Fig 2. Coherent rotation of cells on circular geometry.

(a) The time evolution of polarization vector, $\widehat{\mathbf{p}}$ and velocity vector $\widehat{\mathbf{v}}$ is shown for ξ = 0.1. The evolution rule for polarization is chosen in such a way that, from an initial random orientation, $\widehat{\mathbf{p}}$ will try to orient along velocity vector with time. (b) The coordination between $\widehat{\mathbf{p}}$ and $\widehat{\mathbf{v}}$ is decided by the parameter ξ. The higher the value of ξ, higher is the tendency of $\widehat{\mathbf{p}}$ to orient along $\widehat{\mathbf{v}}$. The orientation of $\widehat{\mathbf{p}}$ and $\widehat{\mathbf{v}}$ at steady state for ξ = 0.5 and ξ = 1 are also shown. (c) Mean vorticity for systems with different ξ is plotted as a function of time. (d) The tendency of polarization vector to orient with velocity vector is shown by the plot between $\widehat{\mathbf{p}}.\widehat{\mathbf{v}}$ and time. As the value of ξ increases, value of $\widehat{\mathbf{p}}.\widehat{\mathbf{v}}$ approaches 1, indicating perfect alignment between two vectors. (e) A plot of velocity correlation length for varying system size shows that correlation length equal to the confinement size. (f) A plot of correlation function with time shows that the velocity correlation length increases with time, till the coherent rotation sets in.