Poisson-bracket formulation of the dynamics of fluids of deformable particles

Using the Poisson-bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified terms fields: an anisotropy density field that captures deformations individual from regular shapes and tensor quantifies both particle elongation nematic alignment elongated shapes. We explicitly consider example dense biological tissue as described by Vertex model energy, where cell has been proposed structural order parameter liquid-solid transition. The hydrodynamic here coupling to flow provides starting point modeling rheology tissue.