Nikolayenko S. Theory of relaxation processes in systems of particles interacting with hydrodynamic media

The thesis is devoted to the construction of the microscopic theory that describes dynamics of particles interacting with hydrodynamic media. The specific example of such system are neutrons or brownian particles, propagating in liquid or gas-like media. Dynamic equations dercribing such sustem on mixed kinetic - hydrodynamic and hydrodynamic stages of evolution where obtained. The role of particles interacting with hydrodynamic media in dissipation processes was evaluated. The effect of non-equilibrium long wave fluctuations on the system relaxation where considered. The long wave fluctuations generated by randomness of initial conditions for the systems where studied, and the "long hydrodynamic tails" theory, which predicts slow relaxation by the power low of t^{-3/2} for the system has been constructed. The effect of long wave fluctuations generated by external random force in particle-multiplying media has been studied. In was shown that long wave fluctuations may increase the increment of instabilty growth by the factor of 2. Keywords: neutrons, multiplying media, capturing media, reduced description method, kinetics, hydrodynamics, non-equilibrium long wave fluctuations, slow relaxation, external random force.