Abstract
This paper deals with the process of crystallization.We first present two major models that describe this phenomenon either as a birth-and-growth process or in terms of a Johnson-Mehl random tessellation. Then, we estimate the parameters of these models and we establish the asymptotic law of the estimators for the geometrical aspect of this phenomenon. Simulations of these laws are also provided in some cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersen, P.K. Borgan, Ø., Gill, R.D., Keiding, N.: Statistical models based on counting processes. Springer Series in Statistics. Springer-Verlag, New York, 1993.
Aletti, G., Saada, D.: Survival analysis in Johnson-Mehl tessellation. To appear on Stat. Inference Stoch. Process, 2006.
Bolthausen, E.: On the central limit theorem for stationary mixing random .elds. Ann. Probab., 10(4):1047–1050, 1982.
Capasso, V., Burger, M., Micheletti, A.: An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes. This volume.
Capasso, V., Burger, M., Micheletti, A., Salani, C.: Mathematical models for polymer crystallization processes. In Mathematical modelling for polymer processing, volume 2 of Math. Ind., pages 167–242, 313–315. Springer, Berlin, 2003.
Capasso, V., Micheletti, A.: On the hazard function for inhomogeneous birthand-growth processes. This volume.
Gill, R.D.: Lectures on survival analysis. In Lectures on probability theory (Saint-Flour, 1992), volume 1581 of Lecture Notes in Math., pages 115–241. Springer, Berlin, 1994.
Guyon, X., Richardson, S.: Vitesse de convergence du théoréme de la limite centrale pour des champs faiblement dépendants. Z. Wahrsch. Verw. Gebiete, 66(2):297–314, 1984.
Møller, J.: Random Johnson-Mehl tessellations. Adv. in Appl. Probab., 24(4):814–844, 1992.
Møller, J.: Topics in Voronoi and Johnson-Mehl tessellations. In Stochastic geometry (Toulouse, 1996), volume 80 of Monogr. Statist. Appl. Probab., pages 173–198. Chapman & Hall/CRC, Boca Raton, FL, 1999.
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic geometry and its applications. John Wiley & Sons Ltd., Chichester, 1987. With a foreword by D.G. Kendall.
Slivnjak, I.M.: Some properties of stationary streams of homogeneous random events. Teor. Verojatnost. i Primenen., 7:347–352, 1962.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Aletti, G., Saada, D. (2007). Polymer Crystallization Processes. In: Aletti, G., Micheletti, A., Morale, D., Burger, M. (eds) Math Everywhere. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44446-6_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-44446-6_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44445-9
Online ISBN: 978-3-540-44446-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)