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Hydrodynamic limit of the Fokker-Planck-equation describing fiber lay-down processes

  • In this paper, a stochastic model [5] for the turbulent fiber laydown 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. 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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Author:L. Bonilla, T. Götz, A. Klar, N. Marheineke, R. Wegener
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15342
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (112)
Document Type:Report
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Creating Corporation:Fraunhofer ITWM
Date of the Publication (Server):2008/05/28
Tag:Asymptotic Expansion; Fokker-Planck Equation; Ornstein-Uhlenbeck Process; Stochastic Differential Equations
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011