Elasticity in the Gauge Theory of Active Nematics with Topological Defects

We analyze the phase behavior of lyotropic nematic liquid crystals in the self-organizing flow, viz. so called active nematics (AN). Their elastic properties are mutually caused by evolution of topological defects (for instance, disclinations and boojums) and the flow regime. Such changes in elasticity of AN comparing with conventional inactive ones set the new working characteristics of these materials, have an influence on their switchable and tunable properties. In this work, we study the uniaxial droplet AN phases with topological defects in their collective flow, we apply the gauge string-like theory using the method of differential forms on a lattice interchanging the drive-force concept. The results of our numerical modeling with Monte Carlo method show, that under certain conditions, the type of the phase transition from nematic to isotropic (N-I) phase and the thermodynamical characteristics in an active regime may differ from such one in the conventional lyotropic nematcis.