Dynamic mathematical model of the crystallization kinetics of fats

Foubert, Imogen; Vanrolleghem, Peter A.; Vanhoutte, Bert; Dewettinck, Koen

doi:10.1016/s0963-9969(02)00157-6

Cited by 72 publications

(63 citation statements)

References 12 publications

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“…Even though the AIC is considered not to be a ''consistent'' information criterion unlike the BIC or LILC (Foubert et al 2002;Wagenmakers and Farrell 2004;Stone 2005), the results presented show that AIC and BIC all predict the ''best'' model rankings in the same order and demonstrate that the order of superiority of models for fitting the data was Hill 5 [ Hill 4 [ PSO [ Elovich [ Power [ IPD. This was also supported by all other model fitting tests along with the evidence ratios, information criterion weights and BFs.…”

Section: Resultsmentioning

confidence: 92%

“…The AIC is calculated using the Kullback-Leibler discrepancy (a measure of the distance between the probability density generated by the model and reality (Wagenmakers and Farrell 2004)) and takes into account both a model's goodness-of-fit R 2 and its number of parameters. However, it has the disadvantage of not being ''consistent'', meaning it does not guarantee that the probability of selecting the wrong model approaches zero as the number of data points tends to infinity (Foubert et al 2002;Wagenmakers and Farrell 2004;Stone 2005). Information criterion that are ''consistent'' include the Schwarz Bayesian information criterion [BIC, Eq.…”

Section: Introductionmentioning

confidence: 99%

“…3, (Schwarz 1978)] and Khinchin's Law of Iterated Logarithm Criterion [LILC, Eq. 4, (Hannan and Quinn 1979;Foubert et al 2002)].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kinetic model selection and the Hill model in geochemistry

Turner

Henley

Sleap

et al. 2014

Int. J. Environ. Sci. Technol.

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This study introduces the Hill model for modelling sorption kinetics and illustrates its efficacy using formal model selection procedures. Although the coefficient of determination (R 2 ) value can be used to ensure goodness-of-fit of a particular model to a set of data, a measure that incorporates the number of model parameters, such as the Bayesian information criterion, law of iterated logarithm criterion, Akaike information criterion, and the extra sum-of-squares F-test is necessary to undertake reliable model selection. This study undertook a formal model selection procedure based on these criteria, in combination with the coefficient of determination, for a range of candidate kinetics sorption models [the pseudo-second order (PSO), the intra-particle diffusion (IPD), Power, Elovich, and the four and five parameter Hill models]. It was found that the model order that statistically best described the data was Hill 5 [ Hill 4 [ pseudo-second order [ Elovich [ Power [ IPD as given by the evidence ratios, information criterion weights and Bayes factors. The extra sum-of-squares F-test, only applicable to nested models, confirms the best fit order as Hill 5 [ Hill 4 [ PSO models. Two new parameters (T and k Hill ) have also been defined that give the Hill models a mechanistic meaning directly comparable to the well-defined parameters of the pseudo-second-order model, namely, the pseudo-secondorder rate constant k pso and the instantaneous sorption coefficient h pso . In the field of geochemistry the use of the four and five parameter Hill models for describing sorption kinetics has been overlooked with many studies favouring the PSO model. It is strongly recommended that the Hill model be considered more widely as a general predictive tool in geochemistry.

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Section: Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Kinetic model selection and the Hill model in geochemistry

Turner

Henley

Sleap

et al. 2014

Int. J. Environ. Sci. Technol.

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“…In this paper, a stochastic CA-based model describing fat migration is proposed, with CAs being the utter discrete counterpart of PDEs. This model takes into account gradient-driven diffusion and the chemical equilibrium between solid and liquid fat in the chocolate coating, which is regulated by melting and crystallization of the fat [5]. Further, it also incorporates capillary rise and keeps track of the spatial distribution of the fat bloom at the surface.…”

Section: Models Describing Fat Bloommentioning

confidence: 99%

A CA-Based Model Describing Fat Bloom in Chocolate

Weeën

Clercq

Dewettinck

et al. 2012

Lecture Notes in Computer Science

Self Cite

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Abstract. In this paper a stochastic model based on a cellular automaton (CA) for describing the spatio-temporal dynamics of fat migration in chocolate confectionery, as well as the resulting fat bloom, is conceived. Several hypotheses on the underlying mechanisms for fat migration exist, but there is no consensus on the correct ones. Although many researchers are studying this industrially important phenomenon, few models describing it have been developed. Therefore, the incorporation of different mechanisms of fat migration into a stochastic CA-based model is discussed and the model parameters are investigated for a better understanding of both the model and the complex fat migration phenomenon.

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“…The vari a tion of SFC as a func tion of time is ob tained by se quen tial in te gra tion of the crys tal li za tion peak. This SFC func tion is used to es ti mate param e ters of crys tal li za tion with the help of the Avrami model or more com plex ones (Foubert et al, 2002;Kloek et al, 2000;Rousset, 2002). Nu cle ation in duction times can also be de ter mined from iso ther mal crys tal li za tion ex per i ments.…”

Section: Kinetic Parametersmentioning

confidence: 99%