By R. Burkard, P. Deuflhard, A. Jameson, J.-L. Lions, G. Strang, V. Capasso, H.W. Engl, J. Periaux

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**Extra info for Computational mathematics driven by industrial problems: lectures given at the 1st session of the Centro internazionale matematico estivo**

**Example text**

I ........ i ........ ........ : ...... i ........ i ........ i.. i ........ 2 f . 4 ...... : . . 6" -os~ ....... ,i ....... ,i ........ 2 ,i ..... 0 i~ ...... i! 4 ,! 6 i! ii ................. 6 Figure 3: A crystal shape in a typical temperature field. actual time, but not about the history of growth. Hence, this description seems to be suitable not only for the case of growth in a given field, but also for growth in interaction with the field. Fig. , the solution of the heat equation without source term) and data for the growth rate obtained by measurements of i-PP.

1 E v o l u t i o n e q u a t i o n s for t h e e m p i r i c a l d i s t r i b u t i o n s . 2 Simulations . . . . . . . . . . . . References 42 42 44 48 51 51 52 53 54 57 58 61 62 65 V. Capasso 40 1 Introduction Polymer industry raises a large amount of relevant mathematical problems with respect to the quality of manufactured polymer parts. These include in particular questions about the crystallization kinetics of the polymer melt, in presence of a temperature field. The final morphology of the crystallised material is a fundamental factor in the physical properties of the solidified part.

1 S t o c h a s t i c i t y of t h e Causal Cone . . . . . . 2 T h e m u l t i p l e scales . . . . . . . . . . . . 3 A v e r a g i n g . . . . . . . . . . . . . . . 1 N u m e r i c a l simulations . . . . . . . . . 4 A p a r t i c l e m o d e l . . . . . . . . . . . . . 1 E v o l u t i o n e q u a t i o n s for t h e e m p i r i c a l d i s t r i b u t i o n s . 2 Simulations . . . . . . . . . . . . References 42 42 44 48 51 51 52 53 54 57 58 61 62 65 V.