By Giorgio Bertotti, Isaak D. Mayergoyz
Quantity 1 covers:* Mathematical types* Differential equations* Stochastic elements of hysteresis* Binary detection utilizing hysteresis* versions of unemployment in economicsVolume 2 covers:* actual versions of magnetic hysteresis* All facets of magnetisation dynamicsVolume three covers:* Hysteresis phenomena in fabrics * Over 2100 pages, wealthy with aiding illustrations, figures and equations * includes contributions from a world checklist of authors, from a wide-range of disciplines* Covers all points of hysteresis - from differential equations, and binary detection, to types of unemployment and magnetisation dynamics
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Extra info for The Science of Hysteresis : 3-volume set
This process can be regarded as rate-independent, and is responsible for most of hysteresis dissipation in ferromagnetic materials that exhibit a domain structure. For instance, steel may be regarded as iron with uniformly distributed inclusions of carbon and other substances on a microscopic length-scale; it turns out that hysteresis is much more pronounced in this material than in pure iron. Here we describe the effect of inclusions on magnetic dynamics in a way that is reminiscent of Coulomb's dry friction.
Moreover, the state of any of the above models is characterized by the pair (e, a), whereas a number of tests on elasto-plastic materials indicates the occurrence of internal variables. An answer to these exhigences is given by a (scalar) model Prandtl  proposed in 1928, and Ishlinskii  rediscovered in 1944, that is obtained by coupling a family of stops in parallel. The stop-play duality then suggests construction of a dual model by coupling a family of plays in series. These two classes will be respectively named Prandtl-IshlinskiY models of stop- and play-type.
105), this term drives M to move towards H e and is dissipative. The vector M x H e lies in the same tangent plane and is orthogonal to/~I x (s x ~ e ) ; it induces/~ to rotate around H e by forming a constant angle (precession) and with angular velocity proportional to Isel; this contribution is not dissipative. M. The relaxation time is proportional to 1/22. 106), d ~rnag(M) "- dt c~t . 110) which yields the energy balance equation grnag(A~(t)) q- 22 /ot d'c ]A~ x f/el 2 dx - grnag(Ad(0)). 105) yields M x He- 0 in f)T.