Geodesic
Branching of symmetric solution of molecular field equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 246-258 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Branching of a completely symmetric solution of the molecular field equation is investigated under the assumption fnat the configuration space of a molecule is a certain group $Q$. The scheme can be used to describe orientationally ordered and spacemodulated structures. Phase transitions from an isotropic liquid to the nematic, cholesteric, and conic phases are considered. The relationship between the phase-transition characteristics (order, Curie point, symmetry of the newly formed phase) and the potential of the intermolecular interaction is established. Investigation of the isolated isotropic-liquid–two-axis-nematic phase transition point has shown that this is not always a second-order transition. The possible existence of a one-dimensional modulated structure having smectic-$A$ symmetry is predicted. The corresponding phase transition follows a scenario different from that of the isotropie-liquid–smectic-$A$ phase transition. 
@article{TMF_1992_90_2_a8,
     author = {A. N. Shramkov and P. P. Shtifanyuk},
     title = {Branching of symmetric solution of molecular field equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {246--258},
     year = {1992},
     volume = {90},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a8/}
}
TY  - JOUR
AU  - A. N. Shramkov
AU  - P. P. Shtifanyuk
TI  - Branching of symmetric solution of molecular field equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 246
EP  - 258
VL  - 90
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a8/
LA  - ru
ID  - TMF_1992_90_2_a8
ER  - 
%0 Journal Article
%A A. N. Shramkov
%A P. P. Shtifanyuk
%T Branching of symmetric solution of molecular field equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 246-258
%V 90
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a8/
%G ru
%F TMF_1992_90_2_a8
A. N. Shramkov; P. P. Shtifanyuk. Branching of symmetric solution of molecular field equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 2, pp. 246-258. http://geodesic.mathdoc.fr/item/TMF_1992_90_2_a8/

[1] Tyablikov S. V., ZhETF, 17:5 (1947), 386–389

[2] Vlasov A. A., Nelokalnaya statisticheskaya mekhanika, Nauka, M., 1978 | MR | Zbl

[3] Weeks J. D., Rice S. A., Kozak J. J., J. Chem. Phys., 52:5 (1970), 2416–2426 | DOI | MR

[4] Brout R., Physica, 29:10 (1963), 1041–1056 | DOI

[5] Tareeva E. E., TMF, 21:3 (1974), 343–353 | MR | Zbl

[6] Kayser R. E., Raveche J. R., Phys. Rev. A, 17:6 (1978), 2067–2072 | DOI

[7] Tareeva E. E., Trapezina T. I., DAN SSSR, 223:4 (1975), 823–826

[8] Tareeva E. E., Trapezina T. I., TMF, 26:2 (1976), 269–276

[9] Trapezina T. I., TMF, 29:1 (1976), 136–142

[10] Mulder B., Phys. Rev. A, 39:1 (1989), 360–370 | DOI

[11] Loginov B. V., Teoriya vetvleniya reshenii nelineinykh uravnenii v usloviyakh gruppovoi invariantnosti, FAN, Tashkent, 1985 | MR | Zbl

[12] Tareyeva E. E., Trapezina T. I., Phys. Lett. A, 60 (1977), 217 | DOI

[13] Sattinger D. H., J. Math. Phys., 19:8 (1978), 1720–1732 | DOI | MR | Zbl

[14] Birman M. Sh., Vilenkin N. Ya., Gorin E. A. i dr., Funktsionalnyi analiz, Nauka, M., 1972 | MR

[15] Varshalovich D. A., Moskalev A. N., Khersonskii V. K., Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975

[16] Kats E. I., UFN, 142:1 (1984), 99–129 | DOI | MR

[17] Straley J. P., Phys. Rev. A, 10:5 (1974), 1881–1887 | DOI

[18] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Nauka, M., 1974 | MR

[19] Brazovskii S. A., Dmitriev S. G., ZhETF, 69:3(9) (1975), 979–989

[20] Rosciszewski K., Acta phys. pol., 67:6 (1986), 999–1034 | MR

[21] Hardouin F., Mery S., Achard M. F., Mauzac M., Davidson P., Keller P., Liq. Cryst., 8:4 (1990), 565–575 | DOI

[22] Keat W. K., Winter B. A., Fontes E., Heiney P. A., Ohba M., Haseltine J. N., Smith A. B., Liq. Cryst., 4:1 (1989), 87–102 | DOI

[23] Chilaya G. S., Lisetski L. N., Mol. Cryst. Liq. Cryst., 140 (1986), 243–286 | DOI