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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 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Symmetry-mediated quantum coherence of W 5+ spins in an oxygen-deficient double perovskite

Elucidating the factors limiting quantum coherence in real materials is essential to the development of quantum technologies. Here we report a strategic approach to determine the effect of lattice dynamics on spin coherence lifetimes using oxygen deficient double perovskites as host materials. In addition to obtaining millisecond T 1 spin-lattice lifetimes at T ~ 10 K, measurable quantum superpositions were observed up to room temperature. We determine that T 2 enhancement in Sr 2 CaWO 6-δ over previously studied Ba 2 CaWO 6-δ is caused by a dynamically-driven increase in effective site symmetry around the dominant paramagnetic site, assigned as W 5+ via electron paramagnetic resonance spectroscopy. Further, a combination of experimental and computational techniques enabled quantification of the relative strength of spin-phonon coupling of each phonon mode. This analysis demonstrates the effect of thermodynamics and site symmetry on the spin lifetimes of W 5+ paramagnetic defects, an important step in the process of reducing decoherence to produce longer-lived qubits.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The critical role of soil moisture in compound hazards

Soil moisture regulates the exchange of energy, water, and carbon across land–vegetation–atmosphere interfaces. Extremes in soil moisture can amplify natural hazards through interactions with diverse Earth system processes. Despite its mechanistic importance, soil moisture remains underrepresented in hazard research and predictive frameworks. Here, in this study, we review our current understanding of the role of soil moisture in the evolution and onset of diverse compound hazards by synthesizing the latest findings from observational and modelling studies. We highlight key soil moisture mechanisms, including atmospheric feedbacks that amplify drought–heatwave–wildfire events, precipitation couplings that promote clustered storms, and threshold responses that drive vegetation die-offs, trigger landslides, and induce flooding. Persistent challenges in observational data, model representation and operational implementation have limited the integration of soil moisture into hazard early-warning systems. Addressing these gaps through advances in observations, data assimilation, and physics-based and data-driven modelling will enhance hazard prediction and preparedness in a rapidly changing world.

Li, Chuxuan [University of California, Los Angeles↗
DOE OSTI2026

Efficiency-optimized relativistic plasma harmonics for extreme fields

Bright harmonic radiation from relativistically oscillating laser plasmas offers a direct route for generating extreme electromagnetic fields. Theory predicts that under optimized conditions, the plasma medium can support strong spatiotemporal compression of laser energy in a coherent harmonic focus (CHF), delivering intensity boosts many orders of magnitude greater than the incident driving laser pulse. Although diffraction-limited performance (spatial compression) and attosecond phase locking (temporal compression) have been demonstrated experimentally, efficient coupling of relativistically intense laser pulse energy into the emitted harmonic cone has not been realized so far. Here we demonstrate that this highly nonlinear interaction can be tailored to deliver the maximum conversion efficiencies predicted from simulations. By fine-tuning the temporal profile of the driving laser on sub-picosecond (<10 −12 s) timescales, energies >9 mJ between the 12th and 47th harmonics are observed. These results are in agreement with the theoretically expected efficiency dependence on harmonic order, verifying that optimal conditions have been achieved in the generation process. This is the important final element required to achieve the expected intensity boosts from a CHF in experiments. Although obtaining spatiotemporal compression and optimal efficiency simultaneously remains challenging, the path to realizing extreme optical field strengths approaching the critical field of quantum electrodynamics (the Schwinger limit at >10 16 V cm −1 or >10 29 W cm −2 ) is now open, permitting all-optical studies of the quantum vacuum and new frontiers for intense attosecond science.

High-harmonic generation↗
DOE OSTI2020

Predicting Microstructural Void Nucleation in Discontinuous Fiber Composites through Coupled in-situ X-ray Tomography Experiments and Simulations

Composite materials have become widely used in engineering applications, in order to reduce the overall weight of structures while retaining their required strength. In this work, a composite material consisting of discontinuous glass fibers in a polypropylene matrix is studied at the microstructural level through coupled experiments and simulations, in order to uncover the mechanisms that cause damage to initiate in the microstructure under macroscopic tension. Specifically, we show how hydrostatic stresses in the matrix can be used as a metric to explain and predict the exact location of microvoid nucleation that occurs during damage initiation within the composite’s microstructure. Furthermore, this work provides evidence that hydrostatic stresses in the matrix can lead to coupled microvoid nucleation and early fiber breakage, and that small fragments of fibers can play an important role in the process of microvoid nucleation. These results significantly improve our understanding of the mechanics that drive the initiation of damage in the complex microstructures of discontinuous fiber reinforced thermoplastics, while also allowing scientists and engineers to predict the microstructural damage behavior of these composites at sub-fiber resolution and with high accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Elucidating the differences in oxidation of high-performance α- and β- diisobutylene biofuels via Synchrotron photoionization mass spectrometry

Abstract Biofuels are a promising ecologically viable and renewable alternative to petroleum fuels, with the potential to reduce net greenhouse gas emissions. However, biomass sourced fuels are often produced as blends of hydrocarbons and their oxygenates. Such blending complicates the implementation of these fuels in combustion applications. Variations in a biofuel’s composition will dictate combustion properties such as auto ignition temperature, reaction delay time, and reaction pathways. A handful of novel drop-in replacement biofuels for conventional transportation fuels have recently been down selected from a list of over 10,000 potential candidates as part of the U.S. Department of Energy’s (DOE) Co-Optimization of Fuels and Engines (Co-Optima) initiative. Diisobutylene (DIB) is one such high-performing hydrocarbon which can readily be produced from the dehydration and dimerization of isobutanol, produced from the fermentation of biomass-derived sugars. The two most common isomers realized, from this process, are 2,4,4-trimethyl-1-pentene (α-DIB) and 2,4,4-trimethyl-2-pentene (β-DIB). Due to a difference in olefinic bond location, the α- and β- isomer exhibit dramatically different ignition temperatures at constant pressure and equivalence ratio. This may be attributed to different fragmentation pathways enabled by allylic versus vinylic carbons. For optimal implementation of these biofuel candidates, explicit identification of the intermediates formed during the combustion of each of the isomers is needed. To investigate the combustion pathways of these molecules, tunable vacuum ultraviolet (VUV) light (in the range 8.1–11.0 eV) available at the Lawrence Berkeley National Laboratory’s Advanced Light Source (ALS) has been used in conjunction with a jet stirred reactor (JSR) and time-of-flight mass spectrometry to probe intermediates formed. Relative intensity curves for intermediate mass fragments produced during this process were obtained. Several important unique intermediates were identified at the lowest observable combustion temperature with static pressure of 93,325 Pa and for 1.5 s residence time. As this relatively short residence time is just after ignition, this study is targeted at the fuels’ ignition events. Ignition characteristics for both isomers were found to be strongly dependent on the kinetics of C 4 and C 7 fragment production and decomposition, with the tert-butyl radical as a key intermediate species. However, the ignition of α-DIB exhibited larger concentrations of C 4 compounds over C 7 , while the reverse was true for β-DIB. These identified species will allow for enhanced engineering modeling of fuel blending and engine design.

09 BIOMASS FUELS↗
DOE OSTI2023

Single-shot X-ray absorption spectroscopy at X-ray free electron lasers

X-ray Absorption Spectroscopy (XAS) is a widely used X-ray diagnostic method for studying electronic and structural properties of matter. At first glance, the relatively narrow bandwidth and the highly fluctuating spectral structure of X-ray Free Electron Lasers (XFEL) sources seem to require accumulation over many shots to achieve high data quality. To date the best approach to implementing XAS at XFEL facilities has been using monochromators to scan the photon energy across the desired spectral range. While this is possible for easily reproducible samples such as liquids, it is incompatible with many important systems. Here, we demonstrate collection of single-shot XAS spectra over 10s of eV using an XFEL source, with error bars of only a few percent. We additionally show how to extend this technique over wider spectral ranges towards Extended X-ray Absorption Fine Structure measurements, by concatenating a few tens of single-shot measurements. Our results pave the way for future XAS studies at XFELs, in particular those in the femtosecond regime. This advance is envisioned to be especially important for many transient processes that can only be initiated at lower repetition rates, for difficult to reproduce excitation conditions, or for rare samples, such as those encountered in high-energy density physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Single-cell stable isotope probing in microbial ecology

Abstract Environmental and host-associated microbiomes are typically diverse assemblages of organisms performing myriad activities and engaging in a network of interactions that play out in spatially structured contexts. As the sum of these activities and interactions give rise to overall microbiome function, with important consequences for environmental processes and human health, elucidating specific microbial activities within complex communities is a pressing challenge. Single-cell stable isotope probing (SC-SIP) encompasses multiple techniques that typically utilize Raman microspectroscopy or nanoscale secondary ion mass spectrometry (NanoSIMS) to enable spatially resolved tracking of isotope tracers in cells, cellular components, and metabolites. SC-SIP techniques are uniquely suited for illuminating single-cell activities in microbial communities and for testing hypotheses about cellular functions generated for example from meta-omics datasets. Here, we illustrate the insights enabled by SC-SIP techniques by reviewing selected applications in microbiology and offer a perspective on their potential for future research.

Alcolombri, Uria (ORCID:0000000335615091)↗
DOE OSTI2021

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

We report nonadiabatic dynamics, which goes beyond the Born–Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The role of the droplet interface in controlling the multiphase oxidation of thiosulfate by ozone

Predicting reaction kinetics in aqueous microdroplets, including aerosols and cloud droplets, is challenging due to the probability that the underlying reaction mechanism can occur both at the surface and in the interior of the droplet. Additionally, few studies directly measure the surface activities of doubly charged anions, despite their prevalence in the atmosphere. Here, deep-UV second harmonic generation spectroscopy is used to probe surface affinities of the doubly charged anions thiosulfate, sulfate, and sulfite, key species in the thiosulfate ozonation reaction mechanism. Thiosulfate has an appreciable surface affinity with a measured Gibbs free energy of adsorption of -7.3 ± 2.5 kJ mol -1 in neutral solution, while sulfate and sulfite exhibit negligible surface propensity. The Gibbs free energy is combined with data from liquid flat jet ambient pressure X-ray photoelectron spectroscopy to constrain the concentration of thiosulfate at the surface in our model. Stochastic kinetic simulations leveraging these novel measurements show that the primary reaction between thiosulfate and ozone occurs at the interface and in the bulk, with the contribution of the interface decreasing from ~65% at pH 5 to ~45% at pH 13. Additionally, sulfate, the major product of thiosulfate ozonation and an important species in atmospheric processes, can be produced by two different pathways at pH 5, one with a contribution from the interface of >70% and the other occurring predominantly in the bulk (>98%). The observations in this work have implications for mining wastewater remediation, atmospheric chemistry, and understanding other complex reaction mechanisms in multiphase environments. Future interfacial or microdroplet/aerosol chemistry studies should carefully consider the role of both surface and bulk chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

BeyondPlanck: I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BEYONDPLANCK project in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building directly on experience from ESA’s Planck mission, we implemented a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a full joint posterior distribution P(ω | d), where ω represents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-ℓ CMB polarization reconstruction with Planck LFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/f correlated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth to τ = 0.066 ± 0.013, with a low-resolution CMB-based χ 2 probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in the Planck LFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide COSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The impact of isospin dependence of pairing on fission barriers in the fission cycling regions

A systematic analysis of the ground state and fission properties of actinides and superheavy nuclei important for the r process modeling has been performed within the framework of covariant density functional theory for the first time in Ref. A brief review of the results related to the heights of primary fission barriers and systematic uncertainties in their prediction is presented. In addition, new results on the potential impact of the isospin dependence of pairing on fission barriers in fission cycling regions is provided for the first time.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Theory and simulations of linear and nonlinear two-dimensional Rayleigh–Taylor dynamics with variable acceleration

Interfacial Rayleigh–Taylor mixing is crucial to describing important natural and engineering processes, such as exploding supernovae, laser micromachining, hot spots in inertial confinement fusion, and optical telecommunications. These require the characterization of the time dependence of the driving acceleration. We compare our theoretical formulation based on group theory foundations with interface-capturing numerical simulations for linear and nonlinear two-dimensional Rayleigh–Taylor instabilities in a finite-sized domain with time-varying acceleration over broad ranges of Atwood numbers and acceleration exponents. Detailed corroboration between theory and simulations is provided for this foundational case. Both demonstrate the strong interfacial nature of Rayleigh–Taylor instabilities, which suggests that practical flow fields can be reconstructed from the derived fluid potential using the proposed theory. A robust agreement is also obtained for the early and late-time evolution of the amplitudes of the bubble and spike, which demonstrate that the Rayleigh–Taylor flow can transition to the mixing regime even for a single-mode initial perturbation. Corroboration with experiments of high energy density plasmas motivated by studies of supernovae is also achieved. In addition, a long-standing puzzle in Rayleigh–Taylor dynamics on the interplay between the acceleration, the shear, and the interface morphology in the theory and simulations is resolved by accounting for finite viscosity of the fluids. The characterization of Rayleigh–Taylor instabilities as a highly interfacial phenomenon provides valuable insight into its multiscale nature, which enhances the design and understanding of numerous processes of practical interest.

42 ENGINEERING↗
DOE OSTI2023

Ferroelectric Al1 − xBxN thin films integrated on Si

Ferroelectric Al0.93B0.07N thin films are prepared (100) Si substrates. The necessary c-axis out-of-plane orientation to observe macroscopic ferroelectric switching was achieved by implementing an initial Ar/N2 plasma treatment, followed by a thin layer of AlN to initiate the desired texture and a 150 nm W layer. The plasma treatment facilitates crystallinity enhancement of the AlN template layer, allowing for subsequent growth of highly oriented W and Al0.93B0.07N layers. The W layer exhibits random in-plane orientation and exclusive (110) out-of-plane orientation with a rocking curve width of 1.4°. When grown on these W surfaces, 175 nm thick Al0.93B0.07N films exhibit random in-plane orientation and exclusive (001) texture with rocking curve full-width-half-max values of 1.6° and RMS roughness values less than 1 nm. Polarization hysteresis measurements show robust hysteresis with coercive field values of 5.4 MV/cm and remanent polarization values of 136 μC/cm2. XPS depth profile analysis suggests that the plasma treatment converts the existing native oxide to a nitrogen rich oxynitride with approximate composition Si3O0.5N3.67. Cross-sectional TEM reveals that the oxynitride interlayer is amorphous and ∼3.4 nm thick, more than double the native oxide thickness measured by multiwavelength ellipsometry, implying that (oxy)nitride growth continues after conversion of the native oxide. This new family of ferroelectric wurtzites is interesting from an integration perspective given their chemical compatibility with mainstream semiconductors. Developing synthesis routes that promote needed texture while preserving compatible processing windows is an important step toward practical integration.

Physics↗
DOE OSTI2022

Interstitial hydrogen enhances the mobility of some grain boundaries in tungsten

Segregation of interstitials at a grain boundary (GB) is known to generally lower its mobility. This phenomenon, called 'solute-drag', has important ramifications on the process of recrystallization and microstructural evolution. Here, we present predictions from molecular dynamics (MD) simulations which demonstrate that interstitial hydrogen in tungsten can in fact increase the mobility of some GBs which exhibit shear coupling. Assuming a disconnection-based mechanism, activation energies and pre-factors for disconnection nucleation are predicted from simulations of shear-coupled motion. In GBs where enhanced mobility is predicted, interstitial H reduces both the activation energy and the pre-factor for disconnection nucleation, thus effectively increasing the mobility. For GBs with diminished mobility, MD predicts that presence of interstitial H reduces the pre-factor and, in some cases, increases the activation energy. The reduction in the activation energy inferred from MD simulations are confirmed by nudged elastic band calculations. Temperature-dependent structural transitions are observed for some GBs, and the effect of interstitial H is found to change with the changes in structure. The effect of interstitial H is predicted to be complex and highly variable, providing some plausible explanations for experimental observations on the recrystallization of tungsten in presence of H-loaded plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

Abstract The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal-quench phase of tokamak disruptions, are numerically investigated with BOUT++’s flux-driven six-field electromagnetic turbulence model. Here, transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens the core temperature profile. Interesting features, such as surging of divertor heat load (up to 50 times) and broadening of heat-flux width (up to four times) on the outer-divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes in divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely, the E × B turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. First, an elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via the E × B convection, which causes the initial divertor heat-load burst, but it also induces amplified magnetic fluctuation B ˜ . Once themagnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, | B ˜ r / B 0 | reaches to 10 −4 level that completely breaks magnetic flux surfaces such that stochastic field lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat-flux width broadening.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Detailed space–time variations of the seismic response of the shallow crust to small earthquakes from analysis of dense array data

SUMMARY We compute high-resolution space–time variations of subsurface seismic properties from autocorrelation functions (ACF’s) of noise and local earthquakes, recorded by the Sage Brush Flat dense array deployed around the Clark branch of the San Jacinto fault. The resolved temporal changes are referred to as apparent velocity changes because they reflect both nonlinear response and variations of material properties such as cracking and damage. Apparent velocity changes are estimated at four frequency bands (10–15, 10–20, 15–30 and 20–40 Hz) for two local earthquake data sets. In one analysis, ACF’s from P- and S-wave windows of 31 small events with magnitudes below 3.1 are used to compute the apparent velocity variations with respect to the mean ACF of each phase, and we also use the mean ACF of noise data as reference to estimate the changes. In a further analysis, the temporal evolution of properties is computed using moving time windows in continuous waveform over one-hour long data with noise and earthquake signals. The apparent velocity changes and recovery times are frequency dependent and present a strong spatial variability across the array. The resolved changes are larger and recovery time shorter with data associated with higher frequencies. At frequencies larger than 15 Hz, and using the mean ACF of noise data as a reference, the apparent average velocity changes across the array during the passage of the P and S waves from the small local events are 2.5 per cent and 6 per cent, respectively. The apparent velocity changes decrease by one order of magnitude when the earthquake data are used as a reference. The relatively large changes in response to very low ground motion have important implications on nonlinear processes involving degradation and healing of the subsurface material during common earthquake shaking.

Geochemistry & Geophysics↗
DOE OSTI2022

Cavitation in a soft porous material

Abstract We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh–Plesset equation to bubbles in soft porous media. The extended Rayleigh–Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

Leng, Yu↗