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NASA NTRS2001

Restraint of Liquid Jets by Surface Tension in Microgravity Modeled

Tension in Microgravity Modeled Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, jets must be contained by surface tension forces. Recent NASA experiments in microgravity (Tank Pressure Control Experiment, TPCE, and Vented Tank Pressure Experiment, VTRE) resulted in a wealth of data about jet behavior in microgravity. VTRE was surprising in that, although it contained a complex geometry of baffles and vanes, the limit on liquid inflow was the emergence of a liquid jet from the top of the vane structure. Clearly understanding the restraint of liquid jets by surface tension is key to managing fluids in low gravity. To model this phenomenon, we need a numerical method that can track the fluid motion and the surface tension forces. The fluid motion is modeled with the Navier-Stokes equation formulated for low-speed incompressible flows. The quantities of velocity and pressure are placed on a staggered grid, with velocity being tracked at cell faces and pressure at cell centers. The free surface is tracked via the introduction of a color function that tracks liquid as 1/2 and gas as -1/2. A phase model developed by Jacqmin is used. This model converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly. Previous attempts at this formulation have been criticized for smearing the interface. However, by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function, interface smearing is avoided. These equations can be rewritten as two coupled Poisson equations that also include the velocity. The method of solution is as follows: first, the phase equations are solved from this solution, a velocity field is generated, then a successive overrelaxation scheme is used to solve for a pressure field consistent with the velocity solution. After the code was implemented in axisymmetric form and verified by several test cases, the drop tower runs of Aydelott were modeled. The model handed the free-surface deformation quite nicely, even to the point of modeling geyser growth in the regime where the free surface was no longer restrained. A representative run is shown.

Chato, David J.↗

NASA NTRS2011

Multi-Segment Radius Measurement Using an Absolute Distance Meter Through a Null Assembly

This system was one of the test methods considered for measuring the radius of curvature of one or more of the 18 segmented mirrors that form the 6.5 m diameter primary mirror (PM) of the James Webb Space Telescope (JWST). The assembled telescope will be tested at cryogenic temperatures in a 17-m diameter by 27-m high vacuum chamber at the Johnson Space Center. This system uses a Leica Absolute Distance Meter (ADM), at a wavelength of 780 nm, combined with beam-steering and beam-shaping optics to make a differential distance measurement between a ring mirror on the reflective null assembly and individual PM segments. The ADM is located inside the same Pressure-Tight Enclosure (PTE) that houses the test interferometer. The PTE maintains the ADM and interferometer at ambient temperature and pressure so that they are not directly exposed to the telescope s harsh cryogenic and vacuum environment. This system takes advantage of the existing achromatic objective and reflective null assembly used by the test interferometer to direct four ADM beamlets to four PM segments through an optical path that is coincident with the interferometer beam. A mask, positioned on a linear slide, contains an array of 1.25 mm diameter circular subapertures that map to each of the 18 PM segments as well as six positions around the ring mirror. A down-collimated 4 mm ADM beam simultaneously covers 4 adjacent PM segment beamlets and one ring mirror beamlet. The radius, or spacing, of all 18 segments can be measured with the addition of two orthogonally-oriented scanning pentaprisms used to steer the ADM beam to any one of six different sub-aperture configurations at the plane of the ring mirror. The interferometer beam, at a wavelength of 687 nm, and the ADM beamlets, at a wavelength of 780 nm, pass through the objective and null so that the rays are normally incident on the parabolic PM surface. After reflecting off the PM, both the ADM and interferometer beams return to their respective instruments on nearly the same path. A fifth beamlet, acting as a differential reference, reflects off a ring mirror attached to the objective and null and returns to the ADM. The spacings between the ring mirror, objective, and null are known through manufacturing tolerances as well as through an in situ null wavefront alignment of the interferometer test beam with a reflective hologram located near the caustic of the null. Since total path length between the ring mirror and PM segments is highly deterministic, any ADM-measured departures from the predicted path length can be attributed to either spacing error or radius error in the PM. It is estimated that the path length measurement between the ring mirror and a PM segment is accurate to better than 100 m. The unique features of this invention include the differential distance measuring capability and its integration into an existing cryogenic and vacuum compatible interferometric optical test.

Merle, Cormic↗

NASA NTRS2000

Context-specific adaptation of pursuit initiation in humans

PURPOSE: To determine if multiple states for the initiation of pursuit, as assessed by acceleration in the "open-loop" period, can be learned and gated by context. METHODS: Four normal subjects were studied. A modified step-ramp paradigm for horizontal pursuit was used to induce adaptation. In an increasing paradigm, target velocity doubled 230 msec after onset; in a decreasing paradigm, it was halved. In the first experiment, vertical eye position (+/-5 degrees ) was used as the context cue, and the training paradigm (increasing or decreasing) changed with vertical eye position. In the second experiment, with vertical position constant, when the target was red, training was decreasing, and when green, increasing. The average eye acceleration in the first 100 msec of tracking was the index of open-loop pursuit performance. RESULTS: With vertical position as the cue, pursuit adaptation differed between up and down gaze. In some cases, the direction of adaptation was in exact accord with the training stimuli. In others, acceleration increased or decreased for both up and down gaze but always in correct relative proportion to the training stimuli. In contrast, multiple adaptive states were not induced with color as the cue. CONCLUSIONS: Multiple values for the relationship between the average eye acceleration during the initiation of pursuit and target velocity could be learned and gated by context. Vertical position was an effective contextual cue but not target color, implying that useful contextual cues must be similar to those occurring naturally, for example, orbital position with eye muscle weakness.

NASA Discipline Neuroscience↗

NASA NTRS1995

A test of a vortex method for the computation of flap side edge noise

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

Martin, James E.↗

NASA NTRS1997

Advanced Signal Processing Methods Applied to Digital Mammography

The work reported here is on the extension of the earlier proposal of the same title, August 1994-June 1996. The report for that work is also being submitted. The work reported there forms the foundation for this work from January 1997 to September 1997. After the earlier work was completed there were a few items that needed to be completed prior to submission of a new and more comprehensive proposal for further research. Those tasks have been completed and two new proposals have been submitted, one to NASA, and one to Health & Human Services WS). The main purpose of this extension was to refine some of the techniques that lead to automatic large scale evaluation of full mammograms. Progress on each of the proposed tasks follows. Task 1: A multiresolution segmentation of background from breast has been developed and tested. The method is based on the different noise characteristics of the two different fields. The breast field has more power in the lower octaves and the off-breast field behaves similar to a wideband process, where more power is in the high frequency octaves. After the two fields are separated by lowpass filtering, a region labeling routine is used to find the largest contiguous region, the breast. Task 2: A wavelet expansion that can decompose the image without zero padding has been developed. The method preserves all properties of the power-of-two wavelet transform and does not add appreciably to computation time or storage. This work is essential for analysis of the full mammogram, as opposed to selecting sections from the full mammogram. Task 3: A clustering method has been developed based on a simple counting mechanism. No ROC analysis has been performed (and was not proposed), so we cannot finally evaluate this work without further support. Task 4: Further testing of the filter reveals that different wavelet bases do yield slightly different qualitative results. We cannot provide quantitative conclusions about this for all possible bases without further support. Task 5: Better modeling does indeed make an improvement in the detection output. After the proposal ended, we came up with some new theoretical explanations that helps in understanding when the D4 filter should be better. This work is currently in the review process. Task 6: N/A. This no longer applies in view of Tasks 4-5. Task 7: Comprehensive plans for further work have been completed. These plans are the subject of two proposals, one to NASA and one to HHS. These proposals represent plans for a complete evaluation of the methods for identifying normal mammograms, augmented with significant further theoretical work.

Stauduhar, Richard P.↗

NASA NTRS1996

Multigrid Methods for EHL Problems

In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of the application of such methods is the recent Effective Influence Method of Dowson and Wang. Multigrid methods have also been used with great success by Venner and Venner and Lubrecht with a good summary being given by Venner. As both these finite difference discretization based approaches appear to provide an efficient way of solving EHL problems, it is important to understand their relative merits. This paper is a first attempt at providing such an understanding in the context of EHL point contact problem, (contact of two spheres), in which the contact zone is a point and an ellipse or circle for unloaded and loaded dry contacts respectively. Since the film thickness and the contact width are generally small compared to the local radius of curvature of the two surfaces, the reduced geometry of the surfaces in the contact area can be accurately approximated to the contact between a paraboloid and a flat surface. The layout of the remainder of this paper is as follows. In section 2 we introduce the form of the equations to be solved. The Effective Influence Newton Method is described in Section 3 while Section 4 describes the Multigrid method to be used. Sections 5 and 6 describe the test problems to be used in the comparison between the two methods and compare the performance of the two methods. Section 7 concludes the paper with an argument of the two methods and suggests some future research directions.

Nurgat, Elyas↗

NASA NTRS2021

Petrology, Geochemistry, and Pairing of Lunar Meteorites from the Dominion Range

Introduction: During the 2018-2019 Antarctic Search for Meteorites (ANSMET) field season in the Dominion Range (DOM), 7 lunar meteorite stones were collected: DOM 18242 (15.1 g), DOM 18244 (25.1 g), DOM 18262 (6.8 g), DOM 18509 (16.5 g), DOM 18543 (13.6 g), DOM 18666 (45.9 g), and DOM 18678 (11.6 g). Here we present the initial results of electron microprobe and X-ray computed tomography (XCT) studies of these stones and look at the details of their petrography and mineral chemistry, as well as investigate possible pairing relationships, both with each other and with previously described lunar meteorites. Most of the work presented here is on the DOM 18509, 18543, and 18678 stones; subsamples of the other stones are in hand and similar measurements will be made on them by the time of the meeting. Methods: Textures in DOM 18509, DOM 18543, and DOM 18678 were characterized in 2D by optical microscopy, backscattered electron (BSE) imaging and elemental X-ray images on thin sections, as well as in 3D by X-ray computed tomography (XCT) on sample chips. Mineral compositions were assessed through a combination of wavelength dispersive spectroscopy EPMA (electron probe microanalysis) and x-ray mapping on the JEOL 8530 at NASA JSC. The bulk composition of all three meteorites was determined based on analyses of the fusion crust glass. XCT analyses were done on the Nikon XTH 320 at NASA JSC. ICP-MS data on bulk rock subsamples for each meteorite will be carried out in the near future. Results: The stones are all similar in macroscopic appearance with a dark aphanitic matrix hosting a variety of small- to medium-sized angular mineral and lithic fragments (often light colored in nature) [1,2]. Based on EPMA and XCT results, the three meteorites are polymict regolith breccias comprised of mineral, glass, and lithic clasts ranging up to several mm in length. Melt veins run through all three meteorite samples. Mineral clasts in all 3 stones are dominated by pyroxene and plagioclase (An82-96), with minor amounts of SiO2, olivine (Fo1-52), and FeTi-oxides. Pyroxene grains are mostly Fe-rich pigeonite and augite, and larger clasts are normally zoned and have fine exsolution lamellae. The lithic clasts in all stones consists of: (1) basalt clasts that contain zoned pyroxene, plagioclase laths, and ilmenite, with minor silica and Fe-rich olivine; (2) granulitic clasts; (3) anorthosite clasts; (4) Si-rich clasts that also contain ilmenite, troilite, high-Ca pyroxene, fayalite, and K-feldspar likely mesostasis from late stage basalts). All three meteorites contain glassy fusion crust that is highly vesicular, high in FeO and Al2O3 (15-17 wt% each), ferroan (Mg# of 23-24), and moderately rich in TiO2 (1.4-1.8 wt%). The composition of the fusion crust can serve as a proxy for the bulk meteorite composition and is identical within error for all three meteorites. Implications: The lithic and mineral clasts in all three stones are similar in clast population and assemblages as well as mineral chemistry. In addition, the fusion crust composition, a proxy for bulk composition, is within error of each other for all three stones. Thus DOM 18509, DOM 18543, and DOM 18678 are almost certainly paired. Based on similarities in macroscopic description as well as preliminary classification data [1,2], all 7 lunar stones from DOM are likely paired, though additional quantitative analyses are needed to confirm this. The presence of spherules and vesicular fusion crusts indicates that the DOM pairing group is a regolith breccia. The presence of basaltic and gabbroic clasts as well as more feldspathic materials, suggest that the regolith from which these meteorites formed contained a mixture of feldspathic highland material and mare material, suggesting a possible provenance near a marehighlands boundary. No evidence of KREEPy lithologies have been observed so far in these meteorites, however, future ICP-MS data on bulk rock chips for the stones will reveal any KREEP component if present. The DOM pairing group has many similarities to previously described lunar breccia meteorite MET 01210, however more detailed compositional data will be needed to make a definitive comparison.

R.A. Zeigler↗

NASA NTRSDate not supplied

Pink Spinel in Apollo Impact Melt Rock 68815: Implications for Mg-Suite Magmatism

Introduction: Magnesian rocks from the lunar highlands are collectively termed the Mg-suite. Characterized by high (>60) Mg# (molar 100×Mg/[Mg+Fe]) in mafic phases and calcic plagioclase, these rocks are plutonic to hypabyssal in origin, and include a range of bulk mineralogies such as troctolites, dunites, norites, gabbronorites, and spinel troctolites [1]. These Mg-suite lithologies have distinct trace element concentrations and ratios that differentiate them from other lunar rock types. These rocks are ancient, generally dated to between 4.5 and 4.1 Ga, although it is unknown if this represents the full range of Mg-suite ages [1–2]. Among the Mg-suite lithologies, the spinel troctolites are relatively rare, to date only found in polymict breccias [3]. Spinel troctolites, as their name suggests, consist of calcic plagioclase and forsteritic olivine, with minor amounts of spinel (MgAl2O4), ± pyroxene and cordierite [1,4]. This form of spinel is often called ‘pink’ spinel because of its appearance in thin section under plane polarized light (PPL; Fig. 1), due to minor amounts of Cr. Spinel troctolites are generally plutonic or hypabyssal in origin (subsequently exhumed and incorporated into polymict breccias), or formed through impact processes (e.g., crystalline impact melt) [5]. A spinel-rich lithology has also been found in the Moscoviense region of the Moon via the Moon Mineralogy Mapper (M3) and lacks other mafic phases [6]. Finally, while the Mg-suite sampled thus far consists of plutonic (or hypabyssal) rocks, the question remains if such magmas could have erupted on the surface of the Moon [7]. These magmas have much lower density than mare basalts, but little sample or remote sensing evidence has been found to support the idea that extrusive Mg-suite volcanism occurred [7]. Here, we present a coordinated microanalytical study of spinel-bearing lithic and mineral clasts found in Apollo sample 68815. These data will be used to understand their petrogenesis (magmatic or impact) and modification histories, and to shed light on the existence of volcanic Mg-suite rocks. Sample Description: Apollo sample 68815 is a polymict impact melt breccia containing a variety of lithic and mineral fragments embedded in devitrified impact melt. This sample was chipped off the top of a boulder at Station 8 during the Apollo 16 mission and had an original weight of nearly 1.8 kg. In this study, we investigated two polished thin sections of 68815: 68815,17 and 68815,148, both containing spinel. Methods: The thin sections of 68815 were studied using optical light microscopy (PPL, cross-polarized light, and reflected light) with a Keyence VHX-7100 Digital Microscope. Each section was then X-ray mapped for 13–14 elements using a Cameca SX100 electron probe microanalyzer (EPMA) located in the Kuiper Materials Imaging and Characterization Facility (KMICF) at the University of Arizona. We have obtained geochemical information about the phases (olivine, plagioclase, spinel, pyroxene) in the thin sections also using the EPMA. In addition, we have used ThermoScientific Helios NanoLab 660 Focused-Ion-Beam Scanning-Electron Microscope (FIB-SEM) and a Hitachi S-4800 SEM (both in KMICF) to obtain backscattered electron (BSE) images and energy dispersive Xray spectrometry (EDS) maps of areas of interest. Using a JEOL 7900F SEM at the Astromaterials Research & Exploration Science (ARES) at NASA Johnson Space Center (JSC), we have obtained electron backscatter diffraction (EBSD) maps of the spinel-bearing portions of the thin sections. The EBSD data were collected under beam conditions of 20 kV, and ~90 μA, with step sizes varying from 0.05 to 2 μm. Following EBSD data collection, we processed the data using AZtecCrystal and MTEX, a free MATLAB toolbox. Results: We have found clasts with subophitic textures, that consist of primarily olivine and plagioclase, with minor amounts of pink Mg-Al spinel and pyroxene (Fig. 1). These clasts are up to ~1 mm in length and contain spinels up to 50 μm across. We have additionally identified pink Mg-Al spinels within the impact melt (i.e., not contained in lithic clasts) in both thin sections. In one instance, a single spinel grain is approximately 300 μm across (Fig. 1b, 2). The spinel fragments embedded in impact melt have varying compositions, typically distinct from the compositions of spinels in the lithic clasts. Spinel-Bearing Clasts: Ten lithic clasts with similar textures and mineral compositions were identified between 68815,17 (two clasts) and ,148 (eight clasts). These clasts fall into two groups. The first has skeletal olivine with intergranular plagioclase, with minor amounts of pyroxene and spinel (Fig. 1a, 2c, 2d). The spinel in these clasts are found amid the plagioclase. The second group have an intergranular texture of olivine and plagioclase, again with minor spinel and pyroxene. The second group may contain spinels surrounded by plagioclase, and spinels enclosed in olivine. Spinels located within both clast types range from no apparent Cr zoning, to reverse zoning (Cr-enrichment inward; Fig. 2d), to normal zoning (Cr-enrichment outward). In the clasts thus far investigated with EPMA, plagioclase compositions range from An# (molar 100×Ca/[Ca+Na+K]) 92–96. Olivine Mg# ranged from 77 to 94, while pyroxene had Mg# from 54–84. Spinel in the clasts have Cr# (molar 100×Cr/[Cr+Al]) 2–4 and Mg# 88–91, which is within the range of pristine and plutonic spinel troctolites [8]. Isolated Spinels: These crystals are generally euhedral to subhedral, and can exhibit reverse Cr zoning (Cr enrichment inward) or no apparent Cr zoning. The spinels thus far investigated via EPMA have Cr# 9–14 and Mg# 65–82. The Cr# for these spinels is within the range reported by [8], but have lower Mg#. Future Work: We will continue to process the EBSD data for these lithic and mineral clasts. We will also continue to characterize these clasts using EPMA and SEM. By thoroughly characterizing the various spinels and spinel-bearing clasts, we aim to constrain the petrogenesis of these minerals and rock fragments. Acknowledgments: We thank NASA for the loan of these thin sections. We thank Ken Domanik and Jerry Chang for their support with data collection. Work was supported by a University of Arizona RII Core Facilities Pilot Program grant and start-up funds to JJB. We acknowledge support from NASA’s Planetary Science Research program for analysis performed at JSC. References: [1] Shearer C. K. et al. (2015) Am. Min. 100, 294–325. [2] Borg L. E. et al. (2020) GCA 290, 312–332. [3] Warren P. H. (1993) Am. Min. 78, 360–376. [4] Dymek R. F. et al. (1976) LPS VII, 2335–2378. [5] Treiman et al. (2019) Am. Min. 104, 370–384. [6] Pieters et al. (2011) JGR: Plan. 116:E00G08. [7] Prissel et al. (2016) Icarus 277, 319–329. [8] Prissel et al. (2016) Am. Min. 101, 1624–1635.

spinel↗

NASA NTRS1999

Simulating the Formation of Lunar Floor-Fracture Craters Using Elastoviscoplastic Relaxation

Lunar floor-fracture craters formed during the height of mare basalt emplacement. Due to a general temporal and spatial relation with the maria, these craters, numbering some 200, may be diagnostic of the thermal structure of the crust during this time. As the name suggests, these craters exhibit brittle failure, generally limited to the central floor region. That, and a shallower depth than fresh lunar craters, has led to two main theories as to their formation: laccolith emplacement under the crater and viscous relaxation. The implications of each model for the state of the Moon's crust during this time are quite different, so the viability of each model must be checked. Laccolith emplacement has been treated elsewhere. However, previous attempts to study the relaxation of the craters have assumed only a uniform, Newtonian viscous response of the near surface to the topographic driving forces, and simply postulated that the fractures resulted from tensile stresses associated with floor uplift. Here, we use a more sophisticated rheological model that includes not only non-Newtonian viscous behavior (i.e., the viscosity is stress-dependent), but also incorporates elastic behavior and a plastic component to the rheology to directly simulate the formation of the floor fractures. The results of our simulations show that while elastoviscoplastic relaxation is potentially viable for larger floor-fracture craters, it is not viable for craters with diameters < or = 60 km, the size of the majority of floor-fracture craters. We employ the finite element method, a numerical technique well suited for boundary-value problems, via the commercially available MARC software package. To test the viability of topographic relaxation, our goal is to prepare the simulations as to maximize the amount of relaxation. We take advantage of the natural axisymmetry of craters, simulating one radial plane. Initial shapes are based on data for fresh craters from Pike. To simplify implementation, a fourth order polynomial is used for the basin, while a third order inverse function is used for the rim. This form closely approximates the long-wavelength behavior of complex craters, while ignoring higher-frequency topography, save the rim. This approximation is appropriate because crater relaxation is strongly controlled by long-wavelength topography. Loading is accomplished assuming a uniform gravity field (1.62 m/s-square) and a uniform density of 2900 kg/cubic m. The initial stress state is set to be hydrostatic, with an additional pressure term to account for any overlying topography. This additional pressure term is tapered exponentially with depth. While the simulations quickly settle on a preferred stress state, and while the final solution is fairly insensitive to the choice of the e-folding depth of the taper, selecting an e-folding depth close to the diameter of the crater sets the initial stress state near the preferred state. We assume a diuranally averaged surface temperature of -20 C, and allow temperature to increase with depth at a rate of 50 K//km. Assuming a thermal conductivity of 2 W/in/K, this gradient translates to a heat flow of 100mW/square m, an extremely high value for the Moon. Temperature, of course, will not increase without bound. To maximize relaxation, we allow our temperature profile to increase linearly until it reaches the solidus (assumed to be 1200C) at a depth of 24.4 km, at which point it is kept constant. The presence of melt will drop the bulk viscosity; however, we have no rheological control for partial melts. Therefore, we make no attempt to simulate this situation. Elastoviscoplastic rheological model. In general, geologic materials can behave in three main ways: elastically, viscously (via solid-state creep), and brittly (plasticity is a continuum approach to simulate this phenomenon). We combine these three deformation mechanisms in an extended Maxwell solid, where the total strain can be broken down into a simple summation of the elastic, creep, and plastic strains. In relaxation phenomena in general, the system takes advantage of any means possible to eliminate deviatoric stresses by relaxing away the topography. Previous analyses have only modeled the viscous response. Comparatively, the elastic response in our model can augment the relaxation, to a point. This effect decreases as the elastic response becomes stiffer; indeed, in the limit of infinite elastic Young's modulus (and with no plasticity), the solution converges on the purely viscous solution. Igneous rocks common to the lunar near-surface have Young's modulii in the range of 10-100 GPa. To maximize relaxation, we use a Young's modulus of 10 GPa. (There is negligible sensitivity to the other elastic modulus, the Poisson's ratio; we use 0.25.) For the viscous response, we use a flow law for steady-state creep in thoroughly dried Columbia diabase, because the high plagioclase (about 70 vol%) and orthopyroxene (about 17 vol%) content is similar to the composition of the lunar highland crust as described by remote sensing and sample studies: noritic anorthosite. This flow law is highly non-Newtonian, i.e., the viscosity is highly stress dependent. That, and the variability with temperature, stands in strong contrast to previous examinations of lunar floor-fracture crater relaxation. To model discrete, brittle faulting, we assume "Byerlee's rule," a standard geodynamical technique. We implement this "rule" with an-angle of internal friction of about 40 deg, and a higher-than-normal cohesion of about 3.2 MPa (to approximate the breaking of unfractured rock). The actual behavior of geologic materials is more complex than in our rheological model, so the uncertainties in the plasticity do not represent the state-of-the-art error. Additional information is contained in the original.

Dombard, A. J.↗

NASA NTRSDate not supplied

Monitoring Airspace Complexity and Determining Contributing Factors

The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.

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