RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

Universally Applicable Model for the Quantitative Determination of Lake Sediment Composition Using Fourier Transform Infrared Spectroscopy

ABSTRACT: Fourier transform infrared spectroscopy (FTIRS) can provide detailed information on organic and minerogenic constituents of sediment records. Based on a large number of sediment samples of varying age (0�340 000 yrs) and from very diverse lake settings in Antarctica, Argentina, Canada, Macedonia/Albania, Siberia, and Sweden, we have developed universally applicable calibration models for the quantitative determination of biogenic silica (BSi; n = 816), total inorganic carbon (TIC; n = 879), and total organic carbon (TOC; n = 3164) using FTIRS. These models are based on the differential absorbance of infrared radiation at specific wavelengths with varying concentrations of individual parameters, due to molecular vibrations associated with each parameter. The calibration models have low prediction errors and the predicted values are highly correlated with conventionally measured values (R = 0.94�0.99). Robustness tests indicate the accuracy of the newly developed FTIRS calibration models is similar to that of conventional geochemical analyses. Consequently FTIRS offers a useful and rapid alternative to conventional analyses for the quantitative determination of BSi, TIC, and TOC. The rapidity, cost-effectiveness, and small sample size required enables FTIRS determination of geochemical properties to be undertaken at higher resolutions than would otherwise be possible with the same resource allocation, thus providing crucial sedimentological information for climatic and environmental reconstructions.

Fourier transform infrared spectroscopy, a new method for rapid determination of total organic and inorganic carbon and biogenic silica concentration in lake sediments

Abstract We demonstrate the use of Fourier transform infrared spectroscopy (FTIRS) to make quantitative measures of total organic carbon (TOC), total inorganic carbon (TIC) and biogenic silica (BSi) concentrations in sediment. FTIRS is a fast and costeffective technique and only small sediment samples are needed (0.01 g). Statistically significant models were developed using sediment samples from northern Sweden and were applied to sediment records from Sweden, northeast Siberia and Macedonia. The correlation between FTIRS-inferred values and amounts of biogeochemical constituents assessed conventionally varied between r = 0.84–0.99 for TOC, r = 0.85– 0.99 for TIC, and r = 0.68–0.94 for BSi. Because FTIR spectra contain information on a large number of both inorganic and organic components, there is great potential for FTIRS to become an important tool in paleolimnology.

The Value of Adding Optics to Ecosystem Models: A Case Study

Many ecosystem models have been developed to study the ocean's biogeochemical properties, but most of these models use simple formulations to describe light penetration and spectral quality. Here, an optical model is coupled with a previously published ecosystem model that explicitly represents two phytoplankton (picoplankton and diatoms) and two zooplankton functional groups, as well as multiple nutrients and detritus. Surface ocean color fields and subsurface light fields are calculated by coupling the ecosystem model with an optical model that relates biogeochemical standing stocks with inherent optical properties (absorption, scattering); this provides input to a commercially available radiative transfer model (Ecolight). We apply this bio-optical model to the equatorial Pacific upwelling region, and find the model to be capable of reproducing many measured optical properties and key biogeochemical processes in this region. Our model results suggest that non-algal particles largely contribute to the total scattering or attenuation (> 50% at 660 nm) but have a much smaller contribution to particulate absorption (< 20% at 440 nm), while picoplankton dominate the total phytoplankton absorption (> 95% at 440 nm). These results are consistent with the field observations. In order to achieve such good agreement between data and model results, however, key model parameters, for which no field data are available, have to be constrained. Sensitivity analysis of the model results to optical parameters reveals a significant role played by colored dissolved organic matter through its influence on the quantity and quality of the ambient light. Coupling explicit optics to an ecosystem model provides advantages in generating: (1) a more accurate subsurface light-field, which is important for light sensitive biogeochemical processes such as photosynthesis and photo-oxidation, (2) additional constraints on model parameters that help to reduce uncertainties in ecosystem model simulations, and (3) model output which is comparable to basic remotely-sensed properties. In addition, the coupling of biogeochemical models and optics paves the road for future assimilation of ocean color and in-situ measured optical properties into the models.

Microwave radiometer to retrieve temperature profiles from the surface to the stratopause

TEMPERA (TEMPERature RAdiometer) is a new ground-based radiometer which measures in a frequency range from 51–57 GHz radiation emitted by the atmosphere. With this instrument it is possible to measure temperature profiles from ground to about 50 km. This is the first ground-based instrument with the capability to retrieve temperature profiles simultaneously for the troposphere and stratosphere. The measurement is done with a filterbank in combination with a digital fast Fourier transform spectrometer. A hot load and a noise diode are used as stable calibration sources. The optics consist of an off-axis parabolic mirror to collect the sky radiation. Due to the Zeeman effect on the emission lines used, the maximum height for the temperature retrieval is about 50 km. The effect is apparent in the measured spectra. The performance of TEMPERA is validated by comparison with nearby radiosonde and satellite data from the Microwave Limb Sounder on the Aura satellite. In this paper we present the design and measurement method of the instrument followed by a description of the retrieval method, together with a validation of TEMPERA data over its first year, 2012.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Electronic band dispersion of graphene nanoribbons via Fourier-transformed scanning tunneling spectroscopy

The electronic structure of atomically precise armchair graphene nanoribbons of width N=7 (7-AGNRs) are investigated by scanning tunneling spectroscopy (STS) on Au(111). We record the standing waves in the local density of states of finite ribbons as a function of sample bias and extract the dispersion relation of frontier electronic states by Fourier transformation. The wave-vector-dependent contributions from these states agree with density functional theory calculations, thus enabling the unambiguous assignment of the states to the valence band, the conduction band, and the next empty band with effective masses of 0.41±0.08me,0.40±0.18me, and 0.20±0.03me, respectively. By comparing the extracted dispersion relation for the conduction band to corresponding height-dependent tunneling spectra, we find that the conduction band edge can be resolved only at small tip-sample separations and has not been observed before. As a result, we report a band gap of 2.37±0.06 eV for 7-AGNRs adsorbed on Au(111).

Fourier Series by Least Square Minimization

An introduction to Fourier Series based on the minimization of the least square error between an approximate series representation and the exact function.

Janissaire-Tschausch-Fourier d'une oda en Habit de Cérémonies

Croqué d'apres Nature p. le B. de G. ; gravé p. J. C. Kilian