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Titlebook: Hysteresis and Phase Transitions; Martin Brokate,Jürgen Sprekels Book 1996 Springer-Verlag New York, Inc. 1996 Approximation.Convexity.Pha

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發(fā)表于 2025-3-21 16:22:38 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Hysteresis and Phase Transitions
編輯Martin Brokate,Jürgen Sprekels
視頻videohttp://file.papertrans.cn/431/430824/430824.mp4
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Hysteresis and Phase Transitions;  Martin Brokate,Jürgen Sprekels Book 1996 Springer-Verlag New York, Inc. 1996 Approximation.Convexity.Pha
描述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.
出版日期Book 1996
關(guān)鍵詞Approximation; Convexity; Phase Transition; Phase Transitions; differential equation; function space; line
版次1
doihttps://doi.org/10.1007/978-1-4612-4048-8
isbn_softcover978-1-4612-8478-9
isbn_ebook978-1-4612-4048-8Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York, Inc. 1996
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沙發(fā)
發(fā)表于 2025-3-21 23:34:32 | 只看該作者
Applied Mathematical Scienceshttp://image.papertrans.cn/h/image/430824.jpg
板凳
發(fā)表于 2025-3-22 01:41:59 | 只看該作者
https://doi.org/10.1007/978-3-658-03041-4When speaking of ., one usually refers to a relation between two scalar time-dependent quantities that cannot be expressed in terms of a single-valued function, but takes the form of . like the one depicted in Fig. 0.1.
地板
發(fā)表于 2025-3-22 04:36:25 | 只看該作者
5#
發(fā)表于 2025-3-22 11:14:16 | 只看該作者
Introduction,When speaking of ., one usually refers to a relation between two scalar time-dependent quantities that cannot be expressed in terms of a single-valued function, but takes the form of . like the one depicted in Fig. 0.1.
6#
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978-1-4612-8478-9Springer-Verlag New York, Inc. 1996
8#
發(fā)表于 2025-3-22 21:33:54 | 只看該作者
Hysteresis and Phase Transitions978-1-4612-4048-8Series ISSN 0066-5452 Series E-ISSN 2196-968X
9#
發(fā)表于 2025-3-23 04:08:37 | 只看該作者
https://doi.org/10.1057/9780230379572efer to Section 4.4, where we introduced a mathematical model for . phase transitions that explains the possible occurrence of an accompanying hysteresis in the framework of Landau-Ginzburg theory. The kinetic equation for the order parameter e resulting from this approach is given by . while the balance of internal energy becomes ..
10#
發(fā)表于 2025-3-23 05:44:52 | 只看該作者
William Blake and the Myths of Britain are called .. Since we will investigate cooling processes only in this chapter, hysteresis phenomena will not play such a dominant role as before; however, hysteretic effects come immediately into play if a series of alternating cooling and heating periods is applied to the sample.
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