In this thesis we consider the reconstruction of albedo maps of exoplanets. This is done with a new variant of spin-orbit tomography that has been described in [Cowan and Agol, 2008] and more in depth in [Fujii and Kawahara, 2012]. This method reconstructs the albedo map from the reflected-light curve, the total intensity of the light that originates from the host star and is reflected by the planet. In the mentioned papers, the surface map of the planet is modeled as a sum of finite sized surface elements with constant albedo, and the relation between this approximation of the map and the light-curve in the time domain is determined. In this report, we use that the signal is quasi periodic due to diurnal and annual motion, and work with the Fourier peaks of the light-curve. We also approximate the map in a different way, writing it as the sum of spherical harmonics, and neglecting spherical harmonics with high spatial frequencies. This has the advantage that the relation can be worked out analytically (for edge-on and face-on observations) without the use of complex mathematics, and that both the surface map and the light-curve contain a daily frequency. We derive an equation for the reflective light-curve under the assumption that the surface map is not a function of time (no clouds), and that the reflection is Lambertian (equal in magnitude in all directions). This transformation is found to be a linear function of the surface map. This equation is worked out for edge-on and face-on observations with arbitrary axial tilt, which describes the orientation of the spin axis with respect to the observer and the orbital plane. Furthermore, we describe how to invert this relation if the axial tilt is known to the observer. We also aimed at recovering the map if the axial tilt is unknown to the observer, since this would make sure that the reconstruction does not rely on other observations. In contrast to what was found in papers like [Fujii and Kawahara, 2010] and [Fujii and Kawahara, 2012], we did not succeed in this. A number of methods were used for this. The first two looked at the problem from a mathematical perspective: the minimization of the distance between the measured light-curve and the light-curve from the reconstructed map, and Tikhonov regularization. The two failed because both the column space and the singular values respectively are not a function of the axial tilt. The third method that has been treated and tested involved the maximization of the ‘amount’ of positive albedo on the reconstructed map, but a test showed that the distinction that this method makes is in the same order of magnitude as the numerical error, thus proving that this method was not useful as well. Further study might show what causes the results of the two methods to differ in this respect

In this thesis, we consider investment optimization for airport infrastructure which is required charge and refuel electric and hydrogen powered aircraft using battery and hydrogen canister swaps respectively. The task at hand is to determine the most cost-effective infrastructure, consisting of spare batteries, and battery chargers for electric aircraft, and spare hydrogen canisters and fueling points for hydrogen aircraft. Previously developed models are expanded upon in this study by introducing the possibility of slot allocation, where flights that are not yet in possession of landing and take-off rights are assigned to them in such a way that requires the smallest extra infrastructure to be acquired. We derive several (mixed) integer linear programming formulations to solve this problem and develop heuristics which are able to approximate the optimal solution using only open-source resources. These are expanded upon by the introduction of instances where more than one battery type is allowed, electricity pricing becomes dependent on the time-of-use, and storage of electricity at the airport is allowed such that the peak demand can be as low as possible. Finally, we incorporate a distinction between the long-, medium-, and short-term decisions which have to be made by the airport operator into the model analysis. This allows the user to determine the most cost-effective infrastructure combination which can meet a required level of service. When testing these methods, we found that exact solutions can be found within reasonable time for cases with up to 200 batteries. Furthermore, a first-in-first-out policy heuristic has shown to be capable of generating promising results while being applicable to larger instances. The models have been illustrated in a case study at the airports Schiphol (Amsterdam) and Zestienhoven (Rotterdam - The Hague), where they have proven to be able to solve all daily instances to optimality.