The role of intracellular interactions in the collective polarization of tissues and its interplay with cellular geometry
Cellular geometry, initial conditions, and model parameters (other than λ) are identical in (a1) and (a2). The big arrows show the average direction of dipoles over patches of a few cells. Angular distributions of the dipoles in the two cases are shown in (b1) and (b2), which reveal the failure of SLCI in establishing long-range polarization. Time evolutions of , , and , for isotropic systems with SLCI (dash-dotted lines), with NLCI (solid lines), as well as elongated systems with NLCI (dashed lines) are shown in (c1). Correlation lengths are illustrated in (c2); unlike in the NLCI case where the angular correlations extend over tissue scales, the correlation length in the case of SLCI remains limited to a few cell diameters. For clarity, the small fluctuations of all the curves, induced by stochastic noises, are removed through ensemble averaging.