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Author: Arnold, Thomas × WGL Institute: WIAS ×

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    Reflection of plane waves by rough surfaces in the sense of Born approximation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Arnold, Thomas; Rathsfeld, Andreas
    The topic of the present paper is the reflection of electromagnetic plane waves by rough surfaces, i.e., by smooth and bounded perturbations of planar faces. Moreover, the contrast between the cover material and the substrate beneath the rough surface is supposed to be low. In this case, a modification of Stearns' formula based on Born approximation and Fourier techniques is derived for a special class of surfaces. This class contains the graphs of functions if the interface function is a radially modulated almost periodic function. For the Born formula to converge, a sufficient and almost necessary condition is given. A further technical condition is defined, which guarantees the existence of the corresponding far field of the Born approximation. This far field contains plane waves, far-field terms like those for bounded scatterers, and, additionally, a new type of terms. The derived formulas can be used for the fast numerical computations of far fields and for the statistics of random rough
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    A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Arnold, Thomas; Henrion, René; Möller, Andris; Vigerske, Stefan
    We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.