Fig. 6: Modulated formulations for cellular activity mitigate density fluctuations.
From: Mitigating density fluctuations in particle-based active nematic simulations
a The median cell population ρC for all four formulations of cellular activity. Modulated methods result in the system median dropping below the mean density within the turbulence regime. Inset: The standard deviation of cell population \({{\sigma}_{{\rho}_{C}}}\). b The fraction of empty cells with ρC = 0. Particle-carried activity in particular has a large fraction of empty cells at the highest activities, while alternative formulations result in a more homogeneous system. c The density correlation length ℓρ, representative of the width of high density nematic bands throughout the system. Density bands become more dense and thinner as activity is raised, but alternative formulations mitigate this effect. The dotted line indicates a scaling of ℓρ ~ α−1. Inset: The far-field value of the density correlation function Cρ,ρ(R → ∞), indicating the degree of density homogeneity. Modulated methods result in a more homogeneous system. d The temporal average of the instantaneous spatial maxima of local density, \({\left\langle \max {\left[{\rho }_{C}({{{{{{\boldsymbol{r}}}}}}},t)\right]}_{{{{{{{\boldsymbol{r}}}}}}}}\right\rangle }_{t}\). ("Part.'', Eq. (6), blue; “Cell'', Eq. (8), red; “Mod. Part.'', Eq. (12), cyan; “Mod. Cell'', Eq. (11), yellow).
