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NASA NTRS1994

Hydrodynamics of binary coalescence. 1: Polytropes with stiff equations of state

We performed a series of three-dimensional hydrodynamic calculations of binary coalescence using the smoothed particle hydrodynamics (SPH) method. The initial conditions are exact polytropic equilibrium configurations on the verge of dynamical instability. We consider synchronized equilbria only and concentrate on stiff equations of state, with adiabatic Gamma greater than 5/3. We assume that the polytropic constants (K identically equal to P/(rho(exp Gamma)) are the same for both components. These conditions apply well to models of neutron star binaries. Accordingly, we discuss our results in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) project, and we calculate the emission of gravitational radiation in the quadruple approximation. The fully nonlinear development of the instability is followed using SPH until a new equilibrium configuration is reached by the system. We find that the properties of this final configuration depend sensitively on both the compressibility and mass ratio. An axisymmetric merged configuration is always produced when the adiabatic exponent Gamma approximately less than 2.3. As a consequence, the emission of gravitational radiation shuts off abruptly right after the onset of dynamical instability. In contrast, triaxial merged configurations are obtained when Gamma approximately greater than 2.3, and the system continues to emit gravitational waves after the final coalescence. Systems with mass ratios q not equal to 1 typically become dynamically unstable before the onset of mass transfer. Stable mass transfer from one neutron star to another in a close binary is therefore probably ruled out. For a mass ratio q approximately less than 0.5, however, dynamical mass transfer can temporarily retard the coalescence by causing a rapid reexpansion of the binary into a new, slightly eccentric but dynamically stable orbit. The maximum amplitude h(sub max) and peak luminosity L(sub max) of the gravitational waves emitted during the final coalescence are nearly independent of Gamma, but depend sensitively on the mass ratio q. The approximate scalings we find are h(sub max) varies as q(exp 2) and L(sub max) varies as q(exp 6) for q close to unity.

Rasio, Frederic A.↗

NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗

NASA NTRS1994

A comparison of cosmological hydrodynamic codes

We present a detailed comparison of the simulation results of various hydrodynamic codes. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent codes are compared: three of them Eulerian mesh-based and two variants of the smooth particle hydrodynamics 'SPH' Lagrangian approach. The Eulerian codes were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH codes at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH codes and the thermal accuracy in low-density regions better in the Eulerian codes. In the low-density, low-temperature regions the SPH codes have poor accuracy due to statiscal effects, and the Jameson code gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic codes and of suiting their use to problems which exploit their best individual features.

Kang, Hyesung↗

NASA NTRS1995

On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory

The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.

Speziale, Charles G.↗

NASA NTRS1995

IUTAM Symposium on Hydrodynamic Diffusion of Suspended Particles

The focus of the symposium was on multiparticle hydrodynamic interactions which lead to fluctuating motion of the particles and resulting particle migration and dispersion or diffusion. Implications of these phenomena were described for sedimentation, fluidization, suspension flows, granular flows, and fiber suspensions. Computer simulation techniques as well as experimental techniques were described. Each session had an invited leadoff talk which overviewed the session topic as well as described the speaker's own related research. Ample time for discussion was included after each talk as well as at the end of each session. The symposium started with a keynote talk on the first evening on What is so puzzling about hydrodynamic diffusion?, which set the tone for the rest of the meeting by emphasizing both recent advances and unanswered issues.

Davis, R. H.↗

NASA NTRS1958

Low-Speed Aerodynamic and Hydrodynamic Characteristics of a Proposed Supersonic Multijet Water-Based Hydro-Ski Aircraft with Upward-Rotating Engines

The low-speed aerodynamic and hydrodynamic characteristics of a proposed multijet water-based aircraft configuration for supersonic operation have been investigated. The design features include upward-rotating engines, body indentation, a single hydro-ski, and a wing with an aspect ratio of 3.0, a taper ratio of 0.143, 36.90 sweepback of the quarter-chord line, and NACA 65AO04 airfoil sections. For the aerodynamic investigation, with the flaps retracted, the model was longitudinally and directionally stable up to the stall. The all-movable horizontal tail was capable of trimming the model up to a lift coefficient of approximately 0.87. All flap configurations investigated had a tendency to become longitudinally unstable at stall. The effectiveness of the all-movable horizontal tail increased with increasing lift coefficient for all flap configurations investigated; however, with the large static margin of the configuration with the center of gravity at 0.25 mean aerodynamic chord, the all-movable horizontal tail was not powerful enough to trim all the various flapped configurations investigated throughout the angle-of-attack range. For the hydrodynamic investigation, longitudinal stability during take-offs and landings was satisfactory. Decreasing the area of the hydro-ski 60 percent increased the maximum resistance and emergence speed 40 and 70 percent, respectively. Without the jet exhaust, the resistance was reduced by simulating the vertical-lift component of the forward engines rotated upward. However, the jet exhaust of the forward engines increased the maximum resistance approximately 60 percent. The engine inlets and horizontal tail were free from spray for all loads investigated and for both hydro-ski sizes.

Petynia, William W.↗

NASA NTRS1999

Investigation of Diffusion Flame Tip Thermodiffusive and Hydrodynamic Instability under Microgravity Conditions

We employ the opposed flow flame-spread configuration in order to examine flame-front instability of diffusion flames near cold, solid boundaries. The thermo-diffusive and hydrodynamic instabilities can transform an initially planar flame front into an irregularly curved, corrugated, possibly fragmented front. Under ordinary 1-g conditions, the buoyancy-induced flow masks the thermo-diffusive and hydrodynamic instabilities and produces planar flames. Such stable spreading flames have been observed for decades in laboratory experiments. Experiments in zero gravity are necessary to produce unstable flame fronts. The thermo-diffusive/hydrodynamic microgravity instability appears in diffusion flames such as, for example: the candle flame oscillations observed by Dietrich et al.; smolder instabilities on a recent Space Shuttle flight. Drs. T. Kashiwagi and S. Olson have attributed the latter to a lowered oxygen transport rate to the hot, reactive surface. Consider a burning surface near the flame extinction limit. The flow, or stretch, induced by the diffusion flame is weak, hence buoyancy plays a small role, thereby enabling previously secondary mechanisms, such as differential thermo-diffusion, to become the most important mechanisms. The flame leading edge becomes unstable; and diffusion flame breakup, oscillation, and rejoining all occur at a measurable frequency of approximately O(1 Hz). This project has only begun in January of this year, 1999. To date, there have been no flight experiments on flame spread instabilities. However, we have made numerous experiments in the NASA 2.2 and 5 second drop towers on flame spread over very thin cellulosic fuels. We have been very fortunate through a combination of factors, to be explained, to obtain some interesting, perhaps even compelling, results on diffusion flame instability in the presence of heat losses to cold surfaces.

Wichman, I. S.↗

NASA NTRS2001

Effects of Flame Structure and Hydrodynamics on Soot Particle Inception and Flame Extinction in Diffusion Flames

This paper summarizes recent studies of the effects of stoichiometric mixture fraction (structure) and hydrodynamics on soot particle inception and flame extinction in diffusion flames. Microgravity experiments are uniquely suited for these studies because, unlike normal gravity experiments, they allow structural and hydrodynamic effects to be independently studied. As part of this recent flight definition program, microgravity studies have been performed in the 2.2 second drop tower. Normal gravity counterflow studies also have been employed and analytical and numerical models have been developed. A goal of this program is to develop sufficient understanding of the effects of flame structure that flames can be "designed" to specifications - consequently, the program name Flame Design. In other words, if a soot-free, strong, low temperature flame is required, can one produce such a flame by designing its structure? Certainly, as in any design, there will be constraints imposed by the properties of the available "materials." For hydrocarbon combustion, the base materials are fuel and air. Additives could be considered, but for this work only fuel, oxygen and nitrogen are considered. Also, the structure of these flames is "designed" by varying the stoichiometric mixture fraction. Following this line of reasoning, the studies described are aimed at developing the understanding of flame structure that is needed to allow for optimum design.

Axelbaum, R. L.↗

NASA NTRS2002

Inducer Hydrodynamic Load Measurement Devices

Marshall Space Flight Center (MSFC) has demonstrated two measurement devices for sensing and resolving the hydrodynamic loads on fluid machinery. The first - a derivative of the six-component wind tunnel balance - senses the forces and moments on the rotating device through a weakened shaft section instrumented with a series of strain gauges. This rotating balance was designed to directly measure the steady and unsteady hydrodynamic loads on an inducer, thereby defining both the amplitude and frequency content associated with operating in various cavitation modes. The second device - a high frequency response pressure transducer surface mounted on a rotating component - was merely an extension of existing technology for application in water. MSFC has recently completed experimental evaluations of both the rotating balance and surface-mount transducers in a water test loop. The measurement bandwidth of the rotating balance was severely limited by the relative flexibility of the device itself, resulting in an unexpectedly low structural bending mode and invalidating the higher-frequency response data. Despite these limitations, measurements confirmed that the integrated loads on the four-bladed inducer respond to both cavitation intensity and cavitation phenomena. Likewise, the surface-mount pressure transducers were subjected to a range of temperatures and flow conditions in a non-rotating environment to record bias shifts and transfer functions between the transducers and a reference device. The pressure transducer static performance was within manufacturer's specifications and dynamic response accurately followed that of the reference.

Skelley, Stephen E.↗

NASA NTRS2002

Inducer Hydrodynamic Load Measurement Devices

Marshall Space Flight Center (MSFC) has demonstrated two measurement devices for sensing and resolving the hydrodynamic loads on fluid machinery. The first - a derivative of the six component wind tunnel balance - senses the forces and moments on the rotating device through a weakened shaft section instrumented with a series of strain gauges. This "rotating balance" was designed to directly measure the steady and unsteady hydrodynamic loads on an inducer, thereby defining both the amplitude and frequency content associated with operating in various cavitation modes. The second device - a high frequency response pressure transducer surface mounted on a rotating component - was merely an extension of existing technology for application in water. MSFC has recently completed experimental evaluations of both the rotating balance and surface-mount transducers in a water test loop. The measurement bandwidth of the rotating balance was severely limited by the relative flexibility of the device itself, resulting in an unexpectedly low structural bending mode and invalidating the higher frequency response data. Despite these limitations, measurements confirmed that the integrated loads on the four-bladed inducer respond to both cavitation intensity and cavitation phenomena. Likewise, the surface-mount pressure transducers were subjected to a range of temperatures and flow conditions in a non-rotating environment to record bias shifts and transfer functions between the transducers and a reference device. The pressure transducer static performance was within manufacturer's specifications and dynamic response accurately followed that of the reference.

Skelley, Stephen E.↗

NASA NTRS2004

Electrochemical and Hydrodynamic Interferences on the Performances of an Oxygen Microsensor with Built-in Electrochemical Microactuator

A concept of novel electrochemical in situ self-calibration technique for an oxygen microsensor has been proposed to devise a convenient calibration method without an externally coupled apparatus. Systemic investigations on the influences of various electrochemical (pH) and hydrodynamic (solution stirring) conditions on the proposed microsensor performances are presented. The results suggest that: 1) The calibrating microenvironments can be manipulated with carefully engineered sensor designs and optimized generating signals; 2) The external oxygen permeable membrane is needed to minimize the electrochemical and hydrodynamic interferences.

Kim, Chang-Soo↗

NASA NTRS2005

Hydrodynamics of Packed Bed Reactor in Low Gravity

Packed bed reactors are well known for their vast and diverse applications in the chemical industry; from gas absorption, to stripping, to catalytic conversion. Use of this type of reactor in terrestrial applications has been rather extensive because of its simplicity and relative ease of operation. Developing similar reactors for use in microgravity is critical to many space-based advanced life support systems. However, the hydrodynamics of two-phase flow packed bed reactors in this new environment and the effects of one physiochemical process on another has not been adequately assessed. Surface tension or capillary forces play a much greater role which results in a shifting in flow regime transitions and pressure drop. Results from low gravity experiments related to flow regimes and two-phase pressure drop models are presented in this paper along with a description of plans for a flight experiment on the International Space Station (ISS). Understanding the packed bed hydrodynamics and its effects on mass transfer processes in microgravity is crucial for the design of packed bed chemical or biological reactors to be used for water reclamation and other life support processes involving water purification.

Motil, Brian J.↗

NASA NTRS2009

Watershed and Hydrodynamic Modeling for Evaluating the Impact of Land Use Change on Submerged Aquatic Vegetation and Seagrasses in Mobile Bay

There is a continued need to understand how human activities along the northern Gulf of Mexico coast are impacting the natural ecosystems. The gulf coast is experiencing rapid population growth and associated land cover/land use change. Mobile Bay, AL is a designated pilot region of the Gulf of Mexico Alliance (GOMA) and is the focus area of many current NASA and NOAA studies, for example. This is a critical region, both ecologically and economically to the entire United States because it has the fourth largest freshwater inflow in the continental USA, is a vital nursery habitat for commercially and recreational important fisheries, and houses a working waterfront and port that is expanding. Watershed and hydrodynamic modeling has been performed for Mobile Bay to evaluate the impact of land use change in Mobile and Baldwin counties on the aquatic ecosystem. Watershed modeling using the Loading Simulation Package in C++ (LSPC) was performed for all watersheds contiguous to Mobile Bay for land use Scenarios in 1948, 1992, 2001, and 2030. The Prescott Spatial Growth Model was used to project the 2030 land use scenario based on observed trends. All land use scenarios were developed to a common land classification system developed by merging the 1992 and 2001 National Land Cover Data (NLCD). The LSPC model output provides changes in flow, temperature, sediments and general water quality for 22 discharge points into the Bay. These results were inputted in the Environmental Fluid Dynamics Computer Code (EFDC) hydrodynamic model to generate data on changes in temperature, salinity, and sediment concentrations on a grid with four vertical profiles throughout the Bay s aquatic ecosystems. The models were calibrated using in-situ data collected at sampling stations in and around Mobile bay. This phase of the project has focused on sediment modeling because of its significant influence on light attenuation which is a critical factor in the health of submerged aquatic vegetation. The impact of land use change on sediment concentrations was evaluated by analyzing the LSPC and EFDC sediment simulations for the four land use scenarios. Such analysis was also performed for storm and non-storm periods. In- situ data of total suspended sediments (TSS) and light attenuation were used to develop a regression model to estimate light attenuation from TSS. This regression model was used to derive marine light attenuation estimates throughout Mobile bay using the EFDC TSS outputs. The changes in sediment concentrations and associated impact on light attenuation in the aquatic ecosystem were used to perform an ecological analysis to evaluate the impact on seagreasses and Submerged Aquatic Vegetation (SAV) habitat. This is the key product benefiting the Mobile Bay coastal environmental managers that integrates the influences of sediments due to land use driven flow changes with the restoration potential of SAVs.

Estes, Maurice G.↗

NASA NTRS2012

Using Remotely Sensed Data and Watershed and Hydrodynamic Models to Evaluate the Effects of Land Cover Land Use Change on Aquatic Ecosystems in Mobile Bay, AL

Alabama coastal systems have been subjected to increasing pressure from a variety of activities including urban and rural development, shoreline modifications, industrial activities, and dredging of shipping and navigation channels. The impacts on coastal ecosystems are often observed through the use of indicator species. One such indicator species for aquatic ecosystem health is submerged aquatic vegetation (SAV). Watershed and hydrodynamic modeling has been performed to evaluate the impact of land cover land use (LCLU) change in the two counties surrounding Mobile Bay (Mobile and Baldwin) on SAV stressors and controlling factors (temperature, salinity, and sediment) in the Mobile Bay estuary. Watershed modeling using the Loading Simulation Package in C++ (LSPC) was performed for all watersheds contiguous to Mobile Bay for LCLU scenarios in 1948, 1992, 2001, and 2030. Remotely sensed Landsat-derived National Land Cover Data (NLCD) were used in the 1992 and 2001 simulations after having been reclassified to a common classification scheme. The Prescott Spatial Growth Model was used to project the 2030 LCLU scenario based on current trends. The LSPC model simulations provided output on changes in flow, temperature, and sediment for 22 discharge points into the estuary. These results were inputted in the Environmental Fluid Dynamics Computer Code (EFDC) hydrodynamic model to generate data on changes in temperature, salinity, and sediment on a grid throughout Mobile Bay and adjacent estuaries. The changes in the aquatic ecosystem were used to perform an ecological analysis to evaluate the impact on SAV habitat suitability. This is the key product benefiting the Mobile Bay coastal environmental managers that integrates the influences of temperature, salinity, and sediment due to LCLU driven flow changes with the restoration potential of SAVs. Data products and results are being integrated into NOAA s EcoWatch and Gulf of Mexico Data Atlas online systems for dissemination to coastal resource managers and stakeholders.

Al-Hamdan, Mohammad Z.↗

NASA NTRS2012

Using Remotely Sensed Data and Watershed and Hydrodynamic Models to Evaluate the Effects of Land Cover Land Use Change on Aquatic Ecosystems in Mobile Bay, AL

Al-Hamdan, Mohammad↗

NASA NTRS2013

Constraints on Decreases in Eta Carinae's Mass-loss from 3D Hydrodynamic Simulations of Its Binary Colliding Winds

Recent work suggests that the mass-loss rate of the primary star Eta-A in the massive colliding wind binary Eta Carinae dropped by a factor of 2-3 between 1999 and 2010. We present result from large- (+/- 1545 au) and small- (+/- 155 au) domain, 3D smoothed particle hydrodynamics (SPH) simulations of Eta Car's colliding winds for three Eta-A mass-loss rates ( (dot-M(sub Eta-A) = 2.4, 4.8 and 8.5 × 10(exp −4) M(solar)/ yr), investigating the effects on the dynamics of the binary wind-wind collision (WWC). These simulations include orbital motion, optically thin radiative cooling and radiative forces. We find that dot-M Eta-A greatly affects the time-dependent hydrodynamics at all spatial scales investigated. The simulations also show that the post-shock wind of the companion star Eta-B switches from the adiabatic to the radiative-cooling regime during periastron passage (Phi approx.= 0.985-1.02). This switchover starts later and ends earlier the lower the value of dot-M Eta-A and is caused by the encroachment of the wind of Eta-A into the acceleration zone of Eta-B's wind, plus radiative inhibition of Eta-B's wind by Eta-A. The SPH simulations together with 1D radiative transfer models of Eta-A's spectra reveal that a factor of 2 or more drop in dot-M EtaA should lead to substantial changes in numerous multiwavelength observables. Recent observations are not fully consistent with the model predictions, indicating that any drop in dot- M Eta-A was likely by a factor of approx. < 2 and occurred after 2004. We speculate that most of the recent observed changes in Eta Car are due to a small increase in the WWC opening angle that produces significant effects because our line of sight to the system lies close to the dense walls of the WWC zone. A modest decrease in dot-M Eta-A may be responsible, but changes in the wind/stellar parameter of Eta-B, while less likely, cannot yet be fully ruled out. We suggest observations during Eta-Car's next periastron in 2014 to further test for decreases in dot-M Eta-A. If dot-M Eta-A is declining and continues to do so, the 2014 X-ray minimum should be even shorter than that of 2009.

Eta Carinae↗

NASA NTRS2013

Sharp Eccentric Rings in Planetless Hydrodynamical Models of Debris Disks

Exoplanets are often associated with disks of dust and debris, analogs of the Kuiper Belt in our solar system. These "debris disks" show a variety of non-trivial structures attributed to planetary perturbations and utilized to constrain the properties of the planets. However, analyses of these systems have largely ignored the fact that, increasingly, debris disks are found to contain small quantities of gas, a component all debris disks should contain at some level. Several debris disks have been measured with a dust-to-gas ratio around unity where the effect of hydrodynamics on the structure of the disk cannot be ignored. Here we report that dust-gas interactions can produce some of the key patterns seen in debris disks that were previously attributed to planets. Through linear and nonlinear modeling of the hydrodynamical problem, we find that a robust clumping instability exists in this configuration, organizing the dust into narrow, eccentric rings, similar to the Fomalhaut debris disk. The hypothesis that these disks might contain planets, though thrilling, is not necessarily required to explain these systems.

debris disks↗

NASA NTRS2005

Frequency-dependent hydrodynamic inductance and the determination of the thermal and quantum noise of a superfluid gyroscope

We reexamine mass flow in a superfluid gyroscope containing a superfluid Josephson weak link. We introduce a frequency-dependent hydrodynamic inductance to account for an oscillatory flow of the normal fluid component in the sensing loop. With this hydrodynamic inductance, we derive the thermal phase noise, and hence the thermal rotational noise of the gyroscope. We examine the thermodynamic stability of the system based on an analysis of the free energy. We derive a quantum phase noise, which is analogous to the zero-point motion of a simple harmonic oscillator. The configuration of the studied gyroscope is analogous to a conventional superconducting RF SQUID. We show that the gyroscope has very low intrinsic noise (1.9x10(-13) rad s(-1)/root Hz), and it can potentially be applied to study general relativity, Earth science, and to improve global positioning systems (GPS).

Penanen, Konstantin↗