Results for “cluster expansion” — Page 5

NASA NTRS2009

Control of the Diameter and Chiral Angle Distributions during Production of Single-Wall Carbon Nanotubes

Many applications of single wall carbon nanotubes (SWCNT), especially in microelectronics, will benefit from use of certain (n,m) nanotube types (metallic, small gap semiconductor, etc.) Especially fascinating is the possibility of quantum conductors that require metallic armchair nanotubes. However, as produced SWCNT samples are polydisperse, with many (n,m) types present and typical approx.1:2 metal/semiconductor ratio. Nanotube nucleation models predict that armchair nuclei are energetically preferential due to formation of partial triple bonds along the armchair edge. However, nuclei can not reach any meaningful thermal equilibrium in a rapidly expanding and cooling plume of carbon clusters, leading to polydispersity. In the present work, SWCNTs were produced by a pulsed laser vaporization (PLV) technique. The carbon vapor plume cooling rate was either increased by change in the oven temperature (expansion into colder gas), or decreased via "warm-up" with a laser pulse at the moment of nucleation. The effect of oven temperature and "warm-up" on nanotube type population was studied via photoluminescence, UV-Vis-NIR absorption and Raman spectroscopy. It was found that reduced temperatures leads to smaller average diameters, progressively narrower diameter distributions, and some preference toward armchair structures. "Warm-up" shifts nanotube population towards arm-chair structures as well, but the effect is small. Possible improvement of the "warm-up" approach to produce armchair SWCNTs will be discussed. These results demonstrate that PLV production technique can provide at least partial control over the nanotube (n,m) population. In addition, these results have implications for the understanding the nanotube nucleation mechanism in the laser oven.

Nikolaev, Pavel↗

NASA NTRS2003

Furrow microtubules and localized exocytosis in cleaving Xenopus laevis embryos

In dividing Xenopus eggs, furrowing is accompanied by expansion of a new domain of plasma membrane in the cleavage plane. The source of the new membrane is known to include a store of oogenetically produced exocytotic vesicles, but the site where their exocytosis occurs has not been described. Previous work revealed a V-shaped array of microtubule bundles at the base of advancing furrows. Cold shock or exposure to nocodazole halted expansion of the new membrane domain, which suggests that these microtubules are involved in the localized exocytosis. In the present report, scanning electron microscopy revealed collections of pits or craters, up to approximately 1.5 micro m in diameter. These pits are evidently fusion pores at sites of recent exocytosis, clustered in the immediate vicinity of the deepening furrow base and therefore near the furrow microtubules. Confocal microscopy near the furrow base of live embryos labeled with the membrane dye FM1-43 captured time-lapse sequences of individual exocytotic events in which irregular patches of approximately 20 micro m(2) of unlabeled membrane abruptly displaced pre-existing FM1-43-labeled surface. In some cases, stable fusion pores, approximately 2 micro m in diameter, were seen at the surface for up to several minutes before suddenly delivering patches of unlabeled membrane. To test whether the presence of furrow microtubule bundles near the surface plays a role in directing or concentrating this localized exocytosis, membrane expansion was examined in embryos exposed to D(2)O to induce formation of microtubule monasters randomly under the surface. D(2)O treatment resulted in a rapid, uniform expansion of the egg surface via random, ectopic exocytosis of vesicles. This D(2)O-induced membrane expansion was completely blocked with nocodazole, indicating that the ectopic exocytosis was microtubule-dependent. Results indicate that exocytotic vesicles are present throughout the egg subcortex, and that the presence of microtubules near the surface is sufficient to mobilize them for exocytosis at the end of the cell cycle.

Non-NASA Center↗

NASA NTRS1990

Tunable far-IR laser spectroscopy of jet-cooled carbon clusters - The nu-2 bending vibration of C3

Seven rovibrational transitions of the (01/1/0)-(00/0/0) fundamental bending band of C3 have been measured with high precision with the use of a tunable far-infrared laser spectrometer. The C3 molecules were produced by laser vaporization of a graphite rod and cooled in a supersonic expansion. The astrophysically important nu-2 fundamental frequency is determined to be 63.416529(40)/cm. These measurements provide the basis for studies of C3 in the interstellar medium with far-infrared astronomy.

Schmuttenmaer, C. A.↗

NASA NTRS1999

On Multi-Dimensional Unstructured Mesh Adaption

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Wood, William A.↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗

NASA NTRS1999

What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?

Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).

Daniels, Andrew D.↗

NASA NTRS1999

ROSAT PSPC Observations of CL0016+16

NASA Grant NAG5-2156 has supported the analysis of several ROSAT observations, which have resulted in the publications. Contents include the following: 1. X-ray Observations of the Sunyaev-Zeldovich Decrement Clusters Abell 665 and CLOO16+16. 2. Complex Spatial Structures in Sunyaev-Zeldovich Decrement Clusters Abell 665 and CLOO16+16. 3. Discovery of Be/X-ray Stars in Two Supernova Remnants in the Small magellanic Cloud. 4. A New Transient Pulsar in the Small Magellanic Cloud with an Unusual X-ray Spectrum. 5. A New X-ray-Discovered Cluster of Galaxies Associated A,ith CLOO16+16. 6. A new X-ray-Discovered Cluster of Galaxies Associated with C10016+16. 7. The Distance to CLOO16+16 and the Hubble Constant. 8. HST Observations of Oxygen-rich Supernova Remnants in the Magellanic Clouds. I. Narrow-band Imaging of N132D in the LMC. 9. The Expansion of the X-ray Remnant of Tycho's Supernova (SN1572). 10. Supernova Remnants Associated with Molecular Clouds in the Large Magellanic Cloud. 11. A Measurement of the Hubble Constant from the X-ray Properties and the Sunyaev-Zeldovich Effect of CLOO16+16.

Hughes, John P.↗

NASA NTRS1995

CFD assessment of the pollutant environment from RD-170 propulsion system testing

Computational Fluid Dynamics (CFD) technology has been used to assess the exhaust plume pollutant environment of the RD-170 engine hot-firing on the F1 Test Stand at Marshall Space Flight Center. Researchers know that rocket engine hot-firing has the potential for forming thermal nitric oxides (NO(x)), as well as producing carbon monoxide (CO) when hydrocarbon fuels are used. Because of the complicated physics involved, however, little attempt has been made to predict the pollutant emissions from ground-based engine testing, except for simplified methods which can grossly underpredict and/or overpredict the pollutant formations in a test environment. The objective of this work, therefore, has been to develop a technology using CFD to describe the underlying pollutant emission physics from ground-based rocket engine testing. This resultant technology is based on a three-dimensional (3D), viscous flow, pressure-based CFD formulation, where wet CO and thermal NO finite-rate chemistry mechanisms are solved with a Penalty Function method. A nominal hot-firing of a RD-170 engine on the F1 stand has been computed. Pertinent test stand flow physics such as the multiple-nozzle clustered engine plume interaction, air aspiration from base and aspirator, plume mixing with entrained air that resulted in contaminant dilution and afterburning, counter-afterburning due to flame bucket water-quenching, plume impingement on the flame bucket, and restricted multiple-plume expansion and turning have been captured. The predicted total emission rates compared reasonably well with those of the existing hydrocarbon engine hot-firing test data.

Wang, Ten-See↗

NASA NTRS1993

A Grid-resolved Analysis of Base Flowfield for a Four-Engine Clustered Nozzle Configuration

The objective of this study is to propose a computational methodology that can effectively anchor the base flowfield of a four-engine clustered nozzle configuration. This computational methodology is based on a three-dimensional, viscous flow, pressure-based computational fluid dynamics (CFD) formulation. For efficient CFD calculation, a Prandtl-Meyer solution treatment is applied to the algebraic grid lines for initial plume expansion resolution. As the solution evolves, the computational grid is adapted to the pertinent flow gradients. The CFD model employs an upwind scheme in which second- and fourth-order central differencing schemes with artificial dissipation are used. The computed quantitative base flow properties such as the radial base pressure distributions, model centerline static pressure, Mach number and impact pressure variations, and base pressure characteristic curve agreed reasonably well with those of the measurement.

Wang, Ten-See↗

NASA NTRS1993

Generation of monodisperse droplets by spontaneous condensation of flow in nozzles

Submicron size monodisperse particles are of interest in many industrial and scientific applications. These include the manufacture of ceramic parts using fine ceramic particles, the production of thin films by deposition of ionized clusters, monodisperse seed particles for laser anemometry, and the study of size dependence of cluster chemical and physical properties. An inexpensive and relatively easy way to generate such particles is by utilizing the phenomenon of spontaneous condensation. The phenomenon occurs when the vapor or a mixture of a vapor and a noncondensing gas is expanded at a high expansion rate. The saturation line is crossed with the supercooled vapor behaving like a gas, until all of a sudden at the so called Wilson point, condensation occurs, resulting in a large number of relatively monodisperse droplets. The droplet size is a function of the expansion rate, inlet conditions, mass fraction of vapor, gas properties, etc. Spontaneous condensation of steam and water vapor and air mixture in a one dimensional nozzle was modeled and the resulting equations solved numerically. The droplet size distribution at the exit of various one dimensional nozzles and the flow characteristics such as pressure ratio, mean droplet radius, vapor and droplet temperatures, nucleation flux, supercooling, wetness, etc., along the axial distance were obtained. The numerical results compared very well with the available experimental data. The effect of inlet conditions, nozzle expansion rates, and vapor mass fractions on droplet mean radius, droplet size distribution, and pressure ratio were examined.

Lai, Der-Shaiun↗

NASA NTRS1976

Condensation of water vapor in rarefaction waves. I - Homogeneous nucleation

A detailed theoretical investigation has been made of the condensation of water vapor/carrier gas mixtures in the nonstationary rarefaction wave generated in a shock tube. It is assumed that condensation takes place by homogeneous nucleation. The equations of motion together with the nucleation rate and the droplet growth equations were solved numerically by the method of characteristics and Lax's method of implicit artificial viscosity. It is found that, for the case considered, the condensation wave formed by the collapse of the metastable nonequilibrium state is followed by a shock wave generated by the intersection of characteristics of the same family. The expansion is practically isentropic up to the onset of condensation. The condensation front accelerates in the x,t plane. The results of the computations for a chosen case of water vapor/nitrogen mixture are presented by plotting variations of pressure, nucleation rate, number density of critical clusters, and condensate mass-fraction along three particle paths. Some consideration is given to homogeneous condensation experiments conducted in a shock tube. Although a direct comparison of the present theoretical work and these experiments is not possible, several worthwhile interpretative features have resulted nevertheless.

Sislian, J. P.↗

NASA NTRS1992

The cosmological constant

The cosmological constant problem is examined in the context of both astronomy and physics. Effects of a nonzero cosmological constant are discussed with reference to expansion dynamics, the age of the universe, distance measures, comoving density of objects, growth of linear perturbations, and gravitational lens probabilities. The observational status of the cosmological constant is reviewed, with attention given to the existence of high-redshift objects, age derivation from globular clusters and cosmic nuclear data, dynamical tests of Omega sub Lambda, quasar absorption line statistics, gravitational lensing, and astrophysics of distant objects. Finally, possible solutions to the physicist's cosmological constant problem are examined.

Carroll, Sean M.↗

NASA NTRS1960

Experimental Evaluation of Rocket Exhaust Diffusers for Altitude Simulation

An experimental investigation of exhaust diffusers has been conducted to evaluate various methods of minimizing the overall pressure ratio (from chamber to ambient pressure) required to establish and maintain full expansion of the nozzle flow (altitude simulation). Exhaust-diffuser configurations investigated were (1) cylindrical diffusers, (2) diffusers with contraction, and (3) diffusers including a right-angle turn. Cylindrical diffusers were evaluated with primary nozzles of various area ratios and types, as well as two clustered configurations; the other diffusers were evaluated with individual nozzles of constant area ratio and varied type. Air was the working fluid, except for two check points obtained with JP-4 fuel and liquid-oxygen rocket engines and cylindrical diffusers. The minimum length-diameter ratio of cylindrical diffusers was about 6 for minimum pressure-ratio requirements. With cylindrical diffusers of adequate length, the pressure-ratio requirements were primarily a function of the ratio of diffuser to nozzle-throat areas and were essentially independent of primary-nozzle type (including two clustered configurations) or area ratio. The two check points obtained with rocket engines indicated the pressure-ratio requirements at given ratios of diffuser to nozzle-throat areas were lowered, as compared with the requirements with air, as a result of the reduced ratio of specific heats. The minimum length-diameter ratio of the contraction throat of convergent-divergent diffusers was also about 6 for minimum pressure-ratio requirements. With adequate contraction-throat length, the pressure-ratio requirements of such diffusers were appreciably below those of comparable cylindrical diffusers when used with conical and cutoff-isentropic nozzles, but not when used with a bell nozzle. Minimum pressure-ratio requirements of a diffuser including a simple long-radius right-angle turn at maximum diffuser area, obtained with the center of radius of the turn a minimum of 2 diffuser diameters downstream of the nozzle exit, were not appreciably above those of a comparable optimum cylindrical diffuser. A diffuser including a long-radius right-angle turn at a contraction minimum area had somewhat lower pressure-ratio requirements than the aforementioned simple turn.

Sivo, Joseph N.↗

NASA NTRS1990

Adaptive pattern recognition by mini-max neural networks as a part of an intelligent processor

In this decade and progressing into 21st Century, NASA will have missions including Space Station and the Earth related Planet Sciences. To support these missions, a high degree of sophistication in machine automation and an increasing amount of data processing throughput rate are necessary. Meeting these challenges requires intelligent machines, designed to support the necessary automations in a remote space and hazardous environment. There are two approaches to designing these intelligent machines. One of these is the knowledge-based expert system approach, namely AI. The other is a non-rule approach based on parallel and distributed computing for adaptive fault-tolerances, namely Neural or Natural Intelligence (NI). The union of AI and NI is the solution to the problem stated above. The NI segment of this unit extracts features automatically by applying Cauchy simulated annealing to a mini-max cost energy function. The feature discovered by NI can then be passed to the AI system for future processing, and vice versa. This passing increases reliability, for AI can follow the NI formulated algorithm exactly, and can provide the context knowledge base as the constraints of neurocomputing. The mini-max cost function that solves the unknown feature can furthermore give us a top-down architectural design of neural networks by means of Taylor series expansion of the cost function. A typical mini-max cost function consists of the sample variance of each class in the numerator, and separation of the center of each class in the denominator. Thus, when the total cost energy is minimized, the conflicting goals of intraclass clustering and interclass segregation are achieved simultaneously.

Szu, Harold H.↗

NASA NTRS1992

The relation of local measures of Hubble's constant to its global value

The distributions of fractional deviations of local values form global H0 that observers with perfect distance data would find if they surveyed specified volumes of the universe are examined here using new very large scale calculations of cold dark matter (CDM) and primordial isocurvature baryonic (PIB) scenarios for the origin of structure. It is found that the expected deviations due to large-scale motions are larger than quoted observational errors unless very large volumes are surveyed. Even perfect sampling and distances of all galaxies within a sphere extending out to the distances of the Virgo and Coma clusters would leave 45 percent and 3 percent rms uncertainties, respectively, in the global value of H0 in the CDM model. It is shown that the local versus global error in an H0 determination can be roughly estimated by the angular variance seen over the sky in the expansion rate, and that a very rough correction from the local to the global H0 value can be derived.

Turner, Edwin L.↗

NASA NTRS1982

Galaxy clusters with multiple components. I - The dynamics of Abell 98

The nature and evolution of rich galaxy clusters containing multiple condensations is studied. Velocities for 13 members of A98 are presented and the determination of dynamical properties of the individual subclusters is substantially improved. The application of techniques for quantifying gravitational scale lengths are stressed without invocation of the symmetry arguments demanded by the usual parameter fitting procedures. The entire A98 cluster is modeled as a two-body system. The probability that A98 is bound is found to be 98 percent. From this model and the results of previous N-body simulations, it is shown that the most likely description of the system is that it reached maximum expansion about 3.5 billion years ago and is presently in a state of collapse. The subclusters will merge in another three billion years.

Beers, T. C.↗

NASA NTRS1997

Advanced Signal Processing Methods Applied to Digital Mammography

The work reported here is on the extension of the earlier proposal of the same title, August 1994-June 1996. The report for that work is also being submitted. The work reported there forms the foundation for this work from January 1997 to September 1997. After the earlier work was completed there were a few items that needed to be completed prior to submission of a new and more comprehensive proposal for further research. Those tasks have been completed and two new proposals have been submitted, one to NASA, and one to Health & Human Services WS). The main purpose of this extension was to refine some of the techniques that lead to automatic large scale evaluation of full mammograms. Progress on each of the proposed tasks follows. Task 1: A multiresolution segmentation of background from breast has been developed and tested. The method is based on the different noise characteristics of the two different fields. The breast field has more power in the lower octaves and the off-breast field behaves similar to a wideband process, where more power is in the high frequency octaves. After the two fields are separated by lowpass filtering, a region labeling routine is used to find the largest contiguous region, the breast. Task 2: A wavelet expansion that can decompose the image without zero padding has been developed. The method preserves all properties of the power-of-two wavelet transform and does not add appreciably to computation time or storage. This work is essential for analysis of the full mammogram, as opposed to selecting sections from the full mammogram. Task 3: A clustering method has been developed based on a simple counting mechanism. No ROC analysis has been performed (and was not proposed), so we cannot finally evaluate this work without further support. Task 4: Further testing of the filter reveals that different wavelet bases do yield slightly different qualitative results. We cannot provide quantitative conclusions about this for all possible bases without further support. Task 5: Better modeling does indeed make an improvement in the detection output. After the proposal ended, we came up with some new theoretical explanations that helps in understanding when the D4 filter should be better. This work is currently in the review process. Task 6: N/A. This no longer applies in view of Tasks 4-5. Task 7: Comprehensive plans for further work have been completed. These plans are the subject of two proposals, one to NASA and one to HHS. These proposals represent plans for a complete evaluation of the methods for identifying normal mammograms, augmented with significant further theoretical work.

Stauduhar, Richard P.↗