Dynamic phase transition for binary systems in cylindrical geometry

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July 2011, 16(1): 173-188. doi: 10.3934/dcdsb.2011.16.173

Dynamic phase transition for binary systems in cylindrical geometry

I-Liang Chern ^1, and Chun-Hsiung Hsia ^2,

1.	Department of Mathematics and Taidar Institute of Mathematical Science, National Taiwan University, Taipei, 10617, Taiwan
2.	Department of Mathematics and Taidar Institute of Mthematical Science, National Taiwan University, Taipei, 10617, Taiwan

Received February 2010 Revised August 2010 Published April 2011

Abstract
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In this article, we present a dynamic phase transition and stability analysis for the Cahn-Hilliard equations in cylindrical geometry. Two types of phase transitions (the continuous type and the jump type) are determined explicitly in terms of relevant physical and geometric parameters.

Keywords: binary system., bifurcation, Phase transition, stability.

Mathematics Subject Classification: 37G3.

Citation: 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

References:

[1]	Stephen J. Blundell and Katherine M. Blundell, "Concepts in Thermal Physics," Oxford University Press, 2008.
[2]	C. M. Elliott and H. Garcke, Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix, Physica D, 109 (1997), 242-256. doi: 10.1016/S0167-2789(97)00066-3.
[3]	J. E. Hilliard, Spinodal decomposition, in Phase Transformations, American Society for Metal, Cleveland, (1970), 497-560.
[4]	T. Ma and S. Wang, "Bifurcation Theory and Applications," vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises,
[5]	T. Ma and S. Wang, Dynamic phase transition theory in PVT systems, Indiana Univ. Math. J., 57 (2008), 2861-2889. doi: 10.1512/iumj.2008.57.3630.
[6]	T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamics for binary systems, Discrete Contin. Dyn. Syst. Ser. B, 11 (2009), 741-784. doi: 10.3934/dcdsb.2009.11.741.
[7]	T. Ma and S. Wang, Phase separation of binary systems, Phys. Rev. A., 388 (2009), 4811-4817.
[8]	J. Moser, A rapidly convergent iteration method and nonlinear partial differential equation. I, Ann. Sc. Norm. Super. Pisa, 20 (1966), 265-315.
[9]	L. E. Reichl, "A Modern Course in Statistical Physics," (Second ed.) A Wiley-Interscinece Publication. New York: John Wiley & Sons Inc. 1998.

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References:

[1]	Stephen J. Blundell and Katherine M. Blundell, "Concepts in Thermal Physics," Oxford University Press, 2008.
[2]	C. M. Elliott and H. Garcke, Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix, Physica D, 109 (1997), 242-256. doi: 10.1016/S0167-2789(97)00066-3.
[3]	J. E. Hilliard, Spinodal decomposition, in Phase Transformations, American Society for Metal, Cleveland, (1970), 497-560.
[4]	T. Ma and S. Wang, "Bifurcation Theory and Applications," vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises,
[5]	T. Ma and S. Wang, Dynamic phase transition theory in PVT systems, Indiana Univ. Math. J., 57 (2008), 2861-2889. doi: 10.1512/iumj.2008.57.3630.
[6]	T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamics for binary systems, Discrete Contin. Dyn. Syst. Ser. B, 11 (2009), 741-784. doi: 10.3934/dcdsb.2009.11.741.
[7]	T. Ma and S. Wang, Phase separation of binary systems, Phys. Rev. A., 388 (2009), 4811-4817.
[8]	J. Moser, A rapidly convergent iteration method and nonlinear partial differential equation. I, Ann. Sc. Norm. Super. Pisa, 20 (1966), 265-315.
[9]	L. E. Reichl, "A Modern Course in Statistical Physics," (Second ed.) A Wiley-Interscinece Publication. New York: John Wiley & Sons Inc. 1998.

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