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Percolation investigation in the discrete space filled with regular structures

Keywords:

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.
References:

 

  1. Buzmakova M.M. Modelirovanie kontinualnojj perkoljacii sfer i ehllipsoidov // Estestvennye nauki. 2012. T. 41. № 4. S. 123−133.
  2. Milovanov D.S., Prokoshev V.G., Abramov D.V. K voprosu o perkoljacii v strukturakh, formiruemykh protjazhennymi nanoobektami // Materialy IXMezhdunar. konf.-seminara «Vysokoproizvoditelnye parallelnye vychislenija na klasternykh sistemakh». Vladimir. 2009. S. 286−289.
  3. Milovanov D.S. Modelirovanie perkoljacii v zapolnennykh reguljarnykh reshetkakh // Materialy IIMezhdunar. nauchno-prakticheskojj konf. «Progressivnye tekhnologii i perspektivy razvitija». Tambov. 05.11.2010. S. 46.
  4. Arakeljan S.M., Milovanov D.S., Prokoshev V.G. Kompjuternoe modelirovanie processa perkoljacii v nanostrukturirovannykh materialakh s ispolzovaniem parallelnykh vychislenijj // Tezisy dokladov IIMezhdunar. konf./molodezhnojj shkoly-seminara «Sovremennye nanotekhnologii i nanofotonika dlja nauki i proizvodstva». 16−19 nojabrja 2009 g. Vladimir. S. 154−155.
  5. Kim M.S., Song J.I., Park Y.B. Prediction of two-dimensional electrical conductivity of graphene/polymer composites // 18th International conference on composite materials, ICC Jeju, Korea, August 21−26, 2011. [EHlektronnyjjresurs] URL: http://www.iccm-entral.org/Proceedings/ICCM18proceedings/ data/2.%20Oral%20Presentation/Aug22%28Monday%29/M19%20Nanocomposites %20and%20Polymer%20Nanocomposites%20including%20Carbon%20Nanotubes%20or%20Graphene/M19-4-IK0423.pdf (dataobrashhenija: 26.02.2015).
  6. SHamin P.JU., Aleksanjan A.S., Prokoshev V.V. Parallelnyjj setevojj simuljator: koncepcija i perspektivy razvitija // Nauchno-tekhnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. 2009. № 3. S. 18−24.
  7. SHamin P.JU., Prokoshev V.V. Modernizacija parallelnogo setevogo simuljatora PSS // Materialy XII Vseros. konf. «Vysokoproizvoditelnye parallelnye vychislenija na klasternykh sistemakh». N. Novgorod. 26−28 nojabrja 2012 g. / Pod red. prof. V.P. Gergelja. N. Novgorod: Izd‑vo Nizhegorodskogo gosuniversiteta. 2012. S. 440−444.

 

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