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Hysteresis and Phase Transitions

  • Book
  • © 1996

Overview

Authors:
  1. Martin Brokate

    1. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. Jürgen Sprekels

    1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Mathematical Sciences (AMS, volume 121)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Martin Brokate, Jürgen Sprekels
    Pages 1-9

  3. Some Mathematical Tools

    • Martin Brokate, Jürgen Sprekels
    Pages 10-21

  4. Hysteresis Operators

    • Martin Brokate, Jürgen Sprekels
    Pages 22-121

  5. Hysteresis and Differential Equations

    • Martin Brokate, Jürgen Sprekels
    Pages 122-149

  6. Phase Transitions and Hysteresis

    • Martin Brokate, Jürgen Sprekels
    Pages 150-174

  7. Hysteresis Effects in Shape Memory Alloys

    • Martin Brokate, Jürgen Sprekels
    Pages 175-217

  8. Phase Field Models with Non-Conserving Kinetics

    • Martin Brokate, Jürgen Sprekels
    Pages 218-270

  9. Phase Field Models With Conserved Order Parameters

    • Martin Brokate, Jürgen Sprekels
    Pages 271-303

  10. Phase Transitions in Eutectoid Carbon Steels

    • Martin Brokate, Jürgen Sprekels
    Pages 304-331

  11. Back Matter

    Pages 332-358
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Keywords

About this book

Hysteresis is an exciting and mathematically challenging phenomenon that oc­ curs in rather different situations: jt, can be a byproduct offundamental physical mechanisms (such as phase transitions) or the consequence of a degradation or imperfection (like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hys­ teresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually non-smooth and thus not easy to treat mathematically. Hence it was only in the early seventies that the group of Russian scientists around M. A. Krasnoselskii initiated a systematic mathematical investigation of the phenomenon of hysteresis which culminated in the fundamental monograph Krasnoselskii-Pokrovskii (1983). In the meantime, many mathematicians have contributed to the mathematical theory, and the important monographs of 1. Mayergoyz (1991) and A. Visintin (1994a) have appeared. We came into contact with the notion of hysteresis around the year 1980.

Authors and Affiliations

  • Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Martin Brokate

  • Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Sprekels

Bibliographic Information

  • Book Title: Hysteresis and Phase Transitions

  • Authors: Martin Brokate, Jürgen Sprekels

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-4048-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1996

  • Hardcover ISBN: 978-0-387-94763-1Published: 20 June 1996

  • Softcover ISBN: 978-1-4612-8478-9Published: 17 September 2011

  • eBook ISBN: 978-1-4612-4048-8Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: X, 358

  • Topics: Analysis

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