel algorithmssub-Riemannian geometrygeometric phasesnonlinear control theorynonholonomic controlcollective motionsShapere and Wilczek's gauge-theoretical approachsingle organismStokes curvature

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Biomechanics (92C10) Biopropulsion in water and in air (76Z10)

Related Items (20)

Experimental investigations of the controlled motion of a screwless underwater robot ⋮ Influence of vortex structures on the controlled motion of an above-water screwless robot ⋮ Low Reynolds number swimming and controllability ⋮ Micromotions and controllability of a swimming model in an incompressible fluid governed by \(2-D\) or \(3-D\) Navier-Stokes equations ⋮ The Role of SE ( d ) $$\mathop{\mathrm{SE}}\nolimits (d)$$ -Reduction for Swimming in Stokes and Navier-Stokes Fluids ⋮ The Role of Symmetry and Dissipation in Biolocomotion ⋮ The self-propulsion of a body with moving internal masses in a viscous fluid ⋮ Geometric analysis of gaits and optimal control for three-link kinematic swimmers ⋮ Optimal strokes for low Reynolds number swimmers: an example ⋮ Analysis of a model microswimmer with applications to blebbing cells and mini-robots ⋮ Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid ⋮ Micro-swimming without flagella: propulsion by internal structures ⋮ One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls ⋮ Self-propulsion of \(N\)-hinged `animats' at low Reynolds number ⋮ Symmetry and gauge freedom ⋮ On efficiency calculations for nonholonomic locomotion problems: An application to microswimming ⋮ A nonholonomic approach to isoparallel problems and some applications ⋮ On the slow motion of a self-propelled rigid body in a viscous incompressible fluid. ⋮ The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation ⋮ Evaluation of spherical shapes swimming efficiency at low Reynolds number with applications to some biological problems

Cites Work

• On the numerical solution of the biharmonic equation in the plane
• Isoholonomic problems and some applications
• Geometry of self-propulsion at low Reynolds number
• The generation of feeding currents by flagellar motions
• Mechanics of Swimming and Flying
• Hydrodynamic Phenomena in Suspensions of Swimming Microorganisms
• An oscillating-boundary-layer theory for ciliary propulsion
• A porous prolate-spheroidal model for ciliated micro-organisms
• A spherical envelope approach to ciliary propulsion
• Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number
• A model for the micro-structure in ciliated organisms
• Analysis of the swimming of microscopic organisms
• The action of waving cylindrical tails in propelling microscopic organisms
• A Theorem on Holonomy
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Problems and progress in microswimming