The production of filaments and nonwoven materials

We present results from the joint research project ProFil (Stochastic Processes for the Production of Filaments and Non-wovens), which were derived for the optimal design of the polymer distributor. In particular, one is interested in designs which prevent the cooling and degeneration of the polymer due to long occupation times. Since this is directly related to the wall shear stress distribution the questions arise, which wall shear stresses are attainable and how the corresponding design can be computed numerically. Employing the concept of approximate controllability we can answer the first one and characterize the set of attainable wall shear stresses. Further, we present a new numerical approach based on conformal mappings which allows for an optimization in the supremum norm and for an additional incorporation of state constraints. Finally, we show how the real industrial problem is solved by a least-squares optimization using shape gradients.