Topological and geometrical quantities in active cellular structures.

Topological and geometrical properties and the associated topological defects find a rapidly growing interest in studying the interplay between mechanics and the collective behavior of cells on the tissue level. We here test if well studied equilibrium laws for polydisperse passive systems such as Lewis' and Aboav-Weaire's law are applicable also for active cellular structures. Large scale simulations, which are based on a multiphase field active polar gel model, indicate that these active cellular structures follow these laws. If the system is in a state of collective motion, quantitative agreement with typical values for passive systems is also observed. If this state has not developed, quantitative differences can be found. We further compare the model with discrete modeling approaches for cellular structures and show that essential properties, such as T1 transitions and rosettes, are naturally fulfilled.