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Global Summary MGS TES Data and Mars-Gram Validation

Mars Global Reference Atmospheric Model (Mars-GRAM 2001) is an engineering-level Mars atmosphere model widely used for many Mars mission applications. From 0-80 km, it is based on NASA Ames Mars General Circulation Model (MGCM), while above 80 km it is based on University of Arizona Mars Thermospheric General Circulation Model. Mars-GRAM 2001 and MGCM use surface topograph$ from Mars Global Surveyor Mars Orbiting Laser Altimeter (MOLA). Validation studies are described comparing Mars-GRAM with a global summary data set of Mars Global Surveyor Thermal Emission Spectrometer (TES) data. TES averages and standard deviations were assembled from binned TES data which covered surface to approx. 40 km, over more than a full Mars year (February, 1999 - June, 2001, just before start of a Mars global dust storm). TES data were binned in 10-by-10 degree latitude-longitude bins (i.e. 36 longitude bins by 19 latitude bins), 12 seasonal bins (based on 30 degree increments of Ls angle). Bin averages and standard deviations were assembled at 23 data levels (temperature at 21 pressure levels, plus surface temperature and surface pressure). Two time-of day bins were used: local time near 2 or 14 hours local time). Two dust optical depth bins wereused: infrared optical depth either less than or greater than 0.25 (which corresponds to visible optical depth either less than or greater than about 0.5). For interests in aerocapture and precision entry and landing, comparisons focused on atmospheric density. TES densities versus height were computed from TES temperature versus pressure, using assumptions of perfect gas law and hydrostatics. Mars-GRAM validation studies used density ratio (TES/Mars-GRAM) evaluated at data bin center points in space and time. Observed average TES/Mars-GRAM density ratios were generally 1+/-0.05, except at high altitudes (15-30 km, depending on season) and high latitudes (> 45 deg N), or at most altitudes in the southern hemisphere at Ls approx. 90 and 180deg). Compared to TES averages for a given latitude and season, TES data had average density standard deviation about the mean of approx. 65-10.5% (varying with height) for all data, or approx. 5-12%, depending on time of day and dust optical depth. Average standard deviation of TES/Mars-GRAM density ratio was 8.9% for local time 2 hours and 7.1% for local time 14 hours. Thus standard deviation of observed TES/Mars-GRAM density ratio, evaluated at matching positions and times, is about the same as the standard deviation of TES data about the TES mean value at a given position and season.

Justus, C.↗

Shuttle car loading system

A system is described for loading newly mined material such as coal, into a shuttle car, at a location near the mine face where there is only a limited height available for a loading system. The system includes a storage bin having several telescoping bin sections and a shuttle car having a bottom wall that can move under the bin. With the bin in an extended position and filled with coal the bin sections can be telescoped to allow the coal to drop out of the bin sections and into the shuttle car, to quickly load the car. The bin sections can then be extended, so they can be slowly filled with more while waiting another shuttle car.

Collins, E. R., Jr.↗

Demand Capacity Balancing at Vertiports for Initial Strategic Conflict Management of Urban Air Mobility Operations

Urban Air Mobility (UAM) is a new transportation concept that enables highly automated, cooperative, passenger or cargo-carrying air transportation services in and around urban areas. To achieve the high level of operational density and complexity desired by the UAM community, an airspace system that allows UAM operators to readily access and operate safely and efficiently in the airspace is needed. This airspace system will require air traffic management designed to reduce the risk of conflicts and loss of separation between UAM flights. In general, strategic conflict management is considered as the first layer of conflict management for safe flight operations to condition the traffic to reduce the need for airborne separation provision, the second layer of conflict management. Demand Capacity Balancing (DCB) is one of the concept components to achieve strategic conflict management. DCB strategically evaluates traffic demand and resource capacities to allow UAM operators to determine when, where and how they operate, while mitigating conflicting needs for airspace and vertiport capacity. DCB can be applied whenever UAM demand exceeds the capacity in airspace or at vertiports. As the UAM ecosystem evolves with advanced technologies and matured operational procedures, more complicated conflict management will likely be needed. In the current UAM ‘Concept of Operation (ConOps) 1.0’ operational stage defined by FAA, however, it will be meaningful to explore the demand capacity balancing at vertiports only, as an initial strategic conflict management approach for UAM operations because vertiport capacity seems to be a bottleneck of UAM traffic. For this research, we developed a demand-capacity imbalance detection and resolution service for UAM. This DCB service identifies the demand from operators and compares the demand to a given capacity at the shared resources (i.e., vertiports) over the upcoming time horizon which is divided into time bins having a constant interval. When a new flight plan is submitted, the algorithm embedded in the DCB service checks the available time bins based on the desired departure time and estimated arrival time at origin and destination vertiports, respectively. If the time bins for the originally desired times are already occupied by other flights (i.e., demand is at or above capacity), the algorithm finds the next available time bins for takeoff and landing and shifts the conflicting departure time to the earliest time that satisfies the capacity constraints at both origin and destination vertiports. The details of the algorithm will be described in the final manuscript. Figure 1 shows that the proposed DCB algorithm works well for a sample traffic scenario. In this example, a total of 144 flights, split between two operators, are planned over 2 hours, traveling 10 routes between five vertiports. In the heatmaps, the horizontal axis shows 12 time bins where each bin represents a 12-minute interval, and the vertical axis shows five vertiports. The number in each cell shows the number of operations, counting both departures and arrivals, at a specific vertiport in each time bin. For the given capacity of 2 operations/vertiport/bin, Figure 1 shows that the original demand sometimes exceeds the capacity, but the modified demand is reduced to the given capacity after resolving demand-capacity imbalances. When UAM flights are operated, it is expected that many practical issues would arise in the federated system architecture with multiple operators. UAM operators may experience a time synchronization issue due to communication delay between operator and vehicle. UAM vehicles would fly at different flight speeds, depending on vehicle models. Actual departure and arrival times can have large variations, compared to the schedule. The lead time from flight plan submission to desired departure time can vary by service type (e.g., regular shuttle service vs. on-demand service). Using the proposed DCB algorithm, we also investigated how the actual flight schedule and DCB performance are affected by these uncertainties such as unsynchronized times between operators, flight speed differences, lead time differences, and departure time errors. The final manuscript will include the background of this research work, the description of the DCB algorithm and its use cases with traffic scenarios. It will also provide the analytical results about the impact of various uncertainties that can occur in actual UAM operations on the DCB at vertiports, in terms of demand distribution changes, number of simultaneous operations, and delay propagation.

Urban Air Mobility↗

Investigation into alternative statistical auroral oval models, stage 1

The statistical model sensitivity to different methods of binning the NOAA/TIROS data base was examined. Each partial auroral pass was analyzed to locate the latitude of peak electron energy flux. Then using this location as the final reference latitude, all other data was binned relative to it. The next line of attack was to bin according to where the latitudinal profile center of gravity lay. This procedure overcomes the problem of very narrow intense features controlling the binning. Again the same data sets were analyzed and a binning made. These profiles look better and indeed look similar to the original auroral model. The passes were then binned relative to the equatorward boundary. The problems associated with the equatorward edge were resolved.

Bowline, M.↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e.,pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bin model explicitly calculates and allows for the examination of both the mass and number concentration of species in each size categor, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fewer droplets, larger sized develop due to the greater condensational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, r d a U production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembe1 (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and platelike), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗

Evaluating Nighttime CALIOP 0.532 micron Aerosol Optical Depth and Extinction Coefficient Retrievals

NASA Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) Version 3.01 5-km nighttime 0.532 micron aerosol optical depth (AOD) datasets from 2007 are screened, averaged and evaluated at 1 deg X 1 deg resolution versus corresponding/co-incident 0.550 micron AOD derived using the US Navy Aerosol Analysis and Prediction System (NAAPS), featuring two-dimensional variational assimilation of quality-assured NASA Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging Spectroradiometer (MISR) AOD. In the absence of sunlight, since passive radiometric AOD retrievals rely overwhelmingly on scattered radiances, the model represents one of the few practical global estimates available from which to attempt such a validation. Daytime comparisons, though, provide useful context. Regional-mean CALIOP vertical profiles of night/day 0.532 micron extinction coefficient are compared with 0.523/0.532 micron ground-based lidar measurements to investigate representativeness and diurnal variability. In this analysis, mean nighttime CALIOP AOD are mostly lower than daytime (0.121 vs. 0.126 for all aggregated data points, and 0.099 vs. 0.102 when averaged globally per normalised 1 deg. X 1 deg. bin), though the relationship is reversed over land and coastal regions when the data are averaged per normalised bin (0.134/0.108 vs. 0140/0.112, respectively). Offsets assessed within single bins alone approach +/- 20 %. CALIOP AOD, both day and night, are higher than NAAPS over land (0.137 vs. 0.124) and equal over water (0.082 vs. 0.083) when averaged globally per normalised bin. However, for all data points inclusive, NAAPS exceeds CALIOP over land, coast and ocean, both day and night. Again, differences assessed within single bins approach 50% in extreme cases. Correlation between CALIOP and NAAPS AOD is comparable during both day and night. Higher correlation is found nearest the equator, both as a function of sample size and relative signal magnitudes inherent at these latitudes. Root mean square deviation between CALIOP and NAAPS varies between 0.1 and 0.3 globally during both day/night. Averaging of CALIOP along-track AOD data points within a single NAAPS grid bin improves correlation and RMSD, though day/night and land/ocean biases persist and are believed systematic. Vertical profiles of extinction coefficient derived in the Caribbean compare well with ground-based lidar observations, though potentially anomalous selection of a priori lidar ratios for CALIOP retrievals is likely inducing some discrepancies. Mean effective aerosol layer top heights are stable between day and night, indicating consistent layer-identification diurnally, which is noteworthy considering the potential limiting effects of ambient solar noise during day.

aerosol optical depth↗

Intercomparison of global SST fields derived from satellite sensors and ship observations

Near global comparisons were made between binned forms of SST obtained from different instruments, ship meteorological observations, and the output of a meteorological model. Binning hereinafter means gridding by simple summation of data values in a bin, which in this study was a 2 deg. x 2 deg. box or a 10 deg. x 10 box surrounding a grid node. In the binned comparisons, the question is asked: are the binned data from two instruments drawn from the same population? The first two measures of statistical moments of the populations are used to test the hypothesis that they are. Comparisons were also attempted between raw forms of the various SST retrievals, using a structure function analysis. The results of this analysis were relatively uninteresting and are therefore omitted.

Pazan, S. E.↗

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles (i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail). Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region, in the sub-tropics (Florida) and in the mid-latitude using identical thermodynamic conditions but with different concentrations of CCN: a low 'clean' concentration and a high 'dirty' concentration.

Tao, Wei-Kuo↗

The Role of Aerosols on Precipitation Processes: Cloud Resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, a detailed spectral-bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region, the sub-tropics (Florida) and midlatitudes using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CeN case but has less cloud water mass aloft. Because the spectral-bin model explicitly calculates and allows for the examination of both the mass and number concentration of species in each size category, a detailed analysis of the instantaneous size spectrum can be obtained for these cases. It is shown that since the low (CN case produces fewer droplets, larger sizes develop due to greater condensational and collection growth, leading to a broader size spectrum in comparison to the high CCN case. Sensitivity tests were performed to identify the impact of ice processes, radiation and large-scale influence on cloud-aerosol interactive processes, especially regarding surface rainfall amounts and characteristics (i.e., heavy or convective versus light or stratiform types). In addition, an inert tracer was included to follow the vertical redistribution of aerosols by cloud processes. We will also give a brief review from observational evidence on the role of aerosol on precipitation processes.

Tao, Wei-Kuo↗

Precision of FLEET Velocimetry Using High-Speed CMOS Camera Systems

Femtosecond laser electronic excitation tagging (FLEET) is an optical measurement technique that permits quantitative velocimetry of unseeded air or nitrogen using a single laser and a single camera. In this paper, we seek to determine the fundamental precision of the FLEET technique using high-speed complementary metal-oxide semiconductor (CMOS) cameras. Also, we compare the performance of several different high-speed CMOS camera systems for acquiring FLEET velocimetry data in air and nitrogen free-jet flows. The precision was defined as the standard deviation of a set of several hundred single-shot velocity measurements. Methods of enhancing the precision of the measurement were explored such as digital binning (similar in concept to on-sensor binning, but done in post-processing), row-wise digital binning of the signal in adjacent pixels and increasing the time delay between successive exposures. These techniques generally improved precision; however, binning provided the greatest improvement to the un-intensified camera systems which had low signal-to-noise ratio. When binning row-wise by 8 pixels (about the thickness of the tagged region) and using an inter-frame delay of 65 microseconds, precisions of 0.5 meters per second in air and 0.2 meters per second in nitrogen were achieved. The camera comparison included a pco.dimax HD, a LaVision Imager scientific CMOS (sCMOS) and a Photron FASTCAM SA-X2, along with a two-stage LaVision HighSpeed IRO intensifier. Excluding the LaVision Imager sCMOS, the cameras were tested with and without intensification and with both short and long inter-frame delays. Use of intensification and longer inter-frame delay generally improved precision. Overall, the Photron FASTCAM SA-X2 exhibited the best performance in terms of greatest precision and highest signal-to-noise ratio primarily because it had the largest pixels.

Peters, Christopher J.↗

Precision of FLEET Velocimetry Using High-speed CMOS Camera Systems

Femtosecond laser electronic excitation tagging (FLEET) is an optical measurement technique that permits quantitative velocimetry of unseeded air or nitrogen using a single laser and a single camera. In this paper, we seek to determine the fundamental precision of the FLEET technique using high-speed complementary metal-oxide semiconductor (CMOS) cameras. Also, we compare the performance of several different high-speed CMOS camera systems for acquiring FLEET velocimetry data in air and nitrogen free-jet flows. The precision was defined as the standard deviation of a set of several hundred single-shot velocity measurements. Methods of enhancing the precision of the measurement were explored such as digital binning (similar in concept to on-sensor binning, but done in post-processing), row-wise digital binning of the signal in adjacent pixels and increasing the time delay between successive exposures. These techniques generally improved precision; however, binning provided the greatest improvement to the un-intensified camera systems which had low signal-to-noise ratio. When binning row-wise by 8 pixels (about the thickness of the tagged region) and using an inter-frame delay of 65 micro sec, precisions of 0.5 m/s in air and 0.2 m/s in nitrogen were achieved. The camera comparison included a pco.dimax HD, a LaVision Imager scientific CMOS (sCMOS) and a Photron FASTCAM SA-X2, along with a two-stage LaVision High Speed IRO intensifier. Excluding the LaVision Imager sCMOS, the cameras were tested with and without intensification and with both short and long inter-frame delays. Use of intensification and longer inter-frame delay generally improved precision. Overall, the Photron FASTCAM SA-X2 exhibited the best performance in terms of greatest precision and highest signal-to-noise ratio primarily because it had the largest pixels.

Peters, Christopher J.↗

Regolith Simulant Preparation and Geotechnical Characterization for Plume Surface Interaction Testing

Descent engine plumes interact with the lunar surface and accelerate regolith particles to potentially high velocities. These ejecta create risks to surface assets that have yet to be fully assessed. To better understand these risks, plume surface interactions can be simulated on the ground by firing a test engine plume into a bin of lunar regolith simulant under vacuum conditions. The dynamics of the resultant ejecta can then be recorded. In this technical memorandum we discuss the processes used in preparing a 150 kg bin of lunar regolith simulant for plume surface interaction ground tests under vacuum conditions for the NASA STMD Plume Surface Interaction project. We present our approach to mitigating regolith simulant eruptions during pump-down, the methods used to fill and reset the regolith simulant bin for each test, and the techniques used to characterize the consistency of regolith simulant geotechnical properties before each new firing. The challenges of preparing a regolith simulant test bin below an ambient pressure of one atmosphere, particularly on the large scale, could largely be overcome with a system that could fill the test bin with simulant inside the chamber and under vacuum conditions.

lunar regolith↗

Azimuth correlator for real-time synthetic aperture radar image processing

An azimuth correlator architecture is defined wherein a number of serial range-line buffer memories are cascaded such that the output stages of all buffer memories together form a complete and unique range bin in the azimuthal dimension at any given time. A range bin is automatically read out of the last stages of the registers in parallel on a range line sample-by-sample basis for subsequent range migration correction and correlation. Range migration correction is performed on the range bins by effectively varying the length of a delay register at the output of each range-line buffer memory. The corrected range bin output from the delay registers is then correlated with a Doppler reference function to form an image element on a real-time basis.

Arens, W. E.↗

The crater density of a linear feature

The standard method of crater counting presently employed permits determination of the relative ages of areal geologic features on cratered planets and satellites. A new method is presented which calculates the areal density of the craters superposed upon linear features. The method produces an effective synthetic area around the linear feature for each crater bin size, permitting the line counts to be compared directly with standard area counts. The shape of the synthetic area produced by the method is an oval, with the calculation of this area for each in being dependent on the median crater size for that bin, as well as the length and width of the linear feature. Incorporated into the method's equation is a factor to normalize the count to one million square kilometers for each bin. Because of the dependence of the method on the crater sizes, the largest possible number of bins should be counted for the method to be the most effective.

Spong, L.↗

Variability analysis in low count rate sources

A method, based on the chi-square statistics, is described for detecting pulselike time variability in low count rate sources observed with photon-counting instruments. This method can be used even in the presence of observational gaps, takes full advantage of the filtering effect due to binning with different bin sizes, and takes into account the arbitrariness introduced by the binning phase. The procedure developed to limit the dependence of the results on the binning phase and ensure statistically correct results is described along with the application of the proposed procedure to a model of a variable source. Monte Carlo simulations are used to show how the method can be used to derive the characteristic variability time scales and that the method is more sensitive than the nonparametric Kolmogorov-Smirnov test in detecting variability to a given confidence level.

Collura, A.↗

The spiral-compact galaxy pair AM 2208-251: Computer simulations versus observations

The system AM2208-251 is a roughly edge-on spiral extending east-west with a smaller round compact E system about 60 arcsec east of the spiral nucleus along the major axis of the spiral. Bertola, Huchtmeier, and Zeilinger (1990) have presented optical spectroscopic as well as single dish 21 cm observations of this system. Their spectroscopic data show, via emission lines lambda lambda 3727-29A, a rising rotation curve near the nucleus. These spectroscopic observations may indicate a tidal interaction in the system. In order to learn more about such pairs, the authors simulated the interaction using the computer model developed by Miller (1976 a,b, 1978) and modified by the authors (Byrd 1986, 1987, 1988). To do the simulation they need an idea of the mutual orbits of the two galaxies. Their computer model is a two-dimensional polar N-body program. It consists of a self-gravitating disk of particles, within an inert axially symmetric stabilizing halo potential. The particles are distributed in a 24(radial) by 36(azimuthal) polar grid. Self consistent calculations can be done only within the grid area. The disk is modeled with a finite Mestel disk, where all the particles initially move in circular orbits with constant tangential velocities (Mestel 1963), resulting in a flat rotation curve. The gas particles in the spiral's disk, which make up 30 percent of its mass, collide in the following manner. The number of particles in each bin of the polar grid is counted every time step. If it is greater than a given critical density, all the particles in the bin collide, obtaining in the result the same velocities, equal to the average for the bin. This process produces clumps of gas particles-the star formation sites. The authors suppress the collision in the inner part of the disk (within the circle r = 6) to represent the hole seen in the gas in the nuclear bulge of spirals. They thus avoid spurious effects due to collisions in that region. They also varied the size of the collisional bins, which did not affect their conclusions.

Klaric, Mario↗