Hysteresis and Phase Transitions: HYSTERESIS & PHASE TRANSITIONS by Martin BrokateHysteresis and Phase Transitions: HYSTERESIS & PHASE TRANSITIONS by Martin Brokate

Hysteresis and Phase Transitions: HYSTERESIS & PHASE TRANSITIONS

byMartin Brokate, Jürgen Sprekels, J]rgen Sprekels

Hardcover | June 20, 1996

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This book presents a mathematical analysis of hysteretic phenomena, where two complementary viewpoints are taken: at first, scalar rate independent hysteresis is studied in a general setting that is based on the interplay between a discrete diagram-oriented and a function space approach: later, the connections between the occurrence of hysteresis and physical mechanisms like energy dissipation and phase transitions are discussed. The exposition ranges from the thermodynamic foundation of phenomenological theories of phase transitions over the variational formulation of the resulting initial-boundary value problems to the rigorous proof of results concerning existence, uniqueness and numerical approximation.
Title:Hysteresis and Phase Transitions: HYSTERESIS & PHASE TRANSITIONSFormat:HardcoverDimensions:382 pages, 9.21 × 6.14 × 0 inPublished:June 20, 1996Language:English

The following ISBNs are associated with this title:

ISBN - 10:0387947639

ISBN - 13:9780387947631

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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-m