Research Catalog

Hysteresis and phase transitions

Title
Hysteresis and phase transitions / Martin Brokate, Jürgen Sprekels.
Author
Brokate, Martin, 1953-
Publication
New York : Springer, [1996], ©1996.

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Additional Authors
Sprekels, J.
Description
x, 357 pages : illustrations; 24 cm.
Summary
  • This monograph contributes to the mathematical analysis of systems exhibiting hysteresis effects and phase transitions. Its main part begins with a detailed study of models for scalar rate independent hysteresis in the form of hysteresis operators. Applications to ferromagnetism, elastoplasticity and fatigue analysis are presented, and two representative distributed systems with hysteresis operator are discussed.
  • The attention then shifts to the mechanisms of energy dissipation and transformation that induce a hysteretic behavior in continuous media undergoing phase transitions. After an introduction to phenomenological thermodynamic theories of phase transitions, in particular, the Landau-Ginzburg theory and phase field models, several specific models are discussed in detail. These include Falk's model for the hysteresis in shape memory alloys and the phase field models due to Caginalp and Penrose-Fife. The latter are studied both for conserved and non-conserved order parameters.
  • A chapter presenting a mathematical model for the austenite-pearlite and austenite-martensite phase transitions in eutectoid carbon steels concludes the book.
Series Statement
Applied mathematical sciences ; 121
Uniform Title
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 121.
Subject
  • Hysteresis > Mathematics
  • Phase transformations (Statistical physics)
Bibliography (note)
  • Includes bibliographical references (p. 332-352) and index.
Contents
Ch. 1. Some Mathematical Tools -- Ch. 2. Hysteresis Operators -- Ch. 3. Hysteresis and Differential Equations -- Ch. 4. Phase Transitions and Hysteresis -- Ch. 5. Hysteresis Effects in Shape Memory Alloys -- Ch. 6. Phase Field Models With Non-Conserving Kinetics -- Ch. 7. Phase Field Models With Conserved Order Parameters -- Ch. 8. Phase Transitions in Eutectoid Carbon Steels.
ISBN
0387947639 (alk. paper)
LCCN
96015533
OCLC
ocm34669286
Owning Institutions
Columbia University Libraries