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Author: Martin Brokate
Publisher: Springer Science & Business Media
ISBN: 1461240484
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: Martin Brokate
Publisher: Springer Science & Business Media
ISBN: 1461240484
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: M. Brokate
Publisher:
ISBN: 9783540547921
Category :
Languages : en
Pages : 300
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Book Description
Author: Hidetoshi Nishimori
Publisher: Oxford University Press
ISBN: 0199577226
Category : Science
Languages : en
Pages : 373
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Book Description
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.
Author: Mark A. Krasnosel'skii
Publisher: Springer Science & Business Media
ISBN: 3642613020
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Hysteresis phenomena are common in numerous physical, mechanical, ecological and biological systems. They reflect memory effects and process irreversibility. The use of hysteresis operators (hysterons) offers an approach to macroscopic modelling of the dynamics of phase transitions and rheological systems. The applications cover processes in electromagnetism, elastoplasticity and population dynamics in particular. Hysterons are also typical elements of control systems where they represent thermostats and other discontinuous controllers with memory. The book offers the first systematic mathematical treatment of hysteresis nonlinearities. Construction procedures are set up for hysterons in various function spaces, in continuous and discontinuous cases. A general theory of variable hysterons is developed, including identification and stability questions. Both deterministic and non-deterministic hysterons are considered, with applications to the study of feedback systems. Many of the results presented - mostly obtained by the authors and their scientific group - have not been published before. The book is essentially self contained and is addressed both to researchers and advanced students.
Author: Chintamani Nagesa Ramachandra Rao
Publisher: McGraw-Hill Companies
ISBN:
Category : Science
Languages : en
Pages : 346
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Book Description
Author: Praveen Chaddah
Publisher: CRC Press
ISBN: 149878626X
Category : Science
Languages : en
Pages : 174
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Book Description
This book introduces new concepts in the phenomenon of 1st order phase transitions. It discusses the concept of kinetic arrest at a certain temperature, with this temperature being dependent on the second control variable (magnetic field, or pressure). It discusses interesting manifestations of this phenomenon when the 1st order transition is broadened, i.e. occurs over a finite range of temperatures. Many examples of this phenomenon, observed recently in many materials, will also be discussed.
Author: Yuri Mnyukh
Publisher: Directscientific Press
ISBN: 9780615339726
Category : Technology & Engineering
Languages : en
Pages : 338
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Book Description
The author's experimental discoveries in the field of solid-state phase transitions have brought about a thorough explanation of this phenomenon, including the puzzling nature of "lamda-anomalies." These phase transitions are found to be always a nucleation and crystal growth in a solid medium, while "second (or higher) order" phase transitions are a misconception: they do not exist. Ramifications of this new understanding are substatial. In this book the reader will find the first unified account for fundamentals of the three great areas of solid-state physics? Phase transitions, ferromagnetism and ferroelectricity, free of the inconsistencies of the conventional theories.
Author: Pierluigi Colli
Publisher: World Scientific
ISBN: 9812566503
Category : Mathematics
Languages : en
Pages : 321
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Book Description
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity.The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area.This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
Author: A. R. Bishop
Publisher: CRC Press
ISBN: 9782881241215
Category :
Languages : en
Pages : 326
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Book Description
Author: Annick LESNE
Publisher: Springer Science & Business Media
ISBN: 364215123X
Category : Science
Languages : en
Pages : 406
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Book Description
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
