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The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella

Abstract : The inertialess fluid-structure interaction of active and passive inextensible filaments and slender-rods are central in many processes in nature, from the dynamics of semi-flexible polymers to cy-toskeletal filaments, flagella and artificial swimmers, covering a wide range of scales. The nonlinear coupling between the geometry of deformation and the physical effects invariably result on intricate governing equations that negotiate elastohydrodynamical interactions with non-holonomic constraints, as a direct consequence of the filament inextensibility. This triggers numerical instabili-ties and require penalization methods and high-order spatiotemporal propagators. Here, we exploit the the momentum balance in the asymptotic limit of small rod-like elements which are integrated semi-analytically. This bypasses the nonlinearities arising via the inextensibilty constraint, avoiding in this way the need of Langrange multipliers. The equivalence between the continuous and asymp-totic model allows a direct comparison between the two formalisms. The nature of the asymptotic approximation entails that coarse discretisation is possible while having a higher precision when compared with the continuous approach. We show that the asymptotic model is also numerically stable in situations in which the continuous formalism has a very poor performance, while the coarse structure guarantees faster computations, over than a hundred times faster than previous schemes. The asymptotic model is simple and intuitive to implement, and generalisations for complex interaction of multiple rods, Brownian polymer dynamics, active filaments and non-local hydrodynamics are straightforward. We demonstrate these via four exemplars: transient dynamics, force-displacement buckling instability, magnetic artificial swimmer and cross-linked filament-bundle dynamics, and we additionally provide the Matlab codes.
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Contributor : Clément Moreau <>
Submitted on : Monday, January 7, 2019 - 5:07:00 PM
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Clément Moreau, Laetitia Giraldi, Hermes Gadêlha. The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella. Journal of the Royal Society Interface, the Royal Society, 2018, 15 (144), ⟨10.1098/rsif.2018.0235⟩. ⟨hal-01658670v2⟩



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