Geodesic
Construction of generalized thermodynamic potentials by the Lie algebra method
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 239-246 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Lie group and Lie algebra are found basing on the analysis of the linearized system of differential equations describing the Williams domains in the nematic liquid crystal. By means of the algebra found, the nonlinear differential equation is obtained which is at the same time the Euler equation for the generalized thermodynamic potential (GTP) describing dissipative structures, the Williams domains. The GTP is found which describes the low-frequency regime of the Williams domains. The scheme described can also be applied to constructing the GTP of the high-frequency electrohydrodynamic instability. 
@article{TMF_1989_81_2_a8,
     author = {E. D. Belotskii and N. G. Migranov and P. M. Tomchuk},
     title = {Construction of~generalized thermodynamic potentials by~the {Lie} algebra method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {239--246},
     year = {1989},
     volume = {81},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a8/}
}
TY  - JOUR
AU  - E. D. Belotskii
AU  - N. G. Migranov
AU  - P. M. Tomchuk
TI  - Construction of generalized thermodynamic potentials by the Lie algebra method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1989
SP  - 239
EP  - 246
VL  - 81
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a8/
LA  - ru
ID  - TMF_1989_81_2_a8
ER  - 
%0 Journal Article
%A E. D. Belotskii
%A N. G. Migranov
%A P. M. Tomchuk
%T Construction of generalized thermodynamic potentials by the Lie algebra method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1989
%P 239-246
%V 81
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a8/
%G ru
%F TMF_1989_81_2_a8
E. D. Belotskii; N. G. Migranov; P. M. Tomchuk. Construction of generalized thermodynamic potentials by the Lie algebra method. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 239-246. http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a8/

[1] De Zhen P., Fizika zhidkikh kristallov, Mir, M., 1978

[2] Lattindzher Dzh., Kon V., Problemy fiziki poluprovodnikov, IIL, M., 1957, S. 514–539.

[3] Belotskii E. D., Migranov N. G., Tomchuk P. M., Nelineinye protsessy v NZhK v elektricheskikh polyakh, Preprint No 7, IF AN USSR, Kiev, 1983

[4] Graham R., Phys. Rev. A, 10:5 (1974), 1762–1784 | DOI

[5] Belotskii E. D., Tomchuk P. M., ZhETF, 88:5 (1985), 1634–1640

[6] Lowe M., Gollub J. P., Lubensky T. C., Phys. Rev. Lett., 51:9 (1983), 786–789 | DOI

[7] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[8] Ovsyannikov L. V., Dinamika sploshnoi sredy, no. 7, Novosibirskii GU, Novosibirsk, 1971, 5–11

[9] Pikin S. A., Strukturnye prevrascheniya v zhidkikh kristallakh, Nauka, M., 1981

[10] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[11] Belotskii E. D., Migranov N. G., Tomchuk P. M., Obrazovanie dvumernykh nesoizmerimykh struktur v sisteme domenov Vilyamsa, Preprint No 8, IF AN USSR, Kiev, 1986