Geodesic
Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 126-136 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe phase transitions using a one-dimensional fractional differential kinetic equation of the Fokker–Planck type. We find a general solution describing the growth of nuclei during phase transitions in a fractal medium.
Keywords: phase transition of a fractional order, growth of nuclei, fractional differential Fokker–Planck equation. 
@article{TMF_2013_177_1_a5,
     author = {V. N. Borodikhin},
     title = {Phase transitions and peculiarities of the~growth of nuclei of the~new phase of a~substance},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {126--136},
     year = {2013},
     volume = {177},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a5/}
}
TY  - JOUR
AU  - V. N. Borodikhin
TI  - Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 126
EP  - 136
VL  - 177
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a5/
LA  - ru
ID  - TMF_2013_177_1_a5
ER  - 
%0 Journal Article
%A V. N. Borodikhin
%T Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 126-136
%V 177
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a5/
%G ru
%F TMF_2013_177_1_a5
V. N. Borodikhin. Phase transitions and peculiarities of the growth of nuclei of the new phase of a substance. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 126-136. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a5/

[1] Ya. B. Zeldovich, ZhETF, 12 (1942), 525–538

[2] E. M. Lifshits, L. P. Pitaevskii, Teoreticheskaya fizika, v. 10, Fizicheskaya kinetika, Fizmatlit, M., 2002 | MR

[3] V. E. Tarasov, Fractional Dynamics: Applycation of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg; Higher Education Press, Beijing, 2010 | MR | Zbl

[4] G. I. Kapel, S. V. Razorenov, A. V. Utkin, V. E. Fortov, Udarno-volnovye yavleniya v kondensirovannykh sredakh, Yanus-K, M., 1996

[5] L. Petronero, E. Tozatti (red.), Fraktaly v fizike, Trudy VI Mezhdunarodnogo simpoziuma po fraktalam v fizike (MTsTF, Triest, Italiya, 9–12 iyulya 1985), Mir, M., 1988

[6] A. V. Milovanov, L. M. Zelenyi, G. Zimbardo, P. Veltri, J. Geophys. Res., 106:A4 (2001), 6291–6307 | DOI

[7] K. Rypdal, J.-V. Paulsen, O. E. Garcia, S. V. Ratynskaia, V. I. Demidov, Nonlin. Processes Geophys., 10 (2003), 139–149 | DOI

[8] A. V. Milovanov, J. J. Rasmussen, Phys. Rev. B, 66:13 (2002), 134505, 11 pp. | DOI

[9] A. I. Olemskoi, Sinergetika slozhnykh sistem. Fenomenologiya i statisticheskaya teoriya, Editorial URSS, M., 2009

[10] G. M. Zaslavsky, “Fractional kinetics of Hamiltonian chaotic systems”, Application of Fractional Calculus in Physics, ed. R. Hilfer, World Sci., River Edge, NJ, 2000, 203–239 | DOI | MR | Zbl

[11] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Mathematics in Science and Engineering, 198, Academic Press, San Diego, CA, 1999 | MR | Zbl

[12] K. B. Oldham, J. Spanier, The Fractional Calculus. Theory and Applications of Differentiation and Integration to Arbitrary Order, Mathematics in Science and Engineering, 111, Academic Press, New York, London, 1974 | MR | Zbl

[13] A. M. Mathai, R. K. Saxena, H. J. Haubold, The H-Function. Theory and Application, Springer, Dordrecht, 2010 | MR | Zbl

[14] K. Tsallis, Introduction in Nonextensive Statistical Mechanics. Approaching a Complex World, Springer, Berlin, 2009 | MR | Zbl

[15] B. B. Mandelbrot, Fraktalnaya geometriya prirody, IKI, M., 2002

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

[17] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady, v. 3, Spetsialnye funktsii. Dopolnitelnye glavy, Fizmatlit, M., 2003 | MR | Zbl

[18] H. Bateman, Higher Transcedental Function, v. 1, McGraw-Hill, New York, 1953

[19] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 5, Statisticheskaya fizika, Fizmatlit, M., 2002 | MR | Zbl

[20] L. M. Zelënyi, A. V. Milovanov, UFN, 174:8 (2004), 809–852 | DOI | DOI