Numerical solution of stochastic differential equations in the sense of Stratonovich in an amorphization crystal lattice model

Model phase transition /PT/ involves the formation of defects (voids or blisters), their migration into thin layers sample from SiC and Mo, accumulation of defects, and consequently, a change in the crystal lattice strain which leads to amorphization of materials. Mathematical model is related with solution of stochastic differential equations /SDEs/. The scheme used is a two-level modification of the asymptotically unbiased numerical method for solving SDEs in the sense of Stratonovich, which has second order mean-square convergence for SDEs with a single noise or for SDEs with additive noise. Based on example of computer simulation of porosity and amorphization lattice are to be discussed characteristics of phase transition at initial stage as well their influence on protective qualities of SiC thin layer cover subjected by radiation of Xe + + ions.

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