By Giorgio Bertotti and Isaak D. Mayergoyz (Auth.)
Content material:
Preface
, Pages ix-x
Contributors for quantity one
, Pages xi-xii
Contributors for quantity two
, Pages xi-xii
Contributors for quantity three
, Pages xi-xii
Chapter 1 - Mathematical versions of Hysteresis
, Pages 1-123
Chapter 2 - Differential Equations with Hysteresis through a Canonical Example
, Pages 125-291
Chapter three - Scalar Preisach versions of Hysteresis
, Pages 293-446
Chapter four - Vector Preisach types of Hysteresis
, Pages 447-528
Chapter five - Stochastic features of Hysteresis
, Pages 529-603
Chapter 6 - keep an eye on of structures with Hysteresis
, Pages 605-637
Chapter 7 - Binary Detection and oblong Hysteresis Operators
, Pages 639-665
Chapter eight - Hysteresis and Unemployment: A initial Investigation
, Pages 667-699
Chapter 1 - Thermodynamics, Hysteresis, and Micromagnetics
, Pages 1-106
Chapter 2 - Random-Field Ising types of Hysteresis
, Pages 107-179
Chapter three - The Barkhausen Effect
, Pages 181-267
Chapter four - contemporary Analytical advancements in Micromagnetics
, Pages 269-381
Chapter five - Computational elements of Micromagnetics
, Pages 383-433
Chapter 6 - Nonlinear Magnetization Dynamics. Switching and rest Phenomena
, Pages 435-565
Chapter 7 - Nonlinear Magnetization Dynamics. Magnetization Modes and Spin Waves lower than Rotating Fields
, Pages 567-642
Chapter 1 - Hysteresis in Magnetic Materials
, Pages 1-190
Chapter 2 - Magnetic Hysteresis in Nanostructured Materials
, Pages 191-255
Chapter three - Superconducting Hysteresis
, Pages 257-335
Chapter four - Hysteresis in Piezoelectric and Ferroelectric Materials
, Pages 337-465
Chapter five - Hysteresis in Shape-Memory Materials
, Pages 467-553
Chapter 6 - Hysteretic Elastic structures: Geophysical Materials
, Pages 555-688
Chapter 7 - software of the Preisach version to Soil-Moisture Hysteresis
, Pages 689-744
Index of quantity one
, Pages 701-705
Index of quantity two
, Pages 643-648
Index of quantity three
, Pages 745-751
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Extra info for The Science of Hysteresis
Example text
Here we introduce the corresponding hysteresis operator, and review its main properties. 83) T~:= {P-- (Pl, P2) E R 2 " p l < p 2 } " Let us denote by T4 the family of Borel measurable functions T' --~ {-1, 1}, and by {~p}, or just ~, a generic element of T4. For any finite (signed) Borel measure It over T', let us then define the Preisach operator N~. C~ ['/-t~(u, r T]) x 7~ - , L~176 T), (t):= f;, [hp(u, Co)] (t)dIt(p) Vt ~ [0, T]. 84) This construction may be regarded as a sort of spectral resolution of a class of hysteresis operators, that we shall characterize afterwards.
Let us represent the ferromagnet as an array of magnetic moments of prescribed modulus, h4, and variable orientation. According to the above mentioned Heisenberg theory, the ferromagnetic behavior is due to the occurrence of a strong coupling among electronic spins, which induces neighboring moments to be (almost) parallel. By averaging over the mesoscopic length-scale, the constraint on the magnitude is then preserved: IMI - ,M in f2. 100) 48 CHAPTER 1 Mathematical Models of Hysteresis The magnetic coupling and the nonconvexity of this constraint are at the basis of the ferromagnetic behavior, in particular of hysteresis.
This can be constructed by integrating a family of vector relays with respect to a suitable measure v, that is defined over the four parameters that determine vector relays: 191, 192, 01, 02" At the expense of some generality, one can also use the following procedure [6,7,45-47]: (i) project the input onto a generic direction, 0; (ii) apply to it a scalar Preisach operator, which may depend on 0; (iii) average these outputs with respect to a prescribed weight function, 7(0). Characterization of Preisach Operators For any measure/~, the Preisach operator 1 ~ fulfils the congruency and wiping-out properties, that we now outline.
