Range descriptions for the spherical mean Radon transform

The transform considered in the paper averages a function supported in a ball in \RR^n over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, error correction, and other issues. Four different types of complete range descriptions are provided, some of which also suggest inversion procedures. Necessity of three of these (appropriately formulated) conditions holds also in general domains, while the complete discussion of the case of general domains would require another publication.Comment: LATEX file, 55 pages, two EPS figure

Evaluation of Four Advanced Nozzle Concepts for Short Takeoff and Landing Performance

Four advanced nozzle concepts were tested on a canard-wing fighter in the Langley 14- by 22-Foot Subsonic Tunnel. The four vectoring-nozzle concepts were as follows: (1) an axisymmetric nozzle (AXI); (2) an asymmetric, load balanced exhaust nozzle (ALBEN); (3) a low aspect ratio, single expansion ramp nozzle (LASERN); and (4) a high aspect ratio, single expansion ramp nozzle (HASERN). The investigation was conducted to determine the most suitable nozzle concept for short takeoff and landing (STOL) performance. The criterion for the best STOL performance was a takeoff ground roll of less than 1000 ft. At approach, the criteria were high lift and sufficient drag to maintain a glide slope of -3 to -6 deg with enough pitching-moment control from the canards. The test was performed at a dynamic pressure of 45 lb/sq ft and an angle-of-attack range of 0 to 20 deg. The nozzle pressure ratio was varied from 1.0 to 4.3 at both dry power and after burning nozzle configurations with nozzle vectoring to 60 deg. In addition, the model was tested in and out of ground effects. The ALBEN concept was the best of the four nozzle concepts tested for STOL performance

The Langley 14- by 22-Foot Subsonic Tunnel: Description, Flow Characteristics, and Guide for Users

The Langley 14- by 22-foot Subsonic Tunnel is a closed circuit, single-return atmospheric wind tunnel with a test section that can be operated in a variety of configurations (closed, slotted, partially open, and open). The closed test section configuration is 14.5 ft high by 21.75 ft wide and 50 ft long with a maximum speed of about 338 ft/sec. The open test section configuration has a maximum speed of about 270 ft/sec, and is formed by raising the ceiling and walls, to form a floor-only configuration. The tunnel may be configured with a moving-belt ground plane and a floor boundary-layer removal system at the entrance to the test section for ground effect testing. In addition, the tunnel had a two-component laser velocimeter, a frequency modulated (FM) tape system for dynamic data acquisition, flow visualization equipment, and acoustic testing capabilities. Users of the 14- by 22-foot Subsonic Tunnel are provided with information required for planning of experimental investigations including test hardware and model support systems

Birth and growth of cavitation bubbles within water under tension confined in a simple synthetic tree

Water under tension, as can be found in several systems including tree vessels, is metastable. Cavitation can spontaneously occur, nucleating a bubble. We investigate the dynamics of spon- taneous or triggered cavitation inside water filled microcavities of a hydrogel. Results show that a stable bubble is created in only a microsecond timescale, after transient oscillations. Then, a diffusion driven expansion leads to filling of the cavity. Analysis reveals that the nucleation of a bubble releases a tension of several tens of MPa, and a simple model captures the different time scales of the expansion process

Low-speed aerodynamic characteristics of a twin-engine general aviation configuration with aft-fuselage-mounted pusher propellers

An investigation was conducted to determine the aerodynamic characteristics of an advanced turboprop aircraft model with aft-pylon-mounted pusher propellers. Tests were conducted through an angle-of-attack range of -8 to 28 degrees, and an angle-of-sideslip range of -20 to 20 degrees at free-stream conditions corresponding to Reynolds numbers of 0.55 to 2.14 x 10 to the 6th power based on mean aerodynamic chord. Test results show that for the unpowered configurations the maximum lift coefficients for the cruise, takeoff, and landing configurations are 1.45, 1.90, and 2.10, respectively. Nacelle installation results in a drag coefficient increase of 0.01. Increasing propeller thrust results in a significant increase in lift for angles of attack above stall and improves the longitudinal stability. The cruise configuration remains longitudinally stable to an angle of attack 5 degrees beyond the stall angle, the takeoff configuration is stable 4 degrees beyond stall angle, and the landing configuration is stable 3 degrees beyond stall angle. The predominant effect of symmetric thrust on the lateral-directional aerodynamic characteristics is in the post-stall region, where additional rudder control is available with power on

A review of technologies applicable to low-speed flight of high-performance aircraft investigated in the Langley 14- x 22-foot subsonic tunnel

An extensive research program has been underway at the NASA Langley Research Center to define and develop the technologies required for low-speed flight of high-performance aircraft. This 10-year program has placed emphasis on both short takeoff and landing (STOL) and short takeoff and vertical landing (STOVL) operations rather than on regular up and away flight. A series of NASA in-house as well as joint projects have studied various technologies including high lift, vectored thrust, thrust-induced lift, reversed thrust, an alternate method of providing trim and control, and ground effects. These technologies have been investigated on a number of configurations ranging from industry designs for advanced fighter aircraft to generic wing-canard research models. Test conditions have ranged from hover (or static) through transition to wing-borne flight at angles of attack from -5 to 40 deg at representative thrust coefficients

Single-bubble and multi-bubble cavitation in water triggered by laser-driven focusing shock waves

In this study a single laser pulse spatially shaped into a ring is focused into a thin water layer, creating an annular cavitation bubble and cylindrical shock waves: an outer shock that diverges away from the excitation laser ring and an inner shock that focuses towards the center. A few nanoseconds after the converging shock reaches the focus and diverges away from the center, a single bubble nucleates at the center. The inner diverging shock then reaches the surface of the annular laser-induced bubble and reflects at the boundary, initiating nucleation of a tertiary bubble cloud. In the present experiments, we have performed time-resolved imaging of shock propagation and bubble wall motion. Our experimental observations of single-bubble cavitation and collapse and appearance of ring-shaped bubble clouds are consistent with our numerical simulations that solve a one dimensional Euler equation in cylindrical coordinates. The numerical results agree qualitatively with the experimental observations of the appearance and growth of bubble clouds at the smallest laser excitation rings. Our technique of shock-driven bubble cavitation opens novel perspectives for the investigation of shock-induced single-bubble or multi-bubble cavitation phenomena in thin liquids

A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our approach results in an explicit series solution for any closed measuring surface surrounding a region for which the eigenfunctions of the Dirichlet Laplacian are explicitly known - such as, for example, cube, finite cylinder, half-sphere etc. In addition, we present a fast reconstruction algorithm applicable in the case when the detectors (the centers of the integration spheres) lie on a surface of a cube. This algorithm reconsrtucts 3-D images thousands times faster than backprojection-type methods

Subsonic aerodynamic characteristic of semispan commercial transport model with wing-mounted advanced ducted propeller operating in reverse thrust

A test was conducted in the Langley 14 by 22 Foot Subsonic Tunnel to determine the effect of the reverse-thrust flow field of a wing-mounted advanced ducted propeller on the aerodynamic characteristics of a semispan subsonic high-lift transport model. The advanced ducted propeller (ADP) model was mounted separately in position alongside the wing so that only the aerodynamic interference of the propeller and nacelle affected the aerodynamic performance of the transport model. Mach numbers ranged from 0.14 to 0.26; corresponding Reynolds numbers ranged from 2.2 to 3.9 x 10(exp 6). The reverse-thrust flow field of the ADP shielded a portion of the wing from the free-stream airflow and reduced both lift and drag. The reduction in lift and drag was a function of ADP rotational speed and free-stream velocity. Test results included ground effects data for the transport model and ADP configuration. The ground plane caused a beneficial increase in drag and an undesirable slight increase in lift. The ADP and transport model performance in ground effect was similar to performance trends observed for out of ground effect. The test results form a comprehensive data set that supports the application of the ADP engine and airplane concept on the next generation of advanced subsonic transports. Before this investigation, the engine application was predicted to have detrimental ground effect characteristics. Ground effect test measurements indicated no critical problems and were the first step in proving the viability of this engine and airplane configuration