6533b81ffe1ef96bd1277042

RESEARCH PRODUCT

Heavy-tail properties of relaxation time distributions underlying the Havriliak–Negami and the Kohlrausch–Williams–Watts relaxation patterns

Karina WeronPaulina HetmanPaulina HetmanBożena Szabat

subject

PhysicsDistribution (mathematics)Heavy-tailed distributionRelaxation (NMR)Materials ChemistryCeramics and CompositesProbability density functionStatistical physicsCondensed Matter PhysicsElectronic Optical and Magnetic MaterialsCole–Cole equationAbelian and tauberian theorems

description

Abstract A detailed discussion of asymptotic properties of the Havriliak–Negami and the Kohlrausch–Williams–Watts relaxation time distributions is presented. The heavy-tail property of the Havriliak–Negami relaxation time distribution, leading to the infinite mean relaxation time, is discussed. In contrast, the existence of the finite mean relaxation time for the Kohlrausch–Williams–Watts response is shown. The discussion of the Cole–Davidson and the Cole–Cole cases is also included. Using the Tauberian theorems we show that these properties are determined directly by the asymptotic behavior of the considered empirical functions.

yearjournalcountryeditionlanguage
2007-12-01Journal of Non-Crystalline Solids
https://doi.org/10.1016/j.jnoncrysol.2007.01.092