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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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Sub-critical assembly die-away analysis with organic scintillators

Determining the reactivity of systems containing fissile material is essential for verifying safety, and possession and enrichment levels. The goal of this experiment was to characterize a subcritical nuclear fuel assembly irradiated by a pulsed neutron generator through differential die-away analysis. Similar characterizations are commonly performed with thermal neutron detectors, but these detectors are bulky and cumbersome, the materials are not widely available, and timing can be clouded by the required thermalization time. In this work, an organic scintillator capable of detecting both neutrons and photons was used to measure the die-away profiles of both particles. These time profiles were then used to estimate the reactivity of the assembly. Here, the calculated reactivity estimates compare favorably to simulated estimates, and therefore provide a useful tool for fissile material characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Investigating the role of strangeness in baryon–antibaryon annihilation at the LHC

Annihilation dynamics plays a fundamental role in the baryon–antibaryon interaction ($B–\bar{B}$) at low-energy and its strength and range are crucial in the assessment of possible baryonic bound states. Experimental data on annihilation cross sections are available for the $p–\bar{p}$ system but not in the low relative momentum region. Data regarding the $B–\bar{B}$ interaction with strange degrees of freedom are extremely scarce, hence the modeling of the annihilation contributions is mainly based on nucleon–antinucleon ($N–\bar{N}$) results, when available. In this letter we present a measurement of the $p–\bar{p}$, $p–\bar{Λ}$⊕$p–{Λ}$ and $Λ–\bar{Λ}$ interaction using correlation functions in the relative momentum space in high-multiplicity triggered pp collisions at $\sqrt{s}$=13 TeV recorded by ALICE at the LHC. In the $p–\bar{p}$ system the couplings to the mesonic channels in different partial waves are extracted by adopting a coupled-channel approach with recent χEFT potentials. The inclusion of these inelastic channels provides good agreement with the data, showing a significant presence of the annihilation term down to zero momentum. Predictions obtained using the Lednický–Lyuboshits formula and scattering parameters obtained from heavy-ion collisions, hence mainly sensitive to elastic processes, are compared with the experimental $p–\bar{Λ}$⊕$p–{Λ}$ and $Λ–\bar{Λ}$ correlations. The model describes the $Λ–\bar{Λ}$ data and underestimates the $p–\bar{Λ}$⊕$p–{Λ}$ data in the region of momenta below 200 MeV/c. The observed deviation indicates a different contribution of annihilation channels to the two systems containing strange hadrons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Multi-fidelity kinetic theory-based approach for the prediction of particle attrition: Application to jet cup attrition system

The timescale difference between the “fast” flow dynamics of fluidized bed reactors and the relatively “slow” rate of particle degradation makes the direct computational prediction of attrition challenging. An approach to this challenge is a multi-fidelity strategy where a high fidelity model for the flow dynamics is coupled with a lower fidelity model for the long-time resolution of the bulk attrition of the reactor inventory. We implement this approach using high-fidelity kinetic theory simulations to calculate the flow dynamics which are post-processed to calculate the frequency and intensity of the particle-particle and particle-wall collisions (e.g. collision energy spectra). This is combined with the particle breakage properties to construct the coefficients for a low-fidelity model [e.g. Monazam et al., 2018, Powder Technology 340, p. 528-536]. Simulations are performed of a jet cup attrition system containing Canadian hematite (Monazam et al. 2018). Furthermore, these are first analyzed using the collision energy spectra. Quantitative predictions of the mass loss are made using a low-fidelity model derived from the collision-spectra and a calibrated material breakage coefficient. The results are found to compare favorably with the experimental measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Crystallization kinetics and nanoparticle ordering in semicrystalline polymer nanocomposites

There has been considerable interest in the nucleation and crystallization of polymers in the presence of nanoparticles (NPs, or nanofillers in general, NFs). Most of the extensive work in this area has focused on anisotropic, non-Brownian NFs (e.g., clay sheets, carbon nanotubes) whose spatial dispersion state in these nanocomposites is controlled by the process by which they are formed. Hence, NF spatial dispersion is generally limited and often remains poorly characterized. Thermodynamic handles that can be used to control NF dispersion state in the polymer melt include (a) favorable interactions between the polymer chains and the bare NP surfaces, or (b) the density and length of the chains, with the same chemistry as the matrix, grafted to the NP surface. These relatively large NFs merely act as stationary objects that affect the kinetics of nucleation by providing heterogeneous sites, and the crystallization rate by confining the polymer in the melt state. The dispersion state of the NFs can dramatically affect the nucleation and crystallization of the matrix, but in most cases reported, the NFs increase nucleation efficiency relative to the neat polymer. At higher NF loadings, the effect of polymer confinement by the NFs dominates, leading to a decrease in crystal growth rates. This review describes the most important lessons learned from these commonly studied systems and then extends to polymer composite systems containing small, mobile spherical NPs (typically smaller than 100 nm in size). The role of NP mobility, which provides for dynamic confinement of the polymer melt, on the kinetics of polymer crystallization (nucleation, growth, and overall crystallization) and how this behavior is mostly consistent with the case of immobile NF is a second important focus of this review. In addition to the role of NFs on crystallization kinetics, recently reported nanoparticle ordering phenomena such as the effect of matrix crystallization on the organization of small spherical NPs within the amorphous regions of the semicrystalline morphology are discussed. In conclusion, such phenomena are clearly not observed for large NFs and hence provide a point of departure from past works in this area.

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

Machine-learning-aided density functional theory calculations of stacking fault energies in steel

A combined large-scale first principles approach with machine learning and materials informatics is proposed to quickly sweep the chemistry-composition space of advanced high strength steels (AHSS). AHSS are composed of iron and key alloying elements such as aluminum and manganese. A systematic exploration of the distribution of aluminum and manganese atoms in iron is used to investigate low stacking fault energies configurations using first principles calculations. To overcome the computational cost of exploring the composition space, this process is sped up using an automated machine learning tool: DeepHyper. Here our results predict that it is energetically favorable for Al to stay away from a stacking fault, but Mn atoms do not affect the stacking fault energy and can stay in the vicinity of the fault. The distribution of Al and Mn atoms in systems containing stacking faults and the effects of their interactions on the equilibrium distribution are systematically analyzed.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Hydration structure and energetics of iron-exchanged montmorillonite

The interaction between iron released from corroded steel canisters and bentonite is a key process influencing the long-term performance of nuclear waste repositories. In particular, the migration of Fe²⁺ into montmorillonite (Mnt) interlayers may alter its hydration, swelling, and ion-transport properties. In the present study, molecular dynamics simulations were performed to investigate the hydration behavior, structural response, and transport properties of Fe-exchanged montmorillonite (Fe-Mnt) under varying hydration states. The simulations focus on short- to intermediate-time-scale Fe 2+ and Fe 3+ interlayer exchange and hydration effects, and do not consider long-term structural substitution, Fe-bearing clay phase stabilization, or secondary iron mineral precipitation. Systems containing Na + -, Fe 2+ -, and Fe 3+ -Mnt were examined using both periodic and edge-exposed configurations to evaluate interlayer structure, ion exchange, and free energy of Fe intercalation. The results show that Fe ions influence the interlayer spacing primarily at low water contents (<1 bilayer), where Fe-Mnt exhibits a d-spacing 1–2 Å larger than Na-Mnt due to stronger hydration. The calculated hydration energies follow the order Fe 2+ $<$Fe 3+ $<$Na + . Both water and ion diffusion coefficients decrease upon Fe ion intercalation, with Fe 2+ ions diffusing an order of magnitude more slowly than those of Na + . Free energy profiles further confirm that Fe 2+ and Fe 3+ ions are thermodynamically favored in the interlayer, with Fe 3+ being the most stable. In conclusion, these findings provide molecular-scale insights into the mechanisms of Fe–Na exchange and their implications for bentonite alteration in repository environments.

clay↗
DOE OSTI2018

Observation of Anisotropic Charge Density Wave in Layered 1T-TiSe 2

Material systems containing charge density waves (CDWs) are ideal for studying structural symmetry breaking induced by electron modulation that would give rise to unconventional macroscopic phenomena such as high-T c superconductivity and colossal magnetoresistance. Layered 1T-TiSe 2 has attracted particular research interests given its rich phase diagram consisting of commensurate and incommensurate CDWs, as well as superconductivity. These phases can be tuned by temperature, pressure, electric field, or intercalation. Moreover, superconductivity is found to be strongly connected to the formation of CDW domain walls. Here, we conduct a full-scale study on 1T-TiSe 2 using an integration of techniques to investigate, at cryogenic temperatures, the real space, reciprocal space, and energy space properties. Our results show that the CDW forms three- dimensional cylinder shape domain, with different in-plane and out-of-plane coherence lengths. First principles density functional theory (DFT) calculations are integrated to explore the electronic feature of CDW in 1T-TiSe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Methylmercury Degradation by Trivalent Manganese

Methylmercury (MeHg) is a potent neurotoxin and has great adverse health impacts on humans. Organisms and sunlight-mediated demethylation are well-known detoxification pathways of MeHg, yet whether abiotic environmental components contribute to MeHg degradation remains poorly known. Here, in this paper, we report that MeHg can be degraded by trivalent manganese (Mn(III)), a naturally occurring and widespread oxidant. We found that 28 ± 4% MeHg could be degraded by Mn(III) located on synthesized Mn dioxide (MnO 2–x ) surfaces during the reaction of 0.91 μg·L –1 MeHg and 5 g·L –1 mineral at an initial pH of 6.0 for 12 h in 10 mM NaNO 3 at 25 °C. The presence of low-molecular-weight organic acids (e.g., oxalate and citrate) substantially enhances MeHg degradation by MnO 2–x via the formation of soluble Mn(III)-ligand complexes, leading to the cleavage of the carbon–Hg bond. MeHg can also be degraded by reactions with Mn(III)-pyrophosphate complexes, with apparent degradation rate constants comparable to those by biotic and photolytic degradation. Thiol ligands (cysteine and glutathione) show negligible effects on MeHg demethylation by Mn(III). This research demonstrates potential roles of Mn(III) in degrading MeHg in natural environments, which may be further explored for remediating heavily polluted soils and engineered systems containing MeHg.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Transformation of Uranyl Peroxide Studtite, [(UO 2 )(O 2 )(H 2 O) 2 ](H 2 O) 2 , to Soluble Nanoscale Cage Clusters

The dissolution behavior of uranyl peroxide studtite, [(UO 2 )(O 2 )(H 2 O) 2 ](H 2 O) 2 , was examined under a wide range of alkaline aqueous environments with and without the addition of hydrogen peroxide. In the absence of added H 2 O 2 , studtite dissolved in aqueous solutions with a tetraethylammonium hydroxide to uranium molar ratio greater than 0.5, and the resulting species in solution characterized by Raman spectroscopy and electrospray ionization mass spectrometry (ESI-MS) is the uranyl peroxide nanocluster U 24 , [(UO 2 )(O 2 )(OH)] 24 24– . This is the first demonstration of the formation of uranyl peroxide nanoclusters from studtite in a solution lacking additional hydrogen peroxide. In similar systems containing added hydrogen peroxide (0.01 M – 1.0 M), studtite dissolved in solutions with a TEAOH to uranium ratio greater than 0.1, and the resulting uranyl peroxide species in solution was U 28 , [(UO 2 )(O 2 ) 1.5 ] 28 28– .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Asynchronous Reciprocal Coupling of Martini 2.2 Coarse-Grained and CHARMM36 All-Atom Simulations in an Automated Multiscale Framework

The appeal of multiscale modeling approaches is predicated on the promise of combinatorial synergy. However, this promise can only be realized when distinct scales are combined with reciprocal consistency. Here, we consider multiscale molecular dynamics (MD) simulations that combine the accuracy and macromolecular flexibility accessible to fixed-charge all-atom (AA) representations with the sampling speed accessible to reductive, coarse-grained (CG) representations. AA-to-CG conversions are relatively straightforward because deterministic routines with unique outcomes are achievable. Conversely, CG-to-AA conversions have many solutions due to a surge in the number of degrees of freedom. While automated tools for biomolecular CG-to-AA transformation exist, we find that one popular option, called Backward, is prone to stochastic failure and the AA models that it does generate frequently have compromised protein structure and incorrect stereochemistry. Although these shortcomings can likely be circumvented by human intervention in isolated instances, automated multiscale coupling requires reliable and robust scale conversion. In this work, we detail an extension to Multiscale Machine-learned Modeling Infrastructure (MuMMI), including an improved CG-to-AA conversion tool called sinceCG. This tool is reliable (~98% weakly correlated repeat success rate), automatable (no unrecoverable hangs), and yields AA models that generally preserve protein secondary structure and maintain correct stereochemistry. We describe how the MuMMI framework identifies CG system configurations of interest, converts them to AA representations, and simulates them at the AA scale while on-the-fly analyses provide feedback to update CG parameters. Application to systems containing the peripheral membrane protein RAS and proximal components of RAF kinase on complex eight-component lipid bilayers with ~1.5 million atoms is discussed in the context of MuMMI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2019

Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum

Here, we develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(N e 5 ) down to O(N e 3 ) where N e is the number of electrons. Finally, this is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to N e ≈ 1000 electrons.

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

Active Thermochemical Tables: Enthalpies of Formation of Bromo- and Iodo-Methanes, Ethenes and Ethynes

Here, the thermochemistry of halocarbon species containing iodine and bromine is examined through an extensive interplay between new Feller–Peterson–Dixon (FPD) style composite methods and a detailed analysis of all available experimental and theoretical determinations using the thermochemical network that underlies the Active Thermochemical Tables (ATcT). From the computational viewpoint, a slower convergence of the components of composite thermochemistry methods is observed relative to species that solely contain first row elements, leading to a higher computational expense for achieving comparable levels of accuracy. Potential systematic sources of computational uncertainty are investigated, and, not surprisingly, spin-orbit coupling is found to be a critical component, particularly for iodine containing molecular species. The ATcT analysis of available experimental and theoretical determinations indicates that prior theoretical determinations have significantly larger uncertainties than originally reported, particularly in cases where molecular spin-orbit effects were ignored. Accurate and reliable heats of formation are reported for 38 halogen containing systems, based on combining the current computations with previous experimental and theoretical work via the ATcT approach.

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

COLUMBUS─An Efficient and General Program Package for Ground and Excited State Computations Including Spin–Orbit Couplings and Dynamics

The COLUMBUS program system provides the tools for performing high-level multireference (MR) computations, including the multireference configuration interaction (MRCI) method and its multireference averaged quadratic coupled cluster (MR-AQCC) extension, allowing computations on a wide range of fascinating atomic and molecular systems, including the treatment of open-shells and complicated excited state phenomena. The inclusion of spin−orbit coupling (SOC) directly within the MRCI step enables the description of systems containing heavy elements, such as lanthanides and actinides, whose properties are strongly influenced by SOC. Analytic energy gradients and nonadiabatic couplings at the correlated MRCI level provide the foundation for a variety of dynamics studies, giving insight into ultrafast photochemistry. New and ongoing method developments in COLUMBUS include the computation of spin densities, improved descriptions of ionic states, enhancements to the AQCC method, and the porting of COLUMBUS to graphical processing units (GPUs). New external interfaces enable an enhanced description of electronic resonances and molecules in strong laser fields. This work highlights these new developments while providing a detailed account of the diverse applications of COLUMBUS in recent years.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molecular Dynamics and Free Energy Calculations of Dicyclohexano-18-crown-6 Diastereoisomers with Sm 2+ , Eu 2+ , Dy 2+ , Yb 2+ , Cf 2+ , and Three Halide Salts in Tetrahydrofuran and Acetonitrile Using the AMOEBA Force Field

With the continual development of lanthanides (Ln) in current technological devices, an efficient separation process is needed that can recover greater amounts of these rare elements. Dicyclohexano-18-crown-6(DCH18C6) is a crown ether that may be a promising candidate for Ln separation, but additional research is required. As such, molecular dynamics(MD) simulations have been performed on four divalent lanthanide halide salts(Sm 2+ , Eu 2+ , Dy 2+ , and Yb 2+ ) and one divalent actinide halide salt (Cf 2+ ) bound to three diastereoisomers of DCH18C6. Dy 2+ , Yb 2+ , Cf 2+ , DCH18C6, and tetrahydrofuran (THF) solvent were parameterized for the AMOEBA polarizable force field for the first time, whereas existing parameters for Sm 2+ and Eu 2+ were utilized from our previous efforts. A coordination number (CN) of six for Ln 2+ /An 2+ –O solvated in THF indicated that the cations interacted almost entirely with the oxygens of the polyether ring. A CN of one for Ln 2+ /An 2+ -N solvated in acetonitrile for systems containing iodide suggested that theN atom of acetonitrile was competitive with I – for cation interactions. Fluctuation between five and six CNs for Dy 2+ and Yb 2+ suggested that although the cations remained in the polyether ring, the size of the ring may not be an ideal fit as these cations possess comparatively smaller ionic radii. Gibbs binding free energies of Sm 2+ in all DCH18C6 diastereoisomers solvated in THF were calculated. The binding free energy of the cis-syn-cis diastereoisomer was the most favorable, followed by cis-anti-cis, and then trans-anti-trans. Lastly, two major types of conformation were observed for each diastereoisomer that were related to the electrostatic interactions and charge density of the cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Interplay Between Membrane Composition and Structural Stability of Membrane-Bound hIAPP

Amyloid aggregates are characteristic of many serious diseases such as Alzheimer’s disease, Parkinson’s, and type 2 diabetes and commonly involve intrinsically disordered proteins (IDPs), those that populate an ensemble of conformations rather than a single folded structure. Human islet amyloid polypeptide (hIAPP or amylin) is an amyloidogenic IDP implicated in pancreatic β-cell death during the pathogenesis of type 2 diabetes. The target of amylin’s toxic activity is thought to be the cell’s lipid membrane, which may also act as a catalyst for aggregation. Since amylin is intrinsically disordered, differing environments can have a large impact on its equilibrium conformational ensemble. We apply atomistic molecular dynamics simulations on multiple systems containing a full-length amylin monomer and a lipid bilayer to study the changes induced by the membrane. Here, we observe stabilized helical conformations structurally similar to those determined by NMR experiments conducted in similar environments. We also find that bilayers of different compositions result in greatly different equilibrium ensembles of amylin. Finally, we discuss how a mixed bilayer containing zwitterionic and anionic lipid headgroups can allow for greater preference toward conformations which are adsorbed below the membrane surface through rearrangement of lipids for more favorable protein–lipid interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Anion Effects on the Interfacial Structure and Bulk Physical Properties in Choline-Based Hydrogen-Bonded Electrolytes

Electrolytes consisting of choline (Ch) salts with acetate (Ac) and oxalate (Ox) anions were studied in mixtures with ethylene glycol (EG), in comparison to chloride (Cl)- and bis(trifluorosulfonyl)imide (TFSI)-containing systems to understand the impact of anion size and charge density on the bulk electrolyte and interfacial properties. These represent hydrogen-bonded concentrated electrolytes where the Ch salts are the H-bond acceptors (HBAs) and EG is the H-bond donor (HBD) in 1:2 and 1:4 HBA:HBD ratios. Increased H-bonding in Ch 2 Ox with EG compacts the liquid compared to ChAc, consistent with the increased dissociation energies of the HBA:HBD clusters with Ox –2 calculated by density functional theory (DFT), thus leading to denser and more viscous liquids. Electrochemical impedance spectroscopy (EIS) and surface-enhanced Raman spectroscopy (SERS) were used to investigate interfacial charge density and the electrode surface species. Differential capacitance curves demonstrate weak dependence on potential except for ChAc:EG, where Ac – is found to adsorb on the Au surface, in particular at +0.055 V vs Ag quasi-reference while no specific adsorption was observed on glassy carbon (GC). In situ SERS measurement confirms the formation of a surface layer in the ChAc:EG systems resulting from a Au–acetate interaction. Despite the structural similarities, Ox –2 did not show specific binding or any dependence of capacitance on potential as a result of strongly solvating EG molecules via H-bonds. Furthermore, this study shows that the charge density of the HBAs impacts both bulk properties and the electrical double-layer formation in concentrated H-bonded electrolytes that is relevant to electrochemical kinetics and morphology in electrodeposition processes and energy storage applications.

25 ENERGY STORAGE↗
DOE OSTI2020

Full-Scale Ab Initio Simulation of Magic-Angle-Spinning Dynamic Nuclear Polarization

Theoretical models aimed at describing magic-angle-spinning (MAS) dynamic nuclear polarization (DNP) NMR have great potential in facilitating the in silico design of DNP polarizing agents and formulations. These models must typically face a trade-off between the accuracy of a strict quantum mechanical description and the need for using realistically large spin systems, for instance, using phenomenological models. In this paper, we show that the use of aggressive state-space restrictions and an optimization strategy allows full-scale ab initio MAS-DNP simulations of spin systems containing thousands of nuclei. Our simulations are shown to reproduce experimental DNP enhancements quantitatively, including their MAS rate dependence, for both frozen solutions and solid materials. They also reveal the importance of a previously unrecognized structural feature found in some polarizing agents that helps minimize the sensitivity losses imposed by the spin diffusion barrier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗