Continuum theory for carpets of model cilia

In biology, fluid transport often emerges from the coordinated activity of

thousands of multi-ciliated cells, each containing hundreds of cilia.  Given the

sheer number of cilia in these system, a continuum theory is needed to fully

analyze large ciliary carpets. Here, we formulate a continuum theory by

systematically coarse graining a simple model for cilia that treats them as

immersed spheres forced along circular trajectories above a surface. We analyze

the stability of isotropic and synchronized states and show that they are

unstable to small perturbations, which implies dynamic pattern formation.

To challenge the theory, we performed numerical simulations on discrete

systems. We report quantitative agreement between theory and in-silico

experiments.