Skip to main content
Log in

Probabilistic metric spaces and hysteresis systems

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

A phenomenological theory of simple hysteresis is constructed with the aid of certain concepts from the theory of probabilistic metric spaces. The predicted forms of the dependence of average energy loss per hysteresis cycle on the maximum excursion of the hysteresis coordinate agree well with experimental results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Paley, R. E. A. C., Wiener, N.: Fourier transforms in the complex domain. Am. Math. Soc. Coll. Publ. v. XIX, 1934.

  2. Kac, M.,et al.: Probability and related topics in physical siences. London, New York: Interscience 1959.

    Google Scholar 

  3. Peierls, R.: Ising's model of ferromagnetism. Proc. Cambridge Phil. Soc.32, 477 (1936).

    Google Scholar 

  4. Feynman, R.: The space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys.20, 367–387 (1948).

    Google Scholar 

  5. Schweizer, B.: Probabilistic metric spaces — the first 25 years. New York Statistician19, no. 2, 3–6 (1967).

    Google Scholar 

  6. ——, Sklar, A.: Statistical metric spaces. Pacific J. Math.10. 313–334 (1960).

    Google Scholar 

  7. Blumenthal, L. M.: Theory and applications of distance geometry. Oxford: Oxford University Press 1953.

    Google Scholar 

  8. Busemann, H.: The geometry of Finsler space. Bull. Am. Math. Soc.56, 5–16 (1950).

    Google Scholar 

  9. Ewing, J. A.: Contributions to the molecular theory of induced magnetism. Proc. Roy. Soc.48, 342 (1890).

    Google Scholar 

  10. Erber, T., Guralnick, S. A., Latal, H. G.: A general phenomenology for hysteresis (in preparation).

  11. ——, Latal, H. G., Harmon, B. N.: The origin of hysteresis in simple magnetic systems. Advance in Chemical Physics, edited by I. Prigogine and S. Rice. London: Wiley (in press).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Erber, T., Schweizer, B. & Sklar, A. Probabilistic metric spaces and hysteresis systems. Commun.Math. Phys. 20, 205–219 (1971). https://doi.org/10.1007/BF01646555

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646555

Keywords

Navigation