Numerical inversion of finite Toeplitz matrices and vector Toeplitz matrices

Numerical technique increases the efficiencies of the numerical methods involving Toeplitz matrices by reducing the number of multiplications required by an N-order Toeplitz matrix from N-cubed to N-squared multiplications. Some efficient algorithms are given

Linear systems of equations solved using mathematical algorithms

New mathematical algorithm solves linear systems of equations, AX equals B, and preserves the integer properties of the coefficients. The algorithms presented can also be used for the efficient evaluation of determinates and their leading minors

Zariski chambers on surfaces of high Picard number

We present an improved algorithm for the computation of Zariski chambers on algebraic surfaces. The new algorithm significantly outperforms the so far available method and allows therefore to treat surfaces of high Picard number, where huge chamber numbers occur. As an application, we efficiently compute the number of chambers supported by the lines on the Segre-Schur quartic

Advances in atomic oxygen simulation

Atomic oxygen (AO) present in the atmosphere at orbital altitudes of 200 to 700 km has been shown to degrade various exposed materials on Shuttle flights. The relative velocity of the AO with the spacecraft, together with the AO density, combine to yield an environment consisting of a 5 eV beam energy with a flux of 10(exp 14) to 10(exp 15) oxygen atoms/sq cm/s. An AO ion beam apparatus that produces flux levels and energy similar to that encountered by spacecraft in low Earth orbit (LEO) has been in existence since 1987. Test data was obtained from the interaction of the AO ion beam with materials used in space applications (carbon, silver, kapton) and with several special coatings of interest deposited on various surfaces. The ultimate design goal of the AO beam simulation device is to produce neutral AO at sufficient flux levels to replicate on-orbit conditions. A newly acquired mass spectrometer with energy discrimination has allowed 5 eV neutral oxygen atoms to be separated and detected from the background of thermal oxygen atoms of approx 0.2 eV. Neutralization of the AO ion beam at 5 eV was shown at the Martin Marietta AO facility

Structure of the isotropic transport operators in three independent space variables

Based on the idea of separation of variables, a spectral theory for the three-dimensional, stationary, isotropic transport operator in a vector space of complex-valued Borel functions results in continuous sets of regular and generalized eigenfunctions

Payload/orbiter contamination control requirement study

The Spacelab carrier induced contaminant environment and Spacelab's ability to meet established contamination control criteria for the shuttle program are determined. The primary areas of on-going activity include updating, refining, and improving the Spacelab Contamination Computer Model and contamination analysis methodology; establishing the resulting adjusted induced environment predictions for comparison with the applicable criteria; determining Spacelab design and operational requirements necessary to meet the criteria; conducting mission feasibility analyses of the combined Spacelab/orbiter contaminant environment for specific proposed missions and payload mixes; and establishing a preliminary Spacelab mission support plan and model interface requirements. A summary is given of these activities conducted to date including any modifications in approach or methodology utilized in the contamination assessment of the Spacelab vehicle. The emphasis is placed on the Spacelab modeling efforts

Technical research and small business

Thesis (M.B.A.)--Boston Universit

The effect of misleading surface temperature estimations on the sensible heat fluxes at a high Arctic site – the Arctic Turbulence Experiment 2006 on Svalbard (ARCTEX-2006)

The observed rapid climate warming in the Arctic requires improvements in permafrost and carbon cycle monitoring, accomplished by setting up long-term observation sites with high-quality in-situ measurements of turbulent heat, water and carbon fluxes as well as soil physical parameters in Arctic landscapes. But accurate quantification and well adapted parameterizations of turbulent fluxes in polar environments presents fundamental problems in soil-snow-ice-vegetation-atmosphere interaction studies. One of these problems is the accurate estimation of the surface or aerodynamic temperature T<sub>(0)</sub> required to force most of the bulk aerodynamic formulae currently used. Results from the Arctic-Turbulence-Experiment (ARCTEX-2006) performed on Svalbard during the winter/spring transition 2006 helped to better understand the physical exchange and transport processes of energy. The existence of an atypical temperature profile close to the surface in the Arctic spring at Svalbard could be proven to be one of the major issues hindering estimation of the appropriate surface temperature. Thus, it is essential to adjust the set-up of measurement systems carefully when applying flux-gradient methods that are commonly used to force atmosphere-ocean/land-ice models. The results of a comparison of different sensible heat-flux parameterizations with direct measurements indicate that the use of a hydrodynamic three-layer temperature-profile model achieves the best fit and reproduces the temporal variability of the surface temperature better than other approaches

Doctor of Philosophy

dissertationThis dissertation solves the collision avoidance problem for single- and multi-robot systems where dynamic effects are significant. In many robotic systems (e.g., highly maneuverable and agile unmanned aerial vehicles) the dynamics cannot be ignored and collision avoidance schemes based on kinematic models can result in collisions or provide limited performance, especially at high operating speeds. Herein, real-time, model-based collision avoidance algorithms that explicitly consider the robots' dynamics and perform real-time input changes to alter the trajectory and steer the robot away from potential collisions are developed, implemented, and verified in simulations and physical experiments. Such algorithms are critical in applications where a high degree of autonomy and performance are needed, for example in robot-assisted first response where aerial and/or mobile ground robots are required to maneuver quickly through cluttered and dangerous environments in search of survivors. Firstly, the research extends reciprocal collision avoidance to robots with dynamics by unifying previous approaches to reciprocal collision avoidance under a single, generalized representation using control obstacles. In fact, it is shown how velocity obstacles, acceleration velocity obstacles, continuous control obstacles, and linear quadratic regulator (LQR)-obstacles are special instances of the generalized framework. Furthermore, an extension of control obstacles to general reciprocal collision avoidance for nonlinear, nonhomogeneous systems where the robots may have different state spaces and different nonlinear equations of motion from one another is described. Both simulations and physical experiments are provided for a combination of differential-drive, differential-drive with a trailer, and car-like robots to demonstrate that the approach is capable of letting a nonhomogeneous group of robots with nonlinear equations of motion safely avoid collisions at real-time computation rates. Secondly, the research develops a stochastic collision avoidance algorithm for a tele-operated unmanned aerial vehicle (UAV) that considers uncertainty in the robot's dynamics model and the obstacles' position as measured from sensors. The model-based automatic collision avoidance algorithm is implemented on a custom-designed quadcopter UAV system with on-board computation and the sensor data are processed using a split-and-merge segmentation algorithm and an approximate Minkowski difference. Flight tests are conducted to validate the algorithm's capabilities for providing tele-operated collision-free operation. Finally, a set of human subject studies are performed to quantitatively compare the performance between the model-based algorithm, the basic risk field algorithm (a variant on potential field), and full manual control. The results show that the model-based algorithm performs significantly better than manual control in both the number of collisions and the UAV's average speed, both of which are extremely vital, for example, for UAV-assisted search and rescue applications. Compared to the potential-field-based algorithm, the model-based algorithm allowed the pilot to operate the UAV with higher average speeds

Spacelab contamination assessment. Payload/orbiter contamination control requirement study

The activities and the results obtained under the payload/orbiter contamination control requirement study were documented, and the integrated shuttle payload contamination evaluation computer model was developed. Spacelab design and development analysis based upon the predicted Spacelab induced contaminant environments were conducted utilizing the space program