The investigation of the flow about general fuselage shapes at high angles of attack

Water tunnel visualization of the flow about bodies at high angles of attack was done. Wind tunnel tests on a series of models with non-circular cross sections are reported

The investigation of flow instabilities on a rotating disk with curvature in the radial direction

The major objective is to explore any visible differences of the flow field with wall curvature of the test body, including possible interaction between Taylor-Gortler instabilities present along concave walls and the inflexional instabilities investigated here. An experimental study was conducted with emphasis placed on making visual observations and recording photographically the flow instabilities present under three different rotating bodies: a flat disk, a concave paraboloid, and a convex paraboloid. The data collected for the three test bodies lead to the conclusion that the wall curvature of the concave and convex paraboloids did not alter the observed flow field significantly from that observed on the flat disk

Long wavelength optical coherence tomography for painted objects

Optical Coherence Tomography has been successfully applied to the imaging of painted objects in recent years. However, a significant limitation is the low penetration depth of OCT in paint because of the high opacity of paint due to either scattering or absorption. It has been shown that the optimum spectral window for OCT imaging of paint layers is around 2.2μm in wavelength. In this paper, we demonstrate a 1950nm OCT for imaging painted objects using a superfluorescent fiber source at low power

High resolution fourier domain optical coherence tomography at 2 microns for painted objects

Optical Coherence Tomography has been successfully applied to the non-invasive imaging of subsurface microstructure of a variety of materials from biological tissues to painted objects of art. One of the limitations of the technique is the low depth of penetration due to the strong scattering and absorption in the material. Previous studies found that for paint materials, the optimum window for large depth of penetration is around 2.2 microns. This is also true for many other materials with low water content. We have previously demonstrated OCT systems in this wavelength regime for imaging with improved depth of penetration. In this paper, we present an improved 2 micron high resolution Fourier domain OCT system using a broadband supercontinuum source. The system achieved a depth resolution of 9 microns in air (or 6 microns in paint or any polymer)

Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second-order. We perform much of our analysis using an index-free `vector-calculus' approach which makes manipulating tensor equations considerably simpler.Comment: 13 pages. Final version to appear in CQ

Ultra-broadband wavelength-swept Tm-doped fiber laser using wavelength-combined gain stages

A wavelength-swept thulium-doped fiber laser system employing two parallel cavities with two different fiber gain stages is reported. The fiber gain stages were tailored to provide emission in complementary bands with external wavelength-dependent feedback cavities sharing a common rotating polygon mirror for wavelength scanning. The wavelength-swept laser outputs from the fiber gain elements were spectrally combined by means of a dichroic mirror and yielded over 500 mW of output with a scanning range from ~1740 nm to ~2070 nm for a scanning frequency of ~340 Hz

Randomized Extended Kaczmarz for Solving Least-Squares

We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input matrix. The proposed algorithm is an extension of the randomized Kaczmarz method that was analyzed by Strohmer and Vershynin.Comment: 19 Pages, 5 figures; code is available at https://github.com/zouzias/RE

Subsonic high-angle-of-attack aerodynamic characteristics of a cone and cylinder with triangular cross sections and a cone with a square cross section

Experiments were conducted in the 12-Foot Pressure Wind Tunnel at Ames Research Center on three models with noncircular cross sections: a cone having a square cross section with rounded corners and a cone and cylinder with triangular cross sections and rounded vertices. The cones were tested with both sharp and blunt noses. Surface pressures and force and moment measurements were obtained over an angle of attack range from 30 deg to 90 deg and selected oil-flow experiments were conducted to visualize surface flow patterns. Unit Reynolds numbers ranged from 0.8x1,000,000/m to 13.0x1,000,000/m at a Mach number of 0.25, except for a few low-Reynolds-number runs at a Mach number of 0.17. Pressure data, as well as force data and oil-flow photographs, reveal that the three dimensional flow structure at angles of attack up to 75 deg is very complex and is highly dependent on nose bluntness and Reynolds number. For angles of attack from 75 deg to 90 deg the sectional aerodynamic characteristics are similar to those of a two dimensional cylinder with the same cross section

Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late

Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late