Abstract
This paper deals with to the modelling and simulation of the crystallization of polymers in an heterogeneous temperature field. Under realistic parameter ranges, of industrial interest, we face a multiple scale phenomenon since the temperature evolution occurs at a faster time scale with respect to the birth-and-growth process of crystallization. We propose a spatially structured stochastic bith-and-growth model for the crystallization process whose kinetics parameters depend locally upon the temperature field, and nonlocally upon the spatial distribution of the crystalline phase. For a large number of crystals the system can be shown to converge to a classical continuum deterministic model. We report here the results of the numerical simulation of the many particle system, and of the corresponding continuum model.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
V. Capasso, D. Morale, Karl Oelschlaeger, C. Salani, “An interacting particle approach for the crystallization of polymers” Proceedings “La Matematica nelle Scienze della Vita e nelle Applicazioni”, (Agnoli, Fabrizio, Vettori Eds. ), Pitagora Editrice Bologna, 2000.
M. Burger, V. Capasso, C. Salani, Modeling multi-dimensional crystallization of polymers in interaction with heat transfer., Nonlinear Analysis (2001), In press.
M. Burger, V. Capasso, A. Micheletti, On the numerical simulation of a stochastic PDE system modelling crystallization of polymers, 2000. In preparation.
M. Burger, V. Capasso, Mathematical modelling and simulation of non-isothermal crystallization of polymers. Math. Models and Methods in Appl. Sciences (2001), In press.
G.Eder, H.Janeschitz-Kriegl, Structure Development During Processing: Crystallization, in Materials Science and Technology, Vol.18 (edited by H.Meijer), Verlag Chemie, Weinheim, 1997.
Morale, D. “Laws of large numbers” for interacting particle systems: from discrete to continuum. An aggregation model., Ph.D. Thesis, Milano, 1999.
Boi, S., Capasso. V, Morale, D. “Modeling the aggregative behavior of ants of the species Polyergus rufescens.”, Nonlinear Analysis: Real World Applications, I, 2000, p. 163–176.
K.Oelschläger, Many-Particle Systems and the continuum Description of their Dynamics Habilitationsschrift, Faculty of Mathematics, University of Heidelberg, Germany, 1989.
C.Salani, Crystallization of polymers with thermal heterogeneities,Thesis for ECMI Diploma, Linz, A.A. 1996/97.
C. Salani, On the mathematics of polymer crystallization processes: stochastic and deterministic models., Ph.D. Thesis, University of Milano, Italy, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Capasso, V., Morale, D., Salani, C. (2002). Modeling and Simulating the Crystallization of Polymers via a Many-Particle System. In: Anile, A.M., Capasso, V., Greco, A. (eds) Progress in Industrial Mathematics at ECMI 2000. Mathematics in Industry, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04784-2_54
Download citation
DOI: https://doi.org/10.1007/978-3-662-04784-2_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07647-3
Online ISBN: 978-3-662-04784-2
eBook Packages: Springer Book Archive