## 15. ÖMG-Kongress

Jahrestagung der Deutschen Mathematikervereinigung

#### 16. bis 22. September 2001 in Wien

**Hauptvortrag**

Dienstag, 18. September 2001, 9.00-11.00, Audimax der Universität Wien

**The Geometry of the Crystallization Process of Polymers**

**Vincenzo Capasso**, **Universita' di Milano**

Crystallization of polymers is composed of two processes, nucleation
(birth) and subsequent growth of crystallites, which are in general both
stochastic in time and space.
If we assume that at points of contact between two growing crystallites they
stop growing, a random division of the relevant region in a d-dimensional space
is obtained, known as a random Johnson-Mehl tessellation, which has been studied
in previous literature with homogeneous parameters.
The coupling of the kinetic parameters of the birth-and-growth process with the
underlying temperature field induces time and space heterogeneities (and
stochastically) of all parameters involved, thus motivating a more general
analysis of the stochastic geometry of the crystallization process.
A complete charaterization of the final spatial structure of the crystallization
(tessellation) can be given in terms of the mean densities of interfaces
(n-facets: cells, faces, edges, verteces) of the random tessellation, at all
different Hausdorff dimensions, with respect to the usual d-dimensional Lebesgue
measure.
Here an analysis of the above quantities in terms of the kinetic parameters of
the process is presented coupled with the evolution equations of the underlying
temperature field.

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