Hierarchy of sigmoid growth models - towards justification of sigmoid treatment of nucleation data

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In the poster we provide a brief introduction to the general problem of fitting the nucleation data – the so called N-t curves, with an hierarchy of sigmoid growth models [1] (HSGM). The special focus of such a treatment is to be on the principal mechanisms of nucleation that could give raise to a positive feedback as demonstrated in the supelinear regime (before the inflection point) of N-t curves.
In the introductory part, we continue the mothodological development of the HSGM by identifying a novel quantitative criterium for “sigmoidness” based on the idea of catastrophe. Here we will use examples of population dynamics.
In the course of implementing the HSGM-approach we revisit several typical datasets reporting sigmoid data [2] and more. A novel tool used in the course of this revisit is the so called Multiple Fitting of a Single Dataset (MFSDS) as first proposed in [3]. Here we also make further refinements of the approach by including datasets generated by the Richards model and Cellular Automata.

In collaboration with: Daniela Tsekova and Feyzim Hodzhaoglu

References
[1] V. Kleshtanova, V. Ivanov, F. Hodzhaoglu, J. Prieto, and V. Tonchev, Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models, Crystals 13, 1690 (2023).
[2] C. N. Nanev and V. D. Tonchev, Sigmoid kinetics of protein crystal nucleation, Journal of Crystal Growth 427, 48 (2015).
[3] V. V. Ivanov, C. Tielemann, K. Avramova, S. Reinsch, and V. Tonchev, Modelling crystallization: When the normal growth velocity depends on the supersaturation, Journal of Physics and Chemistry of Solids 181, 111542 (2023).