Hysteresis and Phase Transitions (Applied Mathematical Sciences, 121, Band 121) - Hardcover

Brokate, Martin; Sprekels, Jürgen

 
9780387947631: Hysteresis and Phase Transitions (Applied Mathematical Sciences, 121, Band 121)
Hardcover
ISBN 10: 0387947639 ISBN 13: 9780387947631
Verlag: Springer, 1996

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

MARTIN BROKATE is Professor of Applied Mathematics at the Technical University, Munich, Germany. He received his PhD in Mathematics at Freie Universität, Berlin, Germany, in 1980, and was appointed to the Chair of Numerical Analysis and Control Theory in 1999. He was the spokesman of Special Research Area 438 "Mathematical Modeling, Simulation and Verification in Material-Oriented Processes and Intelligent Systems" from 2001 to 2004. He was the Dean of the Department of Mathematics in 2003-2006. His interests lie in applied analysis and control theory, with a focus on the mathematical analysis of rate-independent evolutions and hysteresis operators.
PAMMY MANCHANDA is Senior Professor in the Department of Mathematics at the Guru Nanak Dev University, Amritsar, India and Secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM). She has published more than 50 research papers in several international journals of repute, edited4 proceedings for international conferences of the ISIAM and co-authored 3 books. She has visited the International Centre for Theoretical Physics (ICTP) (a UNESCO institution) at Trieste, Italy, many times to carry out her research activities, attended and delivered talks and chaired sessions at several international conferences and workshops across the globe, including the International Council for Industrial and Applied Mathematics (ICIAM) during 1999-2015 and the International Congress of Mathematicians (ICM). She is the managing editor of the Indian Journal of Industrial and Applied Mathematics and a member of the editorial board of the Springer book series Industrial and Applied Mathematics.
ABUL HASAN SIDDIQI is a distinguished scientist and Adjunct Professor at the School of Basic Sciences and Research, and Coordinator at the Centre for Advanced Research in Applied Mathematics and Physics (CARAMP) at Sharda University, Greater Noida, India. He was a visiting consultant at ICTP; Sultan Qaboos University, Muscat, Oman; MIMOS, Kuala Lumpur, Malaysia; and a professor at several reputed universities including Aligarh Muslim University, Aligarh, India; and King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. He has a long association with ICTP (a regular associate, guests of the director and senior associate). He was awarded the German Academic exchange Fellowship thrice to carry out mathematical research in Germany. He has published more than 100 research papers jointly with his research collaborators, 13 books and edited proceedings of 17 international conferences, as well as supervised 29 PhD scholars. He is the founder secretary and the current President of the ISIAM, which celebrated its Silver Jubilee in January 2016. He is the editor-in-chief of the Indian Journal of Industrial and Applied Mathematics (published by ISIAM) and the Springer's book series Industrial and Applied Mathematics.

Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
1996
Sprache
Englisch
ISBN 10 
0387947639
ISBN 13 
9780387947631
Einband
Gebundene Ausgabe
Anzahl der Seiten
368
Kontakt zum Hersteller
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Darmstadt
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Deutschland

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