Matskevych V. Dynamic processes in condensed matters taking into account peculiarities of the internal structure and orientational ordering

The thesis is devoted to the development of the relaxation dynamics of condensed matters in an external field taking into account peculiarities of the internal structure and orientational ordering. The dynamic processes in uniaxial nematic liquid crystals with rod-like and disk-like molecules and in biaxial nematic liquid crystals with ellipsoidal and discoidal molecules are considered. The spectra of collective excitations taking into account the geometry of molecules are investigated and their polarization characteristics are studied. The analytical structure of low-frequency Green's function asymptotics, which depends on spatial anisotropy of medium and geometry of molecules, is determined. The analytical structure of low-frequency Green's function asymptotics for an isotropic solid is obtained. The generalization of the Hamiltonian approach to dynamic processes with relaxation is given. Dissipative Poisson brackets are introduced in terms of the dissipation function. This assertion of the universal structure of relaxation terms in dynamic equations of condensed matters with structure is formulated. The relaxation equations for uniaxial nematic liquid crystals and solid state taking into account the internal structure of the medium are obtained. The explicit form of relaxation Poisson brackets of the dynamic quantities of specified condensed matters is established.