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

Those lecture notes by way of very authoritative scientists survey fresh advances of arithmetic pushed via business software displaying not just how arithmetic is utilized to but additionally how arithmetic has drawn take advantage of interplay with real-word problems.The well-known David record underlines that leading edge excessive know-how relies crucially for its improvement on innovation in arithmetic. The audio system contain 3 fresh presidents of ECMI, certainly one of ECCOMAS (in Europe) and the president of SIAM.

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1 A random evolution equation In an experimental situation, where spatial heterogeneities are caused only by the heat transfer in the material, we may assume that growth and nucleation rates depend upon space and time via suitable functions of the temperature only [13] G(t,x) = G(T(t,x)), (~(t,x) - O N(T(t,x)) +o~l(t,x). Usually it is assumed that the two terms forming the nucleation rate V. Capasso 52 satisfy the following condition: 0h a(x,t) 0T = 0T'07 +a~ = OT s0 (t, x)-b7 + ~1 (t, x). e. when ~ --- 0) at a temperature between the melting and the glass transition p o n t .

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. 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.

E. Burkard and G. J. , Springer Lecture Notes in Computer Science Vol. 1610, pp. 439-452. Berlin, Heidelberg: Springer, 1999. [20] H. Whitney, On the abstract properties of linear dependence. American Journal of Mathematics 57, 1935, 509-533. [21] R. J. Worsley, An improved Bonferroni inequality. Biometrika 69, 1982, 297-302. [22] U. Zimmermann, Linear and Combinatorial Optimization in Ordered Algebraic Structures, Annals of Discrete Mathematics Vol. 10, Amsterdam: North-Holland, 1981. Mathematical Models for Polymer Crystallization Processes Vincenzo Capasso M I R I A M - M i l a n Research C e n t r e for I n d u s t r i a l a n d A p p l i e d M a t h e m a t i c s , Universit~ degli S t u d i di Milano, v i a Saldini 50, 1-20133 Milano, I t a l y e-maih v i n c e n z o .