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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Post-puff SOL broadening on MAST-U under high-recycling conditions: evidence consistent with cross-field transport changes

Transient broadening of the scrape-off layer (SOL) density profile can modify main-chamber first-wall particle fluxes and divertor loading, yet its control parameters remain debated between divertor-regime transitions, neutral dynamics and changes in cross-field transport. We investigate fueling-driven SOL density-profile evolution and post-fueling relaxation on MAST-Upgrade (MAST-U) in ohmic L-mode, using two otherwise similar double-null Conventional Divertor discharges (I p = 450 kA, B T = 0.33 T) with identical 50 ms low-field side gas puffs; the only intentional difference is the puff start time. Upstream Thomson scattering shows that both discharges develop a transient far-SOL density profile modification, expressed as an increased SOL-width metric λ n e and a far-SOL enhancement consistent with a shoulder-like signature. In the earlier-puff case, the SOL-width metric remains elevated after puff termination and the post-puff decay time scales are systematically longer across the analysed radii. Outer-target Langmuir probes indicate high-recycling conditions during the analysed window (few-eV T e with radially peaked j sat,∥ and q ∥ profiles, without signatures of deep detachment). The outer-divertor collisionality proxy Λ div is elevated in both cases and does not discriminate between the different post-puff persistence. The target-integrated ion flux proxy ∫ J sat dA evolves nearly identically in both discharges when aligned to the puff start. Taken together, these observations suggest that the late/post-puff upstream SOL evolution is not set by parallel exhaust to the outer targetalone and is more consistent with upstream cross-field redistribution, with a possible role for plasma–neutral coupling and fueling geometry.

MAST-U↗
DOE OSTI2025

Defect Generation and Evolution in Irradiated Epitaxial Films and Heterostructures of Fe 3 O 4 and Cr 2 O 3

Abstract The functionality of nuclear structural materials, sensors, and microelectronics in harsh environments such as radiation relies on understanding defect generation and evolution processes in oxide layers. The initial radiation response of epitaxial thin films of Fe 3 O 4 (111), Cr 2 O 3 (0001), and Fe 3 O 4 (111)/Cr 2 O 3 (0001) heterostructures deposited on Al 2 O 3 (0001) by oxygen‐assisted molecular beam epitaxy and irradiated with 200 keV He + is characterized. X‐ray diffraction and X‐ray absorption near edge spectroscopy showed that the Cr 2 O 3 layers underwent significant lattice expansion and disordering under irradiation, whereas the Fe 3 O 4 layers do not exhibit noticeable changes. In contrast, positron annihilation spectroscopy revealed an evolution of cation vacancy point defects in the Fe 3 O 4 layers into larger vacancy clusters with increasing irradiation, while the cation vacancies in Cr 2 O 3 remained primarily as single vacancies and small clusters. The results suggest that the Fe 3 O 4 lattice can utilize the free volume of the larger vacancy clusters to relax but the small vacancies in the Cr 2 O 3 lattice do not facilitate relaxation. Comparing defect concentrations in the single layer films versus the heterostructure suggests that point defects may cross the interface from Fe 3 O 4 into Cr 2 O 3 . Together, these results enhance the understanding of the initial defect evolution mechanisms in oxide layers in harsh irradiation environments.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Designing a Dynamic Material via Interlocking Kraft Lignin with Ultrahigh Molecular Weight Poly(ethylene oxide)

The environmental issues stemming from plastic waste and the excessive use of petroleum-based chemicals are both concerning and urgent. To effectively address this problem, we need to adopt a comprehensive approach involving developing more sustainable and renewable materials. These materials should be capable of demonstrating similar or even better performance than functional polymers synthesized from petroleum-based chemicals. Our research aims to develop more sustainable materials by leveraging the intrinsic characteristics of a natural polymer, lignin, a byproduct of the biorefinery industries. We utilized the three-dimensional branching structure of lignin as a material framework. We employed an approach to co-reactive melt processing of kraft lignin with aliphatic flexible chains of soft cross-linkers through the reaction of the cross-linker epoxy chain ends with lignin functional groups. Our study demonstrates that the interlocked structure formed from the co-blending of kraft lignin with ultrahigh molecular weight poly(ethylene oxide) and the cross-linking of lignin chains through a solvent-free process can manipulate the macromolecular interactions and relaxation. This manipulation results in materials that exhibit a wide range of thermomechanical properties and self-healing and shape memory effects, with drastically improved stiffness in a single material. We have explored the fundamental understanding of the macromolecular chain relaxation dynamics originating from the interlocking structure formation. In conclusion, this investigation utilized various techniques, including thermal, mechanical, rheology, and quasi-elastic neutron scattering.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Formation of a Decanuclear Organometallic Dysprosium Complex via a Radical–Radical Cross–Coupling Reaction

Over the years, polynuclear cyclic or torus complexes have attracted increasing interest due to their unique metal topologies and properties. However, the isolation of polynuclear cyclic organometallic complexes is extremely challenging due to their inherent reactivity, which stems from the labile and reactive metal-carbon bonds. In this study, the pyrazine ligand undergoes a radical-radical cross-coupling reaction leading to the formation of a decanuclear [(Cp*) 20 Dy 10 (L1) 10 ] ⋅ 12(C 7 H 8 ) ( 1 ; where L1 = anion of 2-prop-2-enyl-2 H -pyrazine; Cp* = pentamethylcyclopentadienyl) complex, where all Dy III metal centres are bridged by the anionic L1 ligand. Amongst the family of polynuclear Ln organometallic complexes bearing Cp R 2 Ln x units (Cp R = substituted cyclopentadienyl), 1 features the highest nuclearity obtained to date. In-depth computational studies were conducted to elucidate the proposed reaction mechanism and formation of L1, while probing of the magnetic properties of 1 , revealed slow magnetic relaxation upon application of a static dc field.

cross-coupling↗
DOE OSTI2025

Near-ideal relaxed MHD in slab geometry

We investigate the solutions of the relaxed magnetohydrodynamic (MHD) model (RxMHD) of R. Dewar and Z. Qu. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar and Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Axisymmetric gyrokinetic simulation of ASDEX-Upgrade scrape-off layer using a conservative implicit BGK collision operator

Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar–Gross–Krook (BGK) collision operator for use in the discontinuous Galerkin full-f gyrokinetic solver within the Gkeyll framework, which, when combined with Gkeyll's traditional explicit time integrator for collisionless advection, can significantly increase the time step in gyrokinetic simulations of highly collisional regimes. To ensure conservation of density, momentum, and energy, we utilize an iterative scheme to correct the discretized approximation to the equilibrium Maxwellian distribution to which the BGK collision operator relaxes. We have further generalized the BGK infrastructure, both the implicit scheme and the correction routine, to handle cross-species collisions. This improved implicit and conservative BGK operator is benchmarked against the more accurate but more computationally expensive Lenard–Bernstein–Dougherty (LBD) operator, which has been utilized in prior studies with Gkeyll. The implicit BGK operator enables 2D axisymmetric simulations of the ASDEX-Upgrade scrape-off layer to run 56 times faster to completion than the simulations with the LBD operator, because the BGK operator is more robust and converges at a lower resolution than is required by the LBD operator. Additionally, in this more collisional limit, we demonstrate that the results of our simulations utilizing the implicit BGK operator agreed well with simulations utilizing the more computationally expensive LBD operator.

Gyrokinetic simulations↗
DOE OSTI2024

Dynamic Deformation in Nuclear Graphite and Underlying Mechanisms

Time-dependent deformation in nuclear graphite is influenced by the creation and migration of radiation-induced defects in the reactor environment. This study investigates the role of pre-existing defects such as point defect clusters and Mrozowski cracks in nuclear graphite IG-110. Separate specimens were irradiated with a 2.8 MeV Au 2+ beam with a fluence of 4.38 × 10 14 cm −2 and an 8 MeV C 2+ beam with a fluence of 1.24 × 10 16 cm −2 . Microscopic specimens were either mechanically loaded inside a transmission electron microscope (TEM) or subjected to ex situ indentation-based creep loading. In situ TEM tests showed significant plasticity in regions highly localized around the Mrozowski cracks, resembling slip or ripplocation bands. Slip bands were also seen near regions without pre-existing defects but at very high stresses. Ex situ self-ion irradiation embrittled the specimens and decreased the creep displacement and rate, while heavy ion irradiation resulted in the opposite behavior. We hypothesize that the large-sized gold ions (compared to the carbon atoms) induced interplanar swelling as well as cross-plane channels for increased defect mobility. These findings illustrate the role of pre-existing defects in the dynamic relaxation of stresses during irradiation and the need for more studies into the radiation environment’s impact on the mechanical response of nuclear graphite.

creep deformation↗
DOE OSTI2025

Shock-induced chemistry and high strain-rate viscoelastic behavior of a phenolic polymer

We use impact experiments and a finite element model (up to 1.2 GPa), and molecular dynamics simulations (up to 60 GPa), to examine the behavior of a phenolic polymer under shock compression, spanning both nonreactive and reactive regimes. In the nonreactive regime, relaxation following compression at strain rates of ∼105 s−1 can be explained by viscoelasticity observed at ordinary laboratory rates (≲1 s−1) by accounting for the temperature dependence of the phenolic β-transition. Reasonable agreement is found between the measured shock Hugoniot up to 1.2 GPa and molecular dynamics simulation for cross-linked structures of comparable density. We also observed a first-order mechanical transition near 0.36 GPa shock stress and estimated a spall strength of 0.102 GPa and Hugoniot elastic limit of 1–2 GPa. The shock stress is found to vary up to 24% among phenolics made with different resin and/or cure processes. Finally, molecular dynamics simulations are used to identify a reactive regime at shock pressures ≳20 GPa that is characterized by chemically driven, rate-dependent relaxation processes, including dehydrogenation and dehydration reactions that promote the formation of a dense, highly cross-linked carbonaceous solid and the release of light volatiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Low-Lying Excited States of Linear All- Trans Polyenes: Insights from Analytic Gradient and Nonadiabatic Coupling Calculations Based on Multireference Configuration Interaction

Polyenes serve as a rigorous test for theoretical models and electronic structure methods, playing a key role in advancing computational and theoretical chemistry. Here, we present a high-level theoretical investigation of linear, all-trans polyenes using energy gradients and nonadiabatic coupling vectors based on an MR-CISD wave function to describe electronic transitions involving the ground state (1 1 A g – ) and three low-lying excited states (2 1 A g – , 1 1 B u + , and 2 1 B u – ) of hexatriene, octatetraene, and decapentaene. This approach enables accurate evaluation of both adiabatic and vertical excitation and emission energies, yielding results in excellent agreement with experiment, as well as locating minima on the crossing seam between adiabatic states. Our results show that vertical excitation energies to the 1 1 B u + state are blue-shifted by 0.2–0.3 eV relative to the experimental absorption maximum, whereas the vertical emission energy from the 2 1 A g – state is red-shifted by ∼0.2 eV relative to the experimental emission maximum. Upon relaxation from the Franck–Condon geometry, the 2 1 A g – state stabilizes by around 1 eV, compared to 0.2–0.3 eV for the 1 1 B u + state. An analysis of the S 1 /S 0 crossing seam in hexatriene shows that its minimum involves asymmetric backbone deformations and provides an efficient channel for ultrafast internal conversion to the ground state, consistent with the absence of detectable fluorescence in this molecule. These results demonstrate the power of analytic gradients and nonadiabatic coupling vectors based on an MR-CISD wave function for accurately characterizing the electronic structure and photophysics of polyenes.

Excited states↗
DOE OSTI2025

Relaxing constraints on dark matter annihilation near the supermassive black hole in M87

The supermassive black hole at the center of M87 could redistribute dark matter particles within its sphere of influence, creating a high-density region known as a density spike. This spike can significantly enhance dark matter annihilation signals, making M87 a critical target for deriving stringent constraints on annihilation cross sections. In this work, we demonstrate that these constraints are highly sensitive to the choice of the halo density profile for M87. Motivated by recent kinematic studies of M87, we adopt a cored halo model and find that the constraints on dark matter annihilation are significantly relaxed. Specifically, in the cored halo scenario, the smooth part of the halo overwhelmingly dominates the annihilation signals, whereas the commonly assumed cuspy halo model attributes a major contribution to the spike. We demonstrate this effect using a dark matter model with a light mediator.

particle dark matter↗
DOE OSTI2026

Charge Carrier and Spin Diffusion in a Polycrystalline and Single Crystal Lead Halide Perovskite Semiconductor

The directed movement of spin-bearing excitations in semiconductors can enable many potential schemes for spintronic applications. Understanding the mechanism of spin motion, as opposed to charge carrier or exciton motion, may require specialized techniques and sample conditions. Here we employ the noncontact and time-resolved technique of light-induced transient grating spectroscopy (LITG) to measure both carrier and spin motion in a perovskite semiconductor with varying crystallinity. The carrier motion aligns with expectations from past studies undertaken at low fluence, revealing an ambipolar diffusion coefficient on the order of 1 cm 2 /sec and diffusion length of roughly 1.5 μm for single crystals that is strongly attenuated as crystallite size decreases. The spin diffusion is measured with cross-polarized excitation beams and uncovers an intensity-dependent coefficient rising above 100 cm 2 /sec. The fast room-temperature spin relaxation limits the spin diffusion length, but the remarkable speedup of spin over carrier diffusion suggests a mechanism involving a combination of exchange-mediated and doping effects that enhance spin transport.

14 SOLAR ENERGY↗
DOE OSTI2025

Temperature Evolution of the Activation Barriers Leads to Meyer−Neldel Rules for Structural Relaxation and Transport in Polymers

Understanding activation barriers controlling structural relaxation in glass-forming liquids, molecular transport, and ionic conductivity in amorphous polymers is a grand challenge of fundamental scientific and materials engineering interest across disciplines. Over decades, intriguing but puzzling empirical correlations between the elementary time scale of activated barrier crossing and the apparent Arrhenius activation energy, the so-called Meyer−Neldel (MN) rules, have been discovered in diverse liquids and glasses. Here, in this study, we formulate and successfully apply a new experimental analysis and an explicitly dynamical theoretical framework which provides an understanding of the origin, validity, and failure of such correlations, that bridge and unify the three fields of structural relaxation, molecular transport, and ionic conductivity in liquids and quenched glasses. Distinct quasi-universal laws are predicted in equilibrated liquids and nonequilibrium glasses, consistent with experiments. Our analysis reveals that even if the relaxation appears Arrhenius over a limited temperature range, the physical activation barrier is generally temperature-dependent in polymeric systems even below glass transition temperature. In addition, we show that the approximate validity of classical MN rules hinges on a linear temperature dependence of this barrier and the temperature range probed in experiments. Our findings are relevant for controlling the activation barrier in functional soft polymeric materials relevant to molecular separations, barrier coatings, and charge transport, and also provide new constraints on the theoretical understanding of the mechanism underlying slow activated dynamics in glass-forming condensed matter.

Meyer-Neldel rules↗
DOE OSTI2025

Multi-scale Interaction Mechanism for Edge-Localized-Mode Suppression in the Tokamak Edge

A central challenge in fusion energy is reconciling the high-confinement mode required for reactor performance with the intense intermittent relaxation events it produces, known as edge-localized modes. These instabilities arise in the steep pressure pedestal at the plasma edge when magnetohydrodynamic thresholds are crossed, inflicting damaging heat loads on reactor components. Here, we show that multiscale interactions between microscopic turbulence and macroscopic magnetohydrodynamic modes provide encouraging prospects for self-organized edge-localized modes regulation. Using direct quantitative measurements of multiscale modes, eddy dynamics, and turbulent flux, we show that small-scale electron drift wave turbulence actively scatters the large-scale peeling-ballooning modes. This scattering decorrelates the pressure and velocity fields of the instability, so arresting its growth. Our modeling and theoretical analysis confirm this suppression mechanism is effective even when conventional linear stability thresholds are exceeded. This work establishes a nonlinear principle for edge-localized modes stability, revealing how ambient micro-turbulence can be leveraged to maintain a macro-stable, high-performance pedestal for future fusion reactors.

experimental nuclear physics↗
DOE OSTI2025

Cross slip of extended dislocations in face-centered cubic metals through phase-field modeling

Cross slip is a dislocation mechanism that significantly impacts the mechanical behavior of engineering alloys. Here, in this work, we advance a 3D phase-field dislocation dynamics (PFDD) mesoscale technique to simulate cross slip across a broad range of face-centered cubic (FCC) metals. The formulation incorporates elastic anisotropy, an FCC numerical grid, and a high-fidelity representation of the entire γ -surface from density functional theory for eight FCC metals and no adjustable parameters or rules. The relaxed core structures under zero stress for all metals are predicted to extend in plane. The analytical model for stacking fault width agrees well with the PFDD result under the assumption of elastic isotropy but overestimates it under elastic anisotropy, when the degree of anisotropy is large. The dynamic simulations are designed to elucidate the material parameters that influence the propensity for cross slip. Whether cross slip occurs under a non-Schmid stress or to bypass a hard obstacle, the critical stress to cross slip scales strongly with the anisotropic energy coefficient for a screw dislocation.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Sub-melt nanosecond pulsed-laser induced densification and strain-field relaxation in single-crystal diamond

Dislocations and polishing-induced defect networks in synthetic diamond introduce local strain fields and broaden Raman features, limiting performance in optical, thermal, and electronic applications. Laser annealing is emerging as a promising approach to repair surface and near-surface defects in diamond without entering the melt regime, yet surface densification, defect-state modification, and associated structural changes have not been well quantified. In this work, we show that sub-melt nanosecond pulsed-laser annealing (PLA) induces near-surface densification and defect-mediated strain relaxation in single-crystal Chemical Vapor Deposition (CVD) diamond. Single- and two-pulse PLA were applied, and structural evolution was quantified using co-registered ISO 25,178 white-light interferometry, depth-resolved Raman spectroscopy, and cross-sectional STEM with geometric phase analysis (GPA). Across a 5 × 6 grid (n = 30), responsive regions exhibit large reductions in local slope (Sdq 45–65%), developed area (Sdr 60–90%), height spread (Sp, Sz 30–65%), void volume (Vv 57–60%), and roughness amplitude (Sa, Sq 48–57%), consistent with densification of ∼4–6.5 nm. Raman profiling shows narrowing of the diamond line and improved spectral uniformity to depths of ∼2–3 μm. Given that the Raman probing depth significantly exceeds the densified layer thickness, this response is interpreted as consistent with long-range strain-field redistribution originating from the near-surface region. STEM-GPA strain maps further support this interpretation, showing smoother strain fields, suppressed hotspots, and redistribution of localized strain concentrations following PLA. These results are consistent with defect-mediated strain relaxation and densification-driven modification of the near-surface energy state. The approach provides a scalable pathway for improving near-surface structural quality in diamond relevant to electronic, photonic, and quantum applications.

Areal surface metrology (ISO 25,178)↗
DOE OSTI2024

Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers

Distribution of relaxation time (DRT) is used to interpret electrochemical impedance spectroscopy (EIS) for proton exchange membrane (PEM) water electrolyzers, with an attempt to separate overlapped relaxation processes in Nyquist plots. By varying operating conditions and catalyst loadings, four main relaxation peaks arising from EIS can be identified and successfully separated from low to high frequencies as (P1) mass transport, (P2) oxygen evolution reaction kinetics, (P3) reaction kinetics (with faster time constant than P2), and (P4) ionic transport. Here, the shape, height, and frequency of the DRT peaks change with different membrane electrode assembly (MEA) configurations. Electron microscopy reveals distinct features from the cross-sectioned MEAs which verify critical DRT results in that increasing the iridium (Ir)-anode loading from 0.2 mgIr/cm 2 to 1.5 mgIr/cm 2 reduces kinetic losses due to higher site-access; a thick and compacted anode, however, also triggers higher ohmic resistances from membrane/catalyst layer hydration and increases transport losses due to longer ionomer pathways. DRT provides higher resolution to EIS for deconvoluting processes with different relaxation times and the quantification of DRT peaks improves the accounting of total losses from each process.

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

Crack formation in strained β-(AlxGa 1−x ) 2 O 3 films grown on (010) β-Ga 2 O 3 substrates

The cracking and local strain relaxation in (010) (Al x Ga 1−x ) 2 O 3 films grown on Ga 2 O 3 substrates are assessed in terms of film composition and thickness. We utilize x-ray diffraction and electron microscopy techniques combined with simulation and modeling to investigate that film cracking on curvature (flatness) has a directly proportional relationship with film thickness and/or aluminum content. Cross section transmission electron microscopy reveals that cracks along both the (001) and (100) cleavage planes penetrate into the substrate. The diffuse scattered intensity observed in reciprocal space maps (RSMs) is directly correlated with the tilt that is introduced due to the change in the deformation conditions near the cracks. While asymmetric RSMs show that the layers are fully strained, the diffuse scattering distribution in reciprocal space can be interpreted to show that the cracking relaxes and locally tilts the lattice ∼350 nm from the crack edges, which is consistent with the larger radius of curvature associated with the films with higher crack densities. For example, a 200 nm (Al 0.13 Ga 0.87 ) 2 O 3 thick film has an average inter-crack spacing of 3.3 µm, so most of the epitaxial layer is fully strained except near the cracks where it deforms elastically and is consistent with the gallium oxide Poisson ratio. A reciprocal space model was developed, which imports the strain and tilt distributions (based on finite element modeling) to match the features observed in the experimental maps. We also note that previous studies involving (Al x Ga 1−x ) 2 O 3 films may show evidence of cracking as observed in their symmetric and asymmetric RSMs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Bottlebrush Block Copolymers at the Interface of Immiscible Liquids: Adsorption and Lateral Packing

Amphiphilic bottlebrush block copolymers (BBCPs), having a hydrophilic bottlebrush polymer (BP) linked covalently to a hydrophobic BP, were found to segregate to liquid-liquid interfaces to minimize the free energy of the system. The key parameter influencing the outcome of the experiments is the ratio between the degree of polymerization of the backbone (NBB) and that of the side-chain brushes (NSC). Specifically, a spherical, star-like configuration results when NBB < NSC, while a cylindrical, bottlebrush-like shape is preferred when NBB > NSC. Dynamic interfacial tension (γ) and fluorescence recovery after photobleaching (FRAP) measurements show that the BBCP configuration influences the areal density and in-plane diffusion at the fluid interface. The characteristic relaxation times associated with BBCP adsorption (τA) and reorganization (τR) were determined by fitting time-dependent interfacial tension measurements to a sum of two exponential relaxation functions. Both τA and τR initially increased with NBB up to 92 repeat units, due to the larger hydrodynamic radius in solution and slower in-plane diffusivity, attributed to a shorter cross-sectional diameter of the side-chains near the block junction. This trend reversed at NBB = 190, with shorter τA and τR attributed to increased segregation strength and exposure of the bare water/toluene interface due to tilting and/or wiggling of the backbone chains, respectively. The adsorption energy barrier decreased with higher NBB, due to a reduced BBCP packing density at the fluid interface. In conclusion, this study provides fundamental insights into macromolecular assembly at fluid interfaces, as it pertains to unique bottlebrush block architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗