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We present a new approach to the problem of optimal control of solar sails for low-thrust trajectory optimization. The objective was to find the required control torque magnitudes in order to steer a solar sail in interplanetary space. A new steering strategy, controlling the solar sail with generic torques applied about the spacecraft body axes, is integrated into the existing low-thrust trajectory optimization software InTrance. This software combines artificial neural networks and evolutionary algorithms to find steering strategies close to the global optimum without an initial guess. Furthermore, we implement a three rotational degree-of-freedom rigid-body attitude dynamics model to represent the solar sail in space. Two interplanetary transfers to Mars and Neptune are chosen to represent typical future solar sail mission scenarios. The results found with the new steering strategy are compared to the existing reference trajectories without attitude dynamics. The resulting control torques required to accomplish the missions are investigated, as they pose the primary requirements to a real on-board attitude control system.
Analysis of the long-term effect of the MBST® nuclear magnetic resonance therapy on gonarthrosis
(2016)
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.
In most beers, producers strive to minimize haze to maximize visual appeal. To detect the formation of particulates, a measurement system for sub-micron particles is required. Beer haze is naturally occurring, composed of protein or polyphenol particles; in their early stage of growth their size is smaller than 2 µm. Microscopy analysis is time and resource intensive; alternatively, backscattering is an inexpensive option for detecting particle sizes of interest.