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Hysteresis and Phase Transitions

Author: Martin Brokate; Jürgen Sprekels
Publisher: New York, NY : Springer New York, 1996.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), 121.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
This book presents a mathematical analysis of hysteretic phenomena, where two complementary viewpoints are taken: at first, scalar rate independent hysteresis is studied in a general setting that is based on the interplay between a discrete diagram-oriented and a function space approach: later, the connections between the occurrence of hysteresis and physical mechanisms like energy dissipation and phase transitions  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Martin Brokate; Jürgen Sprekels
ISBN: 9781461240488 1461240484
OCLC Number: 852792460
Description: 1 online resource (x, 372 pages 43 illustrations).
Contents: 1. Some Mathematical Tools --
1.1 Measure and Integration --
1.2 Function Spaces --
1.3 Nonlinear Equations --
1.4 Ordinary Differential Equations --
2. Hysteresis Operators --
2.1 Basic Examples --
2.2 General Hysteresis Operators --
2.3 The Play Operator --
2.4 Hysteresis Operators of Preisach Type --
2.5 Hysteresis Potentials and Energy Dissipation --
2.6 Hysteresis Counting and Damage --
2.7 Characterization of Preisach Type Operators --
2.8 Hysteresis Loops in the Prandtl Model --
2.9 Hysteresis Loops in the Preisach Model --
2.10 Composition of Preisach Type Operators --
2.11 Inverse and Implicit Hysteresis Operators --
2.12 Hysteresis Count and Damage, Part II --
3. Hysteresis and Differential Equations --
3.1 Hysteresis in Ordinary Differential Equations --
3.2 Auxiliary Imbedding Results --
3.3 The Heat Equation with Hysteresis --
3.4 A Convexity Inequality --
3.5 The Wave Equation with Hysteresis --
4. Phase Transitions and Hysteresis --
4.1 Thermodynamic Notions and Relations --
4.2 Phase Transitions and Order Parameters --
4.3 Landau and Devonshire Free Energies --
4.4 Ginzburg Theory and Phase Field Models --
5. Hysteresis Effects in Shape Memory Alloys --
5.1 Phenomenology and Falk's Model --
5.2 Well-Posedness for Falk's Model --
5.3 Numerical Approximation --
5.4 Complementary Remarks --
6. Phase Field Models With Non-Conserving Kinetics --
6.1 Auxiliary Results from Linear Elliptic and Parabolic Theory --
6.2 Well-Posedness of the Caginalp Model --
6.3 Well-Posedness of the Penrose-Fife Model --
6.4 Complementary Remarks --
7. Phase Field Models With Conserved Order Parameters --
7.1 Well-Posedness of the Caginalp Model --
7.2 Well-Posedness of the Penrose-Fife Model --
8. Phase Transitions in Eutectoid Carbon Steels --
8.1 Phenomenology of the Phase Transitions --
8.2 The Mathematical Model --
8.3 Well-Posedness of the Model --
8.4 The Jominy Test: A Numerical Study.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), 121.
Responsibility: by Martin Brokate, Jürgen Sprekels.

Abstract:

This book presents a mathematical analysis of hysteretic phenomena, where two complementary viewpoints are taken: at first, scalar rate independent hysteresis is studied in a general setting that is based on the interplay between a discrete diagram-oriented and a function space approach: later, the connections between the occurrence of hysteresis and physical mechanisms like energy dissipation and phase transitions are discussed. The exposition ranges from the thermodynamic foundation of phenomenological theories of phase transitions over the variational formulation of the resulting initial-boundary value problems to the rigorous proof of results concerning existence, uniqueness and numerical approximation.

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