Hydrodynamic limit for the Fokker-Planck equation describing fiber lay-down models

Bonilla LL, Götz T, Klar A, Marheineke N, Wegener R (2007)


Publication Type: Journal article, Original article

Publication year: 2007

Journal

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 68

Pages Range: 648-665

Journal Issue: 3

DOI: 10.1137/070692728

Abstract

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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APA:

Bonilla, L.L., Götz, T., Klar, A., Marheineke, N., & Wegener, R. (2007). Hydrodynamic limit for the Fokker-Planck equation describing fiber lay-down models. SIAM Journal on Applied Mathematics, 68(3), 648-665. https://doi.org/10.1137/070692728

MLA:

Bonilla, Luis L., et al. "Hydrodynamic limit for the Fokker-Planck equation describing fiber lay-down models." SIAM Journal on Applied Mathematics 68.3 (2007): 648-665.

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