Geodesic
Geometric model of the formation of superdiffusion processes
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 430-441 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct a dynamical model of the deformation of a classical diffusion process into superdiffusion implementing the interaction between the diffusion background medium and the external medium. We show how the transformation law of energy characteristics of this deformation is formed gradually.
Mots-clés : superdiffusion, quasiparticles
Keywords: background medium, stationary process, Hausdorff measure, transfer of energy and momentum, Compton scattering. 
@article{TMF_2022_210_3_a7,
     author = {N. S. Arkashov and V. A. Seleznev},
     title = {Geometric model of the~formation of superdiffusion processes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {430--441},
     year = {2022},
     volume = {210},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a7/}
}
TY  - JOUR
AU  - N. S. Arkashov
AU  - V. A. Seleznev
TI  - Geometric model of the formation of superdiffusion processes
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2022
SP  - 430
EP  - 441
VL  - 210
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a7/
LA  - ru
ID  - TMF_2022_210_3_a7
ER  - 
%0 Journal Article
%A N. S. Arkashov
%A V. A. Seleznev
%T Geometric model of the formation of superdiffusion processes
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2022
%P 430-441
%V 210
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a7/
%G ru
%F TMF_2022_210_3_a7
N. S. Arkashov; V. A. Seleznev. Geometric model of the formation of superdiffusion processes. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 430-441. http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a7/

[1] T. Nakayama, K. Yakubo, “Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations”, Rev. Modern Phys., 66:2 (1994), 381–443 | DOI

[2] L. M. Zelenyi, A. V. Milovanov, “Fraktalnaya topologiya i strannaya kinetika: ot teorii perkolyatsii k problemam kosmicheskoi elektrodinamiki”, UFN, 174:8 (2004), 809–852 | DOI | DOI

[3] N. S. Arkashov, V. A. Seleznev, “Ob energeticheskikh kharakteristikakh protsessov anomalnoi diffuzii”, TMF, 199:3 (2019), 479–496 | DOI | DOI | MR

[4] G. Edgar, Measure, Topology, and Fractal Geometry, Springer, New York, 2008 | DOI | MR

[5] I. A. Ibragimov, Yu. V. Linni, Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965

[6] N. S. Arkashov, V. A. Seleznev, “O dinamike statsionarnykh protsessov sdviga s kantorovoi strukturoi”, Sib. matem. zhurn., 58:5 (2017), 972–988 | DOI | DOI

[7] L. Brillouin, Science and Information Theory, Academic Press, New York, 1962 | MR

[8] Yu. A. Rozanov, Sluchainye protsessy, Nauka, M., 1971

[9] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984 | MR | MR | Zbl

[10] N. S. Arkashov, V. A. Seleznev, “O modeli sluchainogo bluzhdaniya na mnozhestvakh s samopodobnoi strukturoi”, Sib. matem. zhurn., 54:6 (2013), 1216–1236 | DOI | MR

[11] N. S. Arkashov, V. A. Seleznev, “O modeli sub- i superdiffuzii na topologicheskikh prostranstvakh s samopodobnoi strukturoi”, Teoriya veroyatn. i ee primen., 60:2 (2015), 209–226 | DOI | DOI