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Progressive nucleation mechanism for the growth behavior of items and its application to cumulative papers and citations of individual authors

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  • Keshra Sangwal

    (Lublin University of Technology)

Abstract

A general expression based on the concepts of the progressive nucleation mechanism is proposed in the form $$ \alpha (t) = \frac{N(t)}{C} = \left[ {1 - \exp \left\{ { - \left( {\frac{t}{\Uptheta }} \right)^{q} } \right\}} \right] $$ to describe the growth behavior of items in an individual system and a collective of systems. In the above relation, α(t) is the ratio of items N(t) at time t to the maximum number C of possible items for the system, Θ is the corresponding time constant and q is the exponent. The above relation is then used to analyze: (1) the growth behavior of cumulative number N(t) of papers published by individual authors and cumulative citations L(t) of N(t) papers of an author as a function of citation duration t, and (2) the relationship between cumulative citations L(t) of papers and cumulative number N(t) of papers. The proposed approach predicts that: (1) the fraction of items produced by successive systems is additive, (2) the cumulative fraction α sum(t) of maximum number of sites is the sum of contributions of fractions of maximum number of items produced by different systems, and (3) the values of time constants Θ and exponent q increase with the addition of fraction of items produced by subsequent systems, but their values are the lowest for individual systems. The approach is applied to explain the growth behavior of cumulative N(t) papers and L(t) citations of four selected Polish professors.

Suggested Citation

  • Keshra Sangwal, 2012. "Progressive nucleation mechanism for the growth behavior of items and its application to cumulative papers and citations of individual authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 92(3), pages 575-591, September.
    • Handle: RePEc:spr:scient:v:92:y:2012:i:3:d:10.1007_s11192-011-0610-8
    DOI: 10.1007/s11192-011-0610-8
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    References listed on IDEAS

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    1. Sangwal, Keshra, 2011. "Progressive nucleation mechanism and its application to the growth of journals, articles and authors in scientific fields," Journal of Informetrics, Elsevier, vol. 5(4), pages 529-536.
    2. Sangwal, K., 2011. "On the growth of citations of publication output of individual authors," Journal of Informetrics, Elsevier, vol. 5(4), pages 554-564.
    3. S. Stremersch & I. Verniers & C. Verhoef, 2006. "The Quest for Citations: Drivers of Article Impact," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/422, Ghent University, Faculty of Economics and Business Administration.
    4. Wong, Chan-Yuan & Goh, Kim-Leng, 2010. "Growth behavior of publications and patents: A comparative study on selected Asian economies," Journal of Informetrics, Elsevier, vol. 4(4), pages 460-474.
    5. Keshra Sangwal, 2012. "Application of progressive nucleation mechanism for the citation behavior of individual papers of different authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 92(3), pages 643-655, September.
    6. Ravichandra Rao, I.K. & Srivastava, Divya, 2010. "Growth of journals, articles and authors in malaria research," Journal of Informetrics, Elsevier, vol. 4(3), pages 249-256.
    7. B.M. Gupta & Suresh Kumar & S. L. Sangam & C.R. Karisiddappa, 2002. "Modeling the growth of world social science literature," Scientometrics, Springer;Akadémiai Kiadó, vol. 53(1), pages 161-164, January.
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    Cited by:

    1. Sangwal, Keshra, 2015. "On the growth dynamics of citations of articles by some Nobel Prize winners," Journal of Informetrics, Elsevier, vol. 9(3), pages 466-476.
    2. Sangwal, Keshra, 2013. "Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors," Journal of Informetrics, Elsevier, vol. 7(1), pages 36-49.
    3. Keshra Sangwal, 2012. "Application of progressive nucleation mechanism for the citation behavior of individual papers of different authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 92(3), pages 643-655, September.

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