Spirals and Phase Transitions

  • Yves Dupain
  • Michel Mendes France
  • Claud Tricot

Abstract

By a stretch of imagination we shall identify spirals with systems of interacting particles. Mimicking the formalism of Statistical Mechanics we shall then discover that spirals go through a phase transition as the “temperature” increases. The inverse critical temperature coincides with the box dimension of the spiral. The article is a restatement of previous joint work [1].

Keywords

Hull 

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References

  1. 1.
    Y. Dupain, M. Mendes France, C. Tricot. Dimensions des spirales, Bull. Soc. Math. Fr. 111, (1983),193–201.MATHGoogle Scholar
  2. 2.
    H. Steinhaus. Sur la portée pratique et théorique de quelque théoréms sur la measure des ensembles de drotes, Comptes rendus du ler congrés des Mathématiciens des pays Slaves, (1930), 353–354.Google Scholar
  3. 3.
    H. Steinhaus. Length, Shape and Area, Colloquium Mathematicum, 3, (1954), 1–13.Google Scholar

Copyright information

© Plenum Press, New York 1995

Authors and Affiliations

  • Yves Dupain
    • 1
  • Michel Mendes France
    • 1
  • Claud Tricot
    • 2
  1. 1.Départment de MatheḿatiquesUniversité Bordeaux ITalence CedexFrance
  2. 2.Départment de Matheḿatiques AppliqueésEcole PolytechniqueMontréalCanada

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