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September  2009, 2(3): 489-502. doi: 10.3934/krm.2009.2.489

A smooth model for fiber lay-down processes and its diffusion approximations

Michael Herty 1, , Axel Klar 2, , Sébastien Motsch 3, and  Ferdinand Olawsky 4,

1. 

Fachbereich Mathematik, RWTH Aachen University, Templergraben 55, D-52074 Aachen, Germany
2. 

Fachbereich Mathematik, Technische Universität Kaiserslautern, PO Box 3049, D-67653 Kaiserslautern
3. 

Institut Mathématique de Toulouse IMT, Université Paul Sabatier deToulouse, 118, route de Narbonne. F-31062 TOULOUSE Cedex, France
4. 

Fraunhofer ITWM, Fraunhofer-Platz 1, D-67663 Kaiserslautern, Germany

Received  March 2009 Revised  May 2009 Published  July 2009

In this paper we improve and investigate a stochastic model and its associated Fokker-Planck equation for the lay-down of fibers on a conveyor belt in the production process of nonwoven materials which has been developed in [2]. The model is based on a stochastic differential equation taking into account the motion of the fiber under the influence of turbulence. In the present paper we remove an obvious drawback of the model, namely the non-differentiability of the paths of the process. We develop a model with smoother trajectories and investigate the relations between the different models looking at different scalings and diffusion approximations. Moreover, we compare the numerical results to simulations of the full physical process.
Keywords: diffusion approximation., Fokker-Planck equations, fiber dynamics.
Mathematics Subject Classification: Primary: 35F10, Secondary: 65Mx.
Citation: Michael Herty, Axel Klar, Sébastien Motsch, Ferdinand Olawsky. A smooth model for fiber lay-down processes and its diffusion approximations. Kinetic and Related Models, 2009, 2 (3) : 489-502. doi: 10.3934/krm.2009.2.489
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