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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Breakdown of the Static Dielectric Screening Approximation of Coulomb Interactions in Atomically Thin Semiconductors

Coulomb interactions in atomically thin materials are remarkably sensitive to variations in the dielectric screening of the environment, which can be used to control exotic quantum many-body phases and engineer exciton potential landscapes. For decades, static or frequency-independent approximations of the dielectric response, where increased dielectric screening is predicted to cause an energy redshift of the exciton resonance, have been sufficient. These approximations were first applied to quantum wells and were more recently extended with initial success to layered transition metal dichalcogenides (TMDs). Here, we use charge-tunable exciton resonances to investigate screening effects in TMD monolayers embedded in materials with low-frequency dielectric constants ranging from 4 to more than 1000, a range of 2 orders of magnitude larger than in previous studies. In contrast to the redshift predicted by static models, we observe a blueshift of the exciton resonance exceeding 30 meV in higher dielectric constant environments. We explain our observations by introducing a dynamical screening model based on a solution to the Bethe-Salpeter equation (BSE). When dynamical effects are strong, we find that the exciton binding energy remains mostly controlled by the low-frequency dielectric response, while the exciton self-energy is dominated by the high-frequency one. Our results supplant the understanding of screening in layered materials and their heterostructures, introduce a knob to tune selected many-body effects, and reshape the framework for detecting and controlling correlated quantum many-body states and designing optoelectronic and quantum devices.

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

Consistent and reproducible computation of the glass transition temperature from molecular dynamics simulations

In many fields, from semiconductors for opto-electronic applications to ionic liquids (ILs) for separations, the glass transition temperature (Tg) of a material is a useful gauge for its potential use in practical settings. As a result, there is a great deal of interest in predicting Tg using molecular simulations. However, the uncertainty and variation in the trend shift method, a common approach in simulations to predict Tg, can be high. This is due to the need for human intervention in defining a fitting range for linear fits of density with temperature assumed for the liquid and glass phases across the simulated cooling. The definition of such fitting ranges then defines the estimate for the Tg as the intersection of linear fits. We eliminate this need for human intervention by leveraging the Shapiro–Wilk normality test and proposing an algorithm to define the fitting ranges and, consequently, Tg. Through this integration, we incorporate into our automated methodology that residuals must be normally distributed around zero for any fit, a requirement that must be met for any regression problem. Consequently, fitting ranges for realizing linear fits for each phase are statistically defined rather than visually inferred, obtaining an estimate for Tg without any human intervention. The method is also capable of finding multiple linear regimes across density vs temperature curves. We compare the predictions of our proposed method across multiple IL and semiconductor molecular dynamics simulation results from the literature and compare other proposed methods for automatically detecting Tg from density–temperature data. We believe that our proposed method would allow for more consistent predictions of Tg. We make this methodology available and open source through GitHub.

Chemistry↗
DOE OSTI2022

Evaluation of UAV-derived multimodal remote sensing data for biomass prediction and drought tolerance assessment in bioenergy sorghum

Screening for drought tolerance is critical to ensure high biomass production of bioenergy sorghum in arid or semi-arid environments. The bottleneck in drought tolerance selection is the challenge of accurately predicting biomass for a large number of genotypes. Although biomass prediction by low-altitude remote sensing has been widely investigated on various crops, the performance of the predictions are not consistent, especially when applied in a breeding context with hundreds of genotypes. In some cases, biomass prediction of a large group of genotypes benefited from multimodal remote sensing data; while in other cases, the benefits were not obvious. In this study, we evaluated the performance of single and multimodal data (thermal, RGB, and multispectral) derived from an unmanned aerial vehicle (UAV) for biomass prediction for drought tolerance assessments within a context of bioenergy sorghum breeding. The biomass of 360 sorghum genotypes grown under well-watered and water-stressed regimes was predicted with a series of UAV-derived canopy features, including canopy structure, spectral reflectance, and thermal radiation features. Biomass predictions using canopy features derived from the multimodal data showed comparable performance with the best results obtained with the single modal data with coefficients of determination (R 2 ) ranging from 0.40 to 0.53 under water-stressed environment and 0.11 to 0.35 under well-watered environment. The significance in biomass prediction was highest with multispectral followed by RGB and lowest with the thermal sensor. Finally, two well-recognized yield-based drought tolerance indices were calculated from ground truth biomass data and UAV predicted biomass, respectively. Results showed that the geometric mean productivity index outperformed the yield stability index in terms of the potential for reliable predictions by the remotely sensed data. Collectively, this study demonstrated a promising strategy for the use of different UAV-based imaging sensors to quantify yield-based drought tolerance.

09 BIOMASS FUELS↗
DOE OSTI2020

Development and validation of the cavitation-induced erosion risk assessment tool

This work presents the development of a cavitation-induced erosion risk assessment (CIERA) tool that links multiphase flow simulation predictions with the progress towards material erosion. To develop a robust erosion modeling tool, the cavitation and erosion predictions for pressurized diesel fuel flow within a channel geometry were validated over a range of Reynolds and cavitation number conditions in two different aluminum channel geometries, one featuring a rounded inlet corner and the other with a sharp inlet corner. The multiphase flow development within the channel was modeled using a compressible mixture model, where phase change was represented with the homogeneous relaxation model and the turbulent flow evolution was modeled using a dynamic structure approach for Large Eddy Simulations. To improve representation of the incubation period before material rupture over existing approaches, a physics-based metric was derived based on the cumulative energy absorbed by the solid material from repeated hydrodynamic impacts. When the average peak pressure was related to the incubation period, the incubation period and its sensitivity to changes in flow conditions were found to be overpredicted. In contrast, predictions from CIERA provided a more accurate means to qualitatively and quantitatively predict the influence of flow conditions on the incubation period before material erosion. When the predicted stored energy was related to the solid material properties to estimate the incubation period, multiphase flow simulations demonstrated accurate representation of the sensitivity of erosion severity to changes in flow conditions. The use of CIERA led to quantitative agreement of the predicted incubation period within 5% of the experimentally measured incubation period.

42 ENGINEERING↗
DOE OSTI2026

Nuclear shell structure governs short-range nucleon pairing

Atomic nuclei are intricate quantum systems in which nucleons (protons and neutrons) are held together by the strong nuclear force. At very short distances, nucleons can momentarily form high-momentum pairs—known as short-range-correlated pairs—that shape the high-momentum structure of nuclear matter. Studying how nucleons form short-range-correlated pairs provides a rare experimental window into the short-distance behaviour of the strong interaction. Here, in this study, we use the scattering of high-energy electrons from 40 Ca, 48 Ca and 54 Fe, chosen for their distinct shell structures, to probe the formation of short-range-correlated pairs. Unexpectedly, we find that short-range-correlated pairing depends far more on the specific quantum orbitals occupied by protons and neutrons than on the nuclear mass or neutron–proton imbalance. This dependence is much stronger than that predicted by theoretical models. Our results point to a need for new angular-momentum quantum selection rules governing short-range nucleon pairing and reveal a deep connection between long-range nuclear shell structure and short-range interactions.

Nguyen, D. [Thomas Jefferson National Accelerator ↗
DOE OSTI2023

Transonic dislocation propagation in diamond

Here, the motion of line defects (dislocations) has been studied for more than 60 years, but the maximum speed at which they can move is unresolved. Recent models and atomistic simulations predict the existence of a limiting velocity of dislocation motion between the transonic and subsonic ranges at which the self-energy of dislocation diverges, though they do not deny the possibility of the transonic dislocations. We used femtosecond x-ray radiography to track ultrafast dislocation motion in shock-compressed single-crystal diamond. By visualizing stacking faults extending faster than the slowest sound wave speed of diamond, we show the evidence of partial dislocations at their leading edge moving transonically. Understanding the upper limit of dislocation mobility in crystals is essential to accurately model, predict, and control the mechanical properties of materials under extreme conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Hydrologic investigations of radar-rainfall error propagation to rainfall-runoff model hydrographs

Rainfall is arguably the most important yet most variable input for rainfall-runoff hydrologic models. In this study, the authors search for the characteristics of radar-rainfall estimates that are most important for skillful streamflow predictions. They perform comprehensive hydrologic investigations of radar-rainfall characteristics, including spatiotemporal resolution, radar range visibility, statistical characterization of rainfall variability, all vis-a-vis basin characteristics such as size and river network topology. Since the true rainfall fields are unknown, the authors exploit a paradigm of using two independently constructed radar-rainfall products i.e., Multi-Radar Multi-Sensor and IFC-ZR used operationally by the Iowa Flood Center (IFC). Using the distributed hydrologic model called the Hillslope-Link Model for the domain of the state of Iowa, they evaluate streamflow prediction at 140 USGS gauge stations that monitor rivers in Iowa. Through spatial and temporal rainfall aggregation experiments, the authors show that the impact of spatial and temporal resolution of rainfall is significant typically for smaller basins while starts reducing significantly for basins larger than 1,000 km 2 . Other rainfall characteristics they explored do not reveal a strong signature in the relationship of rainfall differences between the two products and hydrograph errors. However, exploring the product similarities rather than differences reveals that the basin-wide rainfall volume has the most significant effect on streamflow prediction. The results from this study are generalizable for all rainfall observing systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Predicting Thermal Excursions During in situ Oxidative Regeneration of Packed Bed Catalytic Fast Pyrolysis Catalyst

Ex situ catalytic fast pyrolysis (CFP) uses a secondary reactor to upgrade biomass pyrolysis vapors to stabilized CFP oils with reduced oxygen content. In one configuration, the secondary reactor is operated as a packed-bed swing reactor system which allows coke-deactivated beds to be decarbonized in situ while other beds remain online for vapor upgrading. In situ decarbonization must be done carefully to avoid irreversible deactivation and/or physical degradation of catalyst pellets. Given that packed bed reactors are well known to have poor heat transfer characteristics, this is a critical issue impacting scaleability and commercial viability of the technology. To predict thermal excursions during regeneration, finite element computational models have been built to assist in scaling up oxidative decarbonization of a Pt/TiO2 CFP catalyst (0.5 mm spheres) from a bench scale packed bed with 100 g of catalyst to a pilot scale packed bed with 2 kg of catalyst and internal cooling tubes. Based on transient measurements of outlet temperature and effluent CO2 concentration, and using an assumed coke profile and activation energy, this paper demonstrates that specific combinations of effective thermal conductivity and wall heat transfer coefficient can fit bench scale oxidative regeneration data equally well. For the upscaled 2 kg bed, four bench-scale “best fit” parameter pairs give different predictions for location and magnitude of thermal excursions, with the maximum computed bed temperature gradients ranging from 30 °C cm-1 to as high as 3000 °C cm-1. The larger the fraction of heat removal by conduction through the cooling tubes, the greater the differences between the parameter pairs. The modelling results presented in this paper cast doubt on the industrial viability of the proposed combination of catalyst, bed and regeneration process, and point to the need for alternate reactor designs. However, there is considerable uncertainly in some of the key model parameters. The reliability of model predictions can be increased by adding more temperature measurements at key bed locations, testing additional variations in process conditions, performing careful bed dissections to determine the true coke profile, and perhaps most importantly, directly measuring the effective thermal conductivity of the catalyst pellets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Computationally Predicted High-Throughput Free-Energy Phase Diagrams for the Discovery of Solid-State Hydrogen Storage Reactions

The design of multinary solid-state material systems that undergo reversible phase changes via changes in temperature and pressure provides a potential means of safely storing hydrogen. However, fully mapping the stabilities of known or newly targeted compounds relative to competing phases at reaction conditions has previously required many stringent experiments or computationally demanding calculations of each compound’s change in Gibbs energy with respect to temperature, G(T). Here, we have extended the approach of constructing chemical potential phase diagrams based on ΔG f (T) to enable the analysis of phase stability at non-zero temperatures. We first performed density functional theory calculations to compute the formation enthalpies of binary, ternary, and quaternary compounds within several compositional spaces of current interest for solid-state hydrogen storage. Temperature effects on solid compound stability were then accounted for using our recently introduced machine learned descriptor for the temperature-dependent contribution G δ (T) to the Gibbs energy G(T). From these Gibbs energies, we evaluated each compound’s stability relative to competing compounds over a wide range of conditions and show using chemical potential and composition phase diagrams that the predicted stable phases and H2 release reactions are consistent with experimental observations. This demonstrates that our approach rapidly computes the thermochemistry of hydrogen release reactions for compounds at sufficiently high accuracy relative to experiment to provide a powerful framework for analyzing hydrogen storage materials. This framework based on G(T) enables the accelerated discovery of active materials for a variety of technologies that rely on solid-state reactions involving these materials.

08 HYDROGEN↗
DOE OSTI2025

Search for boosted low-mass resonances decaying into hadrons produced in association with a photon in pp collisions at $ \sqrt{s}$ = 13 TeV with the ATLAS detector

Many extensions of the Standard Model, including those with dark matter particles, propose new mediator particles that decay into hadrons. This paper presents a search for such low mass narrow resonances decaying into hadrons using 140 fb −1 of proton-proton collision data recorded with the ATLAS detector at a centre-of-mass energy of 13 TeV. The resonances are searched for in the invariant mass spectrum of large-radius jets with two-pronged substructure that are recoiling against an energetic photon from initial state radiation, which is used as a trigger to circumvent limitations on the maximum data recording rate. This technique enables the search for boosted hadronically decaying resonances in the mass range 20–100 GeV hitherto unprobed by the ATLAS Collaboration. The observed data are found to agree with Standard Model predictions and 95% confidence level upper limits are set on the coupling of a hypothetical new spin-1 Z′ resonance with Standard Model quarks as a function of the assumed Z′-boson mass in the range between 20 and 200 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

X-ray diffraction from shock driven Sn microjets

Here, in situ x-ray diffraction was performed on shock-generated microjets composed of Sn and Sn–4Ag. Under low pressure drives (~21 GPa), a significant fraction of the jet volume was found to be in the β-Sn phase, and these crystallites were much smaller than the initial grain size of the material. Significant quantities of amorphous (molten) material were observed for higher drive pressures (~25–35 GPa). The extent of melting at these pressures was greater than would be predicted for uniaxial shock loading. Diffraction patterns from the Sn–4Ag alloy showed a peak that is consistent with the expected Ag 3 Sn intermetallic phase. This peak remained evident under drive conditions where the sample was otherwise fully amorphous. This indicates a slushy or a mixed phase of liquid Sn and solid Ag 3 Sn. Given the eutectic character of this alloy, this observation is attributed to a kinetic limitation on the dissolution of Ag 3 Sn. This implies that a much broader range of drive conditions will lead to mixed phase jets and ejecta than would be predicted from the equilibrium melt boundary of such alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Surface Atmosphere Integrated Field Laboratory (SAIL) Campaign

The science of mountainous hydrology spans the atmosphere through the bedrock and inherently crosses physical and disciplinary boundaries: land-atmosphere interactions in complex terrain enhance clouds and precipitation, while watersheds retain and release water over a large range of spatial and temporal scales. Limited observations in complex terrain challenge efforts to improve predictive models of the hydrology in the face of rapid changes. The Upper Colorado River exemplifies these challenges, especially with ongoing mismatches between precipitation, snowpack, and discharge. Consequently, the U.S. Department of Energy’s (DOE) Atmospheric Radiation Measurement (ARM) user facility has deployed an observatory to the East River Watershed near Crested Butte, Colorado between September 2021 and June 2023 to measure the main atmospheric drivers of water resources, including precipitation, clouds, winds, aerosols, radiation, temperature and humidity. This effort, called the Surface Atmosphere Integrated Field Laboratory (SAIL), is also working in tandem with DOE-sponsored surface and subsurface hydrologists and other federal, state, and local partners. SAIL data can be benchmarks for model development by producing a wide range of observational information on precipitation and its associated processes, including those processes that impact snowpack sublimation and redistribution, aerosol direct radiative effects in the atmosphere and in the snowpack, aerosol impacts on clouds and precipitation, and processes controlling surface fluxes of energy and mass. Preliminary data from SAIL’s first year showcase the rich information content in SAIL’s many data-streams and support testing hypotheses that will ultimately improve scientific understanding and predictability of Upper Colorado River hydrology in 2023 and beyond.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Cosmic Supernova Neutrino and Gamma-Ray Backgrounds in the MeV Regime

Cosmic multimessenger backgrounds include relic diffuse components created in the early universe and contributions from individual sources. Here, we study both type Ia supernovae (SNe Ia) and core-collapse supernovae (CCSNe) contributions to the diffuse neutrino and gamma-ray backgrounds in the MeV regime referred to as DSNB and DSGB respectively. We show that the diffuse SN Ia background is 10 6 times lower (for $\overline{v}_e$) than the CCSN background making it negligible. Our predicted DSNB $\overline{v}_e$ flux at earth in the 19.3–32 MeV regime is 0.36 ν cm -2 s -1 . We also find that the DSNB flux in the energy range from 11.3 to 32 MeV varies by +29% with a change in the SFRD model from Madau & Fragos which yielded a minimum predicted flux, to the extragalactic background light reconstruction model (maximum predicted flux). The diffuse SN Ia gamma-ray background and its dependence on the progenitor supernova delay time distribution are also evaluated. Furthermore, we address the origin of the CGB (Cosmic Gamma-ray Background) in the 0.1–7 MeV regime by adding contributions from sources such as SNe Ia, CCSNe, radio-quiet Active Galactic Nuclei, Flat spectrum radio quasars (FSRQs) and Neutron star—neutron star mergers. We find that our modeled background (including uncertainties) matches the observed CGB above 1.0 MeV, but is a factor ≈2 lower than the observed flux in the 0.1–1.0 MeV range, highlighting the need for future MeV missions to establish the CGB spectrum more reliably, and to possibly identify additional sources or even source classes in the underexplored MeV band.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Cloud condensation nuclei activity of internally mixed particle populations at a remote marine free troposphere site in the North Atlantic Ocean

Here, this study reports results from research conducted at the Observatory of Mount Pico (OMP), 2225 m above mean sea level on Pico Island in the Azores archipelago in June and July 2017. We investigated the chemical composition, mixing state, and cloud condensation nuclei (CCN) activities of long-range transported free tropospheric (FT) particles. FLEXible PARTicle Lagrangian particle dispersion model (FLEXPART) simulations reveal that most air masses that arrived at the OMP during the sampling period originated in North America and were highly aged (average plume age > 10 days). We probed size-resolved chemical composition, mixing state, and hygroscopicity parameter ($\mathcal{κ}$) of individual particles using computer-controlled scanning electron microscopy with an energy-dispersive X-ray spectrometer (CCSEM-EDX). Based on the estimated individual particle mass from elemental composition, we calculated the mixing state index, $χ$. During our study, FT particle populations were internally mixed ($χ$ of samples are between 53% and 87%), owing to the long atmospheric aging time. We used data from a miniature Cloud Condensation Nucleus Counter (miniCCNC) to derive the hygroscopicity parameter, $\mathcal{κ}$ CCNC . Combining $\mathcal{κ}$ CCNC and FLEXPART, we found that air masses recirculated above the North Atlantic Ocean with lower mean altitude had higher $\mathcal{κ}$ CCNC due to the higher contribution of sea salt particles. We used CCSEM-EDX and phase state measurements to predict single-particle $\mathcal{κ}$ ($\mathcal{κ}$ CCSEM-EDX ) values, which overlap with the lower range of $\mathcal{κ}$ CCNC measured below 0.15 % SS. Therefore, CCSEM-EDX measurements can be useful in predicting the lower bound of $\mathcal{κ}$, which can be used in climate models to predict CCN activities, especially in remote locations where online CCN measurements are unavailable.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Search for a resonance decaying into a scalar particle and a Higgs boson in the final state with two bottom quarks and two photons with 199 fb −1 of data collected at $\sqrt{s}$ = 13 and 13.6 TeV with the ATLAS detector

A search for the resonant production of a heavy scalar X decaying into a lighter scalar S and a Higgs boson, through the process X → S (→ $b\bar{b}$) H (→ γγ) , where the two photons are consistent with the Higgs boson decay, is performed. The search is conducted using integrated luminosities of 140 and 59 fb −1 of proton–proton collision data at centre-of-mass energies of 13 and 13.6 TeV, respectively, recorded with the ATLAS detector at the LHC. The search is performed over the mass ranges of 170 ≤ m X ≤ 1000 GeV and 15 ≤ m S ≤ 500 GeV. No significant excess over the Standard Model background predictions is observed and limits at 95% confidence level are set on the product of cross section and branching fraction for the process X → S (→ $b\bar{b}$) H (→ γγ) at 13 TeV, ranging from 9 fb to 0.06 fb.

Aad, G. (ORCID:0000000266654934)↗
DOE OSTI2020

Infrared spectroscopic method for uranium isotopic analysis

A high performance infrared (HPIR) system was developed and demonstrated for the infrared absorption analysis of {sup 235}U and {sup 238}U isotopes in uranium hexafluoride gas samples. Sweeping the quantum cascade laser light source over the spectral range and sampling via a high-rate analog-to-digital converter provided 0.0005 cm-1 spectral resolution, which allowed for high-precision measurements of the isotopic peak shift. A data analysis method was developed using principal component analysis to predict the isotope weight % content of {sup 235}U. The HPIR precision, accuracy, and error were evaluated for a wide range of isotopic ratio samples (0.287 – 93.7 weight % {sup 235}U), and the results were compared to the International Target Values (ITVS) set forth by the International Atomic Energy Agency (IAEA) for non-destructive and destructive analytical techniques. The method meets or surpasses the IAEA ITVs for non-destructive analysis of samples with isotopic content of depleted to highly enriched. The results also demonstrated the capability of the HPIR system to correctly predict the {sup 235}U weight % content of a mislabeled sample whose isotopic distribution was validated by mass spectroscopic measurements. The HPIR measurement is nondestructive and, thus, allows for confirmatory analyses of the exact sample at a designated IAEA lab if higher-resolution or a certified analysis is needed. (author)

07 ISOTOPE AND RADIATION SOURCES↗