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NASA NTRS1980

Strouhal number influence on flight effects on jet noise radiated from convecting quadrupoles

The paper reports a complementary extension of previous work to include the high-frequency features reflected in the discussion of the higher Strouhal number influence on flight effects. It is found that, in addition to the usual features of flight effects on noise from ordinary flows, the high Strouhal number flows exhibit some more interesting features which are uniquely characteristic to them. The additional features are as follows: (1) Flight effects are more favorable to hot jets than to cold jets; (2) the higher the Strouhal number of the jet flow, the lesser the forward arc amplification due to flight; (3) as the Strouhal number increases, the peak amplification angle in the forward quadrant and the peak suppression angle in the aft quadrant move toward 90 deg and get closer, thus reducing the amplification exposure to a constricted angular region; (4) the silence zone is disturbed and displaced from its normal position parallel to the jet flow to give rise to multiple crossings of flight curves with the static line; and (5) the occurrence of multiple crossings is a strange phenomenon solely characteristic of high Strouhal number with high subcritical jet flows in flight.

Dash, R.↗

NASA NTRS2000

Design and Evaluation of a New Boundary-Layer Rake for Flight Testing

A new boundary-layer rake has been designed and built for flight testing on the NASA Dryden Flight Research Center F-15B/Flight Test Fixture. A feature unique to this rake is its curved body, which allows pitot tubes to be more densely clustered in the near-wall region than conventional rakes allow. This curved rake design has a complex three-dimensional shape that requires innovative solid-modeling and machining techniques. Finite-element stress analysis of the new design shows high factors of safety. The rake has passed a ground test in which random vibration measuring 12 g rms was applied for 20 min in each of the three normal directions. Aerodynamic evaluation of the rake has been conducted in the NASA Glenn Research Center 8 x 6 Supersonic Wind Tunnel at Mach 0-2. The pitot pressures from the new rake agree with conventional rake data over the range of Mach numbers tested. The boundary-layer profiles computed from the rake data have been shown to have the standard logarithmic-law profile. Skin friction values computed from the rake data using the Clauser plot method agree with the Preston tube results and the van Driest II compressible skin friction correlation to approximately +/-5 percent.

Bui, Trong T.↗

NASA NTRS2008

Fluorescence Imaging Study of Impinging Underexpanded Jets

An experiment was designed to create a simplified simulation of the flow through a hole in the surface of a hypersonic aerospace vehicle and the subsequent impingement of the flow on internal structures. In addition to planar laser-induced fluorescence (PLIF) flow visualization, pressure measurements were recorded on the surface of an impingement target. The PLIF images themselves provide quantitative spatial information about structure of the impinging jets. The images also help in the interpretation of impingement surface pressure profiles by highlighting the flow structures corresponding to distinctive features of these pressure profiles. The shape of the pressure distribution along the impingement surface was found to be double-peaked in cases with a sufficiently high jet-exit-to-ambient pressure ratio so as to have a Mach disk, as well as in cases where a flow feature called a recirculation bubble formed at the impingement surface. The formation of a recirculation bubble was in turn found to depend very sensitively upon the jet-exit-to-ambient pressure ratio. The pressure measured at the surface was typically less than half the nozzle plenum pressure at low jet pressure ratios and decreased with increasing jet pressure ratios. Angled impingement cases showed that impingement at a 60deg angle resulted in up to a factor of three increase in maximum pressure at the plate compared to normal incidence.

Inman, Jennifer A.↗

NASA NTRS2018

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗

NASA NTRS1979

HF-induced parametric decay in presence of field-aligned irregularities

A nonlinear theory for the saturation of the HF-induced parametric decay instability is formulated in terms of the normal modes of a field-aligned plasma wave duct. Coupling coefficients between modes are derived, and a saturation spectrum is computed numerically for a typical irregularity. The computed spectrum shows that unstable waves may propagate at larger angles to the magnetic field than would be the case in a regular medium. The relevance of this work to the experiment of Muldrew and Showen (1977), concerning the height of the HF-induced plasma line at Arecibo, is discussed. A possible explanation is also found for the 'decay line' feature in comparison with the 'broad bump' in the observed backscatter spectrum.

Rypdal, K.↗

NASA NTRS1981

Ultraviolet observations of hot stars with circumstellar dust shells

Absolute fluxes over the wavelength range 1200-3200 A are presented for 13 normal early-type stars and 12 early-type stars known to have large IR excess; the data were obtained to study the UV spectral modifications produced by absorbing circumstellar dust particles. It is found that all the Be/shell stars whose spectral types are later than B6 exhibit greatly enhanced line absorption due to circumstellar Fe II. The circumstellar gaseous line absorption in stars cooler than B6 severely complicates the study of circumstellar dust absorption. However, those B and A stars that exhibit the circumstellar 9.7-micron emission feature have a very large increase in circumstellar absorption for 1800 A; such absorption is expected from circumstellar silicate particles.

Sitko, M. L.↗

NASA NTRS2000

SeaWinds Scatterometer on QuikSCAT Mission and the Emerging Land and Ocean Applications

Spaceborne scatterometers are active microwave radar instruments designed to acquire near-simultaneous, spatially collocated measurements of the normalized radar backscattering cross section (sigma0) of the global surface from several azimuth and/or incidence angles. The primary objective of the scatterometer mission is to measure the near-surface wind speed and direction over the global ocean using sigma0 measurements together with a wind geophysical model function. However, since sigma0 measurements are collected globally all the time, sigma0 data can also be used for global land and ice applications. In this paper, we will first present the objectives of the QSCAT mission, the instrument design, and the unique features of the Ku-band scatterometer currently in operation, called SeaWinds on QuikSCAT (QSCAT). We will then present some emerging land and ocean applications of the QSCAT data, which include (1) global snow detection and monitoring, (2) melt region mapping on the Greenland ice sheet, (3) Monsoon flood detection and monitoring, (4) soil wetness application at large scale, and (5) hurricane monitoring and tracking.

Tsai, W.-Y.↗

NASA NTRS2003

Touch and gravitropic set-point angle interact to modulate gravitropic growth in roots

Plant roots must sense and respond to a variety of environmental stimuli as they grow through the soil. Touch and gravity represent two of the mechanical signals that roots must integrate to elicit the appropriate root growth patterns and root system architecture. Obstacles such as rocks will impede the general downwardly directed gravitropic growth of the root system and so these soil features must be sensed and this information processed for an appropriate alteration in gravitropic growth to allow the root to avoid the obstruction. We show that primary and lateral roots of Arabidopsis do appear to sense and respond to mechanical barriers placed in their path of growth in a qualitatively similar fashion. Both types of roots exhibited a differential growth response upon contacting the obstacle that directed the main axis of elongation parallel to the barrier. This growth habit was maintained until the obstacle was circumvented, at which point normal gravitropic growth was resumed. Thus, the gravitational set-point angle of the primary and lateral roots prior to encountering the barrier were 95 degrees and 136 degrees respectively and after growing off the end of the obstacle identical set-point angles were reinstated. However, whilst tracking across the barrier, quantitative differences in response were observed between these two classes of roots. The root tip of the primary root maintained an angle of 136 degrees to the horizontal as it traversed the barrier whereas the lateral roots adopted an angle of 154 degrees. Thus, this root tip angle appeared dependent on the gravitropic set-point angle of the root type with the difference in tracking angle quantitatively reflecting differences in initial set-point angle. Concave and convex barriers were also used to analyze the response of the root to tracking along a continuously varying surface. The roots maintained the a fairly fixed angle to gravity on the curved surface implying a constant resetting of this tip angle/tracking response as the curve of the surface changed. We propose that the interaction of touch and gravity sensing/response systems combine to strictly control the tropic growth of the root. Such signal integration is likely a critical part of growth control in the stimulus-rich environment of the soil. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Discipline Plant Biology↗

NASA NTRS2007

Radiation Test Results for a MEMS Microshutter Operating at 60 K

The James Webb Space Telescope (JWST), the successor to the Hubble Space Telescope, is due to be launched in 2013 with the goal of searching the very distant Universe for stars that formed shortly after the Big Bang. Because this occurred so far back in time, the available light is strongly red-shifted, requiring the use of detectors sensitive to the infrared portion of the electromagnetic spectrum. HgCdTe infrared focal plane arrays, cooled to below 30 K to minimize noise, will be used to detect the faint signals. One of the instruments on JWST is the Near Infrared Spectrometer (NIRSPEC) designed to measure the infrared spectra of up to 100 separate galaxies simultaneously. A key component in NIRSPEC is a Micro-Electromechanical System (MEMS), a two-dimensional micro-shutter array (MSA) developed by NASA/GSFC. The MSA is inserted in front of the detector to allow only the light from the galaxies of interest to reach the detector and to block the light from all other sources. The MSA will have to operate at 30 K to minimize the amount of thermal radiation emitted by the optical components from reaching the detector array. It will also have to operate in the space radiation environment that is dominated by the MSA will be exposed to a large total ionizing dose of approximately 200 krad(Si). Following exposure to ionizing radiation, a variety of MEMS have exhibited performance degradation. MEMS contain moving parts that are either controlled or sensed by changes in electric fields. Radiation degradation can be expected for those devices where there is an electric field applied across an insulating layer that is part of the sensing or controlling structure. Ionizing radiation will liberate charge (electrons and holes) in the insulating layers, some of which may be trapped within the insulating layer. Trapped charge will partially cancel the externally applied electric field and lead to changes in the operation of the MEMS. This appears to be a general principle for MEMS. Knowledge of the above principle has raised the concern at NASA that the MSA might also exhibit degraded performance because, i) each shutter flap is a multilayer structure consisting of metallic and insulating layers and ii) the movement of the shutter flaps is partially controlled by the application of an electric field between the shutter flap and the substrate (vertical support grid). The whole mission would be compromised if radiation exposure were to prevent the shutters from opening and closing properly. energetic ionizing particles. Because it is located A unique feature of the MSA is that, as outside the spacecraft and has very little shielding, previously mentioned, it will have to operate at temperatures near 30 K. To date, there are no published reports on how very low temperatures (- 30K) affect the response of MEMS devices to total ionizing dose. Experiments on SiO2 structures at low temperatures (80 K) indicate that the electrons generated by the ionizing radiation are mobile and will move rapidly under the application of an external electric field. Holes, on the other hand, that would normally move in the opposite direction through the SiO2 via a "thermal hopping" process, are effectively immobile at low electric fields as they are trapped close to their generation sites. However, for sufficiently large electric fields (greater than 3 MV/cm) holes are able to move through the SiO2. The larger the field, the more rapidly the holes move. The separation of the electrons and holes leads to a reduced electric field within the insulating layer. To overcome this reduction in electric field, a greater external voltage will have to be applied that alters the normal operation of the device. This report presents the results of radiation testing of the MSA at 60 K. The temperature was higher than the targeted temperature because of a faulty electrical interconnect on the test board. Specifically, our goal was to determine whether the MSA would function propey after a TID of 200 krad(Si).

Rapchun, David A.↗

NASA NTRS2010

Tracing the Inter-Hemispheric Coupling During Polar Summer Periods of 2002-2010 Using TIMED/SABER Measurements

It has been found that for more than one polar summer season between 2002-2010, the northern polar mesospheric region near and above the mesospheric maximum was warmer than normal. The strongest warming effect of this type was observed to occur during northern summer 2002. Theoretical studies have implied that these "anomalies" were preceded by unusual dynamical processes occurring in the southern hemisphere. We have analyzed temperature distributions measured by the SABER limb scanning infrared radiometer aboard the NASA TIMED satellite between 2002-2010 at altitudes from 15 to 110 km and for latitudes between 83 deg. S to 83 deg. N. We describe the approach to trace the inter-hemispheric temperature correlatoins and to identify the global features that were unique for the "anomalous" northern polar summers.

Goldberg, Richard↗

NASA NTRS1976

A normal shock-wave turbulent boundary-layer interaction at transonic speeds

Experimental results, including surveys of the mean and fluctuating flow, and measurements of surface pressure, skin friction, and separation length, are compared with solutions to the Navier-Stokes equations utilizing various algebraic eddy viscosity models to describe the Reynolds shear stresses. The experimental data, obtained at a free-stream Mach number of 1.5 and Reynolds numbers between 10 million and 80 million, show that a separated zone forms near the foot of the shock and that its length is proportional to the initial boundary-layer thickness; that a supersonic region forms downstream of the shock; and that the shear stress increases significantly through the interaction and subsequently decays downstream. The computations adequately represent the qualitative features of the flow field throughout the interaction but quantitatively underpredict the extent of separation and the downstream level of skin friction.

Mateer, G. G.↗

NASA NTRS1976

Ultraviolet absorption lines associated with the Vela supernova remnant

Two stars behind the Vela supernova remnant and two stars offset from the remnant have been observed with the UV spectrometer aboard the Copernicus satellite. Over 200 interstellar atomic and molecular absorption features between 1000 and 1400 A have been identified and measured for radial velocity and equivalent width. In many cases, additional information was obtained by studying the detailed shapes of the recorded profiles. Most of the stars show several absorption components, with clouds of the highest radial velocity appearing in the spectra of stars behind the remnant. For each component, column densities were derived using velocity dispersion parameters which yielded the most self-consistent results. Qualitatively, the gas toward the remnant exhibits a number of unusual properties, when compared with normal interstellar material. First, abnormally high radial velocities were evident. Second, the degree of ionization of some elements suggested the existence of ionizing processes significantly more potent than those found in general regions of space. Finally, an investigation of electron densities shows that much of the gas, especially that at high velocity, must exist in the form of relatively thin sheets or filaments. If cosmic abundances prevail, the column densities of high-velocity excited material suggest that H-alpha emission measures could be as large as 100 sq cm/cu pc.

Jenkins, E. B.↗

NASA NTRS1985

AC motor and generator requirements for isolated WECS

After surveying electrically driven loads used on productive farms, the investigators chose three pumps for testing at voltages and frequencies far outside the normal operating range. These loads extract and circulate water and move heat via air, and all are critical to farm productivity. The object was to determine the envelope of supply voltage and frequency over which these loads would operate stably for time intervals under 1 hour. This information is among that needed to determine the feasibility of supplying critical loads, in case of a utility outage, from a wind driven alternator whose output voltage and frequency will vary dramatically in most continental wind regimes. Other related work is surveyed. The salient features and limitations of the test configurations used and the data reduction are described. The development of simulation models suitable for a small computer are outlined. The results are primarily displayed on the voltage frequency plane with the general conclusion that the particular pump models considered will operate over the range of 50 to 90 Hz and a voltage band which starts below rated, decreases as frequency decreases, and is limited on the high side by excessive motor heating. For example, centrifugal pump operating voltage ranges as extensive .4 to 1.4 appear possible. Particular problems with starting, stalling due to lack of motor torque, high speed cavitation, and likely overheating are addressed in a listing of required properties for wind driven alternators and their controllers needed for use in the isolated or stand alone configuration considered.

Park, G. L.↗

NASA NTRS1990

Amplification of a high-frequency electromagnetic wave by a relativistic plasma

The amplification of a high-frequency transverse electromagnetic wave by a relativistic plasma component, via the synchrotron maser process, is studied. The background plasma that supports the transverse wave is considered to be cold, and the energetic component whose density is much smaller than that of the background component has a loss-cone feature in the perpendicular momentum space and a finite field-aligned drift speed. The ratio of the background plasma frequency squared to the electron gyrofrequency squared is taken to be sufficiently larger than unity. Such a parameter regime is relevant to many space and astrophysical situations. A detailed study of the amplification process is carried out over a wide range of physical parameters including the loss-cone index, the ratio of the electron mass energy to the temperature of the energetic component, the field-aligned drift speed, the normalized density, and the wave propagation angle.

Yoon, Peter H.↗

NASA NTRS1999

The Effects of Partial Mechanical Loading and Ibandronate on Skeletal Tissues in the Adult Rat Hindquarter Suspension Model for Microgravity

We report initial data from a suspended rat model that quantitatively relates chronic partial weightbearing to bone loss. Chronic partial weightbearing is our simulation of the effect of limited artificial gravity aboard spacecraft or reduced planetary gravity. Preliminary analysis of bone by PQCT, histomorphometry, mechanical testing and biochemistry suggest that chronic exposure to half of Earth gravity is insufficient to prevent severe bone loss. The effect of episodic full weightbearing activity (Earth Gravity) on rats otherwise at 50% weightbearing was also explored. This has similarity to treatment by an Earth G-rated centrifuge on a spacecraft that normally maintained artificial gravity at half of Earth G. Our preliminary evidence, using the above techniques to analyze bone, indicate that 2 hours daily of full weightbearing was insufficient to prevent the bone loss observed in 50% weightbearing animals. The effectiveness of partial weightbearing and episodic full weightbearing as potential countermeasures to bone loss in spaceflight was compared with treatment by ibandronate. Ibandronate, a long-acting potent bisphosphonate proved more effective in preventing bone loss and associated functionality based upon structure than our first efforts at mechanical countermeasures. The effectiveness of ibandronate was notable by each of the testing methods we used to study bone from gross structure and strength to tissue and biochemistry. These results appear to be independent of generalized systemic stress imposed by the suspension paradigm. Preliminary evidence does not suggest that blood levels of vitamin D were affected by our countermeasures. Despite the modest theraputic benefit of mechanical countermeasures of partial weightbearing and episodic full weightbearing, we know that some appropriate mechanical signal maintains bone mass in Earth gravity. Moreover, the only mechanism that correctly assigns bone mass and strength to oppose regionally specific force applied to bone is mechanical, a process based upon bone strain. Substantial evidence indicates that the specifics of dynamic loading i.e. time-varying forces are critical. Bone strain history is a predictor of the effect that mechanical conditions have on bone structure mass and strength. Using servo-controlled force plates on suspended rats with implanted strain gauges we manipulated impact forces of ambulation in the frequency (Fourier) domain. Our results indicate that high frequency components of impact forces are particularly potent in producing bone strain independent of the magnitude of the peak force or peak energy applied to the leg. Because a servo-system responds to forces produced by the rat's own muscle activity during ambulation, the direction of ground-reaction loads act on bone through the rat's own musculature. This is in distinction to passive vibration of the floor where forces reach bone through the natural filters of soft tissue and joints. Passive vibration may also be effective, but it may or may not increase bone in the appropriate architectural pattern to oppose the forces of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of the rat forelimb as a transfer function between impact force and bone strain to predict optimal dynamic loading conditions for this system. We plan additional studies of mechanical counter-measures that incorporate improved dynamic loading, features relevant to anticipated evaluation of artificial gravity, exercise regimens and exposure to Martian gravity, The combination of mechanical countermeasures with ibandronate will also be investigated for signs of synergy.

Schultheis, Lester W.↗

NASA NTRS1992

Structural review of the Vredefort dome

The structure of the older-than-3.2-Ga Archean basement and Archean-to-Precambrian sedimentary/volcanic rocks (3.07 to ca. 2.2 Ga) in the center of the Witwatersrand Basin to the southwest of Johannesburg (South Africa) is dominated by the ca. 2.0-Ga megascopic Vredefort 'Dome' structure. The effect of the 'Vredefort event' is demonstrably large and is evident within a northerly arc of about 100 km radius around the granitic core of the structure. Northerly asymmetric overturning of the strata is observed within the first 17 km (strata is horizontal in the south), followed by a 40-km-wide rim synclinorium. Fold and fault structures (normal, reverse, and strike-slip) are locally as well as regionally concentrically arranged with respect to the northern and western sides of the structure. The unusual category of brittle deformation, the so-called 'shock deformation', observed in the collar strata has attracted worldwide attention over the past two decades. These deformation phenomena include the presence of coesite and stishovite, mylonites, and pseudotachylites, cataclasis at a microscopic scale, and the ubiquitous development of multiply striated joint surfaces (which include shatter cones, orthogonal, curviplanar, and conjugate fractures). The macroscopic to microscopic deformation features have led to the formulation of various hypotheses to account for the origin of the Vredefort structure: (1) tectonic hypotheses--deep crustal shear model, doming and N-directed thrust fault model, fold interference model, and diapir model; (2) the exogenous bolide impact hypothesis; and (3) the endogenous cryptoexplosion model.

Colliston, W. P.↗

NASA NTRS1993

Functional patterns in an annual grassland during an AVIRIS overflight

This study relates Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) imagery to ground measurements of vegetation distribution, physiology, and productivity at Stanford University's Jasper Ridge Biological Preserve. Primary efforts focused on a 9-ha region of annual grassland where we completed a detailed ground-based study in conjunction with a 15 May 1991 AVIRIS overflight. Spectral mixture analysis and the normalized difference vegetation index (NDVI) calculated from AVIRIS data were used to evaluate spatial patterns of vegetation type, productivity, and potential physiological activity. Concurrent ground sampling revealed a high degree of correlation between NDVI and estimates of canopy chemistry, structure, productivity, and CO2 flux, supporting the use of imaging spectrometry to estimate spatial and temporal trends in vegetation physiology and productivity in this relatively simple grassland ecosystem. Geostatistical analyses of both ground and AVIRIS data supported the conclusion that the AVIRIS pixel size was suitable for describing the influence of major landscape features in this grassland and that spatial detail would be lost at slightly larger pixel sizes typical of other imaging spectrometers.

Gamon, John A.↗

NASA NTRS1997

Characteristics of Seamounts Near Hawaii as Viewed by GLORIA

Using images and data acquired from the GLORIA sonar system, 390 seamounts within the U.S. Hawaiian Exclusive Economic Zone (HEEZ) off Hawaii have been studied. Their diameters range from 1 to 57 km. with most less than 15 km. Seamount abundance increases exponentially with decreasing size. The areal density of observed seamounts having diameters greater than 1 km is 182/10(exp 6) sq km. The theoretical abundance of seamounts of all sizes normalized to a unit area is (309 +/- 17)/10(exp 6) sq km, about an order of magnitude less than other surveyed areas of the Pacific. This may reflect a lower abundance of Cretaceous seamounts in this region, the covering of small seamounts by sediment, or discrepancies from the use of different data sets to derive the abundance statistics. The seamounts have morphologies ranging from steep-sided, flat-topped structures to cones to more amorphous structures; they are similar to volcanoes found elsewhere on the seafloor. A suite of secondary features associated with the seamounts includes summit craters, summit mounds, coalesced boundaries, landslides, and graben. Several seamount chains are aligned parallel to Cretaceous fracture zones, consistent with an origin close to the ancestral East Pacific Rise. Others are aligned parallel to the Necker Ridge, suggesting that they formed contemporaneously with Necker in the plate interior. This observation, together with high abundances of seamounts where other intraplate igneous processes have occurred, suggests some seamounts formed since leaving the spreading center.

Bridges, Nathan T.↗