Distributions of citations of papers of individual authors publishing in different scientific disciplines: Application of Langmuir-type function

The distribution of cumulative citations L and contributed citations Lf to individual multiauthored papers published by selected authors working in different scientific disciplines is analyzed and discussed using Langmuir-type function: yn=y0[1−αKn/(1+Kn)], where yn denotes the total number of normalized cumulative citations ln* and normalized contributed citations lnf* received by individual papers of rank n, y0 is the maximum value of yn when n=0, α≥1 is an effectiveness parameter, and K is the Langmuir constant related to the dimensionless differential energy Q=ln(KNc), with Nc as the number of papers receiving citations. Relationships between the values of the Langmuir constant K of the distribution function, the number Nc of papers of an individual author receiving citations and the effectiveness parameter α of this function, obtained from analysis of the data of rank-size distributions of the authors, are investigated. It was found that: (1) the quantity KNc obtained from the real citation distribution of papers of various authors working in different disciplines is inversely proportional to (α−1) with a proportional constant (KNc)0<1, (2) the relation KNc=(KNc)0/(α−1) also holds for the citation distribution of journals published in countries of two different groups, investigated earlier (Sangwal, K. (2013). Journal of Informetrics, 7, 487–504), and (3) deviations of the real citation distribution from curves predicted by the Langmuir-type function are associated with changing activity of sources of generation of items (citations).