Model of radiation-stimulated growth of coherent structures in a crystalline medium with fast relaxation and slow diffusion 

Vitaliy M. Morozov, Junior researcher, Samara National Research University (34 Moskovskoye highway, Samara, Russia), E-mail: aieler@rambler.ru 

Background. In this research constructed a model for the radiation-stimulated growth of coherent structures based on the nonlinear diffusion of point defects in a crystalline medium. Materials and methods. The main results were obtained with using the method of multiscale expansions and the qualitative theory of differential equations. Results. A model of nonlinear diffusion of point defects with a limited source were formulated. Regimes of growth of coherent structures in a medium with nonlinear diffusion were revealed. Conditions for the formation of a periodic macrostructure and conditions for amplification of the amplitude of the initial periodic distribution of defects were obtained. Conclusions. Accounting for the influence of defects on the process of their generation in the model of irradiation of a crystalline material with a high-energy and high-density particle beam leads to a description of the growth of coherent structures. In this case, there are two modes of growth corresponding to the initial stage of irradiation—relaxation, associated with an increase in the amplitude of the initial distribution of defects, and asymptotic, when the structure is preserved when dynamic equilibrium is established. 

Functional substitution method, exact solutions of nonlinear wave and diffusion equations, nonlinear diffusion processes and models 

Morozov V.M. Model of radiation-stimulated growth of coherent structures in a crystalline medium with fast relaxation and slow diffusion. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2022;(2):99–133. (In Russ.). doi:10.21685/2072-3040-2022-2-7