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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Electrofracturing of Shale at Elevated Pressure

Electrofracturing deeply buried shale formations could be used to increase reservoir permeability and improve reservoir production without requiring large volumes of freshwater. This paper describes a novel experimental system and initial test results to electrofracture shale under high confining pressures. Core-scale laboratory testing was performed on twelve rock samples recovered from a shale gas reservoir. Each sample was subjected to confining pressures of 20.7 MPa (3000 psi) or 58.6 MPa (8000 psi), representative of overburden pressures at depth. Samples were then subjected to application of high voltage until specimen fracture. The experiments produced deformed samples with multiple fracture types, both parallel and oblique to bedding planes. Electrofracturing increased permeabilities by up to nine orders of magnitude for extended time periods. Rock fracture and throughgoing fractures were demonstrated. Computed tomography images revealed the creation of fractures and tube/tunnel flow channels, which resisted closure under hydrostatic pressures up to 58.6 MPa. The breakdown energy and permeability changes in the sample were independent of applied confining pressure. The cumulative energy input required for fracture depended on applied confining pressure and sample length. The energy required to fracture samples up to 9 cm in length is generally more than 0.5 kJ/cm, but no greater than 1 kJ/cm. Our results show that electrofracture of shales under confining pressure is possible and could be a possible water-free mechanism for reservoir stimulation.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2024

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (<15%) and GPU memory (<35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. Furthermore, we observed that Fourier-MIONet can maintain good accuracy when predicting out-of-distribution (OOD) data. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Furthermore, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

Geological carbon sequestration (GCS) involves injecting CO2 into subsurface geological formationsfor permanent storage. Numerical simulations could guide decisions in GCS projects by predictingCO 2 migration pathways and the pressure distribution in storage formation. However, these simula-tions are often computationally expensive due to highly coupled physics and large spatial-temporalsimulation domains. Surrogate modelling with data-driven machine learning has become a promis-ing alternative to accelerate physics-based simulations. Among these, the Fourier neural operator(FNO) has been applied to three-dimensional synthetic subsurface models. Despite its good accuracyin simulating CO 2 plume migration, it requires large computational resources in training and alsolacks generalizability. Here, to further improve performance, we have developed a nested Fourier-DeepONet by combining the expressiveness of the FNO with the modularity of a deep operatornetwork (DeepONet). This new framework is twice as efficient as a nested FNO for training and has atleast 80% lower GPU memory requirement due to its flexibility to treat temporal coordinates sepa-rately. These performance improvements are achieved without compromising prediction accuracy.In addition, the generalization and extrapolation ability of nested Fourier-DeepONet beyond thetraining range has been thoroughly evaluated. Nested Fourier-DeepONet outperformed the nestedFNO for extrapolation in time with more than 50% reduced error. It also exhibited good extrapolationaccuracy beyond the training range in terms of reservoir properties, number of wells, and injectionrate.

Lee, Jonathan E. [Department of Chemical and Envir↗
DOE OSTI2026

Optimizing district energy systems by integrating Borehole Thermal Energy Storage Using a Mixed-Integer Linear Programming g-function framework with a Multi-Timescale Rolling Horizon method

Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.

Yang, Jiahui↗
DOE OSTI2025

Material Fracturing and Failure Simulation Datasets

Fracturing is a fundamental physics phenomena with broad relevance across multiple domains, ranging from infrastructure integrity, aerospace durability, reservoir production, and seismic events. We present a diverse dataset of simulated fracture evolution and material failure generated from two numerical solvers: the phase-field method and the combined finite-discrete element method (FDEM). These solvers differ in formulation, physical fidelity, and computational efficiency. The dataset includes five materials: PBX, anisotropic shale, tungsten, aluminum, and steel. For each, phase-field simulations span 400,000 cases: 200,000 under uniaxial tension and 200,000 under biaxial tension. The computationally expensive FDEM simulations include 90,000 split evenly among PBX, shale, and tungsten under uniaxial loading. All simulations begin with randomized initial fracture patterns. Each entry includes temporal data capturing fracture propagation dynamics. This comprehensive dataset is designed to support the development of foundational or surrogate machine learning approaches for predicting material failure. While no such models are introduced here, the dataset lays a robust foundation for advancing future research and innovation in these areas.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Failure Analysis–Informed Risk Assessment Framework for Geological Carbon Storage Using Numerical Simulation and Machine Learning

Geological carbon storage (GCS) is recognized as a critical technology for achieving large-scale reductions in anthropogenic carbon dioxide (CO 2 ) emissions. Ensuring long-term containment and safety requires robust risk assessment frameworks that account for geological uncertainty and identify potential failure scenarios. Among various indicators, the area of review (AoR) serves as a key metric for evaluating storage performance, regulatory compliance, and monitoring design, as it delineates the spatial extent impacted by pressure buildup and plume migration. However, conventional AoR-based risk assessments typically perturb parameters within narrow uncertainty bounds, potentially overlooking rare but high-impact events arising from extreme geological conditions. In this study, we present a failure analysis–informed risk assessment framework for large-scale GCS projects to improve site prescreening and monitoring design. A suite of 300 numerical simulations was generated using stochastic geological models that vary five key parameters: net-to-gross ratio, anisotropy azimuth, porosity multiplier, permeability multiplier, and vertical-to-horizontal permeability ratio. Among these, 200 realizations represent normal geological uncertainty, while 100 additional cases explore extreme yet plausible conditions for failure-case analysis. The AoR was simulated and computed from pressure and CO 2 saturation fields, where the baseline AoR boundary, representing the extent predicted under typical geological uncertainty, was defined as the union of 200 normal-range simulations, and failure was identified when extreme-range cases exceeded this baseline. Results show that incorporating broader parameter uncertainty produces significantly larger AoR extents, underscoring the potential underestimation of risk under conventional uncertainty ranges. Furthermore, spatial probability maps derived from failure-induced AoR exceedance identify regions requiring enhanced monitoring attention. Various machine learning (ML)–based classifiers were developed to predict failure occurrence from geological parameters, with the random forest model achieving the highest performance (F1-score of 0.986). Consistent findings from correlation coefficient, feature importance, and Sobol sensitivity analyses reveal that low net-to-gross ratios and permeability multipliers are the dominant risk drivers, reflecting reduced reservoir connectivity and limited pressure dissipation. Altogether, these results provide a novel framework for risk-informed site prescreening and monitoring design that explicitly considers rare but high-impact geological scenarios in GCS projects.

25 ENERGY STORAGE↗
NASA NTRS1997

Automated Liquid-Level Control of a Nutrient Reservoir for a Hydroponic System

A microprocessor-based system for control of the liquid level of a nutrient reservoir for a plant hydroponic growing system has been developed. The system uses an ultrasonic transducer to sense the liquid level or height. A National Instruments' Multifunction Analog and Digital Input/Output PC Kit includes NI-DAQ DOS/Windows driver software for an IBM 486 personal computer. A Labview Full Development system for Windows is the graphical programming system being used. The system allows liquid level control to within 0.1 cm for all levels tried between 8 and 36 cm in the hydroponic system application. The detailed algorithms have been developed and a fully automated microprocessor based nutrient replenishment system has been described for this hydroponic system.

Smith, Boris↗
NASA NTRS1978

A scene-analysis approach to remote sensing

The author has identified the following significant results. Geometric correspondance between a sensed image and a symbolic map is established in an initial stage of processing by adjusting parameters of a sensed model so that the image features predicted from the map optimally match corresponding features extracted from the sensed image. Information in the map is then used to constrain where to look in an image, what to look for, and how to interpret what is seen. For simple monitoring tasks involving multispectral classification, these constraints significantly reduce computation, simplify interpretation, and improve the utility of the resulting information. Previously intractable tasks requiring spatial and textural analysis may become straightforward in the context established by the map knowledge. The use of map-guided image analysis in monitoring the volume of water in a reservoir, the number of boxcars in a railyard, and the number of ships in a harbor is demonstrated.

Tenenbaum, J. M.↗
DOE OSTI2025

Continuous operation of a coherent 3,000-qubit system

Neutral atoms are a promising platform for quantum science, enabling advances in areas ranging from quantum simulations and computation to metrology, atomic clocks and quantum networking. Although atom losses typically limit these systems to a pulsed mode, continuous operation could substantially enhance cycle rates, remove bottlenecks in metrology and enable deep-circuit quantum evolution through quantum error correction. Here we demonstrate an experimental architecture for high-rate reloading and continuous operation of a large-scale atom-array system while realizing coherent storage and manipulation of quantum information. Our approach utilizes a series of two optical lattice conveyor belts to transport atom reservoirs into the science region, where atoms are repeatedly extracted into optical tweezers without affecting the coherence of qubits stored nearby. Using a reloading rate of 300,000 atoms in tweezers per second, we create over 30,000 initialized qubits per second, which we leverage to assemble and maintain an array of over 3,000 atoms for more than 2 hours. Furthermore, we demonstrate persistent refilling of the array with atomic qubits in either a spin-polarized or a coherent superposition state while preserving the quantum state of stored qubits. Our results pave the way for the realization of large-scale continuously operated atomic clocks, sensors and fault-tolerant quantum computers.

atomic and molecular physics↗
DOE OSTI2024

Pore-scale visualization of natural hydrate-bearing sediments

Accurate modeling of gas hydrate reservoir productivity and geomechanical risks associated with subsurface dissociation of natural gas hydrates (NGH) requires the determination of model parameters through physical testing on natural hydrate-bearing sediments (HBS). This involves investigating the hydro-mechanical behavior of undisturbed hydrate samples from nature under in situ conditions using pressure core characterization and analysis, which provides a unique opportunity for research. By employing state-of-the-art micro computed tomography imagery on cryogenically preserved, hydrate-bearing sediment samples, we can determine hydrate saturation as well as permeability with and without the presence of hydrates in the sediment. Furthermore, utilizing a machine learning based image segmentation technique, it is possible to extract pore space and grain information. Subsections of the entire image volume were used to determine anisotropic permeabilities using a finite-difference method Stokes solver (FDMSS). Additionally, permeability measurements on whole pressure and temperature preserved hydrate-bearing core were analyzed by utilizing the National Energy Technology Laboratory’s (NETL) Pressure Core Characterization and X-ray CT Visualization Tool (PCXT) to manipulate, cut, and analyze pressure preserved sediment. Permeabilities were measured under a broad range of vertical stress states to simulate expected pressure changes during production scenarios, and the results show that permeabilities derived from images are in agreement with those from traditional core derived experiments. The collected stress-dependent permeability, permeability anisotropy, and corresponding gas hydrate saturations provide valuable input into numerical simulations of reservoir productivity. These properties have been proven to be key parameters determining a long-term reservoir response under depressurization.

Liu, Mengwei [Oak Ridge Institute for Science and ↗
NASA NTRS1990

Intraocular pressure, retinal vascular, and visual acuity changes during 48 hours of 10-deg head-down tilt

Intraocular pressures, retinal vascular diameters, and visual acuities of nine men, were repeatedly measured while the subjects were tilted 10 deg head-down for 48 h and while they were seated before (baseline), and after the tilt. An immediate increase in intraocular pressure, measured by pneumatonometer was recorded when subjects assumed the head-down position, and diurnal variations in intraocular pressures were observed for the 48 h. The initial and final head-down intraocular pressures were not significantly different. However, when subjects resumed the sitting position, intraocular pressures fell below the initial sitting values. Computer image analysis of the retinal vasculature detected a 6 percent and 2 percent reduction in the caliber of arteries and veins, respectively, as compared with sitting baseline values. No changes in visual acuity were documented during the 48 h of head-down tilt. The data suggest that the choroidal blood reservoir increases in volume over 48 h at continuous head-down position with a compensatory decrease in aqueous volume. These findings may explain intraocular pressure changes noted in astronauts during previous space missions and in studies associated with change in body position.

Mader, Thomas H.↗
NASA NTRS2015

Core Analysis Combining MT (TIPPER) and Dielectric Sensors (Sans EC) in Earth and Space

On terrestrial planets and moons of our solar system cores reveal details about a geological structure's formation, content, and history. The strategy for the search for life is focused first on finding water which serves as a universal solvent, and identifying the rocks which such solvent act upon to release the constituent salts, minerals, ferrites, and organic compounds and chemicals necessary for life. Dielectric spectroscopy measures the dielectric properties of a medium as a function of frequency. Reflection measurements in the frequency range from 300 kHz to 300 MHz were carried out using RF and microwave network analyzers interrogating SansEC Sensors placed on clean geological core samples. These were conducted to prove the concept feasibility of a new geology instrument useful in the field and laboratory. The results show that unique complex frequency spectra can be acquired for a variety of rock core samples. Using a combination of dielectric spectroscopy and computer simulation techniques the magnitude and phase information of the frequency spectra can be converted to dielectric spectra. These low-frequency dielectric properties of natural rock are unique, easily determined, and useful in characterizing geology. TIPPER is an Electro-Magnetic Passive-Source Geophysical Method for Detecting and Mapping Geothermal Reservoirs and Mineral Resources. This geophysical method uses distant lightning and solar wind activity as its energy source. The most interesting deflections are caused by the funneling of electrons into more electrically conductive areas like mineralized faults, water or geothermal reservoirs. We propose TIPPER to be used with SansEC for determining terrain/ocean chemistry, ocean depth, geomorphology of fracture structures, and other subsurface topography characteristics below the ice crust of Jovian moons. NASA envisions lander concepts for exploration of these extraterrestrial icy surfaces and the oceans beneath. One such concept would use a nuclear powered heated tip for melting through the ice sheath of Europa and inserting a down hole SansEC with TIPPER interface. NASA's Juno space probe already on the way to Jupiter as part of the Exploration New Frontiers Program and the planned Europa mission will conduct detailed reconnaissance of Jupiter's moon Europa and investigate whether the icy moon could harbor conditions suitable for life. It has already been observed that Jovian moons have auroras that may serve as naturally occurring active energy sources for a TIPPER instrument.

Mound, Michael C.↗
NASA NTRS1992

Flow characterization in the NASA Ames 16-inch Shock Tunnel

Flow characteristics of NASA's 16-Inch Shock Tunnel are determined for purposes of providing hypersonic propulsion simulation capability. The key tunnel operating parameters are the incident shock speed and reservoir pressure and enthalpy. Flow characteristics of concern are the nozzle exit pressure, temperature, Mach number, Reynolds number, chemical composition, and flow uniformity. Surface mounted gages (for pressure and heat transfer) and nonintrusive optical flow diagnostics (emission and absorption spectroscopy and holographic interferometry) are used to verify tunnel conditions. Experimental measurements are used to validate computational analysis for predicting facility performance, and CFD is used to interpret the free stream optical diagnostic measurements.

Cavolowsky, John A.↗
NASA NTRS2007

Quantum Chemical Evaluation of the Astrochemical Significance of Reactions between S Atom and Acetylene or Ethylene

Addition-elimination reactions of S atom in its P-3 ground state with acetylene (C2H2) and ethylene (C2H4) were characterized with both molecular orbital and density functional theory calculations employing correlation consistent basis sets in order to assess the likelihood either reaction might play a general role in astrochemistry or a specific role in the formation of S2 (X (sup 3 SIGMA (sub g) (sup -)) via a mechanism proposed by Saxena and Misra (Mon. Not. R. Astron. Soc. 1995, 272, 89). The acetylene and ethylene reactions proceed through C2H2S ((sup 3)A")) and C2H4S ((sup 3)A")) intermediates, respectively, to yield HCCS ((sup 2)II)) and C2H3S ((sup 2)A')). Substantial barriers were found in the exit channels for every combination of method and basis set considered in this work, which effectively precludes hydrogen elimination pathways for both S + C2H2 and S + C2H4 in the ultracold interstellar medium where only very modest barriers can be surmounted and processes without barriers tend to predominate. However, if one or both intermediates is formed and stabilized efficiently under cometary or dense interstellar cloud conditions, they could serve as temporary reservoirs for S atom and participate in reactions such as S + C2H2S (right arrow) S2 = C2H2 or S + C2H4S (right arrow) S2 + C2H4. For formation and stabilization to be efficient, the reaction must possess a barrier height small enough to be surmountable at low temperatures yet large enough to prevent redissociation to reactants. Barrier heights computed with B3LYP and large basis sets are very low, but more rigorous QCISD(T) and RCCSD(T) results indicate that the barrier heights are closer to 3-4 kcal/mol. The calculations therefore indicate that S + C2H2 or S + C2H4 could contribute to the formation of S2 in comets and may serve as a means to gauge coma temperature. The energetics of the ethylene reaction are more favorable.

Woon, David E.↗
NASA NTRS1973

Applications of ERTS-1 Data Collection System (DCS) in the Arizona Regional Ecological Test Site (ARETS)

The author has identified the following significant results. The DCS water-stage data from the USGS streamflow gaging station on the Verde River near Camp Verde furnished information sufficient for the accurate computation of daily mean streamflow rates during the first 2 months of operation. Daily mean flow rates computed from the DCS data agreed with those computed from the digital recorder data within + or - 5% during periods of stable or slowly changing flow and within + or - 10% during periods of rapidly changing high flow. The SRP was furnished near-real time DCS information on snow moisture content and streamflow rates for use in the management and operation of the multiple-use reservoir system. The SRP, by prudent water management and the use of near-real time hydrologic data furnished by microwave and ERTS DCS telemetry, was successful in anticipating the amount of flow into the Salt and Verde Rivers and in the subsequent release of water at rates that did not create flooding in metropolitan Phoenix. Only minor flooding occurred along the Gila River west of Phoenix. According to the Maricopa County Civil Defense agency, wage and salary losses of about $11,400,000 resulted from closing of roads across the Salt River in the winter and spring of 1972-73; however, the number and duration of the closing were minimized by use of DCS data.

Schumann, H. H.↗
NASA NTRS1992

Computational and numerical analysis of hypersonic nozzle flows with comparisons to wind tunnel calibration data

Navier-Stokes (NS), parabolized NS codes, and classical method of characteristics prediction techniques are employed to compute hypersonic nozzle flowfields for the 15 in Mach 6 High Temperature Tunnel and the 16 in Mach 17 Nitrogen Tunnel, which are part of the Langley Research Center. The study focuses on defining the accuracy of these techniques by comparing the computational results to wind tunnel pitot pressure measurements conducted in the newly designed nozzle of the Mach 6 tunnel and in the original nozzle of the Mach 17 tunnel. The comparisons between predicted results and test section pitot surveys for the Mach 6 nozzle are in good agreement and show highly uniform flow over a range of reservoir pressures and temperatures.

Hackett, Charles M.↗
DOE OSTI2024

3D modeling of deep borehole electromagnetic measurements with energized casing source for fracture mapping at the Utah Frontier Observatory for Research in Geothermal Energy

Here, we present a 3D numerical modelling analysis evaluating the deployment of a borehole electromagnetic measurement tool to detect and image a stimulated zone at the Utah Frontier Observatory for Research in Geothermal Energy geothermal site. As the depth to the geothermal reservoir is several kilometres and the size of the stimulated zone is limited to several 100 m, surface-based controlled-source electromagnetic measurements lack the sensitivity for detecting changes in electrical resistivity caused by the stimulation. To overcome the limitation, the study evaluates the feasibility of using a three-component borehole magnetic receiver system at the Frontier Observatory for Research in Geothermal Energy site. To provide sufficient currents inside and around the enhanced geothermal reservoir, we use an injection well as an energized casing source. To efficiently simulate energizing the injection well in a realistic 3D resistivity model, we introduce a novel modelling workflow that leverages the strengths of both 3D cylindrical-mesh-based electromagnetic modelling code and 3D tetrahedral-mesh-based electromagnetic modelling code. The former is particularly well-suited for modelling hollow cylindrical objects like casings, whereas the latter excels at representing more complex 3D geological structures. In this workflow, our initial step involves computing current densities along a vertical steel-cased well using a 3D cylindrical electromagnetic modelling code. Subsequently, we distribute a series of equivalent current sources along the well's trajectory within a complex 3D resistivity model. We then discretize this model using a tetrahedral mesh and simulate the borehole electromagnetic responses excited by the casing source using a 3D finite-element electromagnetic code. This multi-step approach enables us to simulate 3D casing source electromagnetic responses within a complex 3D resistivity model, without the need for explicit discretization of the well using an excessive number of fine cells. We discuss the applicability and limitations of this proposed workflow within an electromagnetic modelling scenario where an energized well is deviated, such as at the Frontier Observatory for Research in Geothermal Energy site. Using the workflow, we demonstrate that the combined use of the energized casing source and the borehole electromagnetic receiver system offer measurable magnetic field amplitudes and sensitivity to the deep localized stimulated zone. The measurements can also distinguish between parallel-fracture anisotropic reservoirs and isotropic cases, providing valuable insights into the fracture system of the stimulated zone. Besides the magnetic field measurements, vertical electric field measurements in the open well sections are also highly sensitive to the stimulated zone and can be used as additional data for detecting and imaging the target. We can also acquire additional multiple-source data by grounding the surface electrode at various locations and repeating borehole electromagnetic measurements. This approach can increase the number of monitoring data by several factors, providing a more comprehensive dataset for analysing the deep-localized stimulated zone. The numerical analysis indicates that it is feasible to use the combination of the energized casing and downhole electromagnetic measurements in monitoring localized stimulated zone at large depths.

58 GEOSCIENCES↗