Numerical simulation of anomalous diffusion in polygonal billiard gas channel
Matematičeskoe modelirovanie, Tome 25 (2013) no. 5, pp. 3-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

Some problems of applying fractional calculus for models of anomalous diffusion in polygonal billiard gas channels are considered. It is shown that results of microscale modeling and numerical solution for corresponding fractional equations are in good agreement.
Mots-clés : anomalous diffusion, fractional calculus, billiard gas channel, space-time particles evolution.
Keywords: microscale modeling
@article{MM_2013_25_5_a0,
     author = {D. L. Reviznikov and Y. V. Slastushenskiy},
     title = {Numerical simulation of anomalous diffusion in polygonal billiard gas channel},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {25},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_5_a0/}
}
TY  - JOUR
AU  - D. L. Reviznikov
AU  - Y. V. Slastushenskiy
TI  - Numerical simulation of anomalous diffusion in polygonal billiard gas channel
JO  - Matematičeskoe modelirovanie
PY  - 2013
SP  - 3
EP  - 14
VL  - 25
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2013_25_5_a0/
LA  - ru
ID  - MM_2013_25_5_a0
ER  - 
%0 Journal Article
%A D. L. Reviznikov
%A Y. V. Slastushenskiy
%T Numerical simulation of anomalous diffusion in polygonal billiard gas channel
%J Matematičeskoe modelirovanie
%D 2013
%P 3-14
%V 25
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2013_25_5_a0/
%G ru
%F MM_2013_25_5_a0
D. L. Reviznikov; Y. V. Slastushenskiy. Numerical simulation of anomalous diffusion in polygonal billiard gas channel. Matematičeskoe modelirovanie, Tome 25 (2013) no. 5, pp. 3-14. http://geodesic.mathdoc.fr/item/MM_2013_25_5_a0/

[1] Olemskoi A. I., Kharchenko D. O., Samoorganizatsiya samopodobnykh stokhasticheskikh sistem, NITs «Regulyarnaya i khaoticheskaya dinamika», Institut kompyuternykh issledovanii, M.–Izhevsk, 2007, 296 pp.

[2] Uchaikin V. V., Metod drobnykh proizvodnykh, «Artishok», Ulyanovsk, 2008, 512 pp.

[3] Baowen Li, Jiao Wang, Lei Wang, Gang Zhang, “Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels”, Chaos, 15 (2005), 015121 | DOI

[4] Maruyama Sh., “CVD growth and heat transfer of carbon nanotubes”, Proceedings of the 14th International Heat Transfer Conference IHTC14 (August 8–13, 2010, Washington, DC, USA), 23350

[5] Nuo Yang, Gang Zhang, Baowen Li., “Violation of Fourier`s law and anomalous heat diffusion in silicon nanowires”, Nano Today, 5 (2010), 85–90 | DOI

[6] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp. | MR | Zbl

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

[8] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 199 pp. | MR | Zbl

[9] Tarasov V. E., Modeli teoreticheskoi fiziki s integrodifferentsirovaniem drobnogo poryadka, RKhD, M.–Izhevsk, 2010, 568 pp.

[10] Meerschaert M. M., Tadjeran C., “Finite difference approximations for fractional advection-dispersion flow equations”, Journal of Computational and Applied Mathematics, 172 (2004), 65–77 | DOI | MR | Zbl

[11] Petukhov A. A., Reviznikov D. L., “Algoritmy chislennogo resheniya drobno-differentsialnykh uravnenii”, Vestnik MAI, 16:6 (2009), 228–234

[12] Goloviznin V. M., Kiselev V. P., Korotkin I. A., Yurkov Yu. P., Nekotorye osobennosti vychislitelnykh algoritmov dlya uravnenii drobnoi diffuzii, preprint IBRAE-2002-01, IBRAE RAN, M., 2002

[13] Reviznikov D. L., Slastushenskii Yu. V., “Primenenie drobno-differentsialnogo ischisleniya dlya opisaniya anomalnoi diffuzii”, Vestnik MAI, 18:4 (2011), 76–82

[14] Gorenflo R., Mainardi F., “Random Walk Models for Space-Fractional Diffusion Processes”, Fractional Calculus Applied Analysys, 1:2 (1998), 167–191 | MR | Zbl

[15] Slastushenskii Yu. V., “Model sluchainogo bluzhdaniya dlya uravneniya anomalnoi diffuzii”, Nauchno-tekhnicheskii Vestnik Povolzhya, 2011, no. 5, 242–246