A mathematical characterization of the gel point in sol-gel transition

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Bilge, A.H.^1 ; Pekcan, O.^1

Kadir Has University, Faculty of Engineering and Natural Sciences, Cibali, Istanbul, Turkey^1

关键词: Accumulation points;    Extreme value;    Gel point;    Mathematical characterization;    Sigmoidal curves;    Sol-gel transitions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012005/pdf
DOI  :  10.1088/1742-6596/574/1/012005

来源: IOP

【 摘 要 】

We model the sol-gel transition in terms of Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models and compare with experimental results. We show, numerically, that the "gel point" described as the onset of the gelation phenomena and measured experimentally, corresponds to an accumulation point of the extreme values of the derivatives of the gelation curve. We define the "critical point of a sigmoidal curve" as the limit of the points where the derivatives reach their extreme values, provided that this limit exists.