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Research in X-ray Astronomy

This research grant supported an active sounding rocket program at Penn State University over a period of over 10 years. During this period, the grant supported at least 8 graduate students in Astronomy & Astrophysics for at least a portion of their research. During the same period, our group was involved in seven sounding rocket flights, launched from White Sands, New Mexico, and from Woomera, Australia. Most of these rocket flights, and most of the work supported by this grant, involved the use of X-ray CCD cameras. The first X-ray CCD camera ever flown in space was our sounding rocket observation of SN1987A (flight 36.030 in 1987). Subsequent flights utilized improved CCD detectors, culminating in the'state-of-the-art EEV detector developed for our CUBIC mission, which was flown on 36.093 last May. Data from the last three flights, which observed the diffuse X-ray background with CCDS, include detection of the OVII He(alpha) line in the high latitude diffuse background and detection of the Mg XI He(alpha) line in the North Polar Spur. These results have been reported at meetings of the American Astronomical Society and the SPIE. The analysis of flights 36.092 and 36.106 is part of Jeff Mendenhall's PhD thesis and will be published in the Astrophysical Journal next year. The 36.093 data are currently being analyzed by PhD student Laura Cawley. From 1990 to 1996 this grant supported our development and launch of the CUBIC instrument on the SAC-B satellite, which was designed to measure the spectrum of the soft X-ray diffuse background with moderate energy resolution and high S/N ratio. Unfortunately, this mission terminated shortly after launch due to a failure of the Pegasus XL launch vehicle. This work resulted in publication of 4 papers in the SPIE Proceedings and four others in refereed journals, in addition to several other conference proceedings and contributed papers. In addition to the CCD flights described above, this grant has supported preliminary development of a new sounding rocket payload utilizing a replicated Ni mirror that is being developed at PSU in collaboration with MSFC. Initial testing of the coating technology has produced promising results.

Source record↗

Airborne Submillimeter Spectroscopy

This is the final technical report for NASA-Ames grant NAG2-1068 to Caltech, entitled "Airborne Submillimeter Spectroscopy", which extended over the period May 1, 1996 through January 31, 1998. The grant was funded by the NASA airborne astronomy program, during a period of time after the Kuiper Airborne Observatory was no longer operational. Instead. this funding program was intended to help develop instrument concepts and technology for the upcoming SOFIA (Stratospheric Observatory for Infrared Astronomy) project. SOFIA, which is funded by NASA and is now being carried out by a consortium lead by USRA (Universities Space Research Association), will be a 747 aircraft carrying a 2.5 meter diameter telescope. The purpose of our grant was to fund the ongoing development of sensitive heterodyne receivers for the submillimeter band (500-1200 GHz), using sensitive superconducting (SIS) detectors. In 1997 July we submitted a proposal to USRA to construct a heterodyne instrument for SOFIA. Our proposal was successful [1], and we are now continuing our airborne astronomy effort with funding from USRA. A secondary purpose of the NAG2-1068 grant was to continue the anaIN'sis of astronomical data collected with an earlier instrument which was flown on the NASA Kuiper Airborne Observatory (KAO). The KAO instrument and the astronomical studies which were carried out with it were supported primarily under another grant, NAG2-744, which extended over October 1, 1991 through Januarv 31, 1997. For a complete description of the astronomical data and its anailysis, we refer the reader to the final technical report for NAG2-744, which was submitted to NASA on December 1. 1997. Here we report on the SIS detector development effort for SOFIA carried out under NAG2-1068. The main result of this effort has been the demonstration of SIS mixers using a new superconducting material niobium titanium nitride (NbTiN), which promises to deliver dramatic improvements in sensitivity in the 700-1200 GHz frequency range.

Zmuidzinas, J.↗

Composition Measurements at the Magnetopause and in the Plasma Mantle

This final report describes activities under NASA grant NAGW-4049 to Lockheed Missiles and Space Company. The report covers the entire period of the grant from 15 August 1994 to 31 January 1998. The original grant was for 3 years ending in August 1997; however the grant was extended 6 months to accomodate additional data analysis that added significantly to the scientific results. This is a grant under the NASA Supporting Research and Technology Program for the analysis and interpretation of the combined scientific data from the ISEE-1 Plasma Composition Experiment and the AMPTE/CCE Hot Plasma Composition Experiment. These combined data sets were used in a study of the Earth's magnetopause to develop a fundamental understanding of plasma entry and dynamics at the boundary and formation and maintenance of the low latitude boundary layer under a variety of solar wind and magnetospheric conditions and at a wide range of local times.

Gary, S. P.↗

Geospatial Education and Research Development: A Laboratory for Remote Sensing and Environmental Analysis (LaRSEA)

Old Dominion University has claimed the title "University of the 21st Century," with a bold emphasis on technology innovation and application. In keeping with this claim, the proposed work has implemented a new laboratory equipped for remote sensing as well as curriculum and research innovations afforded for present and future faculty and students. The developments summarized within this report would not have been possible without the support of the NASA grant and significant cost-sharing of several units within the University. The grant effectively spring-boarded the university into major improvements in its approach to remote sensing and geospatial information technologies. The university has now committed to licensing Erdas Imagine software for the laboratory, a campus-wide ESRI geographic information system (GIS) products license, and several smaller software and hardware utilities available to faculty and students through the laboratory. Campus beneficiaries of this grant have included faculty from departments including Ocean, Earth. and Atmospheric Sciences, Political Science and Geography, Ecological Sciences, Environmental Health, and Civil and Environmental Engineering. High student interest is evidenced in students in geology, geography, ecology, urban studies, and planning. Three new courses have been added to the catalog and offered this year. Cross-cutting curriculum changes are in place with growing enrollments in remote sensing, GIS, and a new co-taught seminar in applied coastal remote sensing. The enabling grant has also allowed project participants to attract external funding for research grants, thereby providing additional funds beyond the planned matching, maintenance and growth of software and hardware, and stipends for student assistants. Two undergraduate assistants and two graduate assistants have been employed by full-time assistantships as a result. A new certificate is offered to students completing an interdisciplinary course sequence in remote sensing and coastal environments. Subsequent phases of the project are under planning. including seminars for regional coastal managers and public dissemination of remote sensing science through the local media and university publications.

Allen, Thomas R., Jr.↗

Deformation of Alaskan Volcanoes, Measured by Satellite Radar Inferometry

The purpose of this project was to determine the suitability of measuring active deformation of volcanoes in Alaska using Interferometric Synthetic Aperture Radar (INSAR) techniques. Work sponsored by this grant supported one graduate student (for almost 2 years) and one postdoc (for several months), and has resulted in two published peer-reviewed papers and a front-page article in EOS. An additional paper is in review and a fourth is in preparation. An additional paper in preparation was based in part on research supported by this grant and in part by a successor grant from NASA's Solid Earth Natural Hazards program. Over the course of this research, we documented measurable uplift of Trident volcano in the Katmai group, conducted a systematic study of the change in phase coherence over time on volcanic surfaces, and measured and modeled the spectacular 1.5 m deflation of Okmok caldera associated with its 1997 eruption. We also generated initial interferograms spanning the 1996 seismic swarm of Akutan volcano; however, during the period covered by this project we were not able to remove topography. That has been done under the subsequent funding and a paper is now in preparation. This report summarizes work done under two separate contracts because both were based on the same proposal to NASA's ADRO (Application Development and Research Opportunity) program. The first year was funded out of a grant from NASA Headquarters and the second and third years out of a grant through Goddard. The work, however, was a continuous three year effort.

Freymueller, Jeff↗

Multidisciplinary Design Investigation of Truss-Braced Wing Aircraft

The subject grant was in effect from 7/l/99 to 10/31/99. The objective of this grant was to complete a strut-braced wing study which began, which was in effect from 6/27/96 until 9/15/99. While the initial grant was on-going, we were also under subcontract to Lockheed-Martin, Aerospace Systems Division, Marietta, GA to do additional studies related to the strut-braced wing grant "A Structural and Aerodynamic Investigation of a Strut-Braced Wing Transonic Aircraft Concept", 4/l/98-11/15/98. Lockheed-Martin was under contract to NASA Langley. Finally the research under this grant has led to a joint proposal from NASA Langley, Locheed-Martin, Virginia Tech and NASA Dryden to develop a transonic strut-braced wing demonstration aircraft in response to Flight Research for Revolutionary Aeronautical Concepts (REVCON). This final report summarizes the research done, augmented by the additional concommitant research projects mentioned above.

Grossman, B.↗

X-Ray, EUV, UV and Optical Emissivities of Astrophysical Plasmas

This grant primarily covered the development of the thermal X-ray emission model code called APEC, which is meant to replace the Raymond and Smith (1977) code. The new code contains far more spectral lines and a great deal of updated atomic data. The code is now available (http://hea-www.harvard.edu/APEC), though new atomic data is still being added, particularly at longer wavelengths. While initial development of the code was funded by this grant, current work is carried on by N. Brickhouse, R. Smith and D. Liedahl under separate funding. Over the last five years, the grant has provided salary support for N. Brickhouse, R. Smith, a summer student (L. McAllister), an SAO predoctoral fellow (A. Vasquez), and visits by T. Kallman, D. Liedahl, P. Ghavamian, J.M. Laming, J. Li, P. Okeke, and M. Martos. In addition to the code development, the grant supported investigations into X-ray and UV spectral diagnostics as applied to shock waves in the ISM, accreting black holes and white dwarfs, and stellar coronae. Many of these efforts are continuing. Closely related work on the shock waves and coronal mass ejections in the solar corona has grown out of the efforts supported by the grant.

Raymond, John C.↗

Synthesis of Two-Photon Materials and Two-Photon Liquid Crystals

The duration of the grant was interrupted by two major accidents that the PI met with-- an auto accident in Pasadena, CA during her second summer at JPL which took almost eight months for recovery and a second accident during Fall 2000 that left her in crutches for the entire semester. Further, the time released agreed by the University was not given in a timely fashion. The candidate has been given post-grant expire time off. In spite of all these problems, the PI synthesized a number of new two-photon materials and studied the structure-activity correlation to arrive at the best-optimized structure. The PI's design proved to be one of the best in the sense that these materials has a hitherto unreported two-photon absorption cross section. Many materials based on PI's design was later made by the NASA colleague. This is Phase 1. Phase II of this grant is to orate liquid crystalline nature into this potentially useful materials and is currently in progress. Recent observations of nano- and pico-second response time of homeotropically aligned liquid crystals suggest their inherent potentials to act as laser hardening materials, i.e., as protective devices against short laser pulses. The objective of the current project is to exploit this potential by the synthesis of liquid crystals with high optical nonlinearity and optimizing their performance. The PI is trying structural variations to bring in liquid crystalline nature without losing the high two-photon cross section. Both Phase I and Phase II led to many invited presentations and publications in reputed journals like 'Science' and 'Molecular Crystals'. The list of presentations and reprints are enclosed. Another important and satisfying outcome of this grant is the opportunity that this grant offered to the budding undergraduate scientists to get involved in a visible research of international importance. All the students had a chance to learn a lot during research, had the opportunity to present their work at the National level conferences. They continue to retain their interest in their research and went on to accomplish further laurels.

Subramaniam, Girija↗

Metrology Mount and Optics Mandrels

This document is the Final Report for NASA Grant NAG8-1198 from NASA Marshall Space Flight Center (MSFC) to the Smithsonian Astrophysical Observatory (SAO). The Grant is entitled "Metrology Mount and Optics Materials." This final report is required by the terms of the Grant. The period of performance was from September 15, 1995 through January 14, 1999. Total funding received by SAO from MSFC for this effort was, $254,000. Mr. Lester Cohen carried out most of the work at SAO, but received limited support from other engineers, technicians, and designers. Dr. Harvey Tananbaum, the Principal Investigator for the grant provided overall direction and work- assessment. The Grant has had two funding augmentations to its basic amount and has, over time, emphasized three different research areas - each of which has been an extension of earlier research. The research activity was in 2 areas: (1) Expert opto-structural studies related to separation mechanics and effects of electro formed nickel X-ray mirrors. and (2) Design, fabrication and evaluation of a low force metrology and assembly station for light weight full shell electroformed X-ray mirrors.

Tananbaum, H.↗

Aeroelastic Modeling and Behavior of Lifting Surfaces Incorporating Aerodynamic and Structural Nonlinearities: Volterra Series and Indicial Function Approach

Within this NASA Grant, the following points should be emphasized: 1) All the objectives stated in the proposal of the grant have been accomplished. Moreover, the activity within the project has addressed additional issues, of the linear and nonlinear aeroelasticity, not included in the objectives of the grant. 2) During the activities within the grant, we have been in a permanent contact with Dr. Walter A. Silva, the monitor of the NASA Project, to whom we have reported continuously our achievements. 3) As a result of the activities within the grant a number of papers: a. have been submitted for publication to the AIAA Journals, namely the AIAA Journal and the Journal of Guidance, Control, and Dynamics, b. have been presented at the specialized National Conferences and an International Congress, and have appeared in the proceedings of these Conferences, 4) A list of papers submitted for publication and presented at Conferences is appended herewith. 5) In all these papers, an acknowledgment to NASA Langley Research Center was included.

Librescu, Liviu↗

Aeroelastic Modeling and Behavior of Lifting Surfaces Incorporating Aerodynamic and Structural Nonlinearities: Volterra Series and Indicial Function Approach

Within this NASA Grant, the following points should be emphasized: 1) All the objectives stated in the proposal of the grant have been accomplished. Moreover. the activity within the project has addressed additional issues, of the linear and nonlinear aeroelasticity, not included in the objectives of the grant. 2) During the activities within the grant, we have been in a permanent contact with Dr. Walter A. Silva, the monitor of the NASA Project, to whom we have reported continuously our achievements. 3) As a result of the activities within the grant a number of papers: a. have been submitted for publication to the AIAA Journals, namely the AIAA Journal and the Journal of Guidance, Control, and Dynamics, and b. have been presented at the specialized National Conferences and an International Congress, and have appeared in the proceedings of these Conferences. 4) A list of papers submitted for publication and presented at Conferences is appended herewith. 5) In all these papers, an acknowledgment to NASA Langley Research Center was included.

Librescu, Liviu↗

Advanced Methods for Aircraft Engine Thrust and Noise Benefits: Nozzle-Inlet Flow Analysis

The Fluid Mechanics and Acoustics Laboratory at Hampton University (HU/FM&AL) jointly with the NASA Glenn Research Center has conducted four connected subprojects under the reporting project. Basically, the HU/FM&AL Team has been involved in joint research with the purpose of theoretical explanation of experimental facts and creation of accurate numerical simulation techniques and prediction theory for solution of current problems in propulsion systems of interest to the NAVY and NASA agencies. This work is also supported by joint research between the NASA GRC and the Institute of Mechanics at Moscow State University (IM/MSU) in Russia under a CRDF grant. The research is focused on a wide regime of problems in the propulsion field as well as in experimental testing and theoretical and numerical simulation analyses for advanced aircraft and rocket engines. The FM&AL Team uses analytical methods, numerical simulations and possible experimental tests at the Hampton University campus. The fundamental idea uniting these subprojects is to use nontraditional 3D corrugated and composite nozzle and inlet designs and additional methods for exhaust jet noise reduction without essential thrust loss and even with thrust augmentation. These subprojects are: (1) Aeroperformance and acoustics of Bluebell-shaped and Telescope-shaped designs; (2) An analysis of sharp-edged nozzle exit designs for effective fuel injection into the flow stream in air-breathing engines: triangular-round, diamond-round and other nozzles; (3) Measurement technique improvement for the HU Low Speed Wind Tunnel; a new course in the field of aerodynamics, teaching and training of HU students; experimental tests of Mobius-shaped screws: research and training; (4) Supersonic inlet shape optimization. The main outcomes during this reporting period are: (l) Publications: The AIAA Paper #00-3170 was presented at the 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 17-19 June, 2000, Huntsville, AL. The AIAA Paper #01-1893 has been accepted for the AIAA/NAL-NASDA-ISAS 10th International Space Planes and Hypersonic Systems and Technologies Conference, 24-27 April 2001, Kyoto, Japan. The AIAA Paper #01 -3204 has been accepted for presentation at the 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, being held on 08-11 July, in Salt Lake City, UT; (2) A U.S. patent #6,082,635 was granted on July 4, 2000; (3) Grants and proposals: The H U/ FM&AL was awarded the NASA grant NAG-3-2495 in October 2000 and the laboratory is a primary U.S. research team in a joint project under the CRDF award granted to the NASA GRC and IM/MSU (Russia) in July 2000; (4) Theory and numerical simulations: Analytical theory, numerical simulation, comparison of theoretical with experimental results, and modification of theoretical approaches, models, grids, etc., have been conducted for several complicated 2D and 3D nozzle and inlet designs using NASA, ICASE, and IM/MSU codes based on full Euler and Navier-Stokes solvers: CFL3D, FLUENT, and GODUNOV, and others; (5) Experimental Tests: (a) A new course: "Advanced Aerodynamics and Aircraft Performance" presented in spring semester, 2001; training and experimental test research using the HU LSWT. (b) Small-scale M6bius-shaped screws were tested in different conditions and their application has shown essential benefits by comparison with traditional designs; (6) Installation in the FM&AL computer system: second software TECPLOT 8.0 for the UNIX SGI workstation and free TECPLOT 7.5 for the PC Dell computer, and 2D and 3D GRIDGEN (version 9) for the UNIX SGI as well as installation of two free NASA codes, 3D MAG and VULCAN; (7) Student Research Activity: Involvement of two undergraduate students as research assistants in the current research project.

Gilinsky, Mikhail↗

Rocket and Laboratory Studies in Astronomy

This is the final report for NASA Grant NAG5-5122 and covers the period from March 1, 1997 to February 28, 2001. This grant was a continuation of a program in rocket and laboratory studies in ultraviolet astronomy that was supported by NASA grant NAG5-619. As of March 1, 2001, this program is continuing under grant NAG5-5315. During the period of the grant, annual status reports have been submitted detailing the scientific achievements and current objectives of each report period. These will not be repeated here. Among the highlights of the program are four successful rocket launches including participation in the campaign to study comet Hale-Bopp in April 1997. We have continued our emphasis on long-slit spectroscopy of extended sources in the shorter wavelength far-ultraviolet, necessitating the development of evacuated telescope/spectrograph payloads. Finally, we also note the use of our ultraviolet calibration facilities in support of other sounding rocket investigators and for other space missions such as the Far Ultraviolet Spectroscopic Explorer. We include a list of the sounding rocket launches performed under NASA sponsorship during this period, a list of Ph.D. degrees awarded to students who worked in this program, and a summary bibliography of publications between 1997 and 2001.

Feldman, Paul D.↗

Physical Studies of Brown Dwarfs and Extrasolar Planets

The main purpose of this grant proposal was to fund the ongoing work on brown dwarfs by Denise Stephens during her tenure at STScI as a postdoctoral researcher. We have completed approximately half of the three-year grant period. Dr. Stephens has now assumed to role of senior research associate at Johns Hopkins University and in this position is eligible to be PI of grants. Because the bulk of the work and funds under this grant have been and will continue to be for the purposes of supporting Dr. Stephens, we are transferring control of the grant to her at JHU. This closeout is a formality to allow that transfer. The largest project was the completion of a major work on the infrared photometry of L and T dwarfs. The paper was published in January 2004.

Noll, Keith↗

Ground Based Studies of the Outer Planets

This report covers progress to date under this grant on our continuing program to conduct ground based studies of the outer solar system planets and satellites, with emphasis on spectroscopy and atmospheric phenomena. The research continues under our new PAST grant, NNG04G131G beginning 5/1/2004. The original period of performance of the subject grant was 3/1/2001 to 2/28/2004, but was extended one year at no cost. Although there is some overlap in the scientific projects conducted during the extended year with those of the new grant, this report is confined to the portion of the work funded under NAG5-10435. The primary goals for this grant period were a comparative study of outer planet thermospheres/ionospheres near solar maximum, extended to the mid-IR, and the investigation of molecular dimers in outer solar system atmospheres. This project supports NASA's planned space missions, Jupiter Polar Orbiter, outer Planet Microprobes, and the recent Cassini flyby of Jupiter. It also supports the OSS strategic plan themes, The Exploration of the Solar System and The Sun-Earth Connection/ Understanding comparative planetary space environments.

Trafton, Laurence M.↗

Mapping Galactic 60Fe Synthesis in Cen CIR Region

This included a 1 year no cost time extension. The grant was for research into the origin of radioactive 60Fe, whose detection was a mission goal for INTEGRAL and RHESSI. During the grant period, both missions ultimately discovered gamma-line emission from this long lived radioactivity at precisely the value that had been predicted years before by Timmes and Woosley (ApJ, 449,204 (1995)). Unfortunately, using "revised" stellar models and cross sections Rauscher et a1 (ApJ, 576, 323 (2002)), had meanwhile predicted a much larger value. During the grant period, Dieter Hartmann (PI on the complementary grant at Clemson) and Woosley corresponded on this discrepancy and Hartmann visited Santa Cruz (November 20 - 28,2004). All of the grant funds in NAG513659 paid for the expenses of that visit. Subsequently, partly motivated by conversations with Hartmann and Diehl, Woosley re-investigated the production of 60Fe and 26A1 in massive stars from 12 - 120 solar masses, with an eye towards determining the relevant, uncertain physics. The chief changes in Rauscher et a1 were "new" Hauser Feshbach cross sections for 59,60Fe(ng) and 26Al(np)26Mg. The latter has an experimental evaluation which was actually better represented in the study of Timmes and Woosley. The iron (ng) cross sections are from theory and the Timmes and Woosley values were just as reliable as those from Rauscher. Experiments need to be done to resolve who is right. In addition uncertainties in stellar winds, opacities and the IMF were explored. The bottom line is that the value predicted by Timmes and Woosley could well be the correct one, but the experimental error bar is larger than was realized. At least half of the uncertainty is nuclear cross sections that can, and should be measured in the laboratory.

Woosley, Stanford↗

Studies of Coronae and Large Volcanoes on Venus: Constraining the Diverse Outcomes of Small-Scale Mantle Upwellings on Venus

Proxemy Research had a grant from NASA to perform science research on upwelling and volcanism on Venus. This was a 3 year Planetary Geology and Geophysics grant to E. Stofan, entitled Coronae and Large volcanoes on Venus. This grant closes on 12/31/05. Here we summarize the scientific progress and accomplishments of this grant. Scientific publications and abstracts of presentations are indicated in the final section. This was a very productive grant and the progress that was made is summarized. Attention is drawn to the publications and abstracts published in each year. The proposal consisted of two tasks, one examining coronae and one studying large volcanoes. The corona task (Task 1) consisted of three parts: 1) a statistical study of the updated corona population, with Sue Smrekar, Lori Glaze, Paula Martin and Steve Baloga; 2) geologic analysis of several specific groups of coronae, with Sue Smrekar and others; and 3) determining the histories and significance of a number of coronae with extreme amounts of volcanism, with Sue Smrekar. Task 2, studies of large volcanoes, consisted of two subtasks. In the first, we studied the geologic history of several volcanoes, with John Guest, Peter Grindrod, Antony Brian and Steve Anderson. In the second subtask, I analyzed a number of Venusian volcanoes with evidence of summit diking along with Peter Grindrod and Francis Nimmo.

Stofan, Ellen R.↗

Nonthermal processes around collapsed objects: High energy gamma ray sources in the radio sky

In our proposal responding to the initial Guest Observer NRA for the Compton Gamma Ray Observatory, 'Nonthermal Processes Around Collapsed Objects: High Energy Gamma Ray Sources in the Radio Sky', we stated that 'At high energies - the identity of the principal Galactic source population remains unknown' although the 'one certain source of high energy emission is young radio pulsars'. These two statements remain true, although at this writing, eighteen months after the beginning of the Compton allsky survey, much of the gamma-ray data required to greatly extend our knowledge of the Galaxy's high energy emission has been collected. The thrust of the program supported by our grant was to collect and analyze a complementary set of data on the Milky Way at radio wavelengths in order to help identify the dominant Pop 1 component of the Galaxy's gamma ray sources, and to pursue theoretical investigations on the origins and emission mechanisms of young pulsars, the one component of this population identified to date. We summarize here our accomplishments under the grant. In Section 2, we describe our VLA surveys of the Galactic Plane along with the current status of the radio source catalogs derived therefrom; unfortunately, owing to the TDRSS antenna problem and subsequent extension of the Sky Survey, we were not able to carry out a comparison with the EGRET data directly, although everything is now in place to do so as soon as it becomes available. In Section 2, we summarize our progress on the theoretical side, including the substantial completion of a dissertation on pulsar origins and work on the high energy emission mechanisms of isolated pulsars. We list the personnel supported by the grant in section 4 and provide a complete bibliography of publications supported in whole or in part by the grant in the final section.

Helfand, David J.↗