Stochastic and deterministic models for fiber lay-down

This work deals with the mathematical modeling of structures of deposited fibers that arise from the industrial production of nonwovens. The models are based on dynamical systems of stochastic differential equations describing the resulting positions of the fibers on a conveyor belt. Starting from the analysis of existing models, new concepts of modeling are developed and investigated. In this context, the main interest lies in the extensions of the models to three dimensions which enable a realistic description of the fiber orientation in space. Therefore, the containing Brownian motion or Ornstein-Uhlenbeck process, respectively, are enhanced to the unit sphere. More general, the fiber lay-down models are formulated for arbitrary dimensions. In addition to several asymptotic considerations, the convergence to equilibrium is investigated using entropy methods. In the end, the applicability of the derived models is discussed by industrial problems.