Hysteresis and Phase Transitions / Edition 1

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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.
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Product Details

  • ISBN-13: 9780387947631
  • Publisher: Springer New York
  • Publication date: 6/20/1996
  • Series: Applied Mathematical Sciences Series, #121
  • Edition description: 1996
  • Edition number: 1
  • Pages: 358
  • Product dimensions: 0.94 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Introduction 1
Ch. 1 Some Mathematical Tools 10
Ch. 2 Hysteresis Operators 22
Ch. 3 Hysteresis and Differential Equations 122
Ch. 4 Phase Transitions and Hysteresis 150
Ch. 5 Hysteresis Effects in Shape Memory Alloys 175
Ch. 6 Phase Field Models With Non-Conserving Kinetics 218
Ch. 7 Phase Field Models With Conserved Order Parameters 271
Ch. 8 Phase Transitions in Eutectoid Carbon Steels 304
Bibliography 332
Index 353
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