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In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured intensity profiles along the laser beam caustic with consideration of intermodal degrees of coherence derived from spectral analysis. To enhance the accuracy of the model, different approaches and strategies are applied and discussed. The presented decomposition into a set of LP modes enables both the wave-optical simulation of radiation transport by highly multi-mode fibers and, additionally, the analysis of free-space propagation with arbitrarily modified complex amplitude distributions., Comment: 11 pages, 9 figures, 1 Visualisation (see DOI)

We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier-Stokes equations we derive a second order weighted residual integral boundary layer equation, which in particular may be used to describe eddies in the troughs of the wavy bottom. We present numerical results which show that our model is qualitatively and quantitatively accurate in wide ranges of parameters, and we use the model to study some new phenomena, for instance the occurrence of a short wave instability for laminar flows which does not exist over flat bottom., Comment: 23 pages, 12 figures. We added a new Section "Regularization" in which we additionally apply a Pade-like regularization to the weighted residual integral boundary layer equation