Comparison of selected mathematical functions for the analysis of growth behavior of items and physical interpretation of Avrami-Weibull function

• Autorzy: Sangwal Keshra

Identyfikatory

DOI

10.35784/jcsi.2775

Warianty tytułu

PL

Porównanie wybranych funkcji matematycznych do analizy przebiegu wzrostu podmiotów oraz interpretacja funkcji Avrami’ego-Weibulla

• Języki publikacji: EN

Abstrakty

EN

Empirical data of sigmoidal-shaped y(t) growth behavior of different types of items, such as papers and citations earned by individual and all successively published papers of selected top-cited authors, germination of tomato seeds and three different bacteria, are analyzed and compared by Avrami-Weibull, Verhulst (logistic) and Gompertz functions. It was found that: (1) Avrami-Weibull function describes different types of the data better than Gompertz and Verhulst funtions, and (2), in comparison with Verhulst and Gompertz functions, Avrami-Weibull function, expressed in the form: y(t)/ymax = 1-exp[(t/Θ)q] (where ymax is the maximum value of y(t) when t→∞, and Θ and q are constants), is equally very versatile in explaining the generation rate dy(t)/dt of items in terms of its parameters Θ and q. Using the basic concepts involved in the derivation of Avrami-Weibull function for overall crystallization from melt and supersaturated solution, the growth behavior of cumulative number y(t) of items produced at time t by individual (simple) sources and collectives or groups of simple sources (i.e. complex or composite sources) is presented. Comparison of the process of receiving of citations by papers with the processes of occurrence of chemical reactions and crystallization of solid phases from melts and supersaturated solutions shows that this process is similar to that of overall crystallization of solid phases from melts and solutions. Analysis of growth of citations using Avrami-Weibull function to individual papers published by different authors shows that 1 < q < 4 for most cases. This suggests that the process of citations to individual articles is mainly determined by progressive nucleation mode involving both diffusion and integration of published knowledge.

PL

Przeanalizowano i porównano stosowalność funkcji Avrami’ego-Weibulla, Verhulsta (logistycznej) i Gompertza do empirycznych danych sygmoidalnego przebiegu wzrostu y(t) takich różnorodnych podmiotów jak: liczba artykułów i cytowań otrzymywanych przez pojedyncze i wszystkie kolejne artykuły publikowane przez wybranych wysokocytowanych autorów, liczba kiełkowań nasion pomidorów i liczba trzech różnych bakterii. Zaobserwowano, że: 1) funkcja Avrami’ego-Weibulla opisuje różne dane lepiej niż funkcje Gompertza i Verhulsta, oraz 2) w porównaniu z funkcjami Verhulsta i Gompertza, funkcja Avrami’ego-Weibulla, wyrażona w postaci: y(t)/ymax = 1exp[(t/)q] (gdzie: ymaxjest maksymalną wartością y(t) gdy t, oraz i q są stałymi), jest równie wszechstronna w wyjaśnieniu szybkości wytwarzania dy(t)/dt wyżej wymienionych podmiotów przy pomocy parametrów i q. Korzystając z podstawowych pojęć zawartych w wyprowadzeniu równania Avrami’ego-Weibulla do opisania całkowitej krystalizacji z fazy roztopionej i z roztworu przesyconego, przedstawiono przebieg wzrostu kumulacyjnej liczby y(t) podmiotów wytwarza-nych w czasie t poprzez pojedyncze (proste) źródła i zbiory lub grupy pojedynczych źródeł (tj. złożonych źródeł). Porównanie procesu otrzymywania cytowań przez artykuły z procesami występowania reakcji chemicznych i krystalizacji ciał stałych ze stopów i roztworów przesyconych pokazuje, iż proces ten jest podobny do całkowitej krystalizacji ciał stałych ze stopów i roztworów. Analiza wzrostu cytowań według równania Avrami’ego-Weibulla pojedynczych artykułów publikowanych przez różnych autorów pokazuje, że w większości przypadków 1 < q< 4. Z powyższego można wnioskować, że proces cytowania pojedynczych artykułów zachodzi w głównej mierze przez zarodkowanie progresywne oparte na dyfuzji i integracji opublikowanej wiedzy.

Słowa kluczowe

EN

Avrami-Weibull function; Gompertz and Verhulst functions; growth behavior of items; citation analysis

PL

funkcja Avrami’ego-Weibulla; funkcje Gompertza I Verhulsta; przebieg wzrostu podmiotów; analiza cytowań

• Wydawca: Wydawnictwo Politechniki Lubelskiej
• Czasopismo: Journal of Computer Sciences Institute
• Rocznik: 2021
• Tom: Vol. 21
• Strony: 259--278
• Opis fizyczny: Bibliogr. 71 poz., fig., tab.

Twórcy

autor

Sangwal Keshra

• Department of Applied Physics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).