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NASA NTRS2014

Searching for Reduced Carbon on the Surface of Mars: The SAM Combustion Experiment

The search for reduced carbon has been a major focus of past and present missions to Mars. Thermal evolved gas analysis was used by the Viking and Phoenix landers and is currently in use by the Sample Analysis at Mars (SAM) instrument suite on the Mars Science Laboratory (MSL) to characterize volatiles evolved from solid samples, including those associated with reduced organic species. SAM has the additional capability to perform a combustion experiment, in which a sample of Mars regolith is heated in the presence of oxygen and the composition of the evolved gases is measured using quadrupole mass spectrometry (QMS) and tunable laser spectrometry (TLS) [1]. Organics detection on the Martian surface has been complicated by oxidation and destruction during heating by soil oxidants [2], including oxychlorine compounds, and terrestrial organics in the SAM background contributed by one of the SAM wet chemistry reagents MTBSTFA (N-Methyl-N-tertbutyldimethylsilyl- trifluoroacetamide) [3,4]. Thermal Evolved Gas Analysis (TEGA) results from Phoenix show a mid temperature CO2 release between 400 C - 680 C speculated to be carbonate, CO2 adsorbed to grains, or combustion of organics by soil oxidants [5]. Low temperature CO2 evolutions (approx. 200 C - 400 C) were also present at all three sites in Gale Crater where SAM Evolved Gas Analysis (EGA) was performed, and potential sources include combustion of terrestrial organics from SAM, as well as combustion and/or decarboxylation either indigenous martian or exogenous organic carbon [4,6]. By performing an experiment to intentionally combust all reduced materials in the sample, we hope to compare the bulk abundance of CO2 and other oxidized species evolved by combustion to that evolved during an EGA experiment to estimate how much CO2 could be contributed by reduced carbon sources. In addition, C, O, and H isotopic compositions of CO2 and H2O measured by TLS can contribute information regarding the potential sources of these volatiles.

Stern, J. C.↗
NASA NTRSDate not supplied

The Solar Neutron TRACking (SONTRAC) Instrument for the Detection of Fast Neutrons

Fast neutrons (energies >0.5 MeV) contribute to the radiation exposure of space hardware and astronaut crew, enable greater understanding of planetary atmospheric and surface compositions and allow unique measurements of solar particle acceleration. Neutrons are challenging to detect and measurements of them typically suffer from high background rates. High energy neutrons (>50 MeV) pose even more challenges, because the traditional double-scatter technique based on a time-of-flight (ToF) measurement. These measurements are challenging due to size constraints on satellites, particularly newer small satellites. The SOlar Neutron TRACking instrument (SONTRAC) is a small satellite neutron detector that utilizes fine-grained scintillating fiber bundles with 1-mm pitch silicon photomultiplier (SiPM) array readout. Signal processing is accomplished with multichannel ASICs. SONTRAC is able to image fast neutron (between 20-200 MeV) scatters in a compact scalable package. We discuss below the numerous applications of this technology and recent progress on the development and performance characteristics of the prototype instrument.

Georgia A de Nolfo↗
NASA NTRSDate not supplied

Desert Research and Technology Studies (D-RATS) 2022 Quicklook Report

This report summarizes the Desert Research and Technology Studies (D-RATS) 2022 analog tests. BACKGROUND - Artemis Challenges – NASA’s concept of operations (ConOps) for the Artemis mission architecture brings new challenges for human exploration of the lunar surface, including: (1) Low-angle, natural lighting at lunar poles; and (2) Exploration sites that challenge communication with Earth. - International Partner Involvement – NASA is working with the Japan Aerospace Exploration Agency (JAXA) to scope mission & functional requirements for an Artemis Pressurized Rover (PR), which JAXA may provide. - Charter – HQ Exploration Systems Development Mission Directorate (ESDMD) Moon to Mars Architecture Development Office (M2MADO) Strategy and Architectures (SA) chartered the Human-in-the-Loop (HITL) test team to investigate Artemis architectural questions related to pressurized rover ConOps. - Rationale – to inform the NASA/JAXA pressurized rover study-agreement. PLAN - Objectives – Analog tests conducted in October 2022 by the D-RATS team addressed three high-level objectives: 1. Investigate pressurized rover (PR) ConOps and capabilities for Artemis exploration 2. Integrate with JAXA engineers & astronauts and incorporate JAXA PR design elements into testing. 3. Re-establish analog field-testing skills & capabilities with rovers to investigate Artemis architecture ConOps. - Secondary Objectives – Work with other groups to leverage D-RATS field test for additional objectives. 4. Work with the Public Affairs Office (PAO) to perform D-RATS public outreach activities. 5. Coordinate with the Human Physiology Performance Protection & Operations (H-3PO) team to facilitate in-field evaluation of human health and performance (HHP) objectives. 6. Share D-RATS field-site and assets with Lunar LTE Studies (Lunar LiTES) team, to aid their study of the use of 4G/LTE communication protocols and devices for astronauts and robotic nodes on the lunar surface. - Team – Fully integrated test team comprised of members from 5 NASA centers, JAXA, and the United States Geological Survey (USGS) - Location – Black Point Lava Flow, ~40 miles north of Flagstaff, AZ HIGH-LEVEL OBJECTIVES ACCOMPLISHED - Investigated Pressurized Rover ConOps & Capabilities for Artemis Exploration (Objective 1) - Completed testing with 4 crew pairs, each spending 3 days and 2 nights in the rover conducting Artemis PR dayin-the-life activities (2 JAXA astronauts, 2 JAXA engineers, 1 NASA astronaut, 3 NASA engineers). - Collected detailed objective & subjective data supporting 10 strategic questions related to Artemis PR operations. - Field geologists present in field observed rover operations & EVAs. - Science team in Houston MCC communicated directly with crew. - Demonstrated crew-led and MCC-led PR teleoperation use cases during EVAs. - Integrated with JAXA Engineers & Astronauts and Incorporated JAXA PR Design Elements into Testing (Objective 2) - NASA & JAXA engineers, flight controllers, scientists, roboticists, and astronauts directly participated in and/or observed testing both in field and in MCC-Houston. - Incorporated JAXA PR design elements into both integrated and standalone testing at JSC and in the field. - Re-established Analog Field-Testing Skills & Capabilities with Rovers to Investigate Artemis Architecture ConOps (Objective 3) - Multiple teams successfully worked to establish and manage field-test base camp, monitor and maintain the rover, and plan and execute 2 weeks of consecutive field-testing with little to no breaks between crews. TEST OUTCOMES - Results will inform Artemis architecture ConOps & capabilities related to pressurized rover operations (see sections 2 for more details) - Summary and team detailed reports will be posted on the D-RATS 2022 wiki

Analog↗
NASA NTRS1976

Surface chemistry of selected lunar regions

A completely new analysis has been carried out on the data from the Apollo 15 and 16 gamma-ray spectrometer experiments. The components of the continuum background have been estimated. The elements Th, K, Fe, and Mg give useful results; for Ti are significant only for a few high-Ti regions. Errors are given, and the results are checked by other methods. Concentrations are reported for about 60 lunar regions; the ground track has been subdivided in various ways. The borders of the maria seem well-defined chemically, while the distribution of KREEP is broad. This wide distribution requires emplacement of KREEP before the era of mare formation. Its high concentration in western mare soils seems to require major vertical mixing.

Bielefeld, M. J.↗
DOE OSTI2021

The UHECR dipole and quadrupole in the latest data from the original Auger and TA surface detectors

The sources of ultra-high-energy cosmic rays are still unknown, but assuming standard physics, they are expected to lie within a few hundred megaparsecs from us. Indeed, over cosmological distances cosmic rays lose energy to interactions with background photons, at a rate depending on their mass number and energy and properties of photonuclear interactions and photon backgrounds. The universe is not homogeneous at such scales, hence the distribution of the arrival directions of cosmic rays is expected to reflect the inhomogeneities in the distribution of galaxies; the shorter the energy loss lengths, the stronger the expected anisotropies. Galactic and intergalactic magnetic fields can blur and distort the picture, but the magnitudes of the largest-scale anisotropies, namely the dipole and quadrupole moments, are the most robust to their effects. Measuring them with no bias regardless of any higher-order multipoles is not possible except with full-sky coverage. In this work, we achieve this in three energy ranges (approximately $8$--$16~EeV$, $16$--$32~EeV$, and $32$--$\infty~EeV$) by combining surface-detector data collected at the Pierre Auger Observatory until 2020 and at the Telescope Array (TA) until 2019, before the completion of the upgrades of the arrays with new scintillator detectors. We find that the full-sky coverage achieved by combining Auger and TA data reduces the uncertainties on the north-south components of the dipole and quadrupole in half compared to Auger-only results.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Compact radio sources in the starburst galaxy M82 and the Sigma-D relation for supernova remnants

We have obtained an 8.4 GHz Very Large Array (VLA) A-array map of the starburst galaxy M82 with a resolution Full Width at Half Maximum (FWHM) approximately 0.182 sec. About 50 compact radio sources in the central region of M82 were detected with a peak surface brightness approximately greater than 10(exp -17) W/Hz/sq m/sr. Comparison with previous observations shows that most sources are declining in flux. Three previously visible sources have faded into the background of our map (approximately less than 0.2 mJy/beam), while a few sources, including the second and third brightest radio sources in M82, may have increased slightly in flux over the last decade. No new radio supernova was found. The birth rate of the compact radio sources is estimated to be 0.11 + or - 0.05/yr. We attribute the population of such bright, small supernova remnants (SNRs) in M82 to the high pressure in the central region that can truncate the mass loss during a red supergiant phase or allow dense ionized clouds to be present. The compact radio sources obey a Sigma(radio surface brightness) - D(diameter) relation which is remarkably similar to that followed by supernova remnants in the Galaxy and the Magellanic Clouds and by two of the strongest known extragalactic radio supernovae: SN 1986J and SN 1979C. A least-squares fit to the SNR data gives: Sigma(sub 8.4 GHz) (W/Hz/sq m/sr) = 4.4 x 10(exp -16) D(sub pc)(exp -3.5 +/- 0.1) covering seven orders of magnitude in Sigma. Possible selection effects are discussed and a theoretical discussion of the correlation is presented.

Huang, Z. P.↗
NASA NTRS2024

Applications of Remote Sensing for Land Use Planning Scenarios with Suitability Analysis

In regions undergoing rapid urbanization, such as West Africa, land use planning (LUP) is vital to accommodate growing population and manage natural resources. Suitability analysis modeling is a widely used tool in LUP to determine the extent to which a land area is suitable for a designated purpose, but there is a gap in the integration of remote sensing time series data into land use decisions. The goal of this study was to incorporate remote sensing time series information with suitability analyses to inform LUP decisions in urban areas. In the study area of Kumasi, Ghana, land cover trends and land surface temperature (LST) from 2000 to 2019 were used to understand climate change trends. Suitability analyses determined the fitness of land areas for predetermined uses. These background processes informed a genetic algorithm to project plausible futures for three land use scenarios. One scenario represented current land use planning practices for addressing population growth, another scenario prioritized minimizing climate change impacts while also accommodating population growth, and the final scenario focused on both of these climate and population goals in addition to high density urban development. Each of these scenarios was successful in achieving population accommodation and respective climate change mitigation goals. The results for these scenarios provide insight into plausible land use distributions in 2050 based on different planning approaches. The genetic algorithm was able to effectively develop results for each scenario through the integration of remotely sensed trends and suitability models, providing a novel approach to land use decision-making.

remote sensing time series↗
NASA NTRS1972

Role of gas surface interactions in the reduction of OGO-6 neutral gas particle mass spectrometer data

The gas-surface interaction effects observed by the quadrupole mass spectrometer are described, and the technique developed to account for them in determining ambient neutral densities is summarized. The total ion current and the ion currents for ions with molecular weights 2, 4, 16, 28, and 32 are sampled for 1.125 sec once every 9.216 sec, for 258 sec out of a 368 sec cycle. An equation is given for the number density of any constituent in the ion source region, and source density data are discussed. The mass 28 background gas is considered to be CO rather than N2, and a CO model is developed. A quasi-equilibrium model of the atomic oxygen interactions is constructed, and a set of surface parameters is determined which provides a reasonable fit to the mass 16 and 32 source densities consistent with the predicted ambient atomic oxygen.

Hedin, A. E.↗
NASA NTRS1993

A stepped-frequency Delta-K microwave radar for oceanographic studies

A stepped-frequency Delta-K (SFDK) radar was developed to remotely sense ocean surface characteristics. This C-band radar uses frequency diversity and real-time signal processing for improved Delta-K measurements. In this paper, we show how frequency diversity can be implemented to enhance the energy of the resonant peak of the cross-product spectrum relative to the background energy. This feature is essential for making real-time measurements of resonant peak frequency over extended time periods. The SFDK was used in a month-long field experiment at N. Truro (Massachusetts). The results presented show that the phase velocity of ocean surface waves could be precisely measured 87 percent of the time.

Popstefanija, Ivan↗
DOE OSTI2020

Direct evidence for low-energy electron emission following O LVV Auger transitions at oxide surfaces

Abstract Oxygen, the third most abundant element in the universe, plays a key role in the chemistry of condensed matter and biological systems. Here, we report evidence for a hitherto unexplored Auger transition in oxides, where a valence band electron fills a vacancy in the 2s state of oxygen, transferring sufficient energy to allow electron emission. We used a beam of positrons with kinetic energies of $$\sim 1$$ ∼ 1 eV to create O 2s holes via matter-antimatter annihilation. This made possible the elimination of the large secondary electron background that has precluded definitive measurements of the low-energy electrons emitted through this process. Our experiments indicate that low-energy electron emission following the Auger decay of O 2s holes from adsorbed oxygen and oxide surfaces are very efficient. Specifically, our results indicate that the low energy electron emission following the Auger decay of O 2s hole is nearly as efficient as electron emission following the relaxation of O 1s holes in $$\hbox {TiO}_2$$ TiO 2 . This has important implications for the understanding of Auger-stimulated ion desorption, Coulombic decay, photodynamic cancer therapies, and may yield important insights into the radiation-induced reactive sites for corrosion and catalysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

The detection of pulsed X-ray emission from a nearby radio pulsar

As part of a search for thermal surface radiation from nearby neutron stars, we have carried out a 45,000 s observation of the nearby radio pulsar PSR 1929+10 with the ROSAT PSPC. After background subtraction, a net of 420 +/- 25 photons in the 0.1 to 2.0 keV band were detected at the position of the pulsar, corresponding to a luminosity of 1.2 x 10(exp 30) ergs/sec for a source distance of 250 pc, or approximately 3 x 10(exp -4) of the pulsar's spin-down luminosity. We find coherent pulsations from PSR 1929+10 at the radio period of 0.2265 s. The folded light curve is well fitted by a sinusoidal oscillation with a pulsed fraction of about 30%. The total spectrum is fitted by a blackbody with a temperature T(sub infinity) approximately equals 3.2 x 10(exp 6) K; the implied emitting area has a radius of less than 50 m. The maximum of the X-ray light curve coincides with the radio pulse, suggesting that we are detecting the hot magnetic polar cap of the star. The temperature limit for the remainder of the stellar surface is T(sub infinity) less than 3 x 10(exp 5) K. The spatial distribution of the photons is consistent with the instrument point-spread function. We discuss the implications of these results for the temperature distribution over the surface of the star and use this detection to constrain various heating mechanisms for rotation-powered neutron stars. We also use a simple model of general relativistic light bending near the stellar surface in conjunction with the radio emission geometry and the X-ray pulsed fraction to derive a radius for the neutron star of R = 9 +/- 3 km.

Yancopoulos, S.↗
NASA NTRSDate not supplied

Development of Luminescence Lifetime-Based Surface Temperature Mapping for Environmental Barrier Coatings

Luminescence lifetime-based temperature mapping for thermal barrier coatings (TBCs) has been previously demonstrated up to temperatures approaching 1200 °C. Advantages of this method include insensitivities to reflected radiation and emissivity uncertainties. Because of a push towards greater efficiency turbine engine operation using higher turbine inlet temperatures, there is an ongoing movement from TBC-coated superalloy turbine engine components to SiC/SiC ceramic matrix composite components protected by environmental barrier coatings (EBCs). The useful application of luminescence lifetime-based temperature mapping to EBCs requires a significant increase in high temperature capability from below 1200 °C up into the 1300 to 1500 °C temperature range where the much higher background thermal radiation is a challenging issue. In addition, the luminescing sensing layer must exhibit thermochemical compatibility with the EBC. To meet these requirements, Er-doped Y 2 SiO 5 was selected as the luminescing sensor layer material both for its enhanced temperature sensitivity above 1300 °C and its compatibility with rare-earth disilicate EBC topcoats. Both localized spot temperature measurements as well as luminescence lifetime imaging-based temperature mapping were demonstrated up to 1560 °C for Er-doped Y 2 SiO 5 disks. In addition, temperature mapping capability was demonstrated from a 15 µm thick Er-doped Y 2 SiO 5 layer at the surface of a Sc 2 Si 2 O 7 based EBC topcoat. Both localized spot and temperature mapping by luminescence lifetime imaging were demonstrated up to 1380 °C (upper temperature limit of this slurry-based layered EBC) with excellent suppression of background thermal radiation and no degradation of the Er-doped Y 2 SiO 5 temperature sensing surface layer. The source of the novel enhanced temperature sensitivity above 1300 °C will be discussed as well as a path towards compatibility between sensing layer and EBC topcoat to higher temperatures.

temperature measurement↗
DOE OSTI2024

Spectroscopic search for optical emission lines from dark matter decay

We search for narrow-line optical emission from dark matter decay by stacking dark-sky spectra from the Dark Energy Spectroscopic Instrument (DESI) at the redshift of nearby galaxies from DESI’s Bright Galaxy and Luminous Red Galaxy samples. Our search uses regions separated by 5 to 20 arcsec from the centers of the galaxies, corresponding to an impact parameter of approximately 50 kpc. No unidentified spectral line shows up in the search, and we place a line flux limit of 10 −19 ergs/s/cm 2 /arcsec 2 on emissions in the wavelength range of 2000–9000⁢ Å. This places the tightest constraints yet on the two-photon decay of dark matter in the mass range of 5 to 12 eV, with a particle lifetime exceeding 3 × 10 25 s. Furthermore, this detection limit also implies that the line surface brightness contributed from all dark matter along the line of sight is at least 2 orders of magnitude lower than the measured extragalactic background light (EBL), ruling out the possibility that narrow optical-line emission from dark matter decay is a major source of the EBL.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Impact Mapping for Geospatial Reasoning and Decision Making

Objective The reported study evaluated a novel approach to aiding geospatial reasoning and decision making. Background Impact mapping aims to alleviate the cognitive demands of geospatial tasks in part by externalizing data in the form of an integrated decision surface. This is achieved by aggregating data across multiple sources of information and visualizing their combined utility rather than objective measurements or individual utility. Previous research has shown that geospatial decisions improve when aided in this manner, but it remains unknown if dynamic decision making, often plagued by fatigue and anchoring bias, would benefit similarly. Method The experiment implemented a systematic manipulation of the presence of a composite impact map and the number of attributes present in a two-stage disaster relief, resource allocation task to investigate when and how impact mapping is beneficial or deleterious to decision makers. Results The presence of the composite impact map increased the utility of selected sites, increased re-planning decisions, reduced information display views, and reduced workload. Generally, the effect of the composite impact map was greater when participants were asked to evaluate more attributes. Conclusion Composite impact maps appear to improve repeated geospatial reasoning and minimize anchoring bias because they alleviate the cognitive demands otherwise necessary to interpret and maintain information from multiple attributes. Application Data visualization techniques, such as impact mapping, can improve repeated geospatial decision making in environments that include high cognitive demand.

Illingworth, David A.↗
DOE OSTI2023

Evaluation of 6-OxP-CD, an Oxime-based cyclodextrin as a viable medical countermeasure against nerve agent poisoning: Experimental and molecular dynamic simulation studies on its inclusion complexes with cyclosarin, soman and VX

The ability of the cyclodextrin-oxime construct 6-OxP-CD to bind and degrade the nerve agents Cyclosarin (GF), Soman (GD) and S -[2-[Di(propan-2-yl)amino]ethyl] O -ethyl methylphosphonothioate (VX) has been studied using 31 P-nuclear magnetic resonance (NMR) under physiological conditions. While 6-OxP-CD was found to degrade GF instantaneously under these conditions, it was found to form an inclusion complex with GD and significantly improve its degradation (t 1/2 ~ 2 hrs) relative over background (t 1/2 ~ 22 hrs). Consequently, effective formation of the 6-OxP-CD:GD inclusion complex results in the immediate neutralization of GD and thus preventing it from inhibiting its biological target. In contrast, NMR experiments did not find evidence for an inclusion complex between 6-OxP-CD and VX, and the agent’s degradation profile was identical to that of background degradation (t 1/2 ~ 24 hrs). As a complement to this experimental work, molecular dynamics (MD) simulations coupled with Molecular Mechanics-Generalized Born Surface Area (MM-GBSA) calculations have been applied to the study of inclusion complexes between 6-OxP-CD and the three nerve agents. These studies provide data that informs the understanding of the different degradative interactions exhibited by 6-OxP-CD with each nerve agent as it is introduced in the CD cavity in two different orientations (up and down). For its complex with GF, it was found that the oxime in 6-OxP-CD lies in very close proximity (P GF …O Oxime ~ 4–5 Å) to the phosphorus center of GF in the ‘down GF ’ orientation for most of the simulation accurately describing the ability of 6-OxP-CD to degrade this nerve agent rapidly and efficiently. Further computational studies involving the center of masses (COMs) for both components (GF and 6-OxP-CD) also provided some insight on the nature of this inclusion complex. Distances between the COMs (ΔCOM) lie closer in space in the ‘down GF ’ orientation than in the ‘up GF ’ orientation; a correlation that seems to hold true not only for GF but also for its congener, GD. In the case of GD, calculations for the ‘down GD ’ orientation showed that the oxime functional group in 6-OxP-CD although lying in close proximity (P GD …O Oxime ~ 4–5 Å) to the phosphorus center of the nerve agent for most of the simulation, adopts another stable conformation that increase this distance to ~ 12–14 Å, thus explaining the ability of 6-OxP-CD to bind and degrade GD but with less efficiency as observed experimentally (t 1/2 ~ 4 hr. vs. immediate). Lastly, studies on the VX:6-OxP-CD system demonstrated that VX does not form a stable inclusion complex with the oxime-bearing cyclodextrin and as such does not interact in a way that is conducive to an accelerated degradation scenario. Collectively, these studies serve as a basic platform from which the development of new cyclodextrin scaffolds based on 6-OxP-CD can be designed in the development of medical countermeasures against these highly toxic chemical warfare agents.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1988

Satellite microwave rainfall simulations with a three-dimensional dynamical cloud model

The three-dimensional, multicloud model of Tao and Soong (1986) is used to generate three-dimensional distribution of pertinent microphysical and state parameters which are used as input into a microwave radiative transfer model. The model is used to calculate upwelling radiance (brightness temperature) at microwave frequencies from 10 to 183 GHz with an ocean background. The model is used to study the relationship between simulated upwell brightness temperature and the cloud-model-generated rain rate at the surface. It is suggested that these calculations can be used to simulate satellite observed brightness temperature values and to make area-averaged rain rates.

Adler, Robert F.↗
NASA NTRS1993

Quark matter droplets in neutron stars

We show that, for physically reasonable bulk and surface properties, the lowest energy state of dense matter consists of quark matter coexisting with nuclear matter in the presence of an essentially uniform background of electrons. We estimate the size and nature of spatial structure in this phase, and show that at the lowest densities the quark matter forms droplets embedded in nuclear matter, whereas at higher densities it can exhibit a variety of different topologies. A finite fraction of the interior of neutron stars could consist of matter in this new phase, which would provide new mechanisms for glitches and cooling.

Heiselberg, H.↗
NASA NTRS1996

The Kirchhoff Formulas for Moving Surfaces in Aeroacoustics - The Subsonic and Supersonic Cases

One of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise predictions. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modem mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a super-sonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions of the Ffowcs Williams-Hawkings equation. In the first part of this memorandum, some introductory remarks are made on generalized functions, the derivation of the Kirchhoff formulas and the development and validation of Kirchhoff codes. Separate lists of references by Lyrintzis, Long, Strawn and their co-workers are given in this memorandum. This publication is aimed at graduate students, physicists and engineers who are in need of the understanding and applications of the Kirchhoff formulas in acoustics and electromagnetics.

Farassat, F.↗