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2019 | OriginalPaper | Buchkapitel

1. Introduction to Dynamic Transitions

verfasst von : Tian Ma, Shouhong Wang

Erschienen in: Phase Transition Dynamics

Verlag: Springer International Publishing

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Abstract

The study of phase transitions is an active field with a long history. This book aims to provide a comprehensive, unified, and balanced account of both dynamic and topological phase transition theories and their applications to statistical systems, quantum systems, classical and geophysical fluid dynamics, biological and chemical systems, and climate dynamics. The dynamic phase transition theory establishes a dynamic transition principle, Principle 1, following the philosophy of searching for a complete set of transition states. We present in this chapter a brief introduction to this dynamic transition theory together with an introduction to first-principle approach to fundamental laws of physics, and to fundamental issues of dynamic phase transitions motivated by problems in the nonlinear sciences.

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Fußnoten
1
For brevity, we use here \(\lambda \in \mathbb R\).
 
2
See the beginning of Chap. 2 for the precise definition, and Ma and Wang (2005b) for more detailed discussions.
 
Literatur
Zurück zum Zitat Cahn, J. and J. E. Hillard (1957). Free energy of a nonuniform system i. interfacial energy. J. Chemical Physics 28, 258–267. Cahn, J. and J. E. Hillard (1957). Free energy of a nonuniform system i. interfacial energy. J. Chemical Physics 28, 258–267.
Zurück zum Zitat Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability. Dover Publications, Inc.MATH Chandrasekhar, S. (1981). Hydrodynamic and Hydromagnetic Stability. Dover Publications, Inc.MATH
Zurück zum Zitat Drazin, P. and W. Reid (1981). Hydrodynamic Stability. Cambridge University Press.MATH Drazin, P. and W. Reid (1981). Hydrodynamic Stability. Cambridge University Press.MATH
Zurück zum Zitat Eckhardt, B., T. M. Schneider, B. Hof, and J. Westerweel (2007). Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.MathSciNetCrossRef Eckhardt, B., T. M. Schneider, B. Hof, and J. Westerweel (2007). Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468.MathSciNetCrossRef
Zurück zum Zitat Fisher, M. (1964). Specific heat of a gas near the critical point. Physical Review 136:6A, A1599–A1604.CrossRef Fisher, M. (1964). Specific heat of a gas near the critical point. Physical Review 136:6A, A1599–A1604.CrossRef
Zurück zum Zitat Ghil, M., T. Ma, and S. Wang (2001). Structural bifurcation of 2-D incompressible flows. Indiana Univ. Math. J. 50(Special Issue), 159–180. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). Ghil, M., T. Ma, and S. Wang (2001). Structural bifurcation of 2-D incompressible flows. Indiana Univ. Math. J. 50(Special Issue), 159–180. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000).
Zurück zum Zitat Ghil, M., T. Ma, and S. Wang (2005). Structural bifurcation of 2-D nondivergent flows with Dirichlet boundary conditions: applications to boundary-layer separation. SIAM J. Appl. Math. 65(5), 1576–1596 (electronic).MathSciNetCrossRef Ghil, M., T. Ma, and S. Wang (2005). Structural bifurcation of 2-D nondivergent flows with Dirichlet boundary conditions: applications to boundary-layer separation. SIAM J. Appl. Math. 65(5), 1576–1596 (electronic).MathSciNetCrossRef
Zurück zum Zitat Glansdorff, P. and I. Prigogine (1971). Structure, stability, and fluctuations. Wiley-Interscience, New York.MATH Glansdorff, P. and I. Prigogine (1971). Structure, stability, and fluctuations. Wiley-Interscience, New York.MATH
Zurück zum Zitat Kleman, M. and O. D. Laverntovich (2007). Soft matter physics: an introduction. Springer Science & Business Media. Kleman, M. and O. D. Laverntovich (2007). Soft matter physics: an introduction. Springer Science & Business Media.
Zurück zum Zitat Landau, L. D. and E. M. Lifshitz (1975). Course of theoretical physics, Vol. 2 (Fourth ed.). Oxford: Pergamon Press. The classical theory of fields, Translated from the Russian by Morton Hamermesh. Landau, L. D. and E. M. Lifshitz (1975). Course of theoretical physics, Vol. 2 (Fourth ed.). Oxford: Pergamon Press. The classical theory of fields, Translated from the Russian by Morton Hamermesh.
Zurück zum Zitat Ma, T. and S. Wang (2001). Structure of 2D incompressible flows with the Dirichlet boundary conditions. Discrete Contin. Dyn. Syst. Ser. B 1(1), 29–41.MathSciNetMATH Ma, T. and S. Wang (2001). Structure of 2D incompressible flows with the Dirichlet boundary conditions. Discrete Contin. Dyn. Syst. Ser. B 1(1), 29–41.MathSciNetMATH
Zurück zum Zitat Ma, T. and S. Wang (2004b). Dynamic bifurcation and stability in the Rayleigh-Bénard convection. Commun. Math. Sci. 2(2), 159–183.MathSciNetCrossRef Ma, T. and S. Wang (2004b). Dynamic bifurcation and stability in the Rayleigh-Bénard convection. Commun. Math. Sci. 2(2), 159–183.MathSciNetCrossRef
Zurück zum Zitat Ma, T. and S. Wang (2005b). Bifurcation theory and applications, Volume 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ. Ma, T. and S. Wang (2005b). Bifurcation theory and applications, Volume 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
Zurück zum Zitat Ma, T. and S. Wang (2005d). Geometric theory of incompressible flows with applications to fluid dynamics, Volume 119 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.CrossRef Ma, T. and S. Wang (2005d). Geometric theory of incompressible flows with applications to fluid dynamics, Volume 119 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.CrossRef
Zurück zum Zitat Ma, T. and S. Wang (2007a). Rayleigh-Bénard convection: dynamics and structure in the physical space. Commun. Math. Sci. 5(3), 553–574.MathSciNetCrossRef Ma, T. and S. Wang (2007a). Rayleigh-Bénard convection: dynamics and structure in the physical space. Commun. Math. Sci. 5(3), 553–574.MathSciNetCrossRef
Zurück zum Zitat Ma, T. and S. Wang (2007b). Stability and Bifurcation of Nonlinear Evolutions Equations. Science Press, Beijing. Ma, T. and S. Wang (2007b). Stability and Bifurcation of Nonlinear Evolutions Equations. Science Press, Beijing.
Zurück zum Zitat Ma, T. and S. Wang (2008a). Dynamic model and phase transitions for liquid helium. Journal of Mathematical Physics 49:073304, 1–18.MathSciNetMATH Ma, T. and S. Wang (2008a). Dynamic model and phase transitions for liquid helium. Journal of Mathematical Physics 49:073304, 1–18.MathSciNetMATH
Zurück zum Zitat Ma, T. and S. Wang (2008b). Dynamic phase transition theory in PVT systems. Indiana University Mathematics Journal 57:6, 2861–2889.MathSciNetCrossRef Ma, T. and S. Wang (2008b). Dynamic phase transition theory in PVT systems. Indiana University Mathematics Journal 57:6, 2861–2889.MathSciNetCrossRef
Zurück zum Zitat Ma, T. and S. Wang (2009a). Boundary-layer and interior separations in the Taylor-Couette-Poiseuille flow. J. Math. Phys. 50(3), 033101, 29.MathSciNetCrossRef Ma, T. and S. Wang (2009a). Boundary-layer and interior separations in the Taylor-Couette-Poiseuille flow. J. Math. Phys. 50(3), 033101, 29.MathSciNetCrossRef
Zurück zum Zitat Ma, T. and S. Wang (2009b). Cahn-Hilliard equations and phase transition dynamics for binary systems. Dist. Cont. Dyn. Systs., Ser. B 11:3, 741–784. Ma, T. and S. Wang (2009b). Cahn-Hilliard equations and phase transition dynamics for binary systems. Dist. Cont. Dyn. Systs., Ser. B 11:3, 741–784.
Zurück zum Zitat Ma, T. and S. Wang (2009c). Phase separation of binary systems. Physica A: Statistical Physics and its Applications 388:23, 4811–4817.CrossRef Ma, T. and S. Wang (2009c). Phase separation of binary systems. Physica A: Statistical Physics and its Applications 388:23, 4811–4817.CrossRef
Zurück zum Zitat Ma, T. and S. Wang (2011e). Third-order gas-liquid phase transition and the nature of Andrews critical point. AIP Advances 1, 042101.CrossRef Ma, T. and S. Wang (2011e). Third-order gas-liquid phase transition and the nature of Andrews critical point. AIP Advances 1, 042101.CrossRef
Zurück zum Zitat Ma, T. and S. Wang (2015a). Mathematical Principles of Theoretical Physics. Science Press, 524 pages. Ma, T. and S. Wang (2015a). Mathematical Principles of Theoretical Physics. Science Press, 524 pages.
Zurück zum Zitat Ma, T. and S. Wang (2017a). Dynamic law of physical motion and potential-descending principle. J. Math. Study 50:3, 215–241; see also HAL preprint: hal--01558752. Ma, T. and S. Wang (2017a). Dynamic law of physical motion and potential-descending principle. J. Math. Study 50:3, 215–241; see also HAL preprint: hal--01558752.
Zurück zum Zitat Nicolis, G. and I. Prigogine (1977). Self-organization in nonequilibrium systems. Wiley-Interscience, New York.MATH Nicolis, G. and I. Prigogine (1977). Self-organization in nonequilibrium systems. Wiley-Interscience, New York.MATH
Zurück zum Zitat Nishikawa, K. and T. Morita (1998). Fluid behavior at supercritical states studied by small-angle X-ray scattering. Journal of Supercritical Fluid 13, 143–148.CrossRef Nishikawa, K. and T. Morita (1998). Fluid behavior at supercritical states studied by small-angle X-ray scattering. Journal of Supercritical Fluid 13, 143–148.CrossRef
Zurück zum Zitat Novick-Cohen, A. and L. A. Segel (1984). Nonlinear aspects of the Cahn-Hilliard equation. Phys. D 10(3), 277–298.MathSciNetCrossRef Novick-Cohen, A. and L. A. Segel (1984). Nonlinear aspects of the Cahn-Hilliard equation. Phys. D 10(3), 277–298.MathSciNetCrossRef
Zurück zum Zitat Philander, S. G. and A. Fedorov (2003). Is el niño sporadic or cyclic? Annu. Rev. Earth Planet. Sci. 31, 579–594.CrossRef Philander, S. G. and A. Fedorov (2003). Is el niño sporadic or cyclic? Annu. Rev. Earth Planet. Sci. 31, 579–594.CrossRef
Zurück zum Zitat Pismen, L. M. (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, Berlin.MATH Pismen, L. M. (2006). Patterns and Interfaces in Dissipative Dynamics. Springer, Berlin.MATH
Zurück zum Zitat Prandtl, L. (1904). In Verhandlungen des dritten internationalen Mathematiker-Kongresses. Heidelberg, Leipeizig, pp. 484–491. Prandtl, L. (1904). In Verhandlungen des dritten internationalen Mathematiker-Kongresses. Heidelberg, Leipeizig, pp. 484–491.
Zurück zum Zitat Prigogine, I. and R. Lefever (1968). Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys. 48, 1695.CrossRef Prigogine, I. and R. Lefever (1968). Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys. 48, 1695.CrossRef
Zurück zum Zitat Raguin, L. G. and J. G. Georgiadis (2004). Kinematics of the stationary helical vortex mode in Taylor-Couette-Poiseuille flow. J. Fluid Mech. 516, 125–154.MathSciNetCrossRef Raguin, L. G. and J. G. Georgiadis (2004). Kinematics of the stationary helical vortex mode in Taylor-Couette-Poiseuille flow. J. Fluid Mech. 516, 125–154.MathSciNetCrossRef
Zurück zum Zitat Rayleigh, L. (1916). On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32(6), 529–46.CrossRef Rayleigh, L. (1916). On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32(6), 529–46.CrossRef
Zurück zum Zitat Reichl, L. E. (1998). A modern course in statistical physics (Second ed.). A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.MATH Reichl, L. E. (1998). A modern course in statistical physics (Second ed.). A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.MATH
Zurück zum Zitat Stanley, H. E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, New York and Oxford. Stanley, H. E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, New York and Oxford.
Zurück zum Zitat Yang, C. N. and R. Mills (1954). Conservation of isotopic spin and isotopic gauge invariance. Physical Review 96, 191–195.MathSciNetCrossRef Yang, C. N. and R. Mills (1954). Conservation of isotopic spin and isotopic gauge invariance. Physical Review 96, 191–195.MathSciNetCrossRef
Metadaten
Titel
Introduction to Dynamic Transitions
verfasst von
Tian Ma
Shouhong Wang
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-29260-7_1

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