Hysteresis and Phase Transitions: 121 (Applied Mathematical Sciences) - Tapa dura

Sprekels, Jürgen; Brokate, Martin

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

Sinopsis

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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De la contraportada

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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Editorial
Springer
Año de publicación
1996
Idioma
Inglés
ISBN 10 
0387947639
ISBN 13 
9780387947631
Encuadernación
Tapa dura
Número de páginas
372
Contacto del fabricante
no disponible
Persona responsable
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Otras ediciones populares con el mismo título

9781461284789: Hysteresis and Phase Transitions: 121 (Applied Mathematical Sciences)

Edición Destacada

ISBN 10:  1461284783 ISBN 13:  9781461284789
Editorial: Springer, 2011
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