Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Let \orig{A} be any matrix and let $A$ be a slight random perturbation of \orig{A}. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).Comment: corrected some minor mistake

Optical spectroscopy study on pressure-induced phase transitions in the three-dimensional Dirac semimetal Cd3_3As2_2

We report a room-temperature optical reflectivity study performed on [112]-oriented Cd$_3$As$_2$ single crystals over a broad energy range under external pressure up to 10 GPa. The abrupt drop of the band dispersion parameter ($z$-parameter) and the interruption of the gradual redshift of the bandgap at $\sim$4~GPa confirms the structural phase transition from a tetragonal to a monoclinic phase in this material. The pressure-induced increase of the overall optical conductivity at low energies and the continuous redshift of the high-energy bands indicate that the system evolves towards a topologically trivial metallic state, although a complete closing of the band gap could not be observed in the studied pressure range. Furthermore, a detailed investigation of the low-pressure regime suggests the possible existence of an intermediate state between 2 and 4~GPa , that might be a precursor of the structural phase transition or due to the lifted degeneracy of the Dirac nodes. Several optical parameters show yet another anomaly at 8~GPa, where low-temperature superconductivity was found in an earlier study.Comment: submitted to PR

Manufacturing and fabrication, part 3

The accessibility of material and energy off the Earth and the leverage that these nonterrestrial resources can exert on the space transportation system are important influences on the long-term goal of exploring the solar system. Research on separation of lunar materials and manufacturing of useful products from them is in its infancy. A few possible processes and products are described in this report. Specific attention is given to oxygen, metal, and silicate products

Blade-mounted trailing edge flap control for BVI noise reduction

Numerical procedures based on the 2-D and 3-D full potential equations and the 2-D Navier-Stokes equations were developed to study the effects of leading and trailing edge flap motions on the aerodynamics of parallel airfoil-vortex interactions and on the aerodynamics and acoustics of the more general self-generated rotor blade vortex interactions (BVI). For subcritical interactions, the 2-D results indicate that the trailing edge flap can be used to alleviate the impulsive loads experienced by the airfoil. For supercritical interactions, the results show the necessity of using a leading edge flap, rather than a trailing edge flap, to alleviate the interaction. Results for various time dependent flap motions and their effect on the predicted temporal sectional loads, differential pressures, and the free vortex trajectories are presented. For the OLS model rotor, contours of a BVI noise metric were used to quantify the effects of the trailing edge flap on the size and directivity of the high/low intensity noise region(s). Average reductions in the BVI noise levels on the order of 5 dB with moderate power penalties on the order of 18 pct. for a four bladed rotor and 58 pct. for a two bladed rotor were obtained

Interacting Hofstadter spectrum of atoms in an artificial gauge field

Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements. The theory also provides an estimate of the critical interaction strength at the transition to the Mott insulator phase.Comment: 4+ pages, 2 figures; v2: published versio

Design of a Thermal and Micrometeorite Protection System for an Unmanned Lunar Cargo Lander

The first vehicles to land on the lunar surface during the establishment phase of a lunar base will be unmanned lunar cargo landers. These landers will need to be protected against the hostile lunar environment for six to twelve months until the next manned mission arrives. The lunar environment is characterized by large temperature changes and periodic micrometeorite impacts. An automatically deployable and reconfigurable thermal and micrometeorite protection system was designed for an unmanned lunar cargo lander. The protection system is a lightweight multilayered material consisting of alternating layers of thermal and micrometeorite protection material. The protection system is packaged and stored above the lander common module. After landing, the system is deployed to cover the lander using a system of inflatable struts that are inflated using residual fuel (liquid oxygen) from the fuel tanks. Once the lander is unloaded and the protection system is no longer needed, the protection system is reconfigured as a regolith support blanket for the purpose of burying and protecting the common module, or as a lunar surface garage that can be used to sort and store lunar surface vehicles and equipment. A model showing deployment and reconfiguration of the protection system was also constructed