Geodesic
Bifurcation effects in thermodynamics of Markovian copolymers away from the critical point
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 696-707 
A. N. Ivanova; L. I. Manevich. Bifurcation effects in thermodynamics of Markovian copolymers away from the critical point. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 696-707. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a13/
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     author = {A. N. Ivanova and L. I. Manevich},
     title = {Bifurcation effects in thermodynamics of {Markovian} copolymers away from the critical point},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {696--707},
     year = {2011},
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     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a13/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical computations of inhomogeneous free-energy extremals on the basis of the thermodynamic model of Markovian copolymers have shown that they exhibit two qualitatively different scenarios of behavior with varying temperature. The first occurs in systems with close points of the trivial and nontrivial spinodals, while the second scenario takes place when the turning point of an extremal is sufficiently far away from the point of the nontrivial spinodal. In this case, as the binodal is approached, the model exhibits a secondary bifurcation point, i.e., the intersection point with the homogeneous nontrivial extremal issuing from the point of the trivial spinodal. At this point, the homogeneous nontrivial extremal becomes unstable with respect to periodic perturbations of frequency $q^*$ corresponding to a bifurcation of inhomogeneous extremals from the trivial state (point of the nontrivial spinodal). This bifurcation is studied for lamellar, hexagonal, and body-centered cubic structures. The evolution of the extremals is numerically computed until an absolutely stable state corresponding to the binodal is reached.

[1] Panyukov S. V., Kuchanov S. I., “Obschii statisticheskii podkhod dlya opisaniya polimerov s proizvolnoi khimicheskoi strukturoi”, Zh. eksperim. i teor. fiz., 1991, no. 2, 659–674

[2] Panjukov S. V., Kuchanov S. I., “New statistical approach to the description of spatial inhomogeneous states inheteropolymer solutuions”, J. Phys. France, 2 (1992), 1973–1993 | DOI

[3] Ivanova A. N., Kuchanov S. I., Manevitch L. I., “Bifurcation analysis for the construction of a phase diagram of heteropolymer liquids”, J. Math. Phys., 46 (2005), 013301, 19 pp. | DOI | MR | Zbl

[4] Ivanova A. N., Kuchanov S. I., Manevich L. I., “Bifurkatsionnye metody v termodinamike sopolimerov”, VMS. Ser. F, 47:6 (2005), 1011–1018

[5] Volpert A. I., Ivanova A. N., “O diffuzionnoi neustoichivosti i dissipativnykh strukturakh v khimicheskoi kinetike”, Avtovolnovye protsessy v sistemakh s diffuziei, Gorkii, 1981, 33–45

[6] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya nelineinykh differentsialnykh uravnenii, Nauka, M., 1969 | MR

[7] Landau L. D., Lifshits E. M., Statisticheskaya fizika, Nauka, M., 1964 | Zbl

[8] Yudovich V. I., “O vozniknovenii konvektsii”, Prikl. matem. i mekhan., 30:6 (1966), 1000–1005

[9] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl