Kinetic partial differential equations of Kolmogorov-Feller and Einstein-Smoluchowski equation with nonlinear coefficients are solved by a new, stable numerical methods. The theory of stochastic dynamic variables establishes the connection of the solution of Ito stochastic equations in the sense of Stratonovich for the trajectories of Wiener random processes with the transition probability density of these processes, or distribution functions of kinetic equations. The classical theory of nucleation (formation of nuclei of the first order phase transition) describes a non-equilibrium stage of the condensation process by a diffusion random process in the space of the size of the nuclei of the phase transition, when fluctuations affect the clustering of the nuclei. The model of formation of vacancy-gas defects (pores, blisters) in the crystal lattice, arising as a result of its irradiation by inert gas ions xenon, is supplemented by the consideration of Brownian motion of non-point lattice defects, occurring under the action of superposition of paired long-range potentials of indirect elastic interaction of pores between themselves and with the boundaries of the layers. Pores coordinates are changing at times of the order of 10 − 100 ms, sustainable algorithms for calculating which provide a self-consistent defnition spatial - temporal structures of porosity in the sample. According to calculations of 106 trajectories, non-equilibrium kinetic functions were found. Pores distribution in size and coordinates in the layers of the irradiated materials, they characterize the fluctuation instability the initial stage of the phase transition, they are estimated local stresses and porosity in the model volume.
Non-equilibrium condensation process in a holographic superconductor
