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NASA NTRS2007

Cryogenic Shrouds for Testing Thermal-Insulation Panels

Cryogenic shrouds have been designed and built for use in thermomechanical testing of samples of thermalinsulation panels on cryogenic vessels. In the original application for which these shrouds were specifically designed, the samples are representative of the large-area thermal-insulation panels on the space-shuttle external tanks that hold liquid hydrogen and liquid oxygen, and the purpose of the testing is to demonstrate the ability of bonded layers in the panels to resist delamination under a combination of applied uniaxial mechanical loads and realistic operational temperatures. Presumably, the shrouds and the tests performed by use of them could be modified to enable similar evaluation of thermomechanical properties of thermal-insulation panels for cryogenic vessels other than the external tanks of the space shuttles. The shrouds are required to enable maintenance of required temperatures on the inner and outer surfaces of the thermal-insulation-panel samples, to enable visual observation of the outer surfaces of the samples, and not to introduce any measurable loads into the panels. For each panel sample, there are two shrouds: one to be mounted on the inner surface (the surface that would be in contact with a tank containing a cryogenic liquid during normal use) and one to be mounted on the outer surface (the surface that would be exposed to ambient air or other warmer environment during normal use). The shrouds for testing specimens of thermal-insulation- panels for the liquid-hydrogen tank are made largely of titanium; the shrouds for testing specimens of thermal- insulation-panels for the liquid-oxygen tank are made largely of an aluminum- lithium alloy. The specific temperature requirements are the following: The inner shroud must make it possible to maintain a temperature of 321 degrees F (196 degrees C) [the approximate temperature of liquid nitrogen] or 453 F (about 269 C) [the approximate temperature of liquid helium] on the inner face of the sample. The outer shroud must make it possible to maintain a temperature between 30 degrees and 0 degrees F (between about 34 degrees and about 18 degrees C) on the outer surface of the sample by blowing a cryogenic gas or missile grade air along that surface. To enable viewing of the outer surface of the sample during testing, the outer shroud includes a window comprising two layers of poly(methyl methacrylate) with a gap between them to reduce fogging. To ensure that the shrouds do not introduce any measurable loads into a panel specimen, the shrouds are cushioned on the specimen by seals made of a fluoropolymer-membrane/fabric composite material and are held in place on the specimen by means of symmetrically placed clamps with poly(tetrafluoroethylene) pads. Instrumentation ports for thermocouples and strain gauges used in the tests are incorporated into the shrouds.

Norris, Jeffrey↗

DOE OSTI2018

High-Pressure Geophysical Properties of Fcc Phase FeH X

Face centered cubic (fcc) FeHX was synthesized at pressures of 18-68 GPa and temperatures exceeding 1,500 K. Thermally quenched samples were evaluated using synchrotron X-ray diffraction (XRD) and nuclear resonant inelastic X-ray scattering (NRIXS) to determine sample composition and sound velocities to 82 GPa. To aid in the interpretation of nonideal (X≠1) stoichiometries, two equations of state for fcc FeH X were developed, combining an empirical equation of state for iron with two distinct synthetic compression curves for interstitial hydrogen. Matching the density deficit of the Earth's core using these equations of state requires 0.8-1.1 wt % hydrogen at the core-mantle boundary and 0.2-0.3 wt % hydrogen at the interface of the inner and outer cores. Furthermore, a comparison of Preliminary Reference Earth Model (PREM) to a Birch's law extrapolation of our experimental results suggests that an iron alloy containing approximate to 0.8-1.3 wt % hydrogen could reproduce both the density and compressional velocity (V P ) of the Earth's outer core.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1973

Aircraft Range Optimization Using Singular Perturbations

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Oconnor, Joseph Taffe↗

NASA NTRS1975

Spinning mode sound propagation in ducts with acoustic treatment

Recent acoustic data show larger noise attenuations than predicted for acoustically treated aircraft engine inlets without splitter rings. A theoretical study of the acoustic propagation of spinning modes in acoustically treated open circular ducts is presented, and a suppressor with splitter rings was modeled by using the rectangular approximation to the annular duct. Theoretical models were used to determine optimum impedance and maximum attenuation for several spinning lobe numbers from 0 to 50. Results of the analysis indicate that for circular ducts the maximum possible attenuation and the optimum wall impedance are strong functions of the lobe number, and for annular ducts the attenuation and optimum wall impedance are insensitive to the spinning lobe number for well cut-on modes. These results explain why suppressors with splitter rings were quite effective in spite of the lack of detailed information on the noise source modal structure. Conversely, effective use of outer wall treatment alone will require expanded knowledge of the noise source structure. Approximate solutions are presented to help interpret the more exact theoretical results.

Rice, E. J.↗

NASA NTRS1995

An instability in planetary rings due to ballistic transport

Ballistic transport in planetary rings is the net radial transport of mass and angular momentum due to exchanges of meteoroid impact ejecta between neighboring ring regions. The detailed linear stability analysis in this paper demonstrates that ballistic transport causes wavelike disturbances to grow and propagate in an otherwise uniform ring. The growth is strongest for intermediate values of the normal ring optical depth tau = 0.1 to 1.0 and goes to zero as tau approaches 0 and tau approaches infinity. For nominal values of various physical parameters, the minimum e-folding time is approximately 10(exp 5) years for tau approximately 0.4. The direction of propagation is opposite to the sense of any asymmetry that may exist in the ejecta direction distribution (inward for prograde ejecta and outward for retrograde ejecta). The additional effect of viscous transport tends to damp wavelike perturbations strongly at short wavelengths and at high values of tau. The quantitative agreement between this analytic work and numerical simulations reported elsewhere is generally quite good. As applied to Saturn's rings, the results in this paper strengthen the earlier conclusion from numerical calculations that the 100-km structure in the inner B Ring is caused by ballistic transport. However, it is also clear that ballistic transport cannot produce the complex structure seen in the outer two-thirds of the B Ring where tau greater than or approximately 1.5. Wavelike structures in the C Ring might also be attributed to ballistic transport; but this requires further study.

Durisen, Richard H.↗

NASA NTRS2017

Evidence for Reduced Species Star Formation Rates in the Centers of Massive Galaxies at zeta = 4

We perform the first spatially-resolved stellar population study of galaxies in the early universe z equals 3.5 -6.5, utilizing the Hubble Space Telescope Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) imaging dataset over the GOODS-S field. We select a sample of 418 bright and extended galaxies at z less than or approximately equal to 3.5-6.5 from a parent sample of approximately 8000 photometric-redshift selected galaxies from Finkelstein et al. We first examine galaxies at 3.5 less than or equal to z less than or approximately equal to 4.0 using additional deep K-band survey data from the HAWK-I UDS and GOODS Survey (HUGS) which covers the 4000 Angstrom break at these redshifts. We measure the stellar mass, star formation rate, and dust extinction for galaxy inner and outer regions via spatially-resolved spectral energy distribution fitting based on a Markov Chain Monte Carlo algorithm. By comparing specific star formation rates (sSFRs) between inner and outer parts of the galaxies we find that the majority of galaxies with the high central mass densities show evidence for a preferentially lower sSFR in their centers than in their outer regions, indicative of reduced sSFRs in their central regions. We also study galaxies at z approximately equal to 5 and 6 (here limited to high spatial resolution in the rest-frame ultraviolet only), finding that they show sSFRs which are generally independent of radial distance from the center of the galaxies. This indicates that stars are formed uniformly at all radii in massive galaxies at z approximately equal to 5-6, contrary tomassive galaxies at z. less than approximately equal to 4.

early universe â€“ galaxies: bulges â€“ galaxies: ↗

NASA NTRS1971

A U-type solar radio burst originating in the outer corona.

The observation of a U-type solar radio burst with a reversing frequency of approximately 0.7 MHz suggests the presence of a magnetic bottle extending out to about 35 solar radii. A possible model of this loop structure is developed from the data. The occurrence of low-frequency U-bursts seems to be extremely rare although magnetic bottles may develop frequently during solar maximum.

Stone, R. G.↗

DOE OSTI2020

Simultaneous 10 kHz three-dimensional CH 2 O and tomographic PIV measurements in a lifted partially-premixed jet flame

High-speed, three-dimensional (3D) scalar-velocity field measurements are demonstrated in a lifted partially-premixed dimethyl-ether/air jet flame using simultaneous laser-induced fluorescence (LIF) of formaldehyde (CH 2 O) and tomographic particle image velocimetry (TPIV). The 3D LIF measurements are performed by raster scanning the laser beam from a 100 kHz pulse-burst laser across the probe volume using an acousto-optic deflector. The volumetric reconstruction of the LIF signal from ten parallel planes provides quasi-instantaneous 3D LIF measurements that are synchronized with 10 kHz TPIV measurements. Here, the temporally resolved CH 2 O-LIF and velocity field data are used to analyze Lagrangian particle trajectories and displacement speeds at the base of the lifted flame. The particle trajectories reveal flow structures that are difficult to observe in an Eulerian reference frame. Positive and negative displacement speeds are observed at the CH 2 O-LIF surfaces at the inner and outer regions of the jet flame with a maximum displacement speed of approximately eight times the laminar flame speed of a stoichiometric dimethyl-ether/air mixture. The observations in present study support formation of lean premixed flames near the flame base whose role in flame stabilization should be investigated in more detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Radio Observations of the Double-relic Galaxy Cluster Abell 1240

We present LOFAR 120 - 168 MHz images of the merging galaxy cluster Abell 1240 that hosts double radio relics. In combination with the GMRT 595-629 MHz and VLA 2- 4 GHz data, we characterised the spectral and polarimetric properties of the radio emission. The spectral indices for the relics steepen from their outer edges towards the cluster centre and the electric field vectors are approximately perpendicular to the major axes of the relics. The results are consistent with the picture that these relics trace large-scale shocks propagating outwards during the merger. Assuming diffusive shock acceleration (DSA), we obtain shock Mach numbers of M = 2.4 and 2.3 for the northern and southern shocks, respectively. For M ≲ 3 shocks, a pre-existing population of mildly relativistic electrons is required to explain the brightness of the relics due to the high (> 10 per cent) particle acceleration efficiency required. However, for M ≳ 4 shocks the required efficiency is ≥ 1% and ≥ 0.5%, respectively, which is low enough for shock acceleration directly from the thermal pool. We used the fractional polarization to constrain the viewing angle to > 53±3° and > 39±5° for the northern and southern shocks, respectively. We found no evidence for diffuse emission in the cluster central region. If the halo spans the entire region between the relics (~ 1.8 Mpc) our upper limit on the power is P1.4 GHz = (1.4 ± 0.6) × 10 23 W Hz -1 which is approximately equal to the anticipated flux from a cluster of this mass. However, if the halo is smaller than this, our constraints on the power imply that the halo is underluminous

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Analytic Thermal Model of an Optical Fiber Based Gamma Thermometer and its Application in a University Research Reactor

This paper describes and validates, by comparison with numerical modeling results, an analytical model of thermal transport in an optical fiber based gamma thermometer (OFBGT) that is appropriate for use in university research reactors. The maximum temperature difference between the thermal mass and the outer sheath ( Δ T ) for the OFBGT design that we have considered is approximately 50 ∘ C , for the OFBGT in the Central Irradiation Facility of the Ohio State University Research Reactor (OSURR) with the reactor operating at full power (450 kW). The maximum value of Δ T that is predicted by the analytic model for the OFBGT design is smaller by approximately 1.1 °C than the value of Δ T which is predicted by the numerical model, for the same OFBGT design, but including all the details of the design. We have used the analytical model of thermal transport in an OFBGT to determine a normalized Modulation Transfer Function M T F ′ ( k ) ) for the OFBGT. We conclude that MTF ′ ( k OSU ) > 0.99 , where k OSU is the spatial frequency for the axial dependence of the reactor power distribution in the

47 OTHER INSTRUMENTATION↗

NASA NTRS1977

Interstellar bubbles. II - Structure and evolution

The detailed structure of the interaction of a strong stellar wind with the interstellar medium is presented. First, an adiabatic similarity solution is given which is applicable at early times. Second, a similarity solution is derived which includes the effects of thermal conduction between the hot (about 1 million K) interior and the cold shell of swept-up interstellar matter. This solution is then modified to include the effects of radiative energy losses. The evolution of an interstellar bubble is calculated, including the radiative losses. The quantitative results for the outer-shell radius and velocity and the column density of highly ionized species such as O VI are within a factor 2 of the approximate results of Castor, McCray, and Weaver (1975). The effect of stellar motion on the structure of a bubble, the hydrodynamic stability of the outer shell, and the observable properties of the hot region and the outer shell are discussed.

Weaver, R.↗

NASA NTRS1989

PROMIS series. Volume 7: GOES 5 and GOES 6 geosynchronous magnetic field data for March - June 1986

This is the seventh in a series of volumes pertaining to the Polar Region Outer Magnetosphere International Study (PROMIS). This volume contains 24 hour plots of approximately 1-minute average magnetic fields from the GOES 5 and GOES 6 spacecraft for the period March 10 through June 16, 1986. Data are displayed in a VDH coordinate system based on a centered dipole with northern hemisphere geographic coordinates of the pole at 78.80 deg latitude and 289.24 deg longitude.

Fairfield, D. H.↗

NASA NTRS1994

Self-gravity and dissipation in polar rings

Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.

Dubinski, John↗

NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗

NASA NTRS2013

Characterizing Uranus with an Ice giant Planetary Origins Probe (Ice-POP)

We now know from studies of planetary transits and microlensing that Neptune-mass planets are ubitquitous and may be the most common class of planets in the Galaxy. As such it is crucial that we understand the formation and evolution of the ice giant planets in our own solar system so that we can better understand planet formation throughout the galaxy. An entry probe mission to Uranus would help accomplish this goal. In fact the Planetary Decadal Survey recommended a Uranus orbiter with entry probe but did not explore in detail the specifications for the entry probe. NASA Ames is currently studying thermal protection system requirements for such a mission and this has led to questions regarding the minimum interesting science payload of such an entry probe. The single most important in-situ measurement for an ice giant entry probe is a measurement of atmospheric composition. For Uranus this would specifically include the methane and noble gas abundances. An in situ measurement of the methane abundance, from below the methane cloud, would constrain the atmospheric carbon abundance, which is believed to be roughly 30 to 50 times solar. There are hints from the transiting planets that extrasolar ice giants show comparable or even greater enhancements of heavy elements compared to their primary stars. However the origin of this carbon enhancement is controversial. Is Uranus a "failed core" of a larger gas giant or was the atmosphere enhanced by accretion of icy planetesimals' Constraining atmospheric abundances of C and perhaps S or even N from below 5 bars would provide badly needed data to address such issues. A measurement of the N abundance would provide clues on the origin of the planetesimals that formed Uranus. Low N-abundance indicates planetesimals from 'warmer' regions where N was mainly in form of NH3, whereas a strong enrichment could indicate planetesimals / cometary material from the colder outer regions of the nebula. Furthermore CO and HCN have been detected in Neptune but not in Uranus. A measurement of the abundance of either would constrain the source mechanisms for these molecules (exogenic or internal). A major surprise from the Galileo Entry Probe was that the heavier noble gases Ar, Kr, and Xe are enhanced in Jupiter's atmosphere at a level comparable to what was seen for the chemically active volatiles N, C, and S. It had been generally expected that Ar, Kr, and Xe would be present in solar abundances, as all were expected to accrete with hydrogen during the gravitational capture of nebular gases. Enhanced abundances of Ar, Kr, and Xe is equivalent to saying that these noble gases have been separated from hydrogen. There are several mechanisms that could accomplish this but these hypotheses require further testing. Measurement of noble gas abundances in an ice giant would constrain the planetary formation and nebular mechanisms responsible for this enhancement. Standard three-layer models of Uranus find that the outer, predominantly H/He layer of Uranus does not reach pressures high enough (approximately 1 Mbar) for H2 to transition to liquid metallic hydrogen. However, valid models can also be constructed with a smaller intermediate water-rich layer, with hydrogen then reaching the metallic hydrogen phase. If this occurs, He should phase separate from the hydrogen and ``rain out," taking along a substantial abundance of Ne, as suggested for Jupiter (and likely also for Saturn). Hence He and Ne depletions could be probes of the planet's structure in the much deeper interior. A determination of Uranus' atmospheric abundances, particularly of the noble gasses, is thus critical to understanding the formation of Uranus, and giant planets in general. These measurements can only be performed with an entry probe. The second key measurement would be a temperature-pressure sounding to provide ground truth for remote measurements of atmospheric temperature and composition and to constrain the internal heat flow. This would also establish that the methane abundance measurements have indeed been made below any possible methane cloud. Finally an ultra stable oscillator would measure wind speeds and constrain atmospheric dynamics. In our presentation we will discuss the importance of all of these measurements and argue that an entry probe is a crucial component of any ice giant mission.

Marley, Mark S.↗

DOE OSTI2018

Measurement of toroidal variation in conducted heat loads in locked mode induced disruptions on DIII-D

Locked mode disruptions with controlled toroidal phase are produced in the DIII-D tokamak by locking to large non-axisymmetric applied magnetic perturbations with different toroidal phases. Additionally, the disruption conducted heat loads are found to go almost completely to the outer divertor region, possibly due to strong inner leg detachment, but possibly also due to plasma motion and limiting on the outer divertor leg shelf. The outer leg conducted heat loads are found to have a significant toroidal variation of order ±30%, with a dominantly n = 1 structure. The heat load phase is shifted from initial locked mode phase in a way that is approximately consistent with heat loss into the scrape-off layer being enhanced at the mode island O-point outer midplane crossing. These measurements suggest that pre-existing locked modes can affect the conducted heat load structure during the thermal quench by affecting the thermal quench MHD phase. This is consistent with previous MHD simulations which indicated that pre-disruption locked mode structures can persist and survive to some degree through the large thermal quench MHD. Finally, this work complements previous work [Shiraki2015] which showed that n = 1 structures in mitigated disruptions can create toroidal variation in the disruption radiated power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1974

Spinning mode sound propagation in ducts with acoustic treatment

Recent acoustic data have shown larger noise attenuations than predicted for acoustically treated aircraft engine inlets without splitter rings. These data have stimulated a more detailed theoretical study of the acoustic propagation of spinning modes in acoustically treated open circular ducts. In addition, the suppressor with splitter rings was modeled by using the rectangular approximation to the annular duct. The theoretical models were used to determine optimum impedance and maximum attenuation for several spinning lobe numbers from 0 to 50. It is found that for circular ducts the maximum possible attenuation and the optimum wall impedance are strong functions of the lobe number. For annular ducts the attenuation and optimum wall impedance are insensitive to the spinning lobe number for well cut-on modes. The results help explain why suppressors with splitter rings have been quite effective in spite of the lack of detailed information on the noise-source modal structure. Conversely, effective use of outer-wall treatment alone will require expanded knowledge of the noise-source structure. Approximate solutions are presented to help interpret the more exact theoretical results.

Rice, E. J.↗

NASA NTRS1977

Nested-crater model of lunar ringed basins

We propose a model for the origin of impact-basin rings whereby the main topographic rim of a basin approximates the limit of excavation and inner rings approximate the rims of craters formed inside the transient crater by some perturbation in the cratering process. The cause of this complexity in transient cavities may be the presence of discontinuities in the target material. The second inward ring may have formed at the seismic discontinuity about 20 km deep in the lunar crust, and the third, innermost ring of a few large basins at the crust-mantle interface about 60 km deep. Slumping increased the original diameters of many rings and split some initially coherent rings into subsidiary or partial rings. Deformation outside the transient crater produced external arcs. This model differs from prevalent hypotheses of ring formation whereby an inner ring approximates the transient crater rim and major faulting of the flank produced the outer ring structures.

Wilhelms, D. E.↗