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A Phase Field System with Memory: Stability and Damped Oscillations

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Continuum Models and Discrete Systems

Part of the book series: NATO Science Series ((NAII,volume 158))

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Abstract

Recently [7] a phenomenological model has been proposed to describe first order phase transitions which take place in the presence of configurational modes which resolve themselves on a slow time scale. This model takes the form of a phase field System with memory. A major feature of this model, as opposed to the classical phase field model, is the possibility of damped oscillations which can appear when considering the stability of steady states as well as in the interfacial motion which occurs during coarsening.

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References

  1. P.W. Bates & P.C. Fife, Spectral comparison principles for the Cahn-Hilliard and Phase-Field equations, and time scales for coarsening, Physica D 43 (1990) 335–348.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Ration. Mech. Anal,. 92 (1986) 205–245.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Grinfeld & A. Novick-Cohen, in preparation.

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  4. P.C. Hohenberg & B.I. Halperin, Theory of dynamical critical phenomena, Rev. Modern Phys. 49 (1977) 435–479.

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  5. J.S. Langer, Models of pattern formation in first-order phase transitions, in Directions in Condensed Matter Physics, G. Grinstein and G. Mazenko, eds., World Scientific, Singa-pore, 1986, pp. 165–186.

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  6. H.G. Rotstein, Phase Transition Dynamics with Memory, Ph.D. thesis, Department of Mathematics, Technion-IIT, Haifa, Israel, 1998.

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  7. H.G. Rotstein, S. Brandon, A. Novick-Cohen & A. Nepomnyashchy, Phase field equations with memory: the hyperbolic case, SIAM J. Appl. Math. 62 (2001) 264–282.

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© 2004 Springer Science+Business Media Dordrecht

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Novick-Cohen, A. (2004). A Phase Field System with Memory: Stability and Damped Oscillations. In: Bergman, D.J., Inan, E. (eds) Continuum Models and Discrete Systems. NATO Science Series, vol 158. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2316-3_7

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  • DOI: https://doi.org/10.1007/978-1-4020-2316-3_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-2315-6

  • Online ISBN: 978-1-4020-2316-3

  • eBook Packages: Springer Book Archive

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