Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “polar vortex”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Ferroelectric switching pathways and domain structure of SrBi 2 ⁢(Ta,Nb) 2 ⁢O 9 from first principles

Several families of layered perovskite oxide ferroelectrics exhibit a coupling between polarization and structural order parameters, such as octahedral rotation distortions. This coupling provides opportunities for novel electric field-based manipulation of material properties, and it also stabilizes complex domain patterns and domain-wall vortices. Among layered perovskites with such coupled orders, the Aurivillius-phase oxides SrBi 2 ⁢B 2 ⁢O 9 (B = Ta,Nb) are well-known for their excellent room-temperature ferroelectric performance. This work combines group theoretic analysis with density functional theory calculations to examine the ferroelectric switching processes of SrBi2⁢B2⁢O9. Low-energy two-step ferroelectric switching paths are identified, with polarization reversal facilitated by structural order-parameter rotations. Analysis of the domain structure reveals how the relative energetics of the coupled order parameters translates into a network of several distinct domain-wall types linked by domain-wall vortex structures. Comparisons are made between the ferroelectric switching and domain structure of SrBi 2 ⁢B 2 ⁢O 9 and those of the layered n = 2 Ruddlesden-Popper hybrid improper ferroelectrics. The results provide insight into how ferroelectric properties may be optimized by engineering the complex crystal structures of Aurivillius-phase oxides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1979

Effects of spanwise blowing on the surface pressure distribution and vortex-lift characteristics of a trapezoidal wing-strake configuration

The effects of spanwise blowing on the surface pressures of a 44 deg swept trapezoidal wing-strake configuration were measured. Wind tunnel data were obtained at a free stream Mach number of 0.26 for a range of model angle of attack, jet thrust coefficient, and nozzle chordwise location. Results showed that spanwise blowing delayed the leading edge vortex breakdown to larger span distances and increased the lifting pressures. Vortex lift was achieved at span stations immediately outboard of the strake-wing junction with no blowing, but spanwise blowing was necessary to achieve vortex lift at increased span distances. Blowing on the wing in the presence of the strake was not as effective as blowing on the wing alone. Spanwise blowing increased lift throughout the angle-of-attack range, improved the drag polars, and extended the linear pitching moment to higher values of lift. The leading edge suction analogy can be used to estimate the effects of spanwise blowing on the aerodynamic characteristics.

Campbell, J. F.↗
NASA NTRS2014

Seasonal Evolution of Saturn's Polar Temperatures and Composition

The seasonal evolution of Saturn's polar atmospheric temperatures and hydrocarbon composition is derived from a decade of Cassini Composite Infrared Spectrometer (CIRS) 7-16 micrometers thermal infrared spectroscopy. We construct a near-continuous record of atmospheric variability poleward of 60 deg from northern winter/southern summer (2004, Ls = 293 deg) through the equinox (2009, Ls= 0 deg) to northern spring/southern autumn (2014, Ls = 56 deg). The hot tropospheric polar cyclones that are entrained by pro-grade jets within 2-3 deg of each pole, and the hexagonal shape of the north polar belt, are both persistent features throughout the decade of observations. The hexagon vertices rotated westward by approx. equal to 30 deg longitude between March 2007 and April 2013, confirming that they are not stationary in the Voyager-defined System III longitude system as previously thought. Tropospheric temperature contrasts between the cool polar zones (near 80-85 deg) and warm polar belts (near 75-80 deg) have varied in both hemispheres, resulting in changes to the vertical wind shear on the zonal jets in the upper troposphere and lower stratosphere. The extended region of south polar stratospheric emission has cooled dramatically poleward of the sharp temperature gradient near 75 deg S (by approximately -5 K/yr), coinciding with a depletion in the abundances of acetylene (0030 +/- 0.005 ppm/yr) and ethane (0.35 +/- 0.1 ppm/yr), and suggestive of stratospheric upwelling with vertical wind speeds of w approx. equal to +0.1 mm/s. The upwelling appears most intense within 5 deg latitude of the south pole. This is mirrored by a general warming of the northern polar stratosphere (+5 K/yr) and an enhancement in acetylene (0.030 +/- 0.003 ppm/yr) and ethane (0.45 +/- 0.1 ppm/yr) abundances that appears to be most intense poleward of 75 deg N, suggesting subsidence at w approx. equal to -0.15 mm/ s. However, the sharp gradient in stratospheric emission expected to form near 75 deg N by northern summer solstice (2017, Ls = 90 deg) has not yet been observed, so we continue to await the development of a northern summer stratospheric vortex. The peak stratospheric warming in the north occurs at lower pressure levels (p less than 1 mbar) than the peak stratospheric cooling in the south (p greater than 1 mbar). Vertical motions are derived from both the temperature field (using the measured rates of temperature change and the deviations from the expectations of radiative equilibrium models) and hydrocarbon distributions (solving the continuity equation). Vertical velocities tend towards zero in the upper troposphere where seasonal temperature contrasts are smaller, except within the tropospheric polar cyclones where w approx. equal to +0.02 mm/s. North polar minima in tropospheric and stratospheric temperatures were detected in 2008-2010 (lagging one season, or 6-8 years, behind winter solstice); south polar maxima appear to have occurred before the start of the Cassini observations (1-2 years after summer solstice), consistent with the expectations of radiative climate models. The influence of dynamics implies that the coldest winter temperatures occur in the 75-80 deg region in the stratosphere, and in the cool polar zones in the troposphere, rather than at the poles themselves. In addition to vertical motions, we propose that the UV-absorbent polar stratospheric aerosols entrained within Saturn's vortices contribute significantly to the radiative budget at the poles, adding to the localized enhancement in the south polar cooling and north polar warming poleward of +/-75 deg.

polar temperatures↗
NASA NTRS1984

An evaluation of the relative merits of wing-canard, wing-tail, and tailless arrangements for advanced fighter applications

Two sets of wind tunnel tests were performed to examine the relative merits of wing-canard, wing-tail and tailless configurations for advanced fighters. Both sessions focused on variable camber using automated, prescheduled leading and trailing edge flap positioning. The trials considered a modified F-16 tail and canard configuration at subsonic, transonic and supersonic speeds, a 60 deg delta wing sweep, a 44 deg leading edge trapezoidal wing at subsonic and supersonic speeds, vortex flow effects, and flow interactions in the canard-wing-tail-tailless variations. The results showed that large negative stabilities would need to be tolerated in wing-canard arrangements to make them competitive with wing-tail arrangements. Subsonic polar shapes for canard and tailless designs were more sensitive to static design margins than were wing-tail arrangements. Canards provided better stability at supersonic speeds. The static margin limits were a critical factor in control surface selection. Finally, a tailless delta wing configuration exhibited the lowest projected gross take-off weight and drag values.

Nicholas, W. U.↗
NASA NTRS1985

Configuration of the high-latitude thermosphere neutral circulation for IMF B(y) negative and positive

Asymmetries in the Northern Hemisphere neutral circulation that are dependent on the sign of the east-west 'B(y)' component of the IMF are presently illustrated by measurements of the neutral wind in the polar F-region which were conducted by the DE-2 spacecraft. The data thus obtained are categorized according to the sign of the hourly averaged IMF B(y) component measured by ISEE-3 for the hour preceding the DE-2 measurements. It is noted that there is (1) an asymmetry in the polar cap neutral flow velocity, with the region of most rapid antisunward flow shifting from the dawn side to the dusk side of the polar cap as B(y) changes from positive to negative; (2) a shift occurs in the magnetic local time of the region of entry of neutral gas into the polar cap, from a location on the dawn side of the moon-midnight meridian for B(y) positive to one more biased, for B(y) negative; and (3) there is an enhancement of velocities associated with the dawn anticlockwise neutral vortex for B(y) negative relative to those observed for B(y) positive.

Mccormac, F. G.↗
NASA NTRS1990

Noise of a simulated installed model counterrotation propeller at angle-of-attack and takeoff/approach conditions

Two modern high-speed advanced counterrotation propellers, F7/A7 and F7/A3 were tested in the NASA Lewis Research Center's 9- by 15-Foot Anechoic Wind Tunnel at simulated takeoff/approach conditions of 0.2 Mach. Both rotors were of similar diameter on the F7/A7 propeller, while the aft diameter of the F7/A3 propeller was 85 percent of the forward propeller to reduce tip vortex-aft rotor interaction. The two propellers were designed for similar performance. The propellers were tested in both the baseline configuration and installed configuration consisting of a simulated upstream nacelle support pylon and fuselage section. Acoustic measurements were made with a polar microphone probe which recorded sideline directivities at various azimuthal locations. Aerodynamic measurements were also made to establish propeller operating conditions. The propellers were run at initial blade setting angles adjusted to achieve equal forward/aft torque ratios at angle of attack with the pylon and fuselage simulation in place. Data are presented for propeller operation at 80 and 90 percent of design speed (the forward rotor design tip speed was 238 m/sec (780 ft/sec). Both propellers were tested at the maximum rotor-rotor spacing of 14.99 cm (5.90 in.) based on the pitch change axis separation.

Woodward, Richard P.↗
NASA NTRS1990

The 1989 Antarctic ozone hole as observed by TOMS

In 1989 the Total Ozone Mapping Spectrometer (TOMS) aboard the Nimbus 7 satellite observed the springtime decrease in Antarctic total ozone for the 11th consecutive year. The 1989 minimum values of total ozone measured by TOMS declined throughout the month of September at a rate nearly identical to 1987. The area of the ozone hole as defined by the 220 DU contour grew rapidly during early September. It reached a mid-September peak of 7.5 percent of the Southern Hemisphere, or 19 million square kilometers, essentially the same as observed in 1987. From mid-October through November 1989, minimum polar total ozone values increased and the area within the 220 DU contour decreased more rapidly than during the comparable period of 1987. The more rapid erosion of the 1989 ozone hole resulted from strong wave number one perturbations of the vortex dynamics in late October.

Stolarski, Richard S.↗
NASA NTRS2012

On the Influence of North Pacific Sea Surface Temperature on the Arctic Winter Climate

Differences between two ensembles of Goddard Earth Observing System Chemistry-Climate Model simulations isolate the impact of North Pacific sea surface temperatures (SSTs) on the Arctic winter climate. One ensemble of extended winter season forecasts is forced by unusually high SSTs in the North Pacific, while in the second ensemble SSTs in the North Pacific are unusually low. High Low differences are consistent with a weakened Western Pacific atmospheric teleconnection pattern, and in particular, a weakening of the Aleutian low. This relative change in tropospheric circulation inhibits planetary wave propagation into the stratosphere, in turn reducing polar stratospheric temperature in mid- and late winter. The number of winters with sudden stratospheric warmings is approximately tripled in the Low ensemble as compared with the High ensemble. Enhanced North Pacific SSTs, and thus a more stable and persistent Arctic vortex, lead to a relative decrease in lower stratospheric ozone in late winter, affecting the April clear-sky UV index at Northern Hemisphere mid-latitudes.

Hurwitz, Margaret M.↗
NASA NTRS1988

Synoptic and chemical evolution of the Antarctic vortex in winter and spring, 1987

The dynamical evolution of the vortex at least up to 50 mb is dominated by synoptic scales in the troposphere. In particular, there is a clear response when poleward extension of tropospheric anticyclones from latitudes of 40 and 50 S to 70 and 80 S occurs. This response is evident in isentropic potential vorticity maps, TOMS ozone fields and SAM II polar stratospheric clouds. An important feature of the high latitude Southern Hemisphere lower stratosphere is a transition at potential temperatures in the 390 to 400 K range. This transition, the vortopause, is clearly marked in aircraft profiles of O3, H2O, N2O and ClO at latitudes 68 to 72 S near the Antarctic peninsula, and also cross-sections of potential vorticity and potential temperature; above it, the isopleths are more closely spaced than below it. The aircraft measurements of H2O, O3, NO sub y, N2O, ClO, and whole air data are examined in material coordinates, theta and P sub theta, backed up by trajectory analysis. The evolution of the chemical mixing ratios is examined in these coordinates as a function of time from mid-August to late September. Conclusions are drawn about the rates of change and their causes. The meteorological and aircraft data are examined for evidence of the following kinds of motion with respect to the vortex: ingress of air aloft, subsidence, peeling off of air to lower latitudes, and folding of the vortopause. Conclusions are presented regarding the evidence for a chemical sink of ozone above and below theta = 400 K, and whether the vortex has a mass flow through it, or if the chemical sink operates on a fixed mass of air. Implications for mid-latitudes are briefly considered in the light of the conclusions.

Tuck, A. F.↗
NASA NTRS2019

Saturn Atmospheric Dynamics One Year After Cassini: Long-Lived Features and Time Variations in the Drift of the Hexagon

We examine Saturn's atmospheric dynamics with observations in the visible range from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018 obtaining drift rates of major meteorological systems from the equator to the North polar hexagon. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until September is analyzed elsewhere [Sanchez-Lavega et al., 2019]. Many of the regular cloud features visible in 2018 are long-lived and can be identified in Saturn images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting long-lived cloud systems are: i) A bright white spot in the Equatorial Zone that can be tracked continuously since 2014 with minimal changes in its zonal velocity, which was 444:3 +or- 3:1 ms(exp -1) in 2014 and 452:4 + or - 1:7 ms(exp -1) in 2018. This velocity is remarkably different from the zonal winds at the cloud level at its latitude during the Cassini mission, and is closer to zonal winds obtained at the time of the Voyagers flybys and to zonal winds from Cassini VIMS infrared images of the lower atmosphere. ii) A large long-lived Anticyclone Vortex, here AV, that formed after the Great White Spot of 2010-2011. This vortex has changed significantly in visual contrast, drift rate and latitude with minor changes in size over the last years. iii) A system of subpolar vortices at latitudes 60-65N present at least since 2011. These vortices and additional atmospheric features here studied follow drift rates consistent with zonal winds obtained by Cassini. We also present a study of the positions of the vertices of Saturn's North polar hexagon from 2015 to 2018. These measurements are compared with previous analyses during the Cassini mission (2007-2014), observations with HST in the 90s, and data from the Voyagers in 1980-1981 to explore the long term variability of the hexagon's drift rate. We find variations in the drift rate of the hexagon through these epochs that can not be fit by seasonal changes in the polar area. Instead, the different drift rates reinforce the role of the North Polar Spot that was present in the Voyager epoch and in the early 90s to cause a faster drift rate of the hexagon at that time compared with the current slower one.

R Hueso↗
DOE OSTI2020

Vortices with magnetic field inversion in noncentrosymmetric superconductors

Superconducting materials with noncentrosymmetric lattices lacking space inversion symmetry exhibit a variety of interesting parity-breaking phenomena, including the magneto-electric effect, spin-polarized currents, helical states, and the unusual Josephson effect. In this paper, we demonstrate, within a Ginzburg-Landau framework describing noncentrosymmetric superconductors with O point group symmetry, that vortices can exhibit an inversion of the magnetic field at a certain distance from the vortex core. In stark contrast to conventional superconducting vortices, the magnetic-field reversal in the parity-broken superconductor leads to non-monotonic intervortex forces, and, as a consequence, to the exotic properties of the vortex matter such as the formation of vortex bound states, vortex clusters, and the appearance of metastable vortex/anti-vortex bound states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Plasma heating, electric fields and plasma flow by electron beam ionospheric injection

The electric fields and the floating potentials of a Plasma Diagnostics Payload (PDP) located near a powerful electron beam injected from a large sounding rocket into the auroral zone ionosphere have been studied. As the PDP drifted away from the beam laterally, it surveyed a region of hot plasma extending nearly to 60 m radius. Large polarization electric fields transverse to B were imbedded in this hot plasma, which displayed large ELF wave variations and also an average pattern which has led to a model of the plasma flow about the negative line potential of the beam resembling a hydrodynamic vortex in a uniform flow field. Most of the present results are derived from the ECHO 6 sounding rocket mission.

Winckler, J. R.↗
NASA NTRS1994

Measurements of stratospheric odd nitrogen at Arrival Heights, Antarctica, in 1991

An FTIR spectrometer was installed at Arrival Heights, Antarctica (78 deg S, 167 deg E) in February 1991 to measure the evolution of stratospheric HNO3 during the year. In particular, it was the intention to make the first observations of HNO3 trends during autumn, concurrently with ongoing measurements of column NO2 made with a grating spectrometer. The time-series of NO2 in the Antarctic shows a rapid decline in the column amount during autumn, and a slow recovery in spring, as the photochemical conditions move the species to and from higher storage reservoirs. The new nitric acid data show for the first time that during autumn the vertical column increases from approximately 1.9 x 10(exp 16) molecule cm(exp -2) at day 30 to approximately 3.1 x 10(exp 16) molecule cm(exp -2) by day 100. When the sun returns in spring, it is found that the column amount has fallen to about half the value at the end of autumn. Spring amounts are variable, but as found in the data from previous years remain low inside the vortex. The autumn increase is attributed to the heterogeneous conversion of N2O5 to gas-phase HNO3 on background aerosols. Low nitric acid column amounts at the start of spring suggest that the HNO3 has moved from the gas to the condensed phase on polar stratospheric clouds with the advent of low temperatures during the polar night.

Keys, J. Gordon↗
NASA NTRS2006

MHD Flow Visualization of Magnetopause and Polar Cusps Vortices

Detailed analysis of Wind, Geotail, and Cluster data shows how magnetopause boundary and polar cusps vortices associated with high speed streams can be a carrier of energy flux to the Earth s magnetosphere. For our analysis time interval, March 29 . - April 5 2002, the Interplanetary Magnetic Field (IMF) is primarily northward and MHD simulations of vortices along the flanks within nine hours of the time interval suggest that a Kelvin Helmholtz (KH) instability is likely present. Vortices were classified by solar wind input provided by the Wind satellite located 70-80 RE upstream from Earth. We present statistics for a total of 304 vortices found near the ecliptic plane on the magnetopause flanks, 273 with northward IMF and 31 with southward IMF. The vortices generated under northward IMF were more driven into the dawnside than into the duskside, being substantially more ordered on the duskside. Most of the vortices were large in scale, up to 10 RE, and with a rotation axis closely aligned with the ZGSE direction. They rotated preferentially clockwise on the dawnside, and. counter-clockwise on the duskside. Those generated under southward IMF were less ordered, fewer in number, and also smaller in diameter. Significant vortex activity occurred on the nightside region of the magnetosphere for these southward cases in contrast to the northward IMF cases on which most of the activity was driven onto the magnetopause flanks. Magnetopause crossings seen by the Geotail spacecraft for the time interval were analyzed and compared with the MHD simulation to validate our results. Vortices over the polar cusps are also being analyzed and the simulation results will be compared to the multi-point measurements of the four Cluster satellites.

Collado-Vega, Y. M.↗
DOE OSTI2022

Interfacial magnetic vortex formation in exchange-coupled hard-soft magnetic bilayers

The exchange coupling between a hard magnetic layer MnBi and a soft magnetic layer Co-Fe has been found to significantly improve the maximum energy product. In this work, the spin structure of exchange coupled MnBi:Co-Fe bilayers is experimentally investigated by X-ray magnetic circular dichroism (XMCD) and polarized neutron reflectometry (PNR). We find that the out-of-plane magnetization reversal process of the MnBi:Co-Fe bilayer structure involves formation of a curling-type twisting of the magnetization in the film plane at low or intermediate reversal fields. Additionally, micromagnetic simulations are further performed to provide a detailed view of the spins at the curling center. Reminiscent of chiral spin structures known as spin bobbers, this curling in the exchange-coupled hard-soft magnetic bilayers is a new type of skyrmionic spin structure and worth further investigation.

36 MATERIALS SCIENCE↗
NASA NTRS2007

MHD Flow Visualization of Magnetopause and Polar Cusps Vortices

Detailed analysis of Wind, Geotail, and Cluster data shows how magnetopause boundary and polar cusps vortices associated with high speed streams can be a carrier of energy flux to the Earth's magnetosphere. For our analysis time interval, March 29 . - April 5 2002, the Interplanetary Magnetic Field (IMF) is primarily northward and MHD simulations of vortices along the flanks within nine hours of the time interval suggest that a Kelvin Helmholtz (KH) instability is likely present. Vortices were classified by solar wind input provided by the Wind satellite located 70-80 RE upstream from Earth. We present statistics for a total of 304 vortices found near the ecliptic plane on the magnetopause flanks, 273 with northward IMF and 31 with southward IMF. The vortices generated under northward IMF were more driven into the dawnside than into the duskside, being substantially more ordered on the duskside. Most of the vortices were large in scale, up to 10 RE, and with a rotation axis closely aligned with the Z(sub GSE) direction. They rotated preferentially clockwise on the dawnside, and. counter-clockwise on the duskside. Those generated under southward IMF were less ordered, fewer in number, and also smaller in diameter. Significant vortex activity occurred on the nightside region of the magnetosphere for these southward cases in contrast to the northward IMF cases on which most of the activity was driven onto the magnetopause flanks. Magnetopause crossings seen by the Geotail spacecraft for the time interval were analyzed and compared with the MHD simulation to validate our results. Vortices over the polar cusps are also being analyzed and the simulation results will be compared to the multi-point measurements of the four Cluster satellites.

Collado-Vega, Y. M.↗
DOE OSTI2022

Atomic Scale Crystal Field Mapping of Polar Vortices in Oxide Superlattices

Polar vortices in oxide superlattices can be utilized as potential candidates for data storage applications due to their unique polarization topologies. The structure and dipole arrangement in polar vortices has been studied via X-ray scattering techniques, (scanning) transmission electron microscopy ((S)/TEM) and computational calculations. However, the fundamental correlation between the atomic structure and the electronic structure (which is manifested in the chemical bonding) has heretofore not been explored. Further, The hybridization between nominally empty $\textit{d}$ orbitals on the B-site with the occupied O 2$\textit{p}$ orbitals favors the condensation of a polar (ferroelectric) state in $\textit{AB}$O 3 perovskite oxides. The complex, continuously rotating local polarization texture of the vortices, in turn, can result in especially intricate $\textit{d}$- orbital interactions. Soft X-ray spectroscopy can probe these interactions at the transition metal $\textit{L}$-edge, but these techniques do not have the spatial resolution to resolve variations within one vortex (~5 nm region). Electron energy loss spectroscopy (EELS) in the STEM mode uses inelastically scattered electrons to probe the core-shell excitations (empty density of states) of transition metals at atomic resolution.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1994

Four years of ground-based total ozone measurements by visible spectrometry in Antarctica

Visible spectrometers SAOZ have been developed at Service d'Aeronomie for permanent ground-based ozone monitoring at all latitudes up to the polar circle in winter. Observations are made by looking at the sunlight scattered at zenith in the visible range, twice a day, at sunrise and sunset. Compared to ozone observations in the UV generally in use, visible observations in the small Chappuis bands at twilight have the advantages of being independent of stratospheric temperature, little contaminated by tropospheric ozone and multiple scattering, and of permitting observations even in winter at the polar circle. SAOZ instruments have been installed since 1988 at several stations in the Antarctic and the Arctic. More than four years data at Dumont d'Urville in Terre Adelie (67 deg S) are now available. The station is generally located at the edge of the vortex in spring and therefore the ozone hole is seen there only occasionally. The lowest values (140 DU) were reported in early October 1991. According to these first regular observations throughout the whole winter ozone seems to increase in late autumn and winter. Its decay does not start before the end of August. Although of smaller amplitude than with the previous version five data, the ratio between the groundbased and satellite/TOMS measurements displays a systematic seasonal variation correlated partly to the sun zenith angle of observations from orbit and partly to the temperature of the stratosphere. Since ground-based measurements are always made at 90 deg SZA, the SZA dependence must come from the satellite data interpretation (TOMS observations are between 43 to 88 deg SZA). The temperature dependence could be partly due to variations of ozone absorption cross-sections in the ultraviolet used by the satellite spectrometer, and partly to a systematic seasonal cycle of the air mass factor use in the interpretation of the ground based observations. However, the last contribution appears to be too small to compensate the ozone increase in winter reported by SAOZ, which is then real.

Goutail, F.↗