Motile Cilia — Metachronal Wave

Hydrodynamically coupled oscillators · Stokes flow · Symplectic/Antiplectic waves

Parameters

Physics

θ̇ᵢ = ω + κΣⱼH(i,j)sin(θⱼ-θᵢ)
Metachronal wave: θᵢ(t) = ωt - i·Δφ
v_fluid ~ N·L·ω·f(Δφ)/η_fluid
Symplectic: wave → power stroke dir
Antiplectic: wave ← power stroke dir
Cilia in the respiratory tract, embryo, etc. synchronize via hydrodynamic coupling to form metachronal waves, dramatically increasing fluid transport efficiency over uncoordinated beating.

Observables

Phase velocity v_φ-
Order param R-
Net flow proxy-
Wave type-