×

The mathematics of hysteresis. (English) Zbl 0546.34009

A survey over three different approaches to model hysteresis phenomena is given. The starting point for mathematical models is (a) memory, (b) population, or (c) spatial distribution. In any case the hysteresis effect is interpreted using an averaging procedure over the inner state of the system in consideration.

MSC:

34A34 Nonlinear ordinary differential equations and systems
92D25 Population dynamics (general)
45A05 Linear integral equations
82B35 Irreversible thermodynamics, including Onsager-Machlup theory
70A05 Axiomatics, foundations
80A30 Chemical kinetics in thermodynamics and heat transfer
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Néel, Cahier Phys. 12 pp 1– (1942)
[2] Néel, Cahiers Phys. 13 pp 1–
[3] Krasnosel’skii, Abh. Akad. Wiss. DDR 3 pp 437– (1977)
[4] DOI: 10.1021/j150029a001 · doi:10.1021/j150029a001
[5] Duhem, Z. Phys. Chemie 34 pp 683– (1900)
[6] Duhem, Z. Phys. Chemie 34 pp 312– (1900)
[7] Duhem, Z. Phys. Chemie 33 pp 641– (1900)
[8] Duhem, Z. Phys. Chemie 28 pp 577– (1899)
[9] Duhem, Z. Phys. Chemie 23 pp 497– (1897) · doi:10.1515/bchm2.1897.23.4-5.497
[10] Duhem, Z. Phys. Chemie 23 pp 193– (1897)
[11] Duhem, Z. Phys. Chemie 22 pp 543– (1897)
[12] Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert (1973)
[13] Hornung, Z. Angew. Math. Mech. 63 pp T324– (1983)
[14] Haverkamp, Soil Sci.
[15] DOI: 10.1098/rspl.1889.0033 · doi:10.1098/rspl.1889.0033
[16] DOI: 10.1039/tf9555101551 · doi:10.1039/tf9555101551
[17] DOI: 10.1039/tf9545001077 · doi:10.1039/tf9545001077
[18] DOI: 10.1039/tf9545000187 · doi:10.1039/tf9545000187
[19] DOI: 10.1039/tf9524800749 · doi:10.1039/tf9524800749
[20] DOI: 10.1039/tf9565200106 · doi:10.1039/tf9565200106
[21] DOI: 10.1039/tf9555100835 · doi:10.1039/tf9555100835
[22] Duhem, Z. Phys. Chemie pp 695– (1903)
[23] Weiss, Arch. Sci. Phys. Nat. 49 pp 5– (1916)
[24] Weiss, J. Phys. 6 pp 661– (1907)
[25] DOI: 10.1007/BF01765153 · Zbl 0494.35052 · doi:10.1007/BF01765153
[26] Rayleigh, Philos. Mag. 23 pp 225– (1887) · doi:10.1080/14786448708628000
[27] DOI: 10.1007/BF01349418 · doi:10.1007/BF01349418
[28] DOI: 10.1029/WR009i005p01324 · doi:10.1029/WR009i005p01324
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.