Hamburger Beiträge zur Angewandten Mathematik A Simplified Model for Non-Isothermal Crystallization of Polymers
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چکیده
Recently, Burger and Capasso [M3AS 11 (2001) 1029–1053] derived a coupled system of partial differential equations to describe non–isothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth–and–growth process describing the nucleation and growth of single crystals. In the present work we reconsider the scaling properties of the dimensional system as well as some special one–dimensional models. Moreover, using an appropriate scaling of the original system, we derive a simplified model which only consists of a reaction–diffusion equation with memory for the underlying temperature, such that the degree of crystallization can be explicitly given by a time integration of the temperature–dependent growth and nucleation rate. Numerical simulations indicate that the reduced model shows at least qualitatively the same behavior like the original model.
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تاریخ انتشار 2004