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Upon based the finite difference methods construct the solutions for Liouville quantum kinetic equation linearized by the external field, in complex with the stationary Schrodinger equation and the Poisson operator equation, for an ensemble of non-interacting hydrogen ions (protons) migrating in the field of a crystal lattice perturbed by a variable polarizing field. The influence of the phonon subsystem is not taken into account. The equilibrium (non-balanced) proton density matrix is calculated using quantum Boltzmann statistics. The temperature spectra of dielectric losses tangent angle for hydrogen bonded crystals (HBC) in a wide temperature range (50–550 K) are calculated. At the theoretical level detected the effects of nano-crystalline states (1–10 nm) during the polarization of HBC in the region of ultra-low temperatures (4–25 K).

Methods of continuum mechanics and equilibrium thermodynamics are used to study a generalized physical and mathematical model of the processes of a working substance (steam, gas) moving in the flow part of an axial turbine stage in the nominal operating mode of the turbine. The mathematical description of the hydrodynamics and thermodynamics of the process is carried out for a one-dimensional model, based on the energy equation in thermomechanical form (the first law of thermodynamics in combination with the Bernoulli equation) for the gas (or steam) flow during its adiabatic (isentropic) expansion in the direction of the axis of the turbine stage. The energy equation is written taking into account both thermodynamic (due to the thermal movement of particles) and hydraulic pressure forces (due to the mechanical action of a continuous medium) of the working substance flow on the walls of the stage flow channel. Numerical calculation of flow rates and enthalpy losses on various elements of the stage (nozzle and working blades) is performed on the example of a model turbine with eight axial-type stages, under specified initial conditions of the process.