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Synopsis
This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat...
Review
From the reviews:
"Have you ever wondered about whether one can define differential derivative of non integer order and how useful these fractal derivatives would be? If the answer is yes this is the book to look at. The book is written by physicists with a pragmatic audience in mind. It contains a very thorough and clearly written discussion of the mathematical foundation as well as the applications to...
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- PublisherSpringer
- Publication date2011
- ISBN 10 144193054X
- ISBN 13 9781441930545
- BindingPaperback
- LanguageEnglish
- Number of pages364
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Physics of Fractal Operators
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Physics of Fractal Operators (Institute for Nonlinear Science)
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Physics of Fractal Operators
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Springer New York Mai 2011, 2011
ISBN 10: 144193054X
ISBN 13: 9781441930545
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In Chapter One we review the foundations of statistieal physies and frac tal functions. Our purpose is to demonstrate the limitations of Hamilton's equations of motion for providing a dynamical basis for the statistics of complex phenomena. The fractal functions are intended as possible models of certain complex phenomena; physical.systems that have long-time mem ory and/or long-range spatial interactions. Since fractal functions are non differentiable, those phenomena described by such functions do not have dif ferential equations of motion, but may have fractional-differential equations of motion. We argue that the traditional justification of statistieal mechan ics relies on aseparation between microscopic and macroscopie time scales. When this separation exists traditional statistieal physics results. When the microscopic time scales diverge and overlap with the macroscopie time scales, classieal statistieal mechanics is not applicable to the phenomenon described. In fact, it is shown that rather than the stochastic differential equations of Langevin describing such things as Brownian motion, we ob tain fractional differential equations driven by stochastic processes. 368 pp. Englisch. Seller Inventory # 9781441930545
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Physics of Fractal Operators
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Springer-Verlag New York Inc., 2011
ISBN 10: 144193054X
ISBN 13: 9781441930545
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Physics of Fractal Operators
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In Chapter One we review the foundations of statistieal physies and frac tal functions. Our purpose is to demonstrate the limitations of Hamilton's equations of motion for providing a dynamical basis for the statistics of complex phenomena. The fractal functions are intended as possible models of certain complex phenomena; physical.systems that have long-time mem ory and/or long-range spatial interactions. Since fractal functions are non differentiable, those phenomena described by such functions do not have dif ferential equations of motion, but may have fractional-differential equations of motion. We argue that the traditional justification of statistieal mechan ics relies on aseparation between microscopic and macroscopie time scales. When this separation exists traditional statistieal physics results. When the microscopic time scales diverge and overlap with the macroscopie time scales, classieal statistieal mechanics is not applicable to the phenomenon described. In fact, it is shown that rather than the stochastic differential equations of Langevin describing such things as Brownian motion, we ob tain fractional differential equations driven by stochastic processes. Seller Inventory # 9781441930545
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Physics of Fractal Operators (Institute for Nonlinear Science)
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as sys. Seller Inventory # 4173515
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Physics of Fractal Operators
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