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Modelling of Polymer Crystallization in Temperature Fields
Author(s) -
Burger M.,
Capasso V.,
Eder G.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200201)82:1<51::aid-zamm51>3.0.co;2-8
Subject(s) - crystallization , crystallization of polymers , statistical physics , crystallinity , bounded function , thermodynamics , degree (music) , heat transfer , scale (ratio) , polymer , materials science , stochastic modelling , partial differential equation , stochastic process , mathematics , physics , mathematical analysis , statistics , quantum mechanics , acoustics , composite material
Abstract This paper is devoted to the mathematical modelling of polymer crystallization processes in a bounded region under heat transfer conditions, i.e. in time‐dependent temperature fields. A stochastic model in a general setup is developed based on the theory of marked point processes, and a hybrid model on a macroscopic scale is derived using expected values. The stochastic modelling part is supplemented by a detailed discussion of the relevant parameters and their dependence upon temperature. In the special case of one‐dimensional crystallization a system of partial differential equations describing the evolution of temperature and of the degree of crystallinity is derived.