Advertisement

Preisach Models

  • Hamid Reza NooriEmail author
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

This chapter intends to familiarize the readers with the Preisach model of hysteresis. Since its publication in the 1930s of the last century (Preisach 1935), the model has been further developed and improved and many valuable facts have been accumulated (Everett and Whitton 1952; Everett 1954, 1955; Enderby 1956; Biorci and Pescetti 1958, 1959, 1966; Brown 1962; Bate 1962; Woodward and Della Torre 1960; Della Torre 1965; Damlanian and Visintin 1983; Visintin 1984; Barker et al. 1985; Brokate and Visintin 1989; Krasnosel’skii and Pokrovskii 1989). Here, no attempt of a complete presentation of the theory is made. Instead, we focus on a systematic introduction of the basic but essential concepts of Preisach model of hysteresis, which will help the reader to easily access this complex mathematical theory and prepare him/her for mathematical modeling of biological processes expressing non-linearities of hysteresis type.

Keywords

Preisach Model Visintin Complex Mathematical Theory First-order Transition Curves Hysteresis Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Barker JA, Schreiber DE, Huth BG, Everett DH (1985) Magnetic hysteresis and minor loops—models and experiments. Proc R Soc London A 386:251–261CrossRefGoogle Scholar
  2. Bate G (1962) Statistical stability of preisach diagram for particles of \(\gamma \)-\(Fe_2O_3\). J Appl Phys 33:2263–2269CrossRefGoogle Scholar
  3. Biorci G, Pescetti D (1958) Analytic theory of the behaviour of ferromagnetic materials. Nuovo Cinento 7:829–842CrossRefGoogle Scholar
  4. Biorci G, Pescetti D (1959) Some consequences of the analytical theory of the ferromagnetic hysteresis. J Phys Radium 20:233–236CrossRefGoogle Scholar
  5. Biorci G, Pescetti D (1966) Some remarks on hysteresis. J Appl Phys 37:425–427CrossRefGoogle Scholar
  6. Brokate M, Visintin A (1989) Properties of the preisach model for hysteresis. J Reine Angew Math 402:1–40MathSciNetzbMATHGoogle Scholar
  7. Brown WF Jr (1962) Failure of local-field concept for hysteresis calculations. J Appl Phys 33:1308–1309CrossRefGoogle Scholar
  8. Damlanian A, Visintin A (1983) A multidimensional generalization of the Preisach model for hysteresis. Compt Rend Acad Sci Paris 297:437–440Google Scholar
  9. Torre Della E (1965) Measurements of interaction in an assembly of \(\gamma \)?iron oxide particles. J Appl Phys 36:518–522Google Scholar
  10. Enderby JA (1956) The domain of hysteresis. 2. Interacting domains. Trans Faraday Soc 52:106–120CrossRefGoogle Scholar
  11. Everett DH (1954) A general approach to hysteresis. 3. A formal treatment of the independent domain model. Trans Faraday Soc 50:1071–1096Google Scholar
  12. Everett DH (1955) A general approach to hysteresis. 4. An alternative formulation of the domain model. Trans Faraday Soc 51:1551–1557CrossRefGoogle Scholar
  13. Everett DH, Whitton WI (1952) A general approach to hysteresis. Trans Faraday Soc 48:749–757CrossRefGoogle Scholar
  14. Krasnosel’skii MA, Pokrovskii AV (1989) Systems with hysteresis. Springer, HeidelbergCrossRefzbMATHGoogle Scholar
  15. Mayergoyz ID (1986) Mathematical models of hysteresis. IEEE Trans Magn 22:603–608Google Scholar
  16. Mayergoyz ID (2003) Mathematical models of hysteresis and their applications. Elsevier, New YorkGoogle Scholar
  17. Preisach F (1935) Über die magnetische Nachwirkung. Z Phys 94:277–302CrossRefGoogle Scholar
  18. Shirley ME, Venkataraman R (2003) On the identication of preisach measures. Proc SPIE 5049, 326–336Google Scholar
  19. Visintin A (1984) On the Preisach model for hysteresis. Nonlinear Anal 8:977–996MathSciNetCrossRefzbMATHGoogle Scholar
  20. Woodward JG, Della Torre E (1960) Particle interaction in magnetic recording tapes. J Appl Phys 31:56–62CrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Central Institute for Mental HealthInstitute for PsychopharmacologyMannheimGermany

Personalised recommendations