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NASA NTRS2000

Analysis of the NASA White Sands Test Facility (WSTF) Test System for Friction-Ignition of Metallic Materials

Friction is a known ignition source for metals in oxygen-enriched atmospheres. The test system developed by the NASA White Sands Test Facility in response to ASTM G-94 has been used successfully to determine the relative ignition from friction of numerous metallic materials and metallic materials pairs. These results have been ranked in terms of a pressure-velocity product (PV) as measured under the prescribed test conditions. A high value of 4.1(exp 8) watts per square meter for Inconel MA 754 is used to imply resistance to friction ignition, whereas a low value of 1.04(exp 8) watts per square meter for stainless steel 304 is taken as indicating material susceptible to friction ignition. No attempt has been made to relate PV values to other material properties. This work reports the analysis of the WSTF friction-ignition test system for producing fundamental properties of metallic materials relating to ignition through friction. Three materials, aluminum, titanium, and nickel were tested in the WSTF frictional ignition instrument system under atmospheres of oxygen or nitrogen. Test conditions were modified to reach a steady state of operation, that is applied, the force was reduced and the rotational speed was reduced. Additional temperature measurements were made on the stator sample. The aluminum immediately galled on contact (reproducible) and the test was stopped. Titanium immediately ignited as a result of non-uniform contact of the stator and rotor. This was reproducible. A portion of the stator sampled burned, but the test continued. Temperature measurements on the stator were used to validate the mathematical model used for estimating the interface (stator/rotor) temperature. These interface temperature measurements and the associate thermal flux into the stator were used to distinguish material-phase transitions, chemical reaction, and mechanical work. The mechanical work was used to analyze surface asperities in the materials and to estimate a coefficient of fiction. The coefficient of fiction was analyzed in terms of material properties that is, hardness, Young's modulus and elasticity/plasticity of the material.

Shoffstall, Michael S.↗
NASA NTRS2000

The Non-Stellar Infrared Continuum of Seyfert Galaxies

JHKL'M (1 - 5 micrometers) imaging of a sample of Seyfert 2 galaxies is presented. We have performed an accurate estimate of the near-infrared non-stellar nuclear fluxes. We confirm that the near-infrared nuclear continuum between 1 and 2.2microns of some Seyfert 2s is dominated by stellar emission, whereas the continuum emission at longer wavelengths (lambda = 3 - 5 micrometers) is almost entirely non-stellar in origin. The non-stellar spectral energy distributions (SED) in the infrared (up to 15 micrometers) of Seyfert galaxies show a variety of shapes, and they are well reproduced with the tapered disk models of Efstathiou & Rowan-Robinson (1995). We have used two models, one including an optically thin cone component found to fit the SED of NGC 1068, and a coneless model. Although our modelling of the SEDs does not allow us to favor either model to account for all the observed SEDs, we find that the viewing angle towards the central source is well constrained by both models. The galaxies in our sample have fitted values of the viewing angle in the range Theta(sub V) = 0 deg - 64 deg, for the assumed model parameters. We have also investigated non-stellar color-color diagrams (L' - M vs. H - M and L' - M vs. H - L'). The colors of the Seyfert galaxies with viewing angles Theta(sub v) less than 30 deg are better reproduced with the cone model. These diagrams provide a good means to separate Seyfert 2s with moderate obscuration (A(sub V) approx. less than 20 mag from hard X-ray observations) from those with high obscuration. The ground-based 4.8 microns and ISO 9.6 microns luminosities are well correlated with the hard X-ray luminosities of Seyfert ls and 2s. These continuum emissions appear as a good indicator of the AGN luminosity, at least in the cases of hard X-ray Compton-thin Seyfert galaxies (N(sub H) less than or = 10(exp 24)/sq cm). We finally stress the finding that some Compton thick galaxies show bright non-stellar emission at 5 microns This suggests that the near-infrared emission in Seyfert galaxies is produced in an extended component illuminated by the central source, that is more visible from all viewing angles, providing a good explanation for the differing N(sub H)/A(sub V) ratios found in some Seyfert 2s. We discuss possible implications of mid-infrared surveys for the search of counterparts of highly obscured hard X-ray sources.

Alonso-Herrero, Almudena↗
NASA NTRS2001

Bridgman Growth of Detached GeSi Crystals

The growth of detached crystals by the Bridgman technique, in which the growing crystal is not in contact with the crucible wall, has been observed both on earth and in microgravity conditions. Such detachment has particularly been in evidence in microgravity experiments, where the pressure head of the molten sample is absent. At present, the mechanisms contributing to the detachment are not completely understood and until recently detachment has not been reproducibly obtained. Key parameters which must be considered are the contact angle between the melt and the crucible and the growth angle. Another essential parameter is the pressure difference between the annular gap around the solid below the melt and the volume above the melt. Here we present results of the growth of Ge(0.98)Si(0.02) using adjustments in the applied temperature profile to control the pressure difference between the bottom and top of the melt. The technique is less susceptible to sample contamination than controlling the pressure by connecting the crucible to external gas sources. Using this technique, a pressure difference is created by decreasing the temperature in the volume above the melt while the sample is molten but prior to growth. A maximum pressure difference approximately equal to the pressure head of the molten sample can thus be obtained. Several GeSi crystals were grown in pyrolitic boron nitride crucibles. When a pressure difference was applied, samples were reproducibly grown mostly detached. For comparison, samples were also grown in a configuration in which gas could pass freely between the gap below the melt and the volume above the melt and no pressure difference could be established. These samples were initially attached. Existence of detachment was determined both by measuring the radius of the samples with a profilometer and by observations of the sample surfaces with optical and electron microscopy. The gap thickness between the crucible and detached crystal was on the order of 10 micron. The surfaces of the attached areas of the crystals had the same shape as the interior crucible wall whereas in the detached areas the crystal facets could usually be observed.

Volz, M. P.↗
NASA NTRS2001

Climate and Ozone Response to Increased Stratospheric Water Vapor

Stratospheric water vapor abundance affects ozone, surface climate, and stratospheric temperatures. From 30-50 km altitude, temperatures show global decreases of 3-6 K over recent decades. These may be a proxy for water vapor increases, as the Goddard Institute for Space Studies (GISS) climate model reproduces these trends only when stratospheric water vapor is allowed to increase. Observations suggest that stratospheric water vapor is indeed increasing, however, measurements are extremely limited in either spatial coverage or duration. The model results suggest that the observed changes may be part of a global, long-term trend. Furthermore, the required water vapor change is too large to be accounted for by increased production within the stratosphere, suggesting that ongoing climate change may be altering tropospheric input. The calculated stratospheric water vapor increase contributes an additional approximately equals 24% (approximately equals 0.2 W/m(exp 2)) to the global warming from well-mixed greenhouse gases over the past two decades. Observed ozone depletion is also better reproduced when destruction due to increased water vapor is included. If the trend continues, it could increase future global warming and impede stratospheric ozone recovery.

Shindell, Drew T.↗
NASA NTRS2001

Ground Based Experiments in Support of Microgravity Research Results-Vapor Growth of Organic Nonlinear Optical Thin Film

This work is specifically focused on explaining previous results obtained for the crystal growth of an organic material in a reduced gravity environment. On STS-59, in April 1994, two experiments were conducted with N,N-dimethyl-p-(2,2-dicyanovinyl) aniline (DCVA), a promising nonlinear optical (NLO) material. The space experiments were set to reproduce laboratory experiments that yielded small, bulk crystals of DCVA. The results of the flight experiment, however, were surprising. Rather than producing a bulk single crystal, the result was the production of two high quality, single crystalline thin films. This result was even more intriguing when it is considered that thin films are more desirable for NLO applications than are bulk single crystals. Repeated attempts on the ground to reproduce these results were fruitless. A second set of flight experiments was conducted on STS-69 in September 1995. This time eight DCVA experiments were flown, with each of seven experiments containing a slight change from the first reference experiment. The reference experiment was programmed with growth conditions identical to those of the STS-59 mission. The slight variations in each of the other seven were an attempt to understand what particular parameter was responsible for the preference of thin film growth over bulk crystal growth in microgravity. Once again the results were surprising. In all eight cases thin films were grown again, albeit with varying quality. So now we were faced with a phenomenon that not only takes place in microgravity, but also is very robust, resisting all attempts to force the growth of bulk single crystals.

Zugrav, M. Ittu↗
NASA NTRS2000

Ammonia Formation by the Reduction of Nitrite/Nitrate by FeS: Ammonia Formation Under Acidic Conditions

FeS reduces nitrite to, ammonia at pHs lower than the corresponding reduction by aqueous Fe+2. The reduction follows a reasonable first order decay, in nitrite concentration, with a half life of about 150 min (room temperature, CO2, pH 6.25). The highest ammonia product yield measured was 53%. Under CO2, the product yield decreases from pH 5.0 to pH 6.9. The increasing concentration of bicarbonate at higher pH interferes with the reaction. Bicarbonate interference is shown by comparing runs under N2 and CO2. The reaction proceeds well in the presence of such species as chloride, sulfate, and phosphate though the yield drops significantly with phosphate. FeS also reduces nitrate and, unlike with Fe+2, the reduction shows more reproducibility. Again, the product yield decreases with increasing pH, from 7% at pH 4.7 to 0% at pH 6.9. It appears as if nitrate is much more sensitive to the presence of added species, perhaps not competing as well for binding sites on the FeS surface. This may be the cause of the lack of reproducibility of nitrate reduction by Fe+2 (which also can be sensitive to binding by certain species).

Summers, David P.↗
NASA NTRS2001

An Improved Model for the Turbulent PBL

Second order turbulence models of the Mellor and Yamada type have been widely used to simulate the PBL. It is however known that these models have several deficiencies. For example, they all predict a critical Richardson number which is about four times smaller than the Large Eddy Simulation (LES) data, they are unable to match the surface data, and they predict a boundary layer height lower than expected. In the present model, we show that these difficulties are all overcome by a single new physical input: the use of the most complete expression for both the pressure-velocity and the pressure-temperature correlations presently available. Each of the new terms represents a physical process that, was not accounted for by previous models. The new model is presented in three different levels according to Mellor and Yamada's terminology, with new, ready-to-use expressions for the turbulent, moments. We show that the new model reproduces several experimental and LES data better than previous models. As far as the PBL is concerned, we show that the model reproduces both the Kansas data as analyzed by Businger et al. in the context of Monin-Obukhov similarity theory for smaller Richardson numbers, as well as the LES and laboratory data up to Richardson numbers of order unity. We also show that the model yields a higher PBL height than the previous models.

Cheng, Y.↗
NASA NTRS1994

Towards Understanding the Fluid Dynamic Phenomenon of Interest to Rocket Base Heating: A Review

The significance of the base heating problem for rockets during ascent is due to the complex interaction between the rocket nozzle plumes and the external-flow which can change the flow characteristics in the base region dramatically. At lower altitudes the external-flow merges with the plume-flow, without the formation of a large separated flow region, and the cooler external-flow promotes convective cooling of the base wall. Under these conditions the majority of the base heating is due to radiative heating from the shock heated plume gases. At higher altitudes, however, the process of base heating is not so straightforward. The plume and the base flow expands dramatically and separated flow regions occur in the base area. Hot exhaust gases from the rocket nozzle will be entrained into the separated flow regions and produce a convective component to the base wall heating. Further, if the rocket exhaust-gas contains soot, the soot can increase the emission from the gas and dramatically increase the wall absorption coefficient for radiative heating if it is deposited on the walls . In addition, if the rocket exhaust gas is fuel rich, the fuel can bum in the separated flow regions and further increase the base heating. The base burning phenomenon, and the increased base heating caused by it at higher altitudes, have been observed for the Space Shuttle and Saturn Rocket. Under these conditions, the total heating is significantly higher than the heating without separated flow in the base region, and the increase in heating is directly attributable to the fluid dynamic complexity of the base region. Realistic simulation of the base heating requires that the calculated flow environment reproduce the fluid dynamic flow features accurately. Thus, it will be necessary to introduce into the CFD codes the capability for the flow to respond to the complex vehicle geometry, the effect of turbulence, the ability to accurately reproduce the plume shock/shear layer structures and capture such phenomenon as shock induced base separation and base-burning phenomenon. A survey of experimental, theoretical and computational work that details the fluid dynamics of the base flow environment will be presented in the proposed paper. CFD simulations of rocket base flows using standard CFD codes such as OVERFLOW or GASP will be explored to capture these phenomenon accurately. Merits and limitations of these codes for base flow environment predictions will be explored.

Venkatapathy, E.↗
NASA NTRS2002

Numerical Simulation of Screech Tones from Supersonic Jets: Physics and Prediction

The objectives of this project are to: (1) perform a numerical simulation of the jet screech phenomenon; and (2) use the data of the simulations to obtain a better understanding of the physics of jet screech. The original grant period was for three years. This was extended at no cost for an extra year to allow the principal investigator time to publish the results. We would like to report that our research work and results (supported by this grant) have fulfilled both objectives of the grant. The following is a summary of the important accomplishments: (1) We have now demonstrated that it is possible to perform accurate numerical simulations of the jet screech phenomenon. Both the axisymmetric case and the fully three-dimensional case were carried out successfully. It is worthwhile to note that this is the first time the screech tone phenomenon has been successfully simulated numerically; (2) All four screech modes were reproduced in the simulation. The computed screech frequencies and intensities were in good agreement with the NASA Langley Research Center data; (3) The staging phenomenon was reproduced in the simulation; (4) The effects of nozzle lip thickness and jet temperature were studied. Simulated tone frequencies at various nozzle lip thickness and jet temperature were found to agree well with experiments; (5) The simulated data were used to explain, for the first time, why there are two axisymmetric screech modes and two helical/flapping screech modes; (6) The simulated data were used to show that when two tones are observed, they co-exist rather than switching from one mode to the other, back and forth, as some previous investigators have suggested; and (7) Some resources of the grant were used to support the development of new computational aeroacoustics (CAA) methodology. (Our screech tone simulations have benefited because of the availability of these improved methods.)

Tam, Christopher K. W.↗
NASA NTRS2001

Modeling Tides, Planetary Waves, and Equatorial Oscillations in the MLT

Applying Hines Doppler Spread Parameterization for gravity waves (GW), our 3D model reproduces some essential features that characterize the observed seasonal variations of tides and planetary waves in the upper mesosphere. In 2D, our model also reproduces the large Semi-Annual Oscillation (SAO) and Quasi Biennial Oscillation (QBO) observed in this region at low latitudes. It is more challenging to describe these features combined in a more comprehensive self consistent model, and we give a progress report that outlines the difficulties and reports some success. In 3D, the GW's are partially absorbed by tides and planetary waves to amplify them. Thus the waves are less efficient in generating the QBO and SAO at equatorial latitudes. Some of this deficiency is compensated by the fact that the GW activity is observed to be enhanced at low latitudes. Increasing the GW source has the desired effect to boost the QBO, but the effect is confined primarily to the stratosphere. With increasing altitude, the meridional circulation becomes more important in redistributing the momentum deposited in the background flow by the GW's. Another factor involved is the altitude at which the GW's originate, which we had originally chosen to be the surface. Numerical experiments show that moving this source altitude to the top of the troposphere significantly increases the efficiency for generating the QBO without affecting much the tides and planetary waves in the model. Attention to the details in which the GW source comes into play thus appears to be of critical importance in modeling the phenomenology of the MLT. Among the suite of numerical experiments reported, we present a simulation that produced significant variations of tides and planetary waves in the upper mesosphere. The effect is related to the QBO generated in the model, and GW filtering is the likely cause.

Mengel, J. G.↗
NASA NTRS2001

Evidence for the Widespread Presence of Liquid-Phase Particles During the 1999-2000 Arctic Winter

In-situ Multi-Angle Spectrometer Probe (MASP) particle measurements have been analyzed to determine the typical behaviour of sulphate particles during the SOLVE campaign. The analysis has focussed on variations in the total particle concentration measured by MASP, which is a diagnostic that is primarily sensitive to the growth of small particles (those which are initially smaller than 0.2 micrometers in radius). At all levels of the stratosphere, the total MASP concentration varies continuously with temperature. This behaviour is well-reproduced by assuming that the sulphate aerosols are liquid ternary solutions, but cannot be reproduced if the aerosol is assumed to be frozen. This liquid-like behaviour is apparent for all measurements made during SOLVE, both inside and outside the vortex, and even at the coldest temperatures sampled during the campaign. The only anomalous measurements were made during the flight of January 14th, 2001; however, this midlatitude flight is very unlikely to contain SAT particles based on the recent warm temperatures experienced by the air. At the levels with the coldest measured temperatures, at least 90% of the particles grow as liquids. Therefore, the freezing that occurred during the 1999-2000 Arctic winter was selective, causing most of the particles to remain liquid even in the presence of a small number of frozen particles.

Drdla, K↗
NASA NTRS2002

Dynamics of Planetary Atmospheres

The PI had nineteen papers either published or in press in 1999 through early 2002. Ten of these (Thomas et al. 1999, Geisler et al. 1999, Vasavada et al. 1999, Little et al. t999, Gierasch et al. 2000, Ingersoll et al. 2000, Thomas et al. 2000, Dyudina et al. 2001, Chang et al. 2001, Wang and Ingersoll 2002) were largely supported by the Mars Global Surveyor project and the Galileo project. The other nine papers were largely supported under this grant, and are listed in boldface below. Six of the nine are research papers. Their titles and abstracts are reproduced below. The New Solar System chapter and the Meteorology at the Millennium chapter are review articles, and the World Book Encyclopedia chapter is a popular article. Their title pages and abstracts are also reproduced below.

Ingersoll, Andrew P.↗
NASA NTRS2002

Impacts of PSC Microphysics on Modelled Ozone Loss

Winter-long simulations of the 1999-2000 winter using a coupled microphysical/chemical model have been carried out to explore how PSC microphysics affects ozone loss. Although many models assures that water ice formation leads to denitrification, these simulations show that observed characteristics of the 1999-2000 winter can not be reproduced by such a denitrification mechanism. Instead, denitrification observations are best reproduced by a small number of particles freezing at temperatures near the nitric acid trihydration condensation point. Implications of such a mechanism for assessments of future ozone loss will be discussed. The simulations have also revealed that ozone loss during the 1999-2000 winter was sensitive to chlorine reactivation that occurred during February. Uncertainties in PSC microphysics and heterogeneous reaction rates both influence the modelled chlorine reactivation. For the 1999-2000 winter, these uncertainties have a larger effect on model ozone loss than denitrification. The role of denitrification would have increased if the Arctic vortex had persisted for a longer period.

Drdla, K.↗
NASA NTRS2002

Simulation of High-Latitude Hydrological Processes in the Torne-Kalix Basin: PILPS Phase 2(e): Equivalent Model Representation and Sensitivity Experiments - 3

The Project for Intercomparison of Land Surface Parameterization Schemes (PILPS) Phase 2(e) showed that in cold regions the annual runoff production in Land Surface Schemes (LSSs) is closely related to the maximum snow accumulation, which in turn is controlled in large part by winter sublimation. To help further explain the relationship between snow cover, turbulent exchanges and runoff production, a simple equivalent model-(SEM) was devised to reproduce the seasonal and annual fluxes simulated by 13 LSSs that participated in PILPS Phase 2(e). The design of the SEM relates the annual partitioning of precipitation and energy in the LSSs to three primary parameters: snow albedo, effective aerodynamic resistance and evaporation efficiency. Isolation of each of the parameters showed that the annual runoff production was most sensitive to the aerodynamic resistance. The SEM was somewhat successful in reproducing the observed LSS response to a decrease in shortwave radiation and changes in wind speed forcings. SEM parameters derived from the reduced shortwave forcings suggested that increased winter stability suppressed turbulent heat fluxes over snow. Because winter sensible heat fluxes were largely negative, reductions in winter shortwave radiation imply an increase in annual average sensible heat.

Bowling, Laura C.↗
NASA NTRS2002

Tactical Defenses Against Systematic Variation in Wind Tunnel Testing

This paper examines the role of unexplained systematic variation on the reproducibility of wind tunnel test results. Sample means and variances estimated in the presence of systematic variations are shown to be susceptible to bias errors that are generally non-reproducible functions of those variations. Unless certain precautions are taken to defend against the effects of systematic variation, it is shown that experimental results can be difficult to duplicate and of dubious value for predicting system response with the highest precision or accuracy that could otherwise be achieved. Results are reported from an experiment designed to estimate how frequently systematic variations are in play in a representative wind tunnel experiment. These results suggest that significant systematic variation occurs frequently enough to cast doubts on the common assumption that sample observations can be reliably assumed to be independent. The consequences of ignoring correlation among observations induced by systematic variation are considered in some detail. Experimental tactics are described that defend against systematic variation. The effectiveness of these tactics is illustrated through computational experiments and real wind tunnel experimental results. Some tutorial information describes how to analyze experimental results that have been obtained using such quality assurance tactics.

DeLoach, Richard↗
NASA NTRS2003

Deviation of Long-Period Tides from Equilibrium: Kinematics and Geostrophy

New empirical estimates of the long-period fortnightly (Mf) tide obtained from TOPEX/Poseidon (T/P) altimeter data confirm significant basin-scale deviations from equilibrium. Elevations in the low-latitude Pacific have reduced amplitude and lag those in the Atlantic by 30 deg or more. These interbasin amplitude and phase variations are robust features that are reproduced by numerical solutions of the shallow-water equations, even for a constant-depth ocean with schematic interconnected rectangular basins. A simplified analytical model for cooscillating connected basins also reproduces the principal features observed in the empirical solutions. This simple model is largely kinematic. Zonally averaged elevations within a simple closed basin would be nearly in equilibrium with the gravitational potential, except for a constant offset required to conserve mass. With connected basins these offsets are mostly eliminated by interbasin mass flux. Because of rotation, this flux occurs mostly in a narrow boundary layer across the mouth and at the western edge of each basin, and geostrophic balance in this zone supports small residual offsets (and phase shifts) between basins. The simple model predicts that this effect should decrease roughly linearly with frequency, a result that is confirmed by numerical modeling and empirical T/P estimates of the monthly (Mm) tidal constituent. This model also explains some aspects of the anomalous nonisostatic response of the ocean to atmospheric pressure forcing at periods of around 5 days.

Egbert, Gary D.↗
NASA NTRS2002

Challenging Cosmic Ray Propagation with Antiprotons: Evidence for a "Fresh" Nuclei Component?

Recent measurements of the cosmic ray (CR) antiproton flux have been shown to challenge existing CR propagation models. It was shown that the reacceleration models designed to match secondary to primary nuclei ratio (e.g., Boron/Carbon) produce too few antiprotons, while the traditional non-reacceleration models can reproduce the antiproton flux but fall short of explaining the low-energy decrease in the secondary to primary nuclei ratio. Matching both the secondary to primary nuclei ratio and antiproton flux requires artificial breaks in the diffusion coefficient and the primary injection spectrum suggesting the need for other approaches. In the present paper we discuss one possibility to overcome these difficulties. Using the measured antiproton flux to fix the diffusion coefficient, we show that the spectra of primary nuclei as measured in the heliosphere may contain a fresh local unprocessed component at low energies, thus decreasing the measured secondary to primary nuclei ratio. A model reproducing antiprotons, B/C ratio, and abundances up to Ni is presented.

Moskalenko, Igor V.↗
NASA NTRS2003

Modelling CLPX IOP3 Radiometric Data by Means of the Dense Media Theory: Preliminary Results for the LSOS Test Site

The capabilities of the Dense Media Radiative Transfer model using the Quasi Crystalline Approximation with Coherent Potential (QCA-CP) to reproduce measured radiometric data were tested using the University of Tokyo Ground Based Microwave Radiometer (GBMR-7) during the third Intensive Observation Period (IOP3) of the NASA Cold-land Processes Field Experiment (CLPX). The data were collected at the Local-Scale Observation Site (LSOS), a 0.8-ha study site consisting of two open meadows separated by trees. Intensive measurements were also made of snow depth and temperature, density, and grain size profiles. A DMRT model is needed to describe radiative transfer in a medium such as snow because the assumption of independent scattering used in classical radiative transfer theory (CRT) is not valid. Validation of the DMRT approach requires a relationship between measured snow grain size and the DMRT approximation of snow grain radius as spherical particles with a mean radius of the log-normal particle-size distribution. This relationship is very important for a better understanding of snow modelling and for practical applications. DMRT simulations were compared with observations of microwave brightnesses at 18.7, 36.5 and 89-GHz (V and H polarizations) collected on February-1 9-25, 2003. Observation angles ranged from 30\deg to 70\deg. Model inputs included measured snow parameters except mean grain size. The average snow temperature, fractional volume and depth were held constant, together with the ice and soil permittivities. The minimum and maximum measured mean grain sizes were used to test the capabilities of the DMRT to reproduce the brightnesses as upper and lower limits. The sensitivity to the largest and smallest measured grain size in the three classes of minimum, medium and maximum observed grain sizes was also investigated. DMRT particle sizes yielding a best-fit to the experimental data for each date were computed. Results show that the measured brightnesses fall within the range of simulated brightnesses using the smallest and largest measured grain size values. The DMRT best-fit radii are comparable to the average radii for the medium observed grain sizes.

Tedesco, Marco↗