Flow visualization in the Langley 0.3-meter Transonic Cryogenic Tunnel and preliminary plans for the National Transonic Facility

Design problems associated with the integration of flow visualization in cryogenic facilities are discussed. The possible effects from the cryogenic environment (i.e., window distortion due to thermal contraction both in the mounts and in the window material itself and turbulence in the flow due to injected LN2) are examined. The flow visualization techniques studied are schlieren, shadowgraph, moire deflectometry, and holographic interferometry. The test beds for this work are a Langley in-house cryogenic test chamber and the 0.3-Meter Transonic Cryogenic Tunnel

Hypothesis testing near singularities and boundaries

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as highlighted by recent work of Drton. Indeed, poor behavior of a $\chi^2$ for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a $\chi^2$.Comment: 32 pages, 12 figure

Flow and thermal effects in continuous flow electrophoresis

In continuous flow electrophoresis the axial flow structure changes from a fully developed rectilinear form to one characterized by meandering as power levels are increased. The origin of this meandering is postulated to lie in a hydrodynamic instability driven by axial (and possibly lateral) temperature gradients. Experiments done at MSFC show agreement with the theory

Pyrotechnic shock at the orbiter/external tank forward attachment

During the initial certification test of the forward structural attachment of the space shuttle orbiter to the external tank, pyrotechnic shock from actuation of the separation device resulted in structural failure of the thermal protection tiles surrounding the attachment. Because of the high shock associated with the separation bolt, the development of alternative low shock separation designs was initiated. Two concepts that incorporate a 5.08 centimeter frangible nut as the release device were developed and tested

Tensor Rank, Invariants, Inequalities, and Applications

Though algebraic geometry over $\mathbb C$ is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the $n\times n\times n$ tensors of rank $n$ over $\mathbb C$, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose non-vanishing distinguishes this orbit from points only in its closure. Together with an explicit subset of the defining polynomials of the variety, this gives a semialgebraic description of the tensors of rank $n$ and multilinear rank $(n,n,n)$. The polynomials we construct coincide with Cayley's hyperdeterminant in the case $n=2$, and thus generalize it. Though our construction is direct and explicit, we also recast our functions in the language of representation theory for additional insights. We give three applications in different directions: First, we develop basic topological understanding of how the real tensors of complex rank $n$ and multilinear rank $(n,n,n)$ form a collection of path-connected subsets, one of which contains tensors of real rank $n$. Second, we use the invariants to develop a semialgebraic description of the set of probability distributions that can arise from a simple stochastic model with a hidden variable, a model that is important in phylogenetics and other fields. Third, we construct simple examples of tensors of rank $2n-1$ which lie in the closure of those of rank $n$.Comment: 31 pages, 1 figur

Development of a Rooftop Collaborative Experimental Space through Experiential Learning Projects

The Solar, Water, Energy, and Thermal Laboratory (SWEAT Lab) is a rooftop experimental space at the University of Texas at Austin built by graduate and undergraduate students in the Cockrell School of Engineering. The project was funded by the Texas State Energy Conservation Office and the University’s Green Fee Grant, a competitive grant program funded by UT Austin tuition fees to support sustainability-related projects and initiatives on campus. The SWEAT Lab is an on-going experiential learning facility that enables engineering education by deploying energy and water-related projects. To date, the lab contains a full weather station tracking weather data, a rainwater harvesting system and rooftop garden. This project presented many opportunities for students to learn first hand about unique engineering challenges. The lab is located on the roof of the 10 story Engineering Teaching Center (ETC) building, so students had to design and build systems with constraints such as weight limitations and wind resistance. Students also gained experience working with building facilities and management for structural additions, power, and internet connection for instruments. With the Bird’s eye view of UT Austin campus, this unique laboratory offers a new perspective and dimension to applied student research projects at UT Austin.Cockrell School of Engineerin

Intrinsic carrier mobility of multi-layered MoS2_2 field-effect transistors on SiO2_2

By fabricating and characterizing multi-layered MoS$_2$-based field-effect transistors (FETs) in a four terminal configuration, we demonstrate that the two terminal-configurations tend to underestimate the carrier mobility $\mu$ due to the Schottky barriers at the contacts. For a back-gated two-terminal configuration we observe mobilities as high as 125 cm$^2$V$^{-1}$s$^{-1}$ which is considerably smaller than 306.5 cm$^2$V$^{-1}$s$^{-1}$ as extracted from the same device when using a four-terminal configuration. This indicates that the intrinsic mobility of MoS$_2$ on SiO$_2$ is significantly larger than the values previously reported, and provides a quantitative method to evaluate the charge transport through the contacts.Comment: 8 pages, 5 figures, typos fixed, and references update

Kato square root problem with unbounded leading coefficients

We prove the Kato conjecture for elliptic operators, $L=-\nabla\cdot\left((\mathbf A+\mathbf D)\nabla\ \right)$, with $\mathbf A$ a complex measurable bounded coercive matrix and $\mathbf D$ a measurable real-valued skew-symmetric matrix in $\mathbb{R}^n$ with entries in $BMO(\mathbb{R}^n)$;\, i.e., the domain of $\sqrt{L}\,$ is the Sobolev space $\dot H^1(\mathbb{R}^n)$ in any dimension, with the estimate $\|\sqrt{L}\, f\|_2\lesssim \| \nabla f\|_2$