Riv. Mat. Univ. Parma, Vol. 10, No. 2, 2019

Axel Klar [a]

Interacting fiber structures: mathematical aspects and applications

Pages: 199-268
Received: 7 December 2018
Accepted in revised form: 9 May 2019
Mathematics Subject Classification (2010): 35B40, 82C22, 37H10, 41A60, 65C05.
Keywords: Fiber dynamics, interacting fibers, stochastic differential equations, mean-field equations, convergence to equilibrium, production processes.
Authors address:
[a]: University of Kaiserslautern, Kaiserslautern, 67663, Germany

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Abstract: Fiber structures resulting from a lay down of fibers have been investigated extensively. Microscopic models have been used to describe fibers in detail, whereas kinetic and macroscopic models have been used for the statistical description of the fiber distribution. We review models based on stochastic differential equations, as well as Fokker-Planck and mean field equations and their approximations. Interaction of the fibers is included in these models and a numerical and analytical investigation of the resulting equations is given. Finally an industrial example is discussed and the applicability in an industrial set-up is illustrated.

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