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.
Similar content being viewed by others
References
Paley, R. E. A. C., Wiener, N.: Fourier transforms in the complex domain. Am. Math. Soc. Coll. Publ. v. XIX, 1934.
Kac, M.,et al.: Probability and related topics in physical siences. London, New York: Interscience 1959.
Peierls, R.: Ising's model of ferromagnetism. Proc. Cambridge Phil. Soc.32, 477 (1936).
Feynman, R.: The space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys.20, 367–387 (1948).
Schweizer, B.: Probabilistic metric spaces — the first 25 years. New York Statistician19, no. 2, 3–6 (1967).
——, Sklar, A.: Statistical metric spaces. Pacific J. Math.10. 313–334 (1960).
Blumenthal, L. M.: Theory and applications of distance geometry. Oxford: Oxford University Press 1953.
Busemann, H.: The geometry of Finsler space. Bull. Am. Math. Soc.56, 5–16 (1950).
Ewing, J. A.: Contributions to the molecular theory of induced magnetism. Proc. Roy. Soc.48, 342 (1890).
Erber, T., Guralnick, S. A., Latal, H. G.: A general phenomenology for hysteresis (in preparation).
——, 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).
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01646555