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At least 1,657 records · Page 92
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NASA NTRS2019

Exploration of Failure and Potential Damage Markers in Ti-6Al-4V

To improve prognostics for predicting component life, coupon tests were conducted on Ti-6Al-4V to investigate the development of damage. Various test types were employed (tension, creep, stress relaxation, and fatigue) under a wide range of temperatures and loading rates to engage various amounts of time-dependent and damage behavior. Both stiffness degradation and Poisson’s ratio were monitored to see if they were useful in indicating the initiation and accumulation of damage and subsequently the onset of failure. Stiffness exhibited large decreases with increasing strain when calculated using engineering stress and strain. However, minimal stiffness change was observed when using the true-stress and true- strain values. Detailed microscopy and image analysis were performed to document the actual physical damage that occurred within the various specimens. Two types of damage were observed: shallow surface cracks and internal pores. The severity of damage was greater in the region of localized necking and diminished further away from the neck. The area fraction of pores was higher in the necked region, yet even there it did not exceed more than a few percent and, in most cases, was significantly lower. It was observed that conditions that induced more time-dependent deformation (e.g., slower strain rate testing) resulted in a larger number of pores and larger pore sizes. The pores were always found to occur in the softer β-phase. The severity of observed damage was inconsistent with the large drop in engineering stiffness, but was more aligned with stiffness changes from the true-stress and -strain values. Poisson’s ratio was monitored on every test and showed promise as a damage indicator. It was found to be more sensitive than either the ultimate tensile strength or the inception of tertiary creep. However, calculation of Poisson’s ratio was found to be more involved than expected because of anisotropy and the presence of strain gradients along the specimen at large applied strains. First, the material had a moderate texture and resulted in anisotropy of the strains. Second, the evolution of Poisson’s ratio as a function of axial strain showed strange and unexpected behaviors, which necessitated more extensive analyses of its development. This led to an investigation on the use of small versus large strain approaches and the importance of making consistent measurements; that is, axial and transverse strain measurements over the same volume of material. Additionally, finite element analysis of a tensile sample indicated that non- uniform strain occurred in the sample prior to attaining the maximum strength. This, along with the location at which transverse strain was measured, had a significant influence on the resulting values of Poisson’s ratio. Based on this, lessons learned are offered for future testing.

Ti-6Al-4V↗
NASA NTRS1991

An experimental study of natural and forced modes in an axisymmetric jet

The experiment consisted of two parts. The first part was an effort to study naturally occurring instability modes in the axisymmetric shear layer of a high Reynolds number turbulent jet. Untripped (transitional) and tripped (turbulent) nozzle exit conditions, both with 0.1 percent core turbulence, were studied. For the turbulent nozzle exit boundary layer case, the core turbulence, was varied systematically from 0.1 to 5 percent of the jet exit velocity. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes grew rapidly but dominated only downstream of the potential core region. For the jet excited by natural disturbances, the energy content of the higher order modes (m is less than 1) was significantly lower than that of the axisymmetric and m = +/-1 modes. The initial boundary layer had a profound effect on the natural jet evolution and its excitability. The shorter potential core allowed the jet in the transitional case to support helical disturbances closer the nozzle exit than the turbulent case. The natural jet evolution was found to remain unaffected for varying initial core turbulence over the range of 0.15 to 5 percent of the jet velocity. Target modes for efficient excitation of the jet were determined from the results of the naturally occurring jet instability mode experiments. The second part of this work describes an effort to control the axisymmetric shear layer by artificially exciting target modes. Under optimum conditions, two-frequency excitation is indeed more effective than single frequency plane wave excitation as far as jet mixing is concerned. At high amplitudes of fundamental and subharmonic forcing, the subharmonic augmentation and the axial location of the peak were independent of the initial phase difference. Two-frequency excitation also has its limitations, since axisymmetric waves are damped beyond the potential core. Higher spreading rates are obtained when multi-modal forcing is applied.

Raman, Ganesh↗
NASA NTRS1995

Analysis of plasma measurements for the Geotail mission

The first phase of the Geotail mission, an exploration of the distant magnetotail, was successfully concluded in October 1994. Geotail is currently engaged in a survey of plasmas at distances from Earth approximately 10 to 30 R(sub E). Throughout the mission the Comprehensive Plasma Instrumentation has functioned well with successful return of data. The analysis of the CPI measurements has resulted in a series of publications, and research efforts are ongoing. Research topics include interaction of the magnetotail with the fields and plasmas of the solar wind, steady-state magnetic reconnection in the distant magnetotail at a neutral line bounded by a pair of slow-mode magnetohydrodynamic shocks, development and evolution of plasmoids in magnetotail and magnetospheric substorms, and cold ion beams coexisting as distinct components in the presence of hot plasma-sheet plasmas.

Frank, Louis A.↗
NASA NTRS1997

Measuring the 511 keV emission in the direction of 1E1740.7-2942 with BATSE

Observations of the 511 keV emission in the direction of 1E 1740.7-2942 (1E) using the earth burst and transient source experiment (BATSE) onboard the Compton Gamma Ray Observatory (CGRO), are presented. The CGRO phase 1 average spectrum of 1E is calculated using a method which assumes that a given source spectrum is the sum of the flux coming directly from the object and the contribution from the surrounding diffuse emission. The 1E light curve is calculated in the 40 to 150 keV range. It presents a constant flux excess of 70 mCrab in comparison with observations from the SIGMA gamma ray telescope onboard the GRANAT observatory. By removing this contribution, the 1E spectral transition from the low state to the high standard state observed by SIGMA is confirmed, and it is shown that the 511 keV flux is independent of the 1E long term evolution from low state to high standard state. It is concluded that the 511 keV emission of (4.2 +/- 1.3) x 140(exp -4) photons/sq cm s observed in the direction of 1E is mainly diffuse and spatially extended.

Wallyn, P.↗
NASA NTRS2001

EGIS - An Environmental GIS Developed for NASA Field Center Applications

As the principal center for Environmental Geographic Information Systems (EGIS), the John C. Stennis Space Center (SSC), located in Hancock County, Mississippi, has been assigned technical support requirements to design and to implement a basic EGIS data base for all NASA Field Centers. The intent of this Phase I effort is to produce a baseline EGIS data base incorporating newly available remotely sensed data as well as existing environmental data. A example application of the use of the data base at Stennis Space Center will be to illustrate baseline environmental conditions for consideration with proposed propulsion test stand development and operation. To effectively answer questions related to environmental issues at each center, organization of the data layers and sources will include the following categories: Cadastral/Geodetic; Geopolitical; Hydrography; Infrastructure; Physical Geography; Socioeconomic; Remote Sensing Imagery; Associated Metadata. As part of a Phase II effort, site-specific data and applications will be implemented and added to the data base at each Field Center. This poster illustrates the framework of the design and implementation of a basic EGIS data base. Shown are example data sources, hardware and software, and data base delivery and installation. The poster also depicts future recommendations for a centrally located server to house each of the NASA Field Center data bases. The server will allow real-time data base updates with additional layers and models for each center. Expansion of the EGIS data base will continue to grow as site-specific applications are developed addressing the ongoing evolution of environmental concerns at all NASA Field Centers.

Smoot, James↗
NASA NTRS1983

Voyager 2 observations of Saturn's northern mid-latitude cloud features - Morphology, motions, and evolution

Voyager 2 images provide a basis for detailed study of the morphology and circulation of Saturn's northern midlatitudes. Both Saturn's large-scale cloud bands and the distribution of its local cloud features have a characteristic zonal organization. The region between 30 N and 45 N contains two oppositely directed jets in close proximity, with many bright, active features in the westward jet, and an unusual ribbonlike wave feature encircling the planet in the eastward jet. Several of the smaller features within the westward jet do not remain at fixed latitudes and interact with each other. One group of v-shaped features is found to have periods of high activity correlated with the passage of a cyclonic bright spot. The ribbon wave was Fourier analyzed to determine its spectral composition. The greatest power is near wave number 9, with significant additional peaks appearing at planetary wave numbers 19, 25-27, 35-38, and 47-51. The phase velocity increases with wave number but is not well described by a Rossby-Haurwitz dispersion relation. The curvature of the mean wind profile obtained from cloud tracking indicates that the westward jet exceeds the standard barotropic instability condition, while the eastward jet marginally exceeds the deep-circulation instability condition of Ingersoll and Pollard (1982). The rms eddy velocities on Saturn are less than half as large as those observed on Jupiter.

Sromovsky, L. A.↗
NASA NTRS1990

Steepening of kinetic magnetosonic waves into shocklets - Simulations and consequences for planetary shocks and comets

The generation and the nonlinear evolution of oblique low-frequency electromagnetic (kinetic magnetosonic) waves which were observed upstream of planetary bow shocks and at the Giacobini-Zinner comet, and referred to as shocklets, were investigated using an electromagnetic hybrid code. The observations show that the waves, which have a sinusoidal form when their amplitude is small, become steepened and linearly polarized as they grow in amplitude. The results of simulations show the original small-amplitude elliptically polarized wave grows and steepens, so that its polarization changes and becomes somewhat linear. The steepening process is associated with the coherent generation of a broad spectrum of waves on the magnetosonic whistler branch, which propagate at various phase and group velocities. It is shown that the presence of shocklets upstream of a planetary bow shock can modify its local structure by changing the solar wind Mach number and temperature, or by colliding with the shock.

Omidi, N.↗
NASA NTRS1998

A Compendium of Wind Statistics and Models for the NASA Space Shuttle and Other Aerospace Vehicle Programs

The wind profile with all of its variations with respect to altitude has been, is now, and will continue to be important for aerospace vehicle design and operations. Wind profile databases and models are used for the vehicle ascent flight design for structural wind loading, flight control systems, performance analysis, and launch operations. This report presents the evolution of wind statistics and wind models from the empirical scalar wind profile model established for the Saturn Program through the development of the vector wind profile model used for the Space Shuttle design to the variations of this wind modeling concept for the X-33 program. Because wind is a vector quantity, the vector wind models use the rigorous mathematical probability properties of the multivariate normal probability distribution. When the vehicle ascent steering commands (ascent guidance) are wind biased to the wind profile measured on the day-of-launch, ascent structural wind loads are reduced and launch probability is increased. This wind load alleviation technique is recommended in the initial phase of vehicle development. The vehicle must fly through the largest load allowable versus altitude to achieve its mission. The Gumbel extreme value probability distribution is used to obtain the probability of exceeding (or not exceeding) the load allowable. The time conditional probability function is derived from the Gumbel bivariate extreme value distribution. This time conditional function is used for calculation of wind loads persistence increments using 3.5-hour Jimsphere wind pairs. These increments are used to protect the commit-to-launch decision. Other topics presented include the Shuttle Shuttle load-response to smoothed wind profiles, a new gust model, and advancements in wind profile measuring systems. From the lessons learned and knowledge gained from past vehicle programs, the development of future launch vehicles can be accelerated. However, new vehicle programs by their very nature will require specialized support for new databases and analyses for wind, atmospheric parameters (pressure, temperature, and density versus altitude), and weather. It is for this reason that project managers are encouraged to collaborate with natural environment specialists early in the conceptual design phase. Such action will give the lead time necessary to meet the natural environment design and operational requirements, and thus, reduce development costs.

Smith, O. E.↗
NASA NTRS1998

Magnetic Field Configuration of Active Region NOAA 6555 at the Time of a Long Duration Flare on 23 March 1991: An Exception to Standard Flare Reconnection Model

The high-resolution H(sub alpha) images observed during the decay phase of a long duration flare on 23 March 1991 are used to study the three-dimensional magnetic field configuration of the active region NOAA 6555. Whereas, all the large flares in NOAA 6555 occurred at the location of high magnetic shear and flux emergence, this long duration flare was observed in the region of low magnetic shear at the photosphere. The H(sub alpha) loop activity started soon after the maximum phase of the flare. There were few long loop at the initial phase of the activity. Some of these were sheared in the chromosphere at an angle of about 45 deg with the east-west axis. Gradually, increasing number of shorter loops, oriented along the east-west axis, started appearing. The chromospheric Dopplergrams show blue-shifts at the end points of the loops. By using different magnetic field models, we have extrapolated the photospheric magnetograms to the chromospheric heights. The magnetic field lines computed by using the potential field model correspond to most of the observed H(sub alpha) loops. The height of the H(sub alpha) loops were derived by comparing them with the computed field lines. From the temporal evolution of the H(sub alpha) loop activity, we derive the negative rate of appearance of H(sub alpha) features as a function of height. It is found that the field lines oriented along one of the neutral lines was sheared and low lying. The higher field lines were mostly potential. The paper also outlines a possible scenario for describing the post-flare stage of the observed long duration flare.

Choudhary, Debi Prasad↗
NASA NTRS2000

Experimental Study of Lunar and SNC Magmas

The research described in this progress report involved the study of petrological, geochemical and volcanic processes that occur on the Moon and the SNC parent body, generally accepted to be Mars. The link between these studies is that they focus on two terrestrial-type parent bodies somewhat smaller than earth, and the fact that they focus on the role of volatiles in magmatic processes and on processes of magma evolution on these planets. The work on the lunar volcanic glasses has resulted in some exciting new discoveries over the years of this grant. During the tenure of the present grant, we discovered a variety of metal blebs in the A17 orange glass. Some of these Fe-Ni metal blebs occur in the glass; others were found in olivine phenocrysts which we find make up about 2 vol % of the orange glass magma. The importance of these metal spheres is that they fix the oxidation state of the parent magma during the eruption, and also indicate changes during the eruption. They also yield important information about the composition of the gas phase present, the gas which drove the lunar fire-fountaining. In an Undergraduate senior thesis project, Nora Klein discovered a melt inclusion that remained in a glassy state in one of the olivine phenocrysts. Analyses of this inclusion gave additional information on the CO2, CO and S contents of the orange glass magma prior to its reaching the lunar surface. The composition of lunar volcanic gases has long been one of the puzzles of lunar magmatic processes. One of the more exciting findings in our research over the past year has been the study of magmatic processes linking the SNC meteorite source magma composition with the andesitic composition rocks found at the Pathfinder site. In this project, graduate student Michelle Minitti showed that there was a clear petrologic link between these two magma types via fractional removal of crystals from the SNC parent melt, but the process only worked if there was at least 1 wt % dissolved water in the melt.

Rutherford, Malcolm J.↗
NASA NTRS2012

GX 3+1: The Stability of Spectral Index as a Function of Mass Accretion Rate

We present an analysis of the spectral and timing properties observed in X-rays from neutron star (NS) binary GX 3+1 (4U 1744-26) during long-term transitions between the faint and bright phases superimposed on short-term transitions between lower banana (LB) and upper banana (UB) branches in terms of its color-color diagram, We analyze all observations of this source obtained with the Rossi X-ray Timing Explorer and BeppoSAX satellites, We find that the X-ray broadband energy spectra during these spectral transitions can be adequately reproduced by a composition of a low-temperature blackbody component, a Comptonized component (COMPTB), and Gaussian component We argue that the electron temperature kTe of the Compton cloud monotonically increases from 2.3 keY to 4.5 keY, when GX 3+1 makes a transition from UB to LB. We also detect an evolution of noise components (a very low frequency noise and a high-frequency noise) during these LB-UB transitions. Using a disk seed photon normalization of COMPTB, which is proportional to the mass accretion rate, we find that the photon power-law index Gamma is almost constant (Gamma = 2.00 +/- 0.02) when mass accretion rate changes by factor four. In addition, we find that the emergent spectrum is dominated by the strong Comptonized component We interpret this quasi-stability of the index Gamma and a particular form of the spectrum in the framework of a model in which the energy release in the transition layer located between the accretion disk and NS surface dominates that in the disk. Moreover, this index stability effect now established for GX 3+ I was previously found in the atoll source 4U 1728-34 and suggested for a number of other low-mass X-ray NS binaries. This intrinsic behavior of NSs, in particular for atoll sources, is fundamentally different from that seen in black hole binary sources where the index monotonically increases during spectral transition from the low state to the high state and then finally saturates at high values of mass accretion rate.

Seifana, Elena↗
NASA NTRS1972

Stellar evolution of high mass based on the Ledoux criterion for convection

Theoretical evolutionary sequences of models for stars of 15 and 30 solar masses were computed from the zero-age main sequence to the end of core helium burning. During the earliest stages of core helium depletion, the envelope rapidly expands into the red-supergiant configuration. At 15 solar mass, a blue loop on the H-R diagram ensues if the initial metals abundance, initial helium abundance, or C-12 + alpha particle reaction rate is sufficiently large, or if the 3-alpha reaction rate is sufficiently small. These quantities affect the opacity of the base of the outer convection zone, the mass of the core, and the thermal properties of the core. The blue loop occurs abruptly and fully developed when the critical value of any of these quantities is exceeded, and the effective temperature range and fraction of the lifetime of core helium burning during the slow phase of the blue loop vary surprisingly little. At 30 solar mass no blue loop occurs for any reasonable set of input parameters.

Stothers, R.↗
NASA NTRS2020

Historical (1850‐2014) Aerosol Evolution and Role on Climate Forcing Using the GISS Modele2.1 Contribution to CMIP6

The Earth’s climate is rapidly changing. Over the past centuries, aerosols, via their ability to absorb or scatter solar radiation and alter clouds, played an important role in counterbalancing some of the greenhouse gas (GHG) caused global warming. The multi-century anthropogenic aerosol cooling effect prevented present-day climate from reaching even higher surface air temperatures and subsequent more dramatic climate impacts. Trends in aerosol concentrations and optical depth show that in many polluted regions such as Europe and the United States of America, aerosol precursor emissions decreased back to levels of the 1950s. More recent polluting countries such as China may have reached a turning point in recent years as well, while India still follows an upward trend. Here we study aerosol trends in the CMIP6 simulations of the GISS ModelE2.1 climate model using a fully coupled atmosphere composition onfiguration, including interactive gas-phase chemistry, and either an aerosol microphysical (MATRIX) or a mass-based (OMA) aerosol module. Results show that whether global aerosol radiative forcing is already declining depends on the aerosol scheme used. Using the aerosol microphysical scheme, where the aerosol system reacts more strongly to the trend in sulfur dioxide (SO2) emissions, global peak direct aerosol forcing was reached in the 1980’s, whereas the mass-based scheme simulates peak direct aerosol forcing around 2010.

Aerosol forcing↗
NASA NTRS2010

DSD Characteristics of a Mid-Winter Tornadic Storm Using C-Band Polarimetric Radar and Two 2D-Video Disdrometers

Drop size distributions in an evolving tornadic storm are examined using C-band polarimetric radar observations and two 2D-video disdrometers. The E-F2 storm occurred in mid-winter (21 January 2010) in northern Alabama, USA, and caused widespread damage. The evolution of the storm occurred within the C-band radar coverage and moreover, several minutes prior to touch down, the storm passed over a site where several disdrometers including two 2D video disdrometers (2DVD) had been installed. One of the 2DVDs is a low profile unit and the other is a new next generation compact unit currently undergoing performance evaluation. Analyses of the radar data indicate that the main region of precipitation should be treated as a "big-drop" regime case. Even the measured differential reflectivity values (i.e. without attenuation correction) were as high as 6-7 dB within regions of high reflectivity. Standard attenuation-correction methods using differential propagation phase have been "fine tuned" to be applicable to the "big drop" regime. The corrected reflectivity and differential reflectivity data are combined with the co-polar correlation coefficient and specific differential phase to determine the mass-weighted mean diameter, Dm, and the width of the mass spectrum, (sigma)M, as well as the intercept parameter , Nw. Significant areas of high Dm (3-4 mm) were retrieved within the main precipitation areas of the tornadic storm. The "big drop" regime assumption is substantiated by the two sets of 2DVD measurements. The Dm values calculated from 1-minute drop size distributions reached nearly 4 mm, whilst the maximum drop diameters were over 6 mm. The fall velocity measurements from the 2DVD indicate almost all hydrometeors to be fully melted at ground level. Drop shapes for this event are also being investigated from the 2DVD camera data.

Thurai, M.↗
NASA NTRS2013

Tropical Atlantic Dust and Smoke Aerosol Variations Related to the Madden-Julian Oscillation in MODIS and MISR Observations

In this study, Moderate Resolution Imaging Spectroradiometer (MODIS) fine mode fraction and Multi-angle Imaging SpectroRadiometer (MISR) nonspherical fraction data are used to derive dust and smoke aerosol optical thickness (T(sub dust) and T(sub smoke)) over the tropical Atlantic in a complementary way: due to its wider swath, MODIS has 3-4 times greater sampling than MISR, but MISR dust discrimination is based on particle shape retrievals, whereas an empirical scheme is used for MODIS. MODIS and MISR show very similar dust and smoke winter climatologies. T(sub dust) is the dominant aerosol component over the tropical Atlantic, accounting for 40-70 percent of the total aerosol optical thickness (AOT), whereas T(sub smoke) is significantly smaller than T(sub dust). The consistency and high correlation between these climatologies and their daily variations lends confidence to their use for investigating the relative dust and smoke contributions to the total AOT variation associated with the Madden-Julian Oscillation (MJO). The temporal evolution and spatial patterns of the τdus anomalies associated with the MJO are consistent between MODIS and MISR: the magnitude of MJO-realted T(sub dust) anomalies is comparable to or even larger than that of the total T, while the T(sub smoke) anomaly represents about 15 percent compared to the total, which is quite different from their relative magnitudes to the total T on the climatological time scale. This suggests that dust and smoke are not influenced by the MJO in the same way. Based on correlation analysis, dust is strongly influenced by the MJO-modulated trade wind and precipitation anomalies, and can last as long as one MJO phase, whereas smoke is less affected.

Madden-Julian Oscillation↗
NASA NTRS2020

NICER Observations Reveal that the X-ray Transient MAXI J1348-630 is a Black Hole X-ray Binary

We studied the outburst evolution and timing properties of the recently discovered X-ray transient MAXI J1348−630 as observed with NICER. We produced the fundamental diagrams commonly used to trace the spectral evolution, and power density spectra to study the fast X-ray variability. The main outburst evolution of MAXI J1348−630 is similar to that commonly observed in blackhole transients. The source evolved from the hard state (HS), through hard- and soft-intermediate states, into the soft state in the outburst rise, and back to the HS in reverse during the outburst decay. At the end of the outburst, MAXI J1348−630 underwent two reflares with peak fluxes approximately one and two orders of magnitude fainter than the main outburst, respectively. During the reflares, the source remained in the HS only, without undergoing any state transitions, which is similar to the so-called ‘failed outbursts’. Different types of quasi-periodic oscillations (QPOs) are observed at different phases of the outburst. Based on our spectral-timing results, we conclude that MAXI J1348−630 is a black hole candidate.

L Zhang↗
NASA NTRS1972

The evolution of water vapor in the atmosphere of Venus.

Examination of the feasibility of loss of water vapor from the Venus atmosphere, assuming H2O as the sole initial constituent. A steady-state model is constructed, and the photochemistry establishes the distribution of important products in the upper atmosphere. Calculations of exospheric temperatures yield values as high as 100,000 K. Such large temperatures result from the large abundance of atomic hydrogen in the exosphere, and imply a dynamic outflow of all constituents from the upper region of the atmosphere. Such an outflow would cause the escape of all hydrogen and some of the oxygen resulting from dissociation of H2O. Little loss of CO2 would result, due to its low abundance in the upper region, permitting its accumulation to the present observed value. It is concluded that if Venus formed from the same mix of materials as the earth, much tectonic activity and fairly rapid outgassing must have occurred during the early phase of its history to account for the loss of water vapor.

Smith, L. L.↗
NASA NTRS2008

Evolution of Indarch (EH4 Chondrite) at 1 GPa and High Temperature

The chondritic meteorites are materials that are as old as the solar system itself characterized by variations in bulk chemical and oxidation state, and have long been considered possible building blocks that accreted to form the terrestrial inner planets. Enstatite chondrites contain nearly FeO free enstatite, silicon-rich kamacite and various sulfides indicating formation under highly reducing conditions. These materials could have participated in the formation of the Earth. However, "fingerprinting" of meteoritic materials has shown that no known meteoritic class corresponds to a hypothetical bulk Earth composition in every aspect. To derive constraints on early accretion and differentiation processes and possibly resolve the debate on the formation of the Earth, it is required to study experimentally a variety of chondritic materials and investigate their melting relations and elemental partitioning behavior at variable pressure (P), temperature (T) and oxygen fugacities (fO2). Variations in fO2 can indeed change chemical features and phase equilibria dramatically. The P-T phase diagrams of peridotites and carbonaceous chondrites have been extensively studied experimentally up to pressures and temperatures corresponding to the transition zone and lower mantle. Even though partial melting experiments have been conducted at ambient pressure on the enstatite chondrite Indarch, enstatite meteorites have never been experimentally investigated at high PT. The following investigation focuses on the effect of the fO2 on the phase relations of Indarch, an EH4 chondrite.

Berthet, S.↗