Abstract
Two examples of physical phenomena, dielectric relaxations and turbulent flows, where the Lévy-stable and extreme value distributions appear naturally, are considered. In the case of dielectric relaxations the common mathematical structure underlying four different definitions of relaxation function, responsible for generating the stretched exponential relaxation law, is found. In the case of turbulent flows, the distribution of velocities in a velocity field produced by randomly distributed sources of circulation is shown to be Lévy-stable with the characteristic exponent \(\frac{D}{2}\), where D denotes the fractal dimension of the turbulence.
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Weron, K., Kosmulski, K., Jurlewicz, A., Mercik, S. (1995). Lévy-Stable and extreme value distributions in modelling of dynamical phenomena in complex physical systems. In: Garbaczewski, P., Wolf, M., Weron, A. (eds) Chaos — The Interplay Between Stochastic and Deterministic Behaviour. Lecture Notes in Physics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60188-0_82
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DOI: https://doi.org/10.1007/3-540-60188-0_82
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