- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
Periodic unimodal Allee maps, the semigroup property and the $\lambda$-Ricker map with Allee effect
Dynamic transitions for Landau-Brazovskii model
1. | School of Mathematical Sciences, Peking University, Beijing, 100871, China, China |
2. | LMAM, CAPT and School of Mathematical Sciences, Peking University, Beijing, 100871, China |
References:
[1] |
S. A. Brazovskii, Phase transition of an isotropic system to a nonuniform state, In 30 Years of the Landau Institute - Selected Papers, volume 11 of World Scientific Series in 20th Century Physics, pages 109-113. World Scientific Publishing, 1995.
doi: 10.1142/9789814317344_0016. |
[2] |
M. Brunella and M. Miari, Topological equivalence of a plane vector field with its principal part defined through newton polyhedra, Journal of differential equations, 85 (1990), 338-366.
doi: 10.1016/0022-0396(90)90120-E. |
[3] |
A. D. Bruno, Local Methods in Nonlinear Differential Equations, Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61314-2. |
[4] |
G. H. Fredrickson and E. Helfand, Fluctuation effects in the theory of microphase separation in block copolymers, Journal Chemical Physics, 87 (1987), 697-705.
doi: 10.1063/1.453566. |
[5] |
H. Jenkins, Chemical Thermodynamics at a Glance, Wiley Online Library, 2008.
doi: 10.1002/9780470697733. |
[6] |
E. I. Kats, V. V. Lebedev and A. R. Muratov, Weak crystallization theory, Physics Reports, 228 (1993), 1-91.
doi: 10.1016/0370-1573(93)90119-X. |
[7] |
L. Leibler, Theory of microphase separation in block copolymers, Macromolecules, 13 (1980), 1602-1617.
doi: 10.1021/ma60078a047. |
[8] |
H. Liu, T. Sengul, S. Wang and P. Zhang, Dynamic Transitions and Pattern Formations for Cahn-Hilliard Model with Long-Range Repulsive Interactions, to be published, 2013. |
[9] |
T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamic for binary systems, Discrete and Continuous Dynamical Systems, Series B, 11 (2009), 741-784.
doi: 10.3934/dcdsb.2009.11.741. |
[10] |
T. Ma and S. Wang, Phase Transition Dynamics, Springer-Verlag, 2014.
doi: 10.1007/978-1-4614-8963-4. |
[11] |
A. Shi, Nature of anisotropic fluctuation modes in ordered systems, Journal of Physics: Condensed Matter, 11 (1999), 10183-10197.
doi: 10.1088/0953-8984/11/50/311. |
[12] |
A. Shi, J. Noolandi and R. C. Desai, Theory of anisotropic fluctuations in ordered block copolymer phases, Macromolecules, 29 (1996), 6487-6504.
doi: 10.1021/ma960411t. |
[13] |
X. Zhang and P. Zhang, An efficient numerical method of Landau-Brazovskii model, Journal of Computational Physics, 227 (2008), 5859-5870.
doi: 10.1016/j.jcp.2008.02.021. |
show all references
References:
[1] |
S. A. Brazovskii, Phase transition of an isotropic system to a nonuniform state, In 30 Years of the Landau Institute - Selected Papers, volume 11 of World Scientific Series in 20th Century Physics, pages 109-113. World Scientific Publishing, 1995.
doi: 10.1142/9789814317344_0016. |
[2] |
M. Brunella and M. Miari, Topological equivalence of a plane vector field with its principal part defined through newton polyhedra, Journal of differential equations, 85 (1990), 338-366.
doi: 10.1016/0022-0396(90)90120-E. |
[3] |
A. D. Bruno, Local Methods in Nonlinear Differential Equations, Springer-Verlag, Berlin, 1989.
doi: 10.1007/978-3-642-61314-2. |
[4] |
G. H. Fredrickson and E. Helfand, Fluctuation effects in the theory of microphase separation in block copolymers, Journal Chemical Physics, 87 (1987), 697-705.
doi: 10.1063/1.453566. |
[5] |
H. Jenkins, Chemical Thermodynamics at a Glance, Wiley Online Library, 2008.
doi: 10.1002/9780470697733. |
[6] |
E. I. Kats, V. V. Lebedev and A. R. Muratov, Weak crystallization theory, Physics Reports, 228 (1993), 1-91.
doi: 10.1016/0370-1573(93)90119-X. |
[7] |
L. Leibler, Theory of microphase separation in block copolymers, Macromolecules, 13 (1980), 1602-1617.
doi: 10.1021/ma60078a047. |
[8] |
H. Liu, T. Sengul, S. Wang and P. Zhang, Dynamic Transitions and Pattern Formations for Cahn-Hilliard Model with Long-Range Repulsive Interactions, to be published, 2013. |
[9] |
T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamic for binary systems, Discrete and Continuous Dynamical Systems, Series B, 11 (2009), 741-784.
doi: 10.3934/dcdsb.2009.11.741. |
[10] |
T. Ma and S. Wang, Phase Transition Dynamics, Springer-Verlag, 2014.
doi: 10.1007/978-1-4614-8963-4. |
[11] |
A. Shi, Nature of anisotropic fluctuation modes in ordered systems, Journal of Physics: Condensed Matter, 11 (1999), 10183-10197.
doi: 10.1088/0953-8984/11/50/311. |
[12] |
A. Shi, J. Noolandi and R. C. Desai, Theory of anisotropic fluctuations in ordered block copolymer phases, Macromolecules, 29 (1996), 6487-6504.
doi: 10.1021/ma960411t. |
[13] |
X. Zhang and P. Zhang, An efficient numerical method of Landau-Brazovskii model, Journal of Computational Physics, 227 (2008), 5859-5870.
doi: 10.1016/j.jcp.2008.02.021. |
[1] |
Matteo Novaga, Enrico Valdinoci. The geometry of mesoscopic phase transition interfaces. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 777-798. doi: 10.3934/dcds.2007.19.777 |
[2] |
Hayato Chiba, Georgi S. Medvedev. The mean field analysis of the kuramoto model on graphs Ⅱ. asymptotic stability of the incoherent state, center manifold reduction, and bifurcations. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3897-3921. doi: 10.3934/dcds.2019157 |
[3] |
I-Liang Chern, Chun-Hsiung Hsia. Dynamic phase transition for binary systems in cylindrical geometry. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 173-188. doi: 10.3934/dcdsb.2011.16.173 |
[4] |
Erwann Delay, Pieralberto Sicbaldi. Extremal domains for the first eigenvalue in a general compact Riemannian manifold. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5799-5825. doi: 10.3934/dcds.2015.35.5799 |
[5] |
Camillo De Lellis, Emanuele Spadaro. Center manifold: A case study. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1249-1272. doi: 10.3934/dcds.2011.31.1249 |
[6] |
Jun Yang. Coexistence phenomenon of concentration and transition of an inhomogeneous phase transition model on surfaces. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 965-994. doi: 10.3934/dcds.2011.30.965 |
[7] |
Pavel Krejčí, Jürgen Sprekels. Long time behaviour of a singular phase transition model. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1119-1135. doi: 10.3934/dcds.2006.15.1119 |
[8] |
Mauro Garavello. Boundary value problem for a phase transition model. Networks and Heterogeneous Media, 2016, 11 (1) : 89-105. doi: 10.3934/nhm.2016.11.89 |
[9] |
Mauro Garavello, Francesca Marcellini. The Riemann Problem at a Junction for a Phase Transition Traffic Model. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5191-5209. doi: 10.3934/dcds.2017225 |
[10] |
Pierluigi Colli, Antonio Segatti. Uniform attractors for a phase transition model coupling momentum balance and phase dynamics. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 909-932. doi: 10.3934/dcds.2008.22.909 |
[11] |
Claudia Valls. The Boussinesq system:dynamics on the center manifold. Communications on Pure and Applied Analysis, 2005, 4 (4) : 839-860. doi: 10.3934/cpaa.2005.4.839 |
[12] |
Hongyu Cheng, Rafael de la Llave. Time dependent center manifold in PDEs. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6709-6745. doi: 10.3934/dcds.2020213 |
[13] |
Katarzyna Grabowska, Paweƚ Urbański. Geometry of Routh reduction. Journal of Geometric Mechanics, 2019, 11 (1) : 23-44. doi: 10.3934/jgm.2019002 |
[14] |
Wei-Ming Ni, Xuefeng Wang. On the first positive Neumann eigenvalue. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 1-19. doi: 10.3934/dcds.2007.17.1 |
[15] |
Robert Brooks and Eran Makover. The first eigenvalue of a Riemann surface. Electronic Research Announcements, 1999, 5: 76-81. |
[16] |
Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks and Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011 |
[17] |
Kousuke Kuto, Tohru Tsujikawa. Stationary patterns for an adsorbate-induced phase transition model I: Existence. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1105-1117. doi: 10.3934/dcdsb.2010.14.1105 |
[18] |
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4255-4281. doi: 10.3934/dcds.2021035 |
[19] |
Sergey V. Bolotin, Piero Negrini. Global regularization for the $n$-center problem on a manifold. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 873-892. doi: 10.3934/dcds.2002.8.873 |
[20] |
Stefano Bianchini, Alberto Bressan. A center manifold technique for tracing viscous waves. Communications on Pure and Applied Analysis, 2002, 1 (2) : 161-190. doi: 10.3934/cpaa.2002.1.161 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]