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. .. Sur-la-vie-À-bas-nombre-de-reynolds, 1 1.1.1 Mécanique des fluides à bas nombre de Reynolds

, Zoologie des déformations des cils et flagelles

. .. , Mécanismes de déformation des cils eukaryotes

.. .. Motivations,

. .. Cils and . .. Le-modèle-historique-de-taylor, 12 1.2.5 Étude mathématique de problèmes d'interaction fluide-structure avec structures actives, Modélisation mathématique des, vol.9

.. .. Positionnement-de-la-thèse,

.. .. Résultats,

. .. Introduction, 29 2.2 A continuum active structure model

. .. , 42 2.3.3 Existence and uniqueness of a weak solution to the linearized fluidstructure interaction problem, A coupled fluid-structure interaction problem with cilia-like structures

. .. , 49 2.4.1 Description of the method, Numerical simulations of active structures in a viscous fluid

, Les micro-organismes possédant des cils sont représentés à l'intérieur du cercle au centre de la figure, Aperçu général de quelques micro-organismes possédant des cils ou des flagelles et autres organismes associéss. Image tirée de [Lighthill, 1976.

. .. , Cils bronchiques (a) et Chlamydomonas reinhardtii (b)

. .. Schéma,

, 35 2.2 Deformation of an elongated structure subjected to the internal activity defined by (2.6) at different times: t = 0s (a), t = 0.012s (b), t = 0.025s (c) and t = 0.037s (d). The activity scenario ? a is represented with the set of parameters be given in Table 2, Bending of an elongated elastic structure with the internal activity given by (2.5) at different times: t = 0s (a), t = 0.012s (b), and t = 0.025s (c)

, The activity scenario ? a is represented with the set of parameters be given in Table 2.3, ducing cilia-like deformations at different time: t = 0s (a), t = 0.015s (b), t = 0.035s (c), t = 0.050s (d), t = 0.050s (h), t = 0.065s (g), t = 0.085s (f), and t = 0.1s (e)

, The activity scenario ? a in represented with the set of parameters be, Elongated three-dimensional structure subjected to the internal activity defined by (2.8) inducing twirling at different time: t = 0s (a), t = 0.052s (b), t = 0.082s (c), t = 0.107s (f), and t = 0.128s (e), p.39

, The activity scenario of the structure is given by (2.7), One cilium beating in a viscous fluid of viscosity µ f = 0.01pN · µm · s at different times: t = 0.091s (a), t = 0.110s (b), t = 0.120s (c), and t = 0.166s (d)

, One cilium beating in a viscous fluid at time t = 0.128s (left) and at time t = 0.171s (right) for different values of the fluid viscosity: µ f = 0.01pN·

, The activity scenario of the structure is given by (2.7), µm ?1 ·s (a, b), µ f = 0.02pN·µm ?1 ·s (c, d) and µ f = 0.04pN · µm ?1 · s (e, f)

, Mean deformation of the solid as a function of the time for different values of the fluid viscosity (in pN · µm ?2 · s)

, Time average of the solid deformation as a function of the viscosity of the fluid, vol.56

, Mean horizontal velocity of the fluid in function of the time for different values of the fluid viscosity (in pN · µm ?2 · s)

. .. , 35 2.2 Set of parameters for the flapping scenario of activity, p.36

, Set of parameters for the non symmetric scenario of activity, p.37

, Set of parameters for the twirling scenario of activity in three space dimensions, p.39

, Comparison of the rates of convergence between the finite element method (FEM) with a conformal mesh, the FEM with a non-conformal mesh and the smooth extension method (SEM) with a non-conformal mesh for different test cases