Hydrodynamic Limit of the Fokker-Planck Equation Describing Fiber Lay-down Processes

In: SIAM Journal on Applied Mathematics. 2007

Authors

• L. L. Bonilla
• T. Götz
• Axel Klar
• N. Marheineke
• Raimund Wegener

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. 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.

BibTeX

 
@Article{ Bonilla.Goetz.EA07hydrodynamic, 
   title = { Hydrodynamic Limit of the Fokker-Planck Equation Describing Fiber Lay-down Processes }, 
   author = { L. L. Bonilla and T. Götz and Axel Klar and N. Marheineke and Raimund Wegener },    
   journal = { SIAM Journal on Applied Mathematics },             
   year = 2007, 
} 

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This publication belongs to the project Fimod.