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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.

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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Magnetic ground state of La 2 LiMoO 6 : A comparison with other Mo 5+ ( S=1/2 ) double perovskites

La 2 LiMoO 6 is a double perovskite (DP) with P2 1 /n symmetry based on the Mo5+ ion, 4d1, t2g1, S=1/2. It is isostructural with Sr 2 YMoO 6 , the magnetic ground state of which is apparently a very unusual collective spin singlet or valence-bond glass state as is the case for cubic (Fm-3m) Ba 2 YMoO 6 . Initial studies of La 2 LiMoO 6 suggested a different ground state from the other DPs but no clear conclusions could be drawn. A more detailed study is presented here including magnetic susceptibility, heat capacity, and elastic neutron-scattering results. This DP is now well characterized as an antiferromagnet, T N =18K, via observation of magnetic Bragg peaks in neutron scattering and an anomaly in the magnetic heat capacity. The ordering wave vector is k=( 1/21/2 0), consistent with a type I face-centered-cubic magnetic structure, and the ordered moment on Mo 5+ is 0.32(11)μ B , much reduced from the spin-only value of 1μ B . The index, f=|v c |/T N ~3, indicates a low level of frustration. The heat-capacity data above T N can be interpreted in terms of a one-dimensional spin-correlation model, as can the low-temperature data which follow a T 1 power law. This is consistent with an earlier suggestion. The difference with isostructural Sr 2 YMoO 6 is attributed to differences in the local distortion of the Mo–O octahedron and the resulting orbital ordering.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Fluid Physics in a Fluctuating Acceleration Environment

Our program of research aims at developing a stochastic description of the residual acceleration field onboard spacecraft (g-jitter) to describe in quantitative detail its effect on fluid motion. Our main premise is that such a statistical description is necessary in those cases in which the characteristic time scales of the process under investigation are long compared with the correlation time of g-jitter. Although a clear separation between time scales makes this approach feasible, there remain several difficulties of practical nature: (i), g-jitter time series are not statistically stationary but rather show definite dependences on factors such as active or rest crew periods; (ii), it is very difficult to extract reliably the low frequency range of the power spectrum of the acceleration field. This range controls the magnitude of diffusive processes; and (iii), models used to date are Gaussian, but there is evidence that large amplitude disturbances occur much more frequently than a Gaussian distribution would predict. The lack of stationarity does not constitute a severe limitation in practice, since the intensity of the stochastic components changes very slowly during space missions (perhaps over times of the order of hours). A separate analysis of large amplitude disturbances has not been undertaken yet, but it does not seem difficult a priori to devise models that may describe this range better than a Gaussian distribution. The effect of low frequency components, on the other hand, is more difficult to ascertain, partly due to the difficulty associated with measuring them, and partly because they may be indistinguishable from slowly changing averages. This latter effect is further complicated by the lack of statistical stationarity of the time series. Recent work has focused on the effect of stochastic modulation on the onset of oscillatory instabilities as an example of resonant interaction between the driving acceleration and normal modes of the system, and on cavity flow as an example of how an oscillatory response under periodic driving becomes diffusive if the forcing is random instead. This paper describes three different topics that illustrate behavior that is peculiar to a stochastic acceleration field. In the first case, we show that g-jitter can induce effective attractive or repulsive forces between a pair of spherical particles that are suspended in an incompressible fluid of different density provided that the momentum diffusion length is larger than the interparticle separation (as in the case in most colloidal suspensions). Second, a stochastic modulation of the control parameter in the vicinity of a pitchfork or supercritical bifurcation is known not to affect the location of the threshold. We show, however, that resonance between the modulation and linearly stable modes close to onset can lead to a shift in threshold. Finally, we discuss the classical problem of vorticity diffusion away from a plane boundary that is being vibrated along its own plane. Periodic motion with zero average vorticity production results in an exponential decay of the vorticity away from the boundary. Random vibration, on the other hand, results in power law decay away from the boundary even if vorticity production averages to zero.

Drolet, Francois↗
DOE OSTI2021

Compositionally graded Ga 1-x In x P buffers grown by static and dynamic hydride vapor phase epitaxy at rates up to 1 μm/min

Here, we demonstrate Ga 1-x In x P compositionally graded buffers (CGBs) grown on GaAs with lattice constants between GaAs and InP by hydride vapor phase epitaxy (HVPE). Growth rates were up to ~1 μm/min and threading dislocation density (TDD) was as low as 1.0 x 10 6 cm -2 . We studied the effect of substrate offcut direction, growth rate, and strain grading rate on CGB defect structure. We compared the effect of a “dynamic grading” style, which creates compositional interfaces via mechanical transfer of a substrate between two growth chambers, vs. “static grading” where the CGB grows in a single chamber. Dynamic grading yielded smoother grades with higher relaxation, but TDD was not significantly different between the two styles. Substrate offcut direction was the most important factor for obtaining CGBs with low defect density. (001) substrates offcut towards (111)B yielded smoother CGBs with lower TDD compared to CGBs grown on substrates offcut towards (111)A. Transmission electron microscopy of static and dynamic CGBs grown on A and B-offcuts only found evidence of phase separation in a static A-offcut CGB, indicating that the B offcut limits phase separation, which in turn keeps TDD low. Reduced growth rate led to the appearance CuPt-type atomic ordering, which affected the distribution of dislocations on the active glide planes but did not alter TDD. Higher growth rates led to smoother CGBs and did not appreciably increase TDD as otherwise predicted by steady-state models of plastic relaxation. These results show HVPE’s promise for lattice-mismatched applications and low-c ost InP virtual substrates on GaAs

36 MATERIALS SCIENCE↗
DOE OSTI2025

On reduced modelling of the modulational dynamics in magnetohydrodynamics

This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Modeling of the Dust and Gas Outflows from OH 26.5+0.6: The Superwind

We have observed the extreme OH/IR star, OH 26.5+0.6, in the infrared dust continuum and in the sub- millimeter rotational lines of CO. Mid-infrared images reveal the compact nature of the circumstellar shell (less than 0.5 sec). A deep 9.7 microns absorption feature and an absorption at 18 microns show that the dust mass-loss rate is very high. However, the low antenna temperatures of CO J = 1-0 and 2-1 lines suggest that the outer part of the circumstellar shell is much more tenuous. In order to resolve this discrepancy, we have observed the J = 3-2 and 4-3 CO rotational transitions. We have developed a model for the circumstellar shell for OH 26.5 + 0.6 which is consistent with the infrared and submillimeter observations. The dust and gas data are well fitted by a two-shell model, consisting of a dense shell surrounded by a more tenuous shell. The former we identify with the superwind (M = 5.5 x 10(exp -4) solar mass/ yr), and the latter we identify with mass loss on the asymptotic giant branch (AGB) (M = 10(exp -6) solar mass/ yr). The transition between the two mass-loss phases is shown to be rather abrupt ((Delta)t less than 150 yr). Depending on the mass of the progenitor, this superwind phase may be the last thermal pulse (for M(sub *) less than 1.5 solar mass), or the first of a series of the superwind phases (for up to 8 solar mass), punctuated by a period of low mass-loss rates, before the star evolves off the AGB.

Justtanont, K.↗
NASA NTRSDate not supplied

Exoplanet Yield Sensitivity for the Hybrid Lyot Coronagraph from end-to-end modeling for LUVOIR-A

NASA's future direct imaging flagship mission will require telescope mirror segmentation to survey a statistically significant population of nearby stellar systems by increasing aperture size beyond that achieved by traditional space-borne monolithic apertures thus far. Segmentation is a path for the size expansion, but it entails a challenge due to the introduction of temporal pupil discontinuities in terms of both phase and amplitude. Modeling of the integrated performance of the coronagraph with the expected dynamical profile of the telescope is an important step toward realistic estimates of the mission's science yields. We present results of a study using the hybrid Lyot coronagraph with a 15-m on-axis, segmented optical telescope assembly (OTA), akin to that of the Large UV / Optical /Infrared (LUVOIR) mission. We have developed a high-fidelity, end-to-end model as part of the Segmented Coronagraph Design and Analysis (SCDA) study that includes diffractive optical propagations at the 1e-10 contrast level across the optical train including the OTA and intermediate re-imaging optics inside the coronagraph instrument. We perform a sensitivity analysis to assess the contrast sensitivity to wavefront perturbations for a set of key telescope terms including segment-level low-order and mid-spatial frequency aberrations and evaluate expected exoplanet yields obtained in the presence of these sets of aberrations. Industry-provided segment-level wavefront aberration datasets involving the following mechanisms are input to the end-to-end model: (1) thermal gradients and accelerations, and (2) telescope dynamics including line-of-sight and segment jitter. Dynamically averaged PSFs in the presence of aberrations are fed into AYO (Altruistic Yield Optimization), a mission design reference simulator, that then assesses the scientific yield sensitivities.

high-contrast imaging↗
NASA NTRS1993

The three-point function as a probe of models for large-scale structure

The consequences of models of structure formation for higher-order (n-point) galaxy correlation functions in the mildly non-linear regime are analyzed. Several variations of the standard Omega = 1 cold dark matter model with scale-invariant primordial perturbations were recently introduced to obtain more power on large scales, R(sub p) is approximately 20 h(sup -1) Mpc, e.g., low-matter-density (non-zero cosmological constant) models, 'tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, etal. It is shown that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes Q(sub J) at large scales, r is approximately greater than R(sub p). Current observational constraints on the three-point amplitudes Q(sub 3) and S(sub 3) can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.

Frieman, Joshua A.↗
NASA NTRS1976

Flowfield analysis for successive oblique shock wave-turbulent boundary layer interactions

A computation procedure is described for predicting the flowfields which develop when successive interactions between oblique shock waves and a turbulent boundary layer occur. Such interactions may occur, for example, in engine inlets for supersonic aircraft. Computations are carried out for axisymmetric internal flows at M 3.82 and 2.82. The effect of boundary layer bleed is considered for the M 2.82 flow. A control volume analysis is used to predict changes in the flow field across the interactions. Two bleed flow models have been considered. A turbulent boundary layer program is used to compute changes in the boundary layer between the interactions. The results given are for flows with two shock wave interactions and for bleed at the second interaction site. In principle the method described may be extended to account for additional interactions. The predicted results are compared with measured results and are shown to be in good agreement when the bleed flow rate is low (on the order of 3% of the boundary layer mass flow), or when there is no bleed. As the bleed flow rate is increased, differences between the predicted and measured results become larger. Shortcomings of the bleed flow models at higher bleed flow rates are discussed.

Sun, C. C.↗
NASA NTRS1990

Rotation of low-mass stars - A new probe of stellar evolution

Models of stars of various masses and rotational parameters were developed and compared with observations of stars in open clusters of various ages in order to analyze the evolution of rotating stars from the early premain sequence to an age of 1.7 x 10 to the 9th yrs. It is shown that, for stars older than 10 to the 8th yrs and less massive than 1.1 solar mass, the surface rotation rates depend most strongly on the properties of the angular momentum loss. The trends of the currently available observations suggest that the rotation periods are a good indicator of the field-star ages.

Pinsonneault, M. H.↗
NASA NTRS2010

The Spectral Energy Distribution of Fermi Bright Blazars

We have conducted a detailed investigation of the broadband spectral properties of the gamma-ray selected blazars of the Fermi LAT Bright AGN Sample (LBAS). By combining our accurately estimated Fermi gamma-ray spectra with Swift, radio, infra-red, optical, and other hard X-ray /gamma-ray data, collected within 3 months of the LBAS data taking period, we were able to assemble high-quality and quasi-simultaneous spectral energy distributions (SED) for 48 LBAS blazars. The SED of these gamma-ray sources is similar to that of blazars discovered at other wavelengths, clearly showing, in the usual log v-log v Fv representation, the typical broadband spectral signatures normally attributed to a combination of low-energy synchrotron radiation followed by inverse Compton emission of one or more components. We have used these SED to characterize the peak intensity of both the low- and the high-energy components. The results have been used to derive empirical relationships that estimate the position of the two peaks from the broadband colors (i.e., the radio to optical, alpha(sub ro) , and optical to X-ray, alpha(sub ox), spectral slopes) and from the gamma-ray spectral index. Our data show that the synchrotron peak frequency (v(sup S) (sub peak)) is positioned between 10(exp 12.5) and 10(exp 14) Hz in broad-lined flat spectrum radio quasars (FSRQs) and between 10(exp 13) and 10(exp 17) Hz in featureless BL Lacertae objects. We find that the gamma-ray spectral slope is strongly correlated with the synchrotron peak energy and with the X-ray spectral index, as expected at first order in synchrotron-inverse Compton scenarios. However, simple homogeneous, one-zone, synchrotron self-Compton (SSC) models cannot explain most of our SED, especially in the case of FSRQs and low energy peaked (LBL) BL Lacs. More complex models involving external Compton radiation or multiple SSC components are required to reproduce the overall SED and the observed spectral variability. While more than 50% of known radio bright high energy peaked (HBL) BL Lacs are detected in the LBAS sample, only less than 13% of known bright FSRQs and LBL BL Lacs are included. This suggests that the latter sources, as a class, may be much fainter gamma-ray emitters than LBAS blazars, and could in fact radiate close to the expectations of simple SSC models. We categorized all our sources according to a new physical classification scheme based on the generally accepted paradigm for Active Galactic Nuclei and on the results of this SED study. Since the LAT detector is more sensitive to flat spectrum gamma-ray sources, the correlation between v(sup S) (sub peak) and gamma-ray spectral index strongly favors the detection of high energy peaked blazars, thus explaining the Fermi overabundance of this type of sources compared to radio and EGRET samples. This selection effect is similar to that experienced in the soft X-ray band where HBL BL Lacs are the dominant type of blazars.

Abdo, A. A.↗
NASA NTRSDate not supplied

Modeling Measurement Error in Dose-Response Models of Community Annoyance to Low-Noise Supersonic Flight

The primary research goal of the forthcoming NASA Quesst mission community test campaign is to collect representative community response data in support of the development of supersonic overflight noise certification standards. Beginning in 2026, NASA will fly the novel X-59 demonstrator aircraft over select communities in United States in order to demonstrate the possibility of low-noise supersonic flight over land and to collect objective measurements and subjective data on the perceptual experience of this new noise source. It is believed that a regression of a binary perceptual response (‘highly annoyed’ or ‘not’) on estimated noise levels (doses, measured in decibels) will provide a useful dose-response relationship for regulators. However, as these estimated doses will be subject to measurement error, naïve estimators of regression coefficients are inconsistent and slopes may be subject to attenuation bias. In this presentation, I contrast functional modeling of measurement error via simulation extrapolation (SIMEX) with structural Bayesian measurement error models. These methods are applied to available data collected during two NASA risk reduction studies in California in 2011 and Texas in 2018. I’ll conclude noting that in the presence of nonnegligible measurement errors, probabilities of annoyance may be overpredicted for low noise levels and underpredicted for high noise levels, therefore, methods of correcting for measurement error will be necessary to improve the utility of the dose-response relationship for policy-making purposes.

simulation↗
NASA NTRS1973

Flowfield analysis for successive oblique shock wave interactions with a turbulent boundary layer

A computation procedure is described for predicting flow fields which develop when successive interactions between oblique shock waves and a turbulent boundary layer occur. Computations were carried out for axisymmetric internal flows at free stream Mach numbers = 3.82 and 2.82. The effect of boundary layer bleed was considered for the free stream Mach number = 2.82 flow. A control volume analysis is used to predict changes in the flow field across the interactions. Two bleed flow models were considered. A turbulent boundary layer program was used to compute changes in the boundary layer between the interactions. The results given are for flows with two shock wave interactions and for bleed at the second interaction site. In principle the method described may be extended to account for additional interactions. The predicted results are compared with measured results and are shown to be in good agreement when the bleed flow rate is low (on the order of 3 percent of the boundary layer mass flow), or when there is no bleed. As the bleed flow rate is increased, differences between the predicted and measured results become larger. Shortcomings of the bleed flow models at higher bleed flow rates are discussed.

Sun, C. C.↗
NASA NTRS1991

On the reconciliation of simultaneous microwave imaging and hard X-ray observations of a solar flare

Microwave imaging data for a small flare with simultaneous hard X-ray spectral observations are compared. The X-ray data suggest that the power-law index delta of the energy distribution of the radiating electrons is 5.3 (thick-target) which differs significantly from the estimate (delta = 1.4) from a homogeneous optically-thin gyrosynchrotron model which fits the radio observations well. In order to reconcile these results, a double power-law energy spectrum is investigated for the energetic electrons in the flare, as assumed by other authors: the power law is steep at low energies and much flatter at the higher energies which produce the bulk of the microwaves. The emission of soft photons by the flat tail strongly contributes to the observed hard X-ray range and would flatten the spectrum there. A thin-target model for the X-ray emission is also inconsistent with radio data. An inhomogenous gyrosychrotron model with a number of free parameters and containing an electron distribution given by the thick-target X-ray model could be made to fit the radio data.

Nitta, N.↗
NASA NTRS1986

On the magnetic structure of the quiet transition region

Existing models of the quiet chromosphere-corona transition region predict a distribution of emission measure over temperature that agrees with observation for a T greater than about 100,000 K. These 'network' models assume that all magnetic field lines that emerge from the photosphere extend into and are in thermal contact with the corona. It is shown that the observed fine-scale structure of the photospheric magnetic network instead suggests a two-component picture in which magnetic funnels that open into the corona emerge from only a fraction of the network. The gas that makes up the hotter transition region is mostly contained within these funnels, as in standard models, but, because the funnels are more constricted in our picture, the heat flowing into the cooler transition region from the corona is reduced by up to an order of magnitude. The remainder of the network is occupied by a population of low-lying loops with lengths less than about 10,000 km. It is proposed that the cooler transition region is mainly located within such loops, which are magnetically insulated from the corona and must, therefore, be heated internally. The fine-scale structure of ultraviolet spectroheliograms is consistent with this proposal, and theoretical models of internally heated loops can explain the behavior of the emission measure below a T of aobut 100,000 K.

Rabin, D.↗
DOE OSTI2020

Estimating Higher-Order Moments Using Symmetric Tensor Decomposition

In this paper, we consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in machine learning. The dth-order empirical moment tensor of a set of p observations of n variables is a symmetric d-way tensor. Our goal is to nd a low-rank tensor approximation comprising r $\ll$ p symmetric outer products. The challenge is that forming the empirical moment tensor costs O(pn d ) operations and O(n d ) storage, which may be prohibitively expensive; additionally, the algorithm to compute the low-rank approximation costs O(n d ) per iteration. Our contribution is avoiding formation of the moment tensor, computing the low-rank tensor approximation of the moment tensor implicitly using O(pnr) operations per iteration and no extra memory. This advance opens the door to more applications of higher-order moments since they can now be efficiently computed. We present numerical evidence of the computational savings and show an example of estimating the means for higher-order moments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

Magnetic Field Measurement on the C/NOFS Satellite: Geomagnetic Storm Effects in the Low Latitude Ionosphere

The Vector Electric Field Investigation (VEFI) suite onboard the Communications/Navigation Outage Forecasting System (C/NOFS) spacecraft includes a sensitive fluxgate magnetometer to measure DC and ULF magnetic fields in the low latitude ionosphere. The instrument includes a DC vector measurement at 1 sample/sec with a range of +/- 45,000 nT whose primary objective is to provide direct measurements of both V x B and E x B that are more accurate than those obtained using a simple magnetic field model. These data can also be used for scientific research to provide information of large-scale ionospheric and magnetospheric current systems, which, when analyzed in conjunction with the C/NOFS DC electric field measurements, promise to advance our understanding of the electrodynamics of the low latitude ionosphere. In this study, we use the magnetic field data to study the temporal and local time variations of the ring currents during geomagnetic storms. We first compare the in situ measurements with the POMME (the POtsdam Magnetic Model of the Earth) model in order to provide an in-flight "calibration" of the data as well as compute magnetic field residuals essential for revealing large scale external current systems. We then compare the magnetic field residuals observed both during quiet times and during geomagnetic storms at the same geographic locations to deduce the magnetic field signatures of the ring current. As will be shown, the low inclination of the C/NOFS satellite provides a unique opportunity to study the evolution of the ring current as a function of local time, which is particularly insightful during periods of magnetic storms. This paper will present the initial results of this study.

Le, Guan↗
NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗
DOE OSTI2022

$T\overline{T}$-deformed free energy of the Airy model

Sharpening the correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff λ through the $T\overline{T}$ deformation is of interest. To proceed, we simplify the problem by considering the Airy model and deform Airy correlators in the same way as in $T\overline{T}$ -deformed JT gravity. We use those correlators to compute the annealed and quenched free energies for both λ > 0 and λ < 0 from an integral representation of the replica trick. At the leading order in λ and low temperatures, we confirm that the genus-zero quenched free energy monotonically decreases as a function of temperature when perturbation theory is valid. We then study the all-genus quenched free energy at low temperatures, where we discover and discuss subtleties due to non-perturbative effects in the Airy model, as well as the contributions from the non-perturbative branch under the $T\overline{T}$ deformation.

2D gravity↗