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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling

Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrator's focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.

buckling↗
NASA NTRS1990

Microwave and optical lunar transponders

The scientific areas which used data from the Lunar Laser Ranging Experiment, collected from measurements to the Apollo 11, 14, and 15 and Lunakhod 2, include lunar science (i.e., studies of variations in the lunar angular orientation from that for uniform rotation, lunar tidal displacements, and the lunar mass distribution), geodynamics, astrometry, and gravitational physics. This paper argues that the placement of microwave and optical transponders on the moon would improve the accuracy of laser range measurements by nearly two orders of magnitude and would simplify the measurements. The K-band microwave transponders would be operated at the lunar base and at two remote sites on the moon surface, yielding much improved lunar libration and tidal displacement measurements. A two-wavelength laser transponder also would be operated at the lunar base, allowing accurate tropospheric propagation corrections to be made. This would introduce major improvements in measurements of the lunar orbit and of the earth's rotation, and in tests of general relativity.

Bender, P. L.↗
NASA NTRS2000

The State and Future of Mars Polar Science and Exploration

As the planet's principal cold traps, the martian polar regions have accumulated extensive mantles of ice and dust that cover individual areas of approx. 10(exp 6)sq km and total as much as 3-4 km thick. From the scarcity of superposed craters on their surface, these layered deposits are thought to he comparatively young-preserving a record of the seasonal and climatic cycling of atmospheric CO2, H2O, and dust over the past approx. 10(exp 5)-10(exp 8) years. For this reason, the martian polar deposits may serve as a Rosetta Stone for understanding the geologic and climatic history of the planet-documenting variations in insolation (due to quasiperiodic oscillations in the planet's obliquity and orbital elements), volatile mass balance, atmospheric composition, dust storm activity, volcanic eruptions, large impacts, catastrophic floods, solar luminosity, supernovae, and perhaps even a record of microbial life. Beyond their scientific value, the polar regions may soon prove important for another reason-providing a valuable and accessible reservoir of water to support the long-term human exploration of Mars. In this paper we assess the current state of Mars polar research, identify the key questions that motivate the exploration of the polar regions, discuss the extent to which current missions will address these questions, and speculate about what additional capabilities and investigations may be required to address the issues that remain outstanding.

Clifford, Stephen M.↗
NASA NTRS1995

Paths and patterns: the biology and physics of swimming bacterial populations

The velocity distribution of swimming micro-organisms depends on directional cues supplied by the environment. Directional swimming within a bounded space results in the accumulation of organisms near one or more surfaces. Gravity, gradients of chemical concentration and illumination affect the motile behaviour of individual swimmers. Concentrated populations of organisms scatter and absorb light or consume molecules, such as oxygen. When supply is one-sided, consumption creates gradients; the presence of the population alters the intensity and the symmetry of the environmental cues. Patterns of cues interact dynamically with patterns of the consumer population. In suspensions, spatial variations in the concentration of organisms are equivalent to variations of mean mass density of the fluid. When organisms accumulate in one region whilst moving away from another region, the force of gravity causes convection that translocates both organisms and dissolved substances. The geometry of the resulting concentration-convection patterns has features that are remarkably reproducible. Of interest for biology are (1) the long-range organisation achieved by organisms that do not communicate, and (2) that the entire system, consisting of fluid, cells, directional supply of consumables, boundaries and gravity, generates a dynamic that improves the organisms' habitat by enhancing transport and mixing. Velocity distributions of the bacterium Bacillus subtilis have been measured within the milieu of the spatially and temporally varying oxygen concentration which they themselves create. These distributions of swimming speed and direction are the fundamental ingredients required for a quantitative mathematical treatment of the patterns. The quantitative measurement of swimming behaviour also contributes to our understanding of aerotaxis of individual cells.

Non-NASA Center↗
NASA NTRS1974

A conceptual design and operational characteristics for a Mars rover for a 1979 or 1981 Viking science mission

The feasibility of a small Mars rover for use on a 1979 or 1981 Viking mission was studied and a preliminary design concept was developed. Three variations of the concept were developed to provide comparisons in mobility and science capability of the rover. Final masses of the three rover designs were approximately 35 kg, 40 kg, and 69 kg. The smallest rover is umbilically connected to the lander for power and communications purposes whereas the larger two rovers have secondary battery power and a 2-way very high frequency communication link to the lander. The capability for carrying Viking rovers (including development system) to the surface of Mars was considered first. It was found to be feasible to carry rovers of over 100 kg. Virtually all rover systems were then studied briefly to determine a feasible system concept and a practical interface with the comparable system of a 1979 or 1981 lander vehicle.

Darnell, W. L.↗
NASA NTRS2019

LEAVES: Lofted Environmental and Atmospheric Venus Sensors

LEAVES (Lofted Environmental Atmospheric Venus Sensors) is a design exercise with the goal of dramatically decreasing the cost of obtaining prioritized chemical and physical data in planetary atmospheres. Through the application of a swarm approach this concept parallelizes atmospheric exploration, with geographic coverage far exceeding what is possible with conventional monolithic platforms or sondes. Each unit in the swarm is exceptionally compact, with a powered payload mass of only a few tens of grams and a high-drag, semi-rigid structure that acts to slow each probe as it descends through the atmosphere. This structural design can collapse into a planar form to allow for efficient stowage prior to arrival at the target body. With a total per-unit mass of only 120 g, a fleet of 100 (or more) units can be very reasonably accommodated on a carrier spacecraft.Science operations, which begin when the LEAVES probes reach an altitude of 100 km, are targeted for the cloud-bearing region of Venus' atmosphere. During the roughly 9 hour, terminal velocity descent through the atmosphere, LEAVES collects data of the state and composition of the atmosphere in parallel across multiple units. These data would represent an unprecedented constraint on the distribution and concentration of targeted chemical species, and the detection of local and regional variations in both chemistry and physical properties.A novel and compelling result of this exercise was that the same optimization that produced a structure with an exceptionally low areal mass density (0.126 kg/m2) also resulted in a probe that can be deployed directly from an aerobraking orbit (~140 km at 5 km/s) without the need for aeroshell protection. This translates to a tremendous mass savings and gives LEAVES the flexibility to be carried as a secondary payload aboard either a descending surface probe or an orbital radar mapper. Because such missions are under active development or have already been proposed (but not flown), we infer that LEAVES is well positioned as a technology

Swarm↗
NASA NTRS2021

Pluto’s Sputnik Planitia: Composition of geological units from infrared spectroscopy

We have compared spectroscopic data of Sputnik Planitia on Pluto, as acquired by New Horizons’ Linear Etalon Imaging Spectral Array (LEISA) instrument, to the geomorphology as mapped by White et al. (2017) using visible and panchromatic imaging acquired by the LOng-Range Reconnaissance Imager (LORRI) and the Multi-spectral Visible Imaging Camera (MVIC). We have focused on 13 of the geologic units identified by White et al. (2017), which include the plains and mountain units contained within the Sputnik basin. We divided the map of Sputnik Planitia into 15 provinces, each containing one or more geologic units, and we use LEISA to calculate the average spectra of the units inside the 15 provinces. Hapke-based modeling was then applied to the average spectra of the units to infer their surface composition, and to determine if the composition resulting from the modeling of LEISA spectra reflects the geomorphologic analyses of LORRI data, and if areas classified as being the same geologically, but which are geographically separated, share a similar composition. We investigated the spatial distribution of the most abundant ices on Pluto’s surface - CH4, N2, CO, H2O, and a non-ice component presumed to be a macromolecular carbon-rich material, termed a tholin, that imparts a positive spectral slope in the visible spectral region and a negative spectral slope longward of ~1.1 μm. Because the exact nature of the non-ice component is still debated and because the negative spectral slope of the available tholins in the near infrared does not perfectly match the Pluto data, for spectral modeling purposes we reference it generically as the negative spectral slope endmember (NSS endmember). We created maps of variations in the integrated band depth (from LEISA data) and areal mass fraction (from the modeling) of the components. The analysis of correlations between the occurrences of the endmembers in the geologic units led to the observation of an anomalous suppression of the strong CH4 absorption bands in units with compositions that are dominated by H2O ice and the NSS endmember. Exploring the mutual variation of the CH4 and N2 integrated band depths with the abundance of crystalline H2O and NSS endmember revealed that the NSS endmember is primarily responsible for the suppression of CH4 absorptions in mountainous units located along the western edge of Sputnik Planitia. Our spectroscopic analyses have provided additional insight into the geological processes that have shaped Sputnik Planitia. A general increase in volatile abundance from the north to the south of Sputnik Planitia is observed. Such an increase first observed and interpreted by Protopapa et al., 2017 and later confirmed by climate modeling (Bertrand et al., 2018) is expressed geomorphologically in the form of preferential deposition of N2 ice in the upland and mountainous regions bordering the plains of southern Sputnik Planitia. Relatively high amounts of pure CH4 are seen at the southern Tenzing Montes, which are a natural site for CH4 deposition owing to their great elevation and the lower insolation they are presently receiving. The NSS endmember correlates the existence of tholins within certain units, mostly those coating the low-latitude mountain ranges that are co-latitudinal with the tholin-covered Cthulhu Macula. The spectral analysis has also revealed compositional differences between the handful of occurrences of northern non-cellular plains and the surrounding cellular plains, all of which are located within the portion of Sputnik Planitia that is presently experiencing net sublimation of volatiles, and which do not therefore exhibit a surface layer of bright, freshly-deposited N2 ice. The compositional differences between the cellular and non-cellular plains here hint at the effectiveness of convection in entraining and trapping tholins within the body of the cellular plains, while preventing the spread of such tholins to abutting non-cellular plains.

Pluto's Sputnik Planitia↗
NASA NTRS1982

The Halley dust model

The properties of dust ejecta from Comet Halley are studied on the basis of (a) evidence from the comet's past apparitions and (b) analogy with recent, physically similar comets. Specifically discussed are the light curve and spectrum, discrete phenomena in the head, the physical properties of the nucleus (size, albedo, rotation, surface temperature, and morphology), and an interaction between the nucleus and dust atmosphere. Also reviewed are constraints on the size and mass distributions of dust particles, information on submicron-size and submillimeter-size grains from the comet's dust tail and antitail, and the apparent existence of more than one particle type. Similarities between the jet patterns of Halley and the parent comet of the Perseid meteor stream are depicted, and effects of the surface heterogeneity (discrete active regions) on the dust flow are assessed. Current dust models for Halley are summarized and the existence of short-term variations in the dust content in the comet's atmosphere is suggested.

Sekanina, Z.↗
NASA NTRS1997

Constraints on the Magnitude of Vertical and Lateral Mass Transport on the Moon

The role of vertical and lateral mass transport of crustal materials on the observed patterns of lunar surface composition, and the effects on our understanding of the geologic evolution of the planet, have been the subject of much debate in the lunar science community. The primary consensus that emerged from analyses of these processes in the 1970's and 1980's was that vertical and lateral mixing through impact gardening was a relatively inefficient process, and not likely to have contributed significantly to compositional units and variations on the Moon. The supporting evidence for this view is that unit boundaries (e.g. mare-highland contacts, contacts between mare color units) are still apparently quite distinct and sharp despite several aeons of impact activity, and cores from the Apollo landing sites did not show any evidence of widespread homogenization of the surface composition, nor distinct compositional gradients across geologic boundaries. In addition, modeling of vertical and lateral transport generally showed that the effects on composition should be confined to horizontal scales of about a kilometer and vertical scales of a meter. The problem with this consensus is that there is ample contradictory evidence. The fundamental discovery of Wood et al. (1970) was made possible by significant horizontal transport of highland material to the center of Mare Tranquillitatis. The continuous and discontinuous ejecta from the crater Copernicus has clearly influenced the surface composition of a large area of the lunar maria, while rays and ejecta from many highland craters are easily recognized in and around the nearside maria. Despite this contrary evidence, there have been few detailed studies to quantify the amount and rate of material redistribution through impact processes (a notable exception is reported in the paper by Pieters et al, 1985), largely because data adequate to critically analyze this process were lacking. However, the multispectral images acquired by the Galileo and Clementine missions now permit the investigation of this process.

Mustard, John F.↗
NASA NTRS1972

Mass spectrometric analysis of organic compounds, water and volatile constituents in the atmosphere and surface of Mars - The Viking Mars Lander.

An experiment centering around a mass spectrometer is described, which is aimed at the identification of organic substances present in the top 10 cm of the surface of Mars and an analysis of the atmosphere for major and minor constituents as well as isotopic abundances. In addition, an indication of the abundance of water in the surface and some information concerning the mineralogy can be obtained by monitoring the gases produced upon heating the soil sample. The organic material will simply be expelled by heating to 150, 300, and 500 C into the carrier gas stream of a gas chromatograph interfaced to the mass spectrometer or by slowly heating the sample in direct communication with the spectrometer. It is planned to analyze a total of up to nine soil samples in order to study diurnal and seasonal variations. The system is designed to give useful data even for minor constituents if the total of organics should be as low as 5 ppm. The spectrometer covers the mass range of 12-200 with adequate resolution.

Anderson, D. M.↗
NASA NTRS2001

Balance Mass Flux and Velocity Across the Equilibrium Line in Ice Drainage Systems of Greenland

Estimates of balance mass flux and the depth-averaged ice velocity through the cross-section aligned with the equilibrium line are produced for each of six drainage systems in Greenland. (The equilibrium line, which lies at approximately 1200 m elevation on the ice sheet, is the boundary between the area of net snow accumulation at higher elevations and the areas of net melting at lower elevations around the ice sheet.) Ice drainage divides and six major drainage systems are delineated using surface topography from ERS (European Remote Sensing) radar altimeter data. The net accumulation rate in the accumulation zone bounded by the equilibrium line is 399 Gt/yr and net ablation rate in the remaining area is 231 Gt/yr. (1 GigaTon of ice is 1090 kM(exp 3). The mean balance mass flux and depth-averaged ice velocity at the cross-section aligned with the modeled equilibrium line are 0.1011 Gt kM(exp -2)/yr and 0.111 km/yr, respectively, with little variation in these values from system to system. The ratio of the ice mass above the equilibrium line to the rate of mass output implies an effective exchange time of approximately 6000 years for total mass exchange. The range of exchange times, from a low of 3 ka in the SE drainage system to 14 ka in the NE, suggests a rank as to which regions of the ice sheet may respond more rapidly to climate fluctuations.

Zwally, H. Jay↗
NASA NTRS2007

Optimization of Crew Shielding Requirement in Reactor-Powered Lunar Surface Missions

On the surface of the moon -and not only during heightened solar activities- the radiation environment As such that crew protection will be required for missions lasting in excess of six months. This study focuses on estimating the optimized crew shielding requirement for lunar surface missions with a nuclear option. Simple, transport-simulation based dose-depth relations of the three (galactic, solar, and fission) radiation sources am employed in a 1-dimensional optimization scheme. The scheme is developed to estimate the total required mass of lunar-regolith separating reactor from crew. The scheme was applied to both solar maximum and minimum conditions. It is shown that savings of up to 30% in regolith mass can be realized. It is argued, however, that inherent variation and uncertainty -mainly in lunar regolith attenuation properties in addition to the radiation quality factor- can easily defeat this and similar optimization schemes.

Barghouty, Abdulnasser F.↗
NASA NTRS2007

Optimization of Crew Shielding Requirement in Reactor-Powered Lunar Surface Missions

On the surface of the moon and not only during heightened solar activities the radiation environment is such that crew protection will be required for missions lasting in excess of six months. This study focuses on estimating the optimized crew shielding requirement for lunar surface missions with a nuclear option. Simple, transport-simulation based dose-depth relations of the three radiation sources (galactic, solar, and fission) are employed in a one-dimensional optimization scheme. The scheme is developed to estimate the total required mass of lunar regolith separating reactor from crew. The scheme was applied to both solar maximum and minimum conditions. It is shown that savings of up to 30% in regolith mass can be realized. It is argued, however, that inherent variation and uncertainty mainly in lunar regolith attenuation properties in addition to the radiation quality factor can easily defeat this and similar optimization schemes.

Barghouty, A. F.↗
NASA NTRS2011

Geomagnetic Variability and Predictability

The Earth's magnetic field varies on time scales from seconds to millions of years. These variations can be measured directly by ground observatories and satellites, and indirectly through laboratories. They are from different electromagnetic processes in magnetosphere and ionosphere (external), ocean and crust (surface), and deep in the Earth's fluid outer core (internal). Of the measured magnetic signals, 95% is from the core, and is called the core field, or internal field. Variation of the core field, often called the geomagnetic secular variation (SV), is the manifestation of the magnetohydrodynamic processes in the core. Therefore, SV provides rich information on the core dynamical state that is then critical for understanding the geophysical mechanisms of the SV, the core-mantle interactions, and contribution of mass transport inside the core on Earth's gravity variation. Traditionally, the core state is probed via two independent methodologies: core flow inversion from the observed SV, and pure numerical dynamo simulation. The former is driven by observations, but does not include necessary interactions among physical variables; the latter is dynamically consistent, but is not constrained by any observation. Therefore, both are very limited in providing appropriate estimates of the core state. To avoid these limitations, a new approach, geomagnetic data assimilation, appears recently. In this approach, simulation results (model forecasts) are constantly corrected with observations, the corrected solutions (analysis), are then used as the initial conditions to make more accurate forecasts of future. Recent studies have demonstrated successfully that assimilation solutions are different from those of free running models. These new solutions are better estimates of the core state, and have been used to provide accurate prediction of SV for the period from 2010 to 2015. This prediction is part of the IGRF field model for international community applications.

Kuang, Weijia↗
NASA NTRS2007

The Use of Tribocharging in the Electrostatic Beneficiation of Lunar Simulant

Any future lunar base and habitat must be constructed from strong dense materials in order to provide for thermal and radiation protection. Lunar soil may meet this need. Lunar regolith has high concentrations of aluminum, silicon, calcium, iron, sodium, and titanium oxides. Refinement or enrichment of specific minerals in the soil before it is chemically processed may be more desirable as it would reduce the size and energy requirements required to produce the virgin material and it may significantly reduce the process' complexity. Also, investigations into the potential production of breathable oxygen from oxidized mineral components are a major research initiative by NASA. In this study. the objective was to investigate the use of tribocharging to charge lunar simulants and pass them through a parallel plate separator to enrich different mineral fractions. This technique takes advantage of the high Lunar vacuum in which much higher voltages can be used on the separation plates than in air. Additionally, the Lunar g1avity, only being 1/6 that of Earth, allows the particles more separation time between the plates and therefore enhances separation. For the separation studies, two lunar stimulants were used. The first simulant was created in-house, labeled KSC-1. using commercially supplied (sieved to 325 mesh) materials, and was composed of 40 wt. % feldspar ((Na,K,Ca)AlSi3O8;SiO2), 40 wt. % olivine ((Mg,Fe)2SiO4), 10 wt. % ilmenite (FeTiO3). and 10 wt. % spodumene (LiAlSi2O6) (pyroxene). The advantage of the in-house mixture is that the composition can he varied to simulate different soil compositions from different areas on the moon. This simulant was used to show proof-of-concept using the designed separator in air. The second stimulant was JSC-1. used for the vacuum experiments. JSC-1 is principally basalts, containing phases of plagioclase. pyroxene. olivine, and ilmenite. The JSC-1 was sieved to provide a 50-75 micron size range to correlate with the mean grain size found on the moon's surface [1]. Four different materials were investigated for the triboelectrification process; aluminum, copper. stainless steel, and PTFE. These materials were selected because they offer a wide variation in work functions (aluminum 4.28 eV, copper 4.65 eV. stainless steel 5.04 eV, and PTFE 5.75 eV). The difference between the work function of each material and the simulant influences the charge obtained by the grains. Each simulant was analyzed before and after separation using X-ray Photoelectron Spectroscopy (XPS) to determine mineral surface composition. In addition. Raman spectroscopy was performed on the JSC-1 before and after separation in vacuum to determine the mineral composition. Charge-to-mass (Q/M) measurements were performed using a fluidizing bed in air and passing the simulant through a static mixer of a particular material and collecting it in a Faraday pail grounded through an electrometer. To measure the Q/M in vacuum, a special device was constructed consisting of a heater/shaker cup that fed into a solid block of material (either PTFE, copper, or aluminum) in which a channel composed of a "zig-zag" series of inclines greater than 50 degrees has been cut. The voltage to the vibrating motor can be varied to control the amount of simulant passing through the channel. Figure I shows the Q/M measurements for JSC-1 tribocharged using the static mixers and the incline plane chargers in air, and the incline plane chargers in vacuum.

Trigwell, S.↗
NASA NTRS2024

Tail-Cone Thruster Fan Rotor Flutter Analysis

The aeroelastic stability of a tail cone thruster fan was analyzed for three structural modes and various nodal diameter patterns. Computational fluid dynamics modeling with blade vibrations was used in the analyses performed at design (peak-efficiency) and two near-stall conditions at the design rotational speed. Aerodynamic damping was used to assess flutter since this integrally bladed rotor design will have minimal structural damping. Aerodynamic damping was found to be low at the design condition. For the first mode, aerodynamic damping was seen to decrease towards stall, vanishing for a zero nodal diameter pattern. Further decrease in mass flow led to negative aerodynamic damping (flutter) for the first and second nodal diameters in the near stall condition. The flowfield at this lowest mass flow rate exhibited some additional unsteadiness at higher frequency. The sensitivity of results to time step and amplitudes of vibration was examined and found to be very satisfactory. The largest uncertainty in the results comes from the observed sensitivity of the aerodynamic damping to details of the variation of grid deformations in the blade passage mesh from the blade passage to the boundaries. For the parametric variations analyzed, the calculated aerodynamic damping is lower if the grid deformations near the blade surface are higher. Further work is needed to understand the cause of this sensitivity and find possible solutions to reduce the effects on flutter predictions.

Fan↗
NASA NTRS1972

Analysis of an electrohydraulic aircraft control surface servo and comparison with test results

An analysis of an electrohydraulic aircraft control-surface system is made in which the system is modeled as a lumped, two-mass, spring-coupled system controlled by a servo valve. Both linear and nonlinear models are developed, and the effects of hinge-moment loading are included. Transfer functions of the system and approximate literal factors of the transfer functions for several cases are presented. The damping action of dynamic pressure feedback is analyzed. Comparisons of the model responses with results from tests made on a highly resonant rudder control-surface servo indicate the adequacy of the model. The effects of variations in hinge-moment loading are illustrated.

Edwards, J. W.↗
NASA NTRS1994

Stratospheric aerosol acidity, density, and refractive index deduced from SAGE 2 and NMC temperature data

Water vapor concentrations obtained by the Stratospheric Aerosol and Gas Experiment 2 (SAGE 2) and collocated temperatures provided by the National Meteorological Center (NMC) from 1986 to 1990 are used to deduce seasonally and zonally averaged acidity, density, and refractive index of stratospheric aerosols. It is found that the weight percentage of sulfuric acid in the aerosols increases from about 60 just above the tropopause to about 86 at 35 km. The density increases from about 1.55 to 1.85 g/cu cm between the same altitude limits. Some seasonal variations of composition and density are evident at high latitudes. The refractive indices at 1.02, 0.694, and 0.532 micrometers increase, respectively, from about 1.425, 1.430, and 1.435 just above the tropopause to about 1.445, 1.455, and 1.458 at altitudes above 27 km, depending on the season and latitude. The aerosol properties presented can be used in models to study the effectiveness of heterogeneous chemistry, the mass loading of stratospheric aerosols, and the extinction and backscatter of aerosols at different wavelengths. Computed aerosol surface areas, rate coefficients for the heterogeneous reaction ClONO2 + H2O yields HOCl + HNO3 and aerosol mass concentrations before and after the Pinatubo eruption in June 1991 are shown as sample applications.

Yue, G. K.↗