M.Yu. Zvjagin - Ph. D. (Phys.-Math.), Associate Professor, Department of functional analysis and its applications, Vladimir State University named after A.&N. Stoletovs. E-mail: muz1953@yandex.ru P.Yu. Shamin - Ph. D. (Eng.), Part-programming engineer, Vladimir State University named after A.&N. Stoletovs. E-mail: spu@vlsu.ru V.G. Prokoshev - Dr. Sc. (Phys.-Math.), Professor, Department of Physics and Applied Mathematics, Vladimir State University named after A.&N. Stoletovs. E-mail: prokoshev_vg@vlsu.ru V.A. Jakovlev - Post-graduate Student, Department of Physics and Applied Mathematics, Vladimir State University named after A.&N. Stoletovs. E-mail: vcrazyv33@gmail.com

One of modern trends in scientific world investigation is retraction from continuous models and usage of discrete models. This paper completed in direction of same trend. In this paper we are continuing investigation of percolation process in discrete space, which was initiated in more earlier works [2−4]. However, unlike these works, in which we are placing in three-dimensional space one-dimensional objects (material nano modification with carbon nanotubes), now we are investigating also space filling with two-dimensional segments, which represents simplified model of one-layered carbon surfaces - graphene. In first paragraph of this paper introduced a description of filling structures and space mathematical model and filling process algorithm. In the second paragraph presented computed simulation model description, which implements introduced mathematical model. Same as in earlier works, we are using our parallel network simulator [6, 7] as modelling tool. In the paper described simulator extension modules, which are implements our mathematical model. In last paragraph presented simulation results. Demonstrated modelling space size impact on simulation result compliance with percolation theory. Presented percolation threshold difference for different discrete space connectivity criteria and different filling models.

 

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