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Phase Transitions and Hysteresis

  • Martin Brokate
  • Jürgen Sprekels
Part of the Applied Mathematical Sciences book series (AMS, volume 121)

Abstract

In the previous chapters, the occurrence of hysteresis has been discussed from a mainly phenomenological and mathematical point of view. The attempt to formalize the input-output behaviour of hysteresis loops gave rise to introduce the notion of hysteresis operators, and we studied their properties and differential equations in which they appear. In this approach, we did not pay much attention to the physical circumstances. In particular, we entirely ignored the fact that in nature hysteresis effects are often caused by phase transitions which are accompanied by abrupt changes of some of the involved physical quantities, as well as by the absorption or release of energy in the form of latent heat. The area of the hysteresis loop itself gives a measure for the amount of energy that has been dissipated or absorbed during the phase transformation.

Keywords

Phase Transition External Field Free Energy Density Stefan Problem Total Free Energy 
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References

  1. 1.
    For a more detailed treatment of the theory of phase transitions, we refer the reader to the monographs of Stanley (1971) and Ma (1976).Google Scholar
  2. 2.
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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Martin Brokate
    • 1
  • Jürgen Sprekels
    • 2
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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