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1	Analyzing data with 1D non-linear shapes using topological methods Wang, Suyi, Wang 14 August 2018 (has links) No description available. Computer Science Computer Engineering Geographic Information Science Neurosciences Shape Analysis Computational Topology Map Reconstruction Neuron Tracing JS-Graph Contour Tree Reeb Graph Persistent Homology 1-Stable Manifold DiMorSC
2	MASCOT Follow-on Mission Concept Study with Enhanced GNC and Propulsion Capability of the Nano-lander for Small Solar System Bodies (SSSB) Missions Chand, Suditi January 2020 (has links) This thesis describes the design, implementation and analysis for a preliminary study for DLR's MASCOT lander's next mission to Small Solar System Bodies (SSSB). MASCOT (Mobile Asteroid Surface Scout) is a nano-lander that flew aboard Hayabusa2 (JAXA) to an asteroid, Ryugu. It is a passive nano-spacecraft that can only be deployed ballistically from a hovering spacecraft. Current research focusses on optimizing similar close-approach missions for deploying landers or small cubesats into periodic orbits but does not provide solutions with semi-autonomous small landers deployed from farther distances. This study aims to overcome this short-coming by proposing novel yet simple Guidance, Navigation and Control (GNC) and Propulsion systems for MASCOT. Due to its independent functioning and customisable anatomy, MASCOT can be adapted for several mission scenarios. In this thesis, a particular case-study is modelled for the HERA (ESA) mission. The first phase of the study involves the design of a landing trajectory to the moon of the Didymos binary asteroid system. For a preliminary analysis, the system - Didymain (primary body), Didymoon (secondary body) and MASCOT (third body) - are modelled as a Planar Circular Restricted Three Body Problem (PCR3BP). The numerical integration methodology used for the trajectory is the variable-step Dormand–Prince (Runge Kutta) ODE-4,5 (Ordinary Differential Equation) solver. The model is built in MATLAB-Simulink (2019a) and refined iteratively by conducting a Monte Carlo analysis using the Sensitivity Analysis Tool. Two models - a thruster-controlled system and an alternative hybrid propulsion system of solar sails and thrusters - are simulated and proven to be feasible. The results show that the stable manifold near Lagrange 2 points proposed by Tardivel et. al. for ballistic landings can still be exploited for distant deployments if a single impulse retro-burn is done at an altitude of 65 m to 210 m above ground with error margins of 50 m in position, 5 cm/s in velocity and 0.1 rad in attitude. The next phase is the conceptual design of a MASCOT-variant with GNC abilities. Based on the constraints and requirements of the flown spacecraft, novel GNC and Propulsion systems are chosen. To identify the overriding factors in using commercial-off-the-shelf (COTS) for MASCOT, a market survey is conducted and the manufacturers of short-listed products are consulted. The final phase of the study is to analyse the proposed equipment in terms of parameter scope and capability-oriented trade-offs. Two traceability matrices, one for devised solutions and system and another for solutions versus capabilities, are constructed. The final proposed system is coherent with the given mass, volume and power constraints. A distant deployment of MASCOT-like landers for in-situ observation is suggested as an advantageous and risk-reducing addition to large spacecraft missions to unknown micro-gravity target bodies. Lastly, the implications of this study and the unique advantages of an enhanced MASCOT lander are explored for currently planned SSSB missions ranging from multiple rendezvous, fly-by or sample-return missions. Concluding, this study lays the foundation for future work on advanced GNC concepts for unconventional spacecraft topology for the highly integrated small landers. / <p>This thesis is submitted as per the requirements for the Spacemaster (Round 13) dual master's degree under the Erasmus Mundus Joint Master's Degree Programme. </p> / MASCOT team, DLR Nanolander small spacecraft technology self-navigating lander self-propelling lander Small Solar System Body (SSSB) MASCOT Didymos GNC Propulsion Mission Design Binary Asteroids Asteroids Comets Microlander Solar Sail Phobos Lagrange 2 Stable Manifold Aerospace Engineering Rymd- och flygteknik
3	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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