Detailed comparison of the Williams–Watts and Cole–Davidson functions

Autor:	G. D. Patterson, C. P. Lindsey
Rok vydání:	1980
Předmět:	Physics Distribution function Distribution (mathematics) General Physics and Astronomy Relaxation (physics) Cutoff Statistical physics Function (mathematics) Physical and Theoretical Chemistry
Zdroj:	The Journal of Chemical Physics. 73:3348-3357
ISSN:	1089-7690 0021-9606
Popis:	The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::13f346224bc5ab2db354a7512bb83f65 https://doi.org/10.1063/1.440530 Zobrazit plný text záznamu