Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 68, Issue 3, Pages 648-665Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070692728
Keywords
stochastic differential equations; Fokker-Planck equation; asymptotic expansion; Ornstein-Uhlenbeck process
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In this paper, a stochastic model for the turbulent fiber lay-down in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corresponding to large noise values, the transient and stationary joint probability distributions are determined using the method of multiple scales and the Chapman-Enskog method. Moreover, exponential convergence towards the stationary solution is proven for the reduced problem. For special choices of the industrial parameters, the stochastic limit process is an Ornstein-Uhlenbeck process. It is a good approximation of the fiber motion even for moderate noise values. Moreover, as shown by Monte-Carlo simulations, the limiting process can be used to assess the quality of nonwoven materials in the industrial application by determining distributions of functionals of the process.
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