TY - RPRT
A1 - Bonilla, L.
A1 - Götz, T.
A1 - Klar, A.
A1 - Marheineke, N.
A1 - Wegener, R.
T1 - Hydrodynamic limit of the Fokker-Planck-equation describing fiber lay-down processes
N2 - 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 112
KW - Stochastic Differential Equations
KW - Fokker-Planck Equation
KW - Asymptotic Expansion
KW - Ornstein-Uhlenbeck Process
Y1 - 2007
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1966
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-15342
ER -