On the parson model of the orientational phase transition for a system of ellipsoidal particles

We study the Parson's nonlinear integral equation for the density of distribution of orientations of the axes of ellipsoidal particles. To construct the solutions describing anisotropic (nematic) states of the system, we use the theory of branching the solutions of nonlinear equations (the Lyapunov–Shmidt's theory) and numerical algorithms. The results obtained are used to study the thermodynamic properties of the system of ellipsoidal particles (the state equation) and to calculate the concentrations in isotropic and anisotropic (nematic) phases coexisting in the equilibrium state.