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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 ,
,
12 1.2.5 Étude mathématique de problèmes d'interaction fluide-structure avec structures actives, Modélisation mathématique des, vol.9 ,
,
,
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) ,
,
, 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