Stochastic birth-and-growth processes modelling crystallization of polymers with spatially heterogeneous parameters

✍ Scribed by V. Capasso; C. Salani

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 180 KB
• Volume: 1
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/s0362-546x(99)00289-8

✦ Synopsis

The morphology of a crystalline polymeric material is characterized by the crystallization process, which occurs during the solidiÿcation from the liquid state. This process includes a stochastic birth process (nucleation) and the growth of crystals. From a mathematical point of view, the nucleation process is a marked point process with a stochastic intensity depending on the history of the proceses of birth and growth. Here we consider an extension of the classical Avrami-Kolmogorov model to the case of space-time heterogeneous kinetic parameters. Concepts from stochastic geometry are used, which include the so called causal cone. The Markov property of the process is also analysed.