Anomalous diffusion simulation of the effects for drainage systems
Matematičeskoe modelirovanie, Tome 25 (2013) no. 12, pp. 44-49.

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A model of filtration in a drainage system that takes into account the anomalous diffusion normality moisture transfer in soil caused by the fractal properties of the medium is considered. It is shown that the use of fractal models of filtration of the soil leads to better compliance with the calculation results of the groundwater profiles with the experimental data.
Keywords: mathematical modeling, fractal geometry, partial differential equations of fractional derivatives
Mots-clés : anomalous diffusion, filtration.
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N. M. Kashchenko; M. A. Nikitin. Anomalous diffusion simulation of the effects for drainage systems. Matematičeskoe modelirovanie, Tome 25 (2013) no. 12, pp. 44-49. http://geodesic.mathdoc.fr/item/MM_2013_25_12_a3/

[1] Fedotov G. N., Tretyakov Yu. D., Ivanov V. K., Kuklin A. I., Pakhomov E. I., Islamov A. Kh., Pochatkova T. N., “Fraktalnye kolloidnye struktury v pochvakh razlichnoi zonalnosti”, DAN, 405:3 (2005), 351–354

[2] Fedotov G. N., Tretyakov Yu. D., Ivanov V. K., Kuklin A. I., Pakhomov E. I., Islamov A. Kh., Pochatkova T. N., “Vliyanie vlazhnosti na fraktalnye svoistva pochvennykh kolloidov”, DAN, 409:2 (2006), 199–201

[3] Lundin K. P., Sverdlova L. B., “Issledovanie strukturnykh por torfa s pomoschyu radioaktivnykh izotopov”, Melioratsiya i ispolzovanie osushennykh zemel, Urozhai, Mn., 1966, 48–67

[4] Vozmozhnosti sovremennykh i buduschikh fundamentalnykh issledovanii v pochvovedenii, GEOS, M., 2000, 135 pp.

[5] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp. | Zbl

[6] Meilanov R. P., Sveshnikova D. A., Shakhbanov O. M., “Metod differentsialnykh uravnenii drobnogo poryadka v opisanii kinetiki sorbtsii”, Zh. fiz. khimii, 77:2 (2003), 260–264

[7] Bedanokova S. Yu., “Matematicheskoe modelirovanie solevogo rezhima pochv s fraktalnoi strukturoi”, Vestnik Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. Nauki, 2:15 (2007), 102–109 | DOI | Zbl

[8] Verigin N. N., Vasilev S. V., Sarkisyan V. S., Sherzhukov B. S., Gidrodinamicheskie i fiziko-khimicheskie svoistva gornykh porod, Nedra, M., 1997, 271 pp.

[9] Iksanov R. G., “Zadacha Stefana o vpityvanii vlagi v pochvu”, Sb. nauchnykh trudov MGUP, M., 2004, 155–160

[10] Rubin J., Steinhardt R., “Soil water relations during rain infiltration. 1: Theory”, Soil Sci. Soc. Am. Proc., 27 (1963), 246–251 | DOI

[11] Zakrzhevskii P. I., Vakhonin N. K., “Eksperimentalnoe issledovanie vodopriemnoi sposobnosti zatoplennykh dren”, Konstruktsii i raschety osushitelno-uvlazhnitelnykh sistem, BelNIIMiVKh, Mn., 1978, 58–66

[12] Nakhusheva V. A., Differentsialnye uravneniya matematicheskikh modelei nelokalnykh protsessov, Nauka, M., 2006, 173 pp. | Zbl