Published in journal "Software systems and computational methods", 2013-4 in rubric "Mathematical models and computer simulation experiment", pages 363-369.
Resume: the percolation theory in sufficient details studied how the problem both nodes and links and the mixed problem of percolation theory. However, several experimental processes show the probability variation of the horizontal and vertical communication in the communication lattice structure with defects. In the real physical models such processes may occur, for example, when spraying the conductive material onto the inclined surface or during gradual solidification of the insulating matrix, which contains the micro-charged microparticles of a conductor, and which is placed in the electric or magnetic fields, etc.. In addition, we can expect that the presence of various defects in the structure aff ects both the mechanical and electrical properties of materials. Unfortunately, due to considerable experimental difficulties it is not always possible to determine the exact quantitative relationship between the number of defects and physical parameters. Modeling of the relation between physical parameters and the number of defects for anisotropic links is an important scientific problem. The number of such problems is large and can be of a great practical value in the case of numerical solution of such problems. The aim of this work is to study computer simulation of the combined problem of nodes and links with the division of the probabilities of formation of horizontal and vertical relations and the possibility of adding the Schottky defects into the lattice. The results of the research should be the numerical values of dependencies of the conductivity G of the 2d square grid on the values of probabilities: of the vertical connection P1, horizontal connection P2 and defects N.
Keywords: Software, percolation, conductivity, modeling, cluster, high-performance computing, Open MP, MPI, parallel computing
1. Shklovskiy B.I., Efros A.L. Elektronnye svoystva legirovannykh poluprovodnikov.
M.: Nauka, 1979.
2. Shklovskiy B.I., Efros A.L. // UFN. 1975. T. 117 (3). S. 401.436.
3. Tarasevich Yu.Yu. Perkolyatsiya: Teoriya, prilozheniya, algoritmy. – M.: Editorial
URSS, 2002.-112 s.
4. Tarasevich Yu.Yu., van derMarck S.C. // Int. J. of Modern Physics. C. 1999. Vol. 10 (7). PP.
5. Frank D.J., Lobb C.J. Highly efficient algorithm for percolative studies in two dimensions
// Phys.Rev.B. 1988.V.37.PP.302-307.
6. Lobb C.J., Frank D.J. Percolative conduction and Alexander-Orbach conjecture in two
dimensions // Phys.Rev.B.1984.V.30, No.7.PP. 4090-4092.
7. L.A.Bulavin, N.V. Vygornitskiy, N.I.Lebovka. Komp'yuternoe modelirlvanie
fizicheskikh sistem: Uchebnoe posobie/ – Dolgoprudnyy: Izdatel'skiy Dom «Intelekt»,
2011.-352 s.ISBN 978-5-91559-101-0.
8. Denisenko V.A., Sotskov V.A. Modelirovanie ob'edinenoy zadachi svyazey i uzlov
s razdeleniem svyazey v teorii perkolyatsii.// Zhurnal tekhnicheskoy fiziki 2009 T79
9. Orlov A. N. Vvedenie v teoriyu defektov v kristallakh. – M.: Vysshaya shkola. 1983.
10. Orlov A. N., Trushin Yu. V., Energii tochechnykh defektov v metallakh, – M.: 1983.80 c.
11. Fizicheskie protsessy v obluchennykh poluprovodnikakh, pod red. L. S. Smirnova, –
Novosibirsk: 1977.-s. 170-185.
Correct link to this article:
just copy this link to clipboard