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Spirals and phase transitions. (English) Zbl 0866.11048
Takahashi, Yoichiro (ed.), Algorithms, fractals, and dynamics. Proceedings of the Hayashibara Forum ’92: International symposium on new bases for engineering science, algorithms, dynamics, and fractals, Okayama, Japan, November 23-28, 1992 and a symposium on algorithms, fractals, and dynamics, November 30–December 2, 1992, Kyoto, Japan. New York, NY: Plenum Press. 59-62 (1995).
The authors restate results of a previous work [Bull. Soc. Math. Fr. 111, 193-201 (1983; Zbl 0529.10049)] by identifying spirals with systems of interacting particles. After this translation of notions they discover a phase transition for spirals at the critical “temperature” that is exactly the inverse of the box dimension of the spiral.
MSC:
11K99Probabilistic theory
82B26Phase transitions (general)
28A78Hausdorff and packing measures
82B21Continuum models (systems of particles, etc.)