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At least 1,027 records · Page 57

Modeling Arctic boundary layer cloud streets at grey-zone resolutions

To better understand how model resolution affects the formation of Arctic boundary layer clouds, we investigated the influence of grid spacing on simulating cloud streets that occurred near Utqiagvik (formerly Barrow), Alaska on 2 May 2013 and were observed by the Moderate Resolution Imaging Spectroradiometer (MODIS). The Weather Research and Forecasting model was used to simulate the clouds using nested domains with increasingly fine resolution ranging from a horizontal grid spacing of 27 km in the boundary-layer-parameterized mesoscale domain to a grid spacing of 0.111 km in the large-eddy-permitting domain. We investigated the model-simulated mesoscale environment, horizontal and vertical cloud structures, boundary layer stability, and cloud properties, all of which were subsequently used to interpret the observed roll-cloud case. Increasing model resolution led to a transition from a more buoyant boundary layer to a more shear-driven turbulent boundary layer. The clouds were stratiform-like in the mesoscale domain, but as the model resolution increased, roll-like structures, aligned along the wind field, appeared with ever smaller wavelengths. A stronger vertical water vapor gradient occurred above the cloud layers with decreasing grid spacing. With fixed model grid spacing at 0.333 km, changing the model configuration from a boundary layer parameterization to a large-eddy-permitting scheme produced a more shear-driven and less unstable environment, a stronger vertical water vapor gradient below the cloud layers, and the wavelengths of the rolls decreased slightly. In this study, only the large-eddy-permitting simulation with gird spacing of 0.111 km was sufficient to model the observed roll clouds.

Lai, Hui-Wen↗

Physical and hydraulic properties of baked ceramic aggregates used for plant growth medium

Baked ceramic aggregates (fritted clay, arcillite) have been used for plant research both on the ground and in microgravity. Optimal control of water and air within the root zone in any gravity environment depends on physical and hydraulic properties of the aggregate, which were evaluated for 0.25-1-mm and 1-2-mm particle size distributions. The maximum bulk densities obtained by any packing technique were 0.68 and 0.64 g cm-3 for 0.25-1-mm and 1-2-mm particles, respectively. Wettable porosity obtained by infiltration with water was approximately 65%, substantially lower than total porosity of approximately 74%. Aggregate of both particle sizes exhibited a bimodal pore size distribution consisting of inter-aggregate macropores and intra-aggregate micropores, with the transition from macro- to microporosity beginning at volumetric water content of approximately 36% to 39%. For inter-aggregate water contents that support optimal plant growth there is 45% change in water content that occurs over a relatively small matric suction range of 0-20 cm H2O for 0.25-1-mm and 0 to -10 cm H2O for 1-2-mm aggregate. Hysteresis is substantial between draining and wetting aggregate, which results in as much as a approximately 10% to 20% difference in volumetric water content for a given matric potential. Hydraulic conductivity was approximately an order of magnitude higher for 1-2-mm than for 0.25-1-mm aggregate until significant drainage of the inter-aggregate pore space occurred. The large change in water content for a relatively small change in matric potential suggests that significant differences in water retention may be observed in microgravity as compared to earth.

NASA Center JSC↗

Characterizing the Architectures, Diversity and Habitability of Nearby Planetary Systems: The HabEx Observatory

Ongoing research, upcoming developments in ground-based facilities, and the launch of new space missions (Transiting Exoplanet Survey Satellite [TESS], James Webb Space Telescope [JWST], and Wide Field Infrared Survey Telescope [WFIRST]) will continue to advance knowledge of the variety and nature of exoplanetary system components over the next decade and a half. However, many key questions will remain: What is the architecture and full diversity of mature planetary systems? What is the linkage between individual planet properties, planetary system architectures and circumstellar dust structures? How diverse are planetary atmospheres over the full range of planet sizes and stellar insulation levels? Are there Earth-sized planets orbiting in the habitable zone (HZ) of nearby sunlike stars, with water vapor in their atmospheres, evidence for surface oceans and signs of life? Are these signs of life really of biotic origin? Answering all of these questions requires direct imaging and spectroscopy from space in reflected light and/or thermal emission. We exclusively discuss reflected light (near ultraviolet [UV] to near infrared [IR]) investigations, identifying some of the observational, technological, and theoretical challenges that must be met to accomplish such a feat. This paper concentrates on one possible implementation strategy currently under study: the HabEx (Habitable Exoplanet) Observatory mission concept.

Mennesson, B.↗

The Habitable Exoplanet Observatory (HabEx): Science Goals and Projected Capabilities

Ongoing research, upcoming developments in ground-based facilities, and the launch of new space missions (Transiting Exoplanet Survey Satellite [TESS], James Webb Space Telescope [JWST], and Wide Field Infrared Survey Telescope [WFIRST]) will continue to advance knowledge of the variety and nature of exoplanetary system components over the next decade and a half. However, many key questions will remain: What is the architecture and full diversity of mature planetary systems? What is the linkage between individual planet properties, planetary system architectures, and circumstellar dust structures? How diverse are planetary atmospheres over the full range of planet sizes and stellar insulation levels? Are there Earth-sized planets orbiting in the habitable zone (HZ) of nearby sun-like stars, with water vapor in their atmospheres, evidence for surface oceans and signs of life? Are these really of biotic origin? Answering all of these questions requires direct imaging and spectroscopy from space in reflected light and/or thermal emission. We exclusively discuss reflected light (near ultraviolet [UV] to near infrared [IR]) investigations, identifying some of the observational, technological, and theoretical challenges that must be met to accomplish such a feat. This paper concentrates on one possible implementation strategy and mission concept currently under study: the HabEx (Habitable Exoplanet) Observatory.

Mennesson, Bertrand↗

Crew Autonomy Through Self-Scheduling: Operational Characterization

NASA’s future long-duration exploration missions (LDEMs) will encounter increasing communication transmission delays as they move farther from Earth-based ground stations. This necessitates a new approach, as crews can no longer rely on real-time support from ground planners and must self-schedule their own operational timelines effectively and efficiently. To enable this transition, our team has developed Playbook, a mission planning and scheduling tool. Our research focuses on quantifying scheduling performance using Playbook to inform the design and development of future features to streamline timeline creation. We also aim to propose standards and guidelines for autonomous crews in LDEMs. In the past year, we have focused on further validating and quantifying the effects of countermeasure aids on self-scheduling performance. There are two software aids in Playbook (self-scheduling platform): Suggested Fixes, which propose an edit to resolve violations within a timeline, and No-Go Zones, which highlight where activities should not be scheduled on a timeline. We have made significant progress in HERA Campaign 7 (C7) data collection, increasing the number of days crew must self-schedule from 4 to 8. As a result, almost 20% of the mission is self-scheduled by the analog astronauts. We have also started data collection on a controlled lab experiment designed to quantify performance effects due to the countermeasures. We expect to present the preliminary results from both efforts. Finally, we have conducted an exploratory analysis of NASA’s HERA Campaign 6 (C6), investigating the mission-level impacts of self-scheduling. We derived basic patterns and descriptive statistics to better characterize crew autonomy through self-scheduling. We also assessed if there are any individual indicators of preference for self-scheduling, such as experience or predilection for autonomy. Preliminary analysis indicates that the HERA C6 crew self-scheduled one out of four flexible activities, indicating unprompted adoption of self-scheduling as a concept of operation for crew autonomy.

analog↗

Supernova remnants in dense clouds. I - Blast-wave dynamics and X-ray irradiation

Simplified models of cooling SNRs in uniform media together with an idealized emission spectrum are used to investigate the X-ray irradiation of the surrounding gas. The radiative transfer of the emitted X-rays through both the dense cooling shell and the unshocked cloud is calculated, with a simplified treatment to allow for an ionized zone surrounding the SNR. Numerical results are presented for SN energy of 10 exp 51 ergs and ambient densities ranging from 100 to 1,000,000 cu cm. It is found that an appreciable fraction of the X-ray energy is absorbed in regions where the X-ray energy deposited per H nucleon is between 1 and 30 eV; if the gas is initially molecular, the X-ray irradiation will result in warm molecular gas in which endothermic chemical reactions may proceed, and from which there may be strong emission in rotation-vibration transitions of H2 and other molecular species.

Draine, B. T.↗

Model Interpretation of Climate Signals: Application to the Asian Monsoon Climate

This is an invited review paper intended to be published as a Chapter in a book entitled "The Global Climate System: Patterns, Processes and Teleconnections" Cambridge University Press. The author begins with an introduction followed by a primer of climate models, including a description of various modeling strategies and methodologies used for climate diagnostics and predictability studies. Results from the CLIVAR Monsoon Model Intercomparison Project (MMIP) were used to illustrate the application of the strategies to modeling the Asian monsoon. It is shown that state-of-the art atmospheric GCMs have reasonable capability in simulating the seasonal mean large scale monsoon circulation, and response to El Nino. However, most models fail to capture the climatological as well as interannual anomalies of regional scale features of the Asian monsoon. These include in general over-estimating the intensity and/or misplacing the locations of the monsoon convection over the Bay of Bengal, and the zones of heavy rainfall near steep topography of the Indian subcontinent, Indonesia, and Indo-China and the Philippines. The intensity of convection in the equatorial Indian Ocean is generally weaker in models compared to observations. Most important, an endemic problem in all models is the weakness and the lack of definition of the Mei-yu rainbelt of the East Asia, in particular the part of the Mei-yu rainbelt over the East China Sea and southern Japan are under-represented. All models seem to possess certain amount of intraseasonal variability, but the monsoon transitions, such as the onset and breaks are less defined compared with the observed. Evidences are provided that a better simulation of the annual cycle and intraseasonal variability is a pre-requisite for better simulation and better prediction of interannual anomalies.

Lau, William K. M.↗

Characterization of Reactant Refill and Detonation Wave Dynamics in a GOx/Natural-gas RDRE Using Simultaneous High Repetition-Rate OH-PLIF and Chemiluminescence

The potential application of rotating detonation engines (RDEs) in rocket combustors hinges on a fundamental understanding of detonation wave structure and injector characteristics with fuel and oxidizer compositions relevant in rocket systems. Simultaneous 300 kHz-rate broadband OH* chemiluminescence and OH-PLIF imaging is employed in a fully optically accessible Natural Gas-GOx rotating detonation rocket engine (RDRE) to visualize reactant refill dynamics and detonation wave structure. A custom-built KTP-type optical parametric oscillator (OPO) is coupled with a nanosecond high-repetition-rate burst-mode laser to output284 nm light and target excitation of the Q1(9) transition in the OH radical. Significant deflagrative burning is observed throughout the chamber as a consequence of the oxygen-rich environment. Trailing Azimuthal Reflected Shock Combustion (ARSC) system, similar to those in a H2-air RDE are observed, burning unburned reactants in the region immediately following the primary detonation wave. Contact burning, as indicated in this study, does not seem to be a primary loss mechanism. The simultaneous measurement of OH and OH* show that axial locations exist in the refill process where OH radicals are present, and produced due to shear layer induced deflagration, however, these zones do not produce excited state OH*. While a deeper understanding of the underlying physics in RDRE systems requires further investigation, this work highlights a first-of-its-kind visualization of the turbulent combustion product field and reactant refill characteristics in this highly unsteady environment.

Propulsion↗

Magnetic properties of the quasi-XY Shastry-Sutherland magnet ER 2 Be 2 SiO 7

Polycrystalline and single-crystal samples of the insulating Shastry-Sutherland compound Er 2 ⁢Be 2 ⁢SiO 7 were synthesized via a solid-state reaction and the floating zone method, respectively. The crystal structure, Er single-ion anisotropy, zero-field magnetic ground state, and magnetic phase diagrams along high-symmetry crystallographic directions were investigated with bulk measurement techniques, x-ray and neutron diffraction, and neutron spectroscopy. Here, we establish that Er 2 ⁢Be 2 ⁢SiO 7 crystallizes in a tetragonal space group with planes of orthogonal Er dimers and a strong preference for the Er moments to lie in the local plane perpendicular to each dimer bond. We also find that this system has a noncollinear ordered ground state in zero field with a transition temperature of 0.841 K consisting of antiferromagnetic dimers and in-plane moments. Finally, we mapped out the H-T phase diagrams for Er 2 ⁢Be 2 ⁢SiO 7 along the directions H ∥ [001], [100], and [110]. While an increasing in-plane field simply induces a phase transition to a field-polarized phase, we identify three metamagnetic transitions in the H ∥ [001] case. Single-crystal neutron diffraction results reveal that the H ∥ [001] phase diagram can be explained predominantly by the expected field-induced behavior of classical, anisotropic moments, although the microscopic origin of one phase requires further investigation.

36 MATERIALS SCIENCE↗

A Data Parallel Multizone Navier-Stokes Code

We have developed a data parallel multizone compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the "chimera" approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. The design choices can be summarized as: 1. finite differences on structured grids; 2. implicit time-stepping with either distributed solves or data motion and local solves; 3. sequential stepping through multiple zones with interzone data transfer via a distributed data structure. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran (HPF). One interesting feature is the issue of turbulence modeling, where the architecture of a parallel machine makes the use of an algebraic turbulence model awkward, whereas models based on transport equations are more natural. We will present some performance figures for the code on the CM-5, and consider the issues involved in transitioning the code to HPF for portability to other parallel platforms.

Jespersen, Dennis C.↗

The Evolution in Coma Molecular Composition of Comet C/2017 K2 (PanSTARRS) Across the H 2 O Sublimation Zone: ALMA Imaging of an H 2 O-Dominated Coma

We report a survey of molecular emission from cometary volatiles using the Atacama Large Millimeter/Submillimeter Array (ALMA) toward comet C/2017 K2 (PanSTARRS) carried out on UT 2022 September 21, 22, and 23 at a heliocentric distance r H 3 OH, and H 2 CO (along with continuum emission from dust) sampled molecular chemistry in C/2017 K2 at the inner edge of the H 2 O sublimation zone, the region from r H 2 O begins vigorously subliming and increasingly dominating comet activity, discerning parent from daughter or extended source species. This work presents spectrally integrated flux maps, production rates, and parent scale lengths for each molecule. CH 3 OH, CO, and HCN were produced within ~250 km of the nucleus, potentially including contributions from sublimation of icy grains. CS was consistent with production from CS 2 photolysis, and H 2 CO required production from extended sources in the coma. An ortho-to-para ratio of 2.9 ± 0.4 for H 2 CO was derived from simultaneously measured transitions of each spin species. The continuum was extended and spatially resolved, consistent with thermal emission from dust in the coma. Analysis of the continuum visibilities provided an upper limit on the nucleus diameter d <6.6 km and coma dust masses of (1.2-2.4) times10 11 kg.

Nathan X Roth↗

Satellite-Based Investigations of the Transition from an Oceanic to Continental Transform Margin

Detailed characterization of neotectonics evolution of the Valle de San Felipe and Arroyo Grande regions in northern Baja California. Reoccupied GEOMEX GPS sites, and occupied a regional GPS (Global Positioning System) network. The Baja California peninsula in Mexico offers a unique setting for studying the kinematic evolution of a complex, active strike-slip/rift plate boundary. We are currently conducting remote sensing, geologic, and geodetic studies of this boundary. The combined data sets will yield instantaneous and time integrated views of its evolution. This proposal solicits renewed funding from NASA to support remote sensing and geologic studies. During the late Cenozoic, Baja California has been the locus of changing fault geometry that has accommodated components of the relative motion between the North America and Pacific plates. Contemporary slip between the two plates occurs in a broad zone that encompasses much of southern California and the Baja California Peninsula. The transfer of slip across this zone in southern California is relatively well understood. South of the border, the geometry and role of specific faults and structural provinces in transferring plate margin deformation across the peninsula is enigmatic. Results We use Landsat Thematic Mapper imagery of the Baja California Peninsula to identify recent and active faults, and then conduct field studies that characterize the temporal and spatial structural evolution of the plate margin. These data address questions concerning the neotectonic development of the Gulf of California, the Baja California Peninsula, and their role in evolution of the post-Miocene Pacific - North American plate boundary. Moreover, these studies provide constraints on the geometry of active faults, allowing more exact understanding of the results of ongoing NASA-supported geodetic experiments. In addition, anticipated publication of the TM scenes will provide a widely available geological data base for relatively little-known peninsula California. Achievements include development of an ArcInfo data base of Landsat and SPOT imagery, detailed field studies of Neogene structures in northeastern Baja California, and new constraint on Pacific - North America plate motion at Baja California latitudes. These results are reported in maps, manuscripts and data products which are published or near completion.

Miller, M. Meghan↗

The structure of a separating turbulent boundary layer. IV - Effects of periodic free-stream unsteadiness

Measurements were obtained of the sinusoidal unsteadiness of the free stream velocity during the separation of the turbulent boundary layer. Data were gathered by single wire and cross-wire, anemometry upstream of flow detachment, by laser Doppler velocimetry to detect the movement of the flow in small increments, and by a laser anemometer in the detached zone to measure turbulence and velocities. The study was restricted to a sinusoidal instability frequency of 0.61 and a ratio of oscillation amplitude to mean velocity of 0.3. Large amplitude and phase variations were found after the detachment, with unsteady effects producing hysteresis in the relationships between flow parameters. The detached shear layer decreased in thickness with increasing free-stream velocity and increases in the Reynolds shear stress. Deceleration of the free stream velocity caused thickening in the shear layer and upstream movement of the flow reversal location. The results are useful for studies of compressor blade and helicopter rotors in transition.

Simpson, R. L.↗

Computational fluid dynamics research in three-dimensional zonal techniques

Patched-grid algorithms for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver were investigated. Conservative and non-conservative approaches for performing zonal interpolations were implemented. The latter approach yields the most flexible technique in that it can handle both patched and overlaid grids. Results for a two-dimensional blunt body problem show that either approach yield accurate steady-state shock locations and jump conditions. In addition, calculations of the turbulent flow through a hypersonic inlet on a three-zone grid show that the numerical prediction is in good agreement with the experimental results. Through the use of a generalized coordinate transformation at the zonal interface between two or more blocks, the algorithm can be applied to highly stretched viscous grids and to arbitrarily-shaped zonal boundaries. Applications were made to the F-18 aircraft at subsonic, high-alpha conditions, in support of the NASA High-Alpha Research Program. The calculations were compared to ground-based and flight test experiments and were used as a guide to understanding the ground-based tests, which are laminar and transitional, and their relationship to flight. Calculations about a complete reconnaissance aircraft were also performed in order to further demonstrate the capability of the patched-grid algorithm.

Walters, Robert W.↗

Absence of a bulk signature of a charge density wave in hard x-ray measurements of UTe 2

The long-sought pair density wave (PDW) is an exotic phase of matter in which charge density wave (CDW) order is intertwined with the amplitude or phase of coexisting, superconducting order. Originally predicted to exist in copper-oxides, circumstantial evidence for PDW order now exists in a variety of materials. Recently, scanning tunneling microscopy (STM) studies have reported evidence for a three-component CDW at the surface of the heavy-fermion superconductor, UTe 2 , persisting below its superconducting transition temperature [Aishwarya et al., Nature 618, 928933 (2023); Gu et al., Nature 618, 921927 (2023); LaFleur et al., Nat. Commun. 15, 4456 (2024)]. Here, in this study, we use hard x-ray diffraction measurements on crystals of UTe 2 at 𝑇 = 1.9 and 12 K to search for a bulk signature of this CDW. Using STM measurements as a constraint, we calculate the expected locations of CDW superlattice peaks and sweep a large volume of reciprocal space in search of a signature. We fail to find any evidence for a CDW near any of the expected superlattice positions in many Brillouin zones. We estimate an upper bound on the CDW lattice distortion of 𝑢 max ≲ 4×10 −3 Å. Our results suggest that the CDW observed in STM is either purely electronic, somehow lacking a signature in the lattice, or is restricted to the material surface.

Kengle, Caitlin S.↗

Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars. II. Planetary Systems Observed During Campaigns 1-7

We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically validate 17 planets (7 of which were previously unpublished), confirm the earlier validation of 22 planets, and announce 17 newly discovered planet candidates. Revising the properties of the associated planet candidates based on the updated host star characteristics and refitting the transit photometry, we find that our sample contains 21 planets or planet candidates with radii smaller than 1.25 solar radii, 18 super-Earths (1.25-2 solar radii), 21 small Neptunes (2-4 solar radii), three large Neptunes (4-6 solar radii), and eight giant planets (greater than 6 solar radii). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, 1.29 from plus 0.19 to minus 0.18 solar radii), EPIC 211988320.01 (perihelion radius equals 2.86 from plus 0.16 to minus 0.15 solar radii), and EPIC 212690867.01 (2.20 from plus 0.19 to minus 0.18 solar radii) orbit within optimistic habitable zone boundaries set by the "recent Venus" inner limit and the "early Mars" outer limit. In total, our planet sample includes eight moderately irradiated 1.5-3 solar radii planet candidates (planetary flux greater than or approximately 20 times Earth's flux) orbiting brighter stars (Ks less than 11) that are well-suited for atmospheric investigations with the Hubble, Spitzer, and/or James Webb Space Telescopes. Five validated planets orbit relatively bright stars (Kp less than 12.5) and are expected to yield radial velocity semi-amplitudes of at least 2 meters per second. Accordingly, they are possible targets for radial velocity mass measurement with current facilities or the upcoming generation of red optical and near-infrared high-precision RV (Radial Velocity) spectrographs.

Dressing, Courtney D.↗

Stellar evolution at high mass with convective core overshooting

The transition from stellar evolution models with no convective core overshooting (CCO) at all to models in which homogeneous mixing due to CCO reaches far beyond the formal convective core boundary is systematically explored. Overshooting is parameterized in terms of the ratio d/H(p), where d is the distance of convective overshoot beyond the formal convective core boundary and H(p) is the local pressure scale height. It is concluded that CCO in very massive main sequence stars produces a great expansion of the stellar envelope if d/H(p) is large but not excessively large. CCO does not entirely suppress convective instability above the overshoot zone in the envelopes of main sequence stars more massive than about 15 solar masses. A general comparison of theoretically constructed isochrones for young stars with observed main sequence turnups indicates that the observed turnups are longer, brighter, and cooler at the tip than those expected on thfe basis of standard evolutionary theory.

Stothers, R. B.↗

An Experimental Investigation on the Static Equilibria and Dynamics of Liquid Bridges

A liquid bridge is a volume of liquid held between two or more solid supports. In the case of small disk supports with a sharp edge, the contact line between the bridge and the support disk will be anchored along the edge of the disk. For these cases the solid presents a geometrical singularity and the contact angle is indeterminate within a given range. This dissertation presents research conducted on liquid bridges with anchored contact lines. The three major topics covered are: determining the role of support geometry on static equilibria, liquid bridge dynamical behavior, and forces exerted by a liquid bridge on a support structure. The work was primarily experimental and conducted in a "Plateau tank" that allowed for the simulation of equivalent low-gravity conditions. The main thrust of the experimental work involved the use of a high resolution optical measurement system for imaging the dynamic zone shape, measurement of the static and dynamic contact angles and non-invasive analysis of excited surface modes. The liquid bridge was manipulated by computer controlled linear actuators which allowed precise control over the physical characteristics of the bridge. Experiments have been carried out to locate a bifurcation point along the maximum volume axisymmetric stability margin. Below the critical slenderness the bifurcation from an axisymmetric to a stable nonaxisymmetric configuration is supercritical. However, above this critical slenderness, the bifurcation is subcritical. A series of experiments analyzed the effect on axisymmetric bridge stability by using support disks of different radii, The shape behavior as transition points were approached, as well as the limiting case of a vanishing support radius was investigated. Experiments were performed to determine the resonant frequencies of axisymmetric bridges subject to lateral vibrations. Anomolous results led to a series of experiments to characterize nonlinearities present in the dynamic bridge shape. Finally, an attempt was made to experimentally measure the force exerted by the bridge on the lower support disk. This was done through use of a force balance apparatus. Particular attention was paid to the behavior of the bridge as the minimum volume stability limit was approached.

Resnick, Andrew Howard↗