Theoretical Justification and Error Analysis for Slender Body Theory with Free Ends

@article{Mori2018TheoreticalJA,
  title={Theoretical Justification and Error Analysis for Slender Body Theory with Free Ends},
  author={Yoichiro Mori and Laurel Ohm and Daniel Spirn},
  journal={Archive for Rational Mechanics and Analysis},
  year={2018},
  volume={235},
  pages={1905-1978}
}
Slender body theory is a commonly used approximation in computational models of thin fibers in viscous fluids, especially in simulating the motion of cilia or flagella in swimming microorganisms. In Mori et al. (Commun Pure Appl Math, 2018. arXiv:1807.00178 ), we developed a PDE framework for analyzing the error introduced by the slender body approximation for closed-loop fibers with constant radius $$\varepsilon $$ ε , and showed that the difference between our closed-loop PDE solution and the… 

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References

SHOWING 1-10 OF 58 REFERENCES

SLENDER BODY THEORY FOR STOKES FLOWS WITH REGULARIZED FORCES

Existing slender body theories for the dynamics of a thin tube in a Stokes flow differ in the way the asymptotic errors depend on a small parameter defined as the radius of the body over its length.

An improved slender-body theory for Stokes flow

The present study examines the flow past slender bodies possessing finite centre-line curvature in a viscous, incompressible fluid without any appreciable inertia effects. We consider slender bodies

Simulating the dynamics and interactions of flexible fibers in Stokes flows

The boundary integral formulation of Stokes flows includes slender-body theory

The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and

Slender-body theory for particles of arbitrary cross-section in Stokes flow

A rigid body whose length (2l) is large compared with its breadth (represented by R0) is straight but is otherwise of arbitrary shape. It is immersed in fluid whose undisturbed velocity, at the

Modeling simple locomotors in Stokes flow

Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct

Modeling slender bodies with the method of regularized Stokeslets

Discrete Cilia Modelling with Singularity Distributions: Application to the Embryonic Node and the Airway Surface Liquid

The first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a ‘posterior tilt’ are presented, and a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid is developed.

Slender-body theory for slow viscous flow

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the
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