Results for “Charging Behavior” — Page 43

NASA NTRS1990

Comparison of currents predicted by NASCAP/LEO model simulations with elementary Langmuir-type bare probe models for an insulated cable containing a single pinhole

The behavior of a defect in the insulation of a short biased section of cable in a Low Earth Orbit (LEO) space environment was examined. Such studies are of the utmost importance for large space power systems where great quantities of cabling will be deployed. An insulated probe containing a pinhole was placed into a hypothetical high speed LEO plasma. The NASA Charging Analyzer Program (NASCAP/LEO) was used to explore sheath growth about the probe as a function of applied voltage and to predict I-V behavior. A set of independent current calculations using Langmuir's formulations for concentric spheres and coaxial cylinders were also performed. The case of concentric spheres was here extended to include the case of concentric hemispheres. Several simple Langmuir-type models were then constructed to bracket the current collected by the cable. The space-charge sheath radius and impact parameters were used to determine the proper current regime. I-V curves were plotted for the models and comparisons were made with NASCAP/LEO results. Finally, NASCAP/LEO potential contours and surface cell potential plots were examined to explain interesting features in the NASCAP/LEO I-V curve.

Galofaro, Joel T.↗

NASA NTRSDate not supplied

Monodisperse Single-Material Granular Tribocharging Modeling and Experimental Validation

Charge transfer between insulating grains has been a topic of interest for many years as this phenomenon is extremely important to many areas in industry. Of particular interest to NASA is the behavior of electrically insulative dust grains such as those found on the lunar surface. Whether poured from a scoop during sample collection activities, agitated inside a drum via mining robots, or fluidized by a gas plume, particle-particle interactions between similar granular materials will be widespread on the Moon. Designers hope to have a predictive model for how dust grains are charged, transported, and deposited on flight systems to better understand issues electrostatics may cause in future missions. While difference in work function is often seen as a driver for charge transfer between two materials, this is an incomplete representation for insulative particles. Other asymmetries in the system can also lead to charge being transferred: one such being the difference between static vs dynamic particles. Experiments performed under vacuum in the Electrostatics and Surface Physics Laboratory (ESPL) clearly show that particles having more contacts with other particles tend to charge positively and particles having fewer contacts tend to charge negatively, despite being made from the same material. During these experiments, monodisperse (population of single diameter) spherical particles were held in a reservoir which was then elevated at one end to slope into a Faraday cup used to measure bulk charge of the grains. Care was taken to limit the number of spheres bouncing out of the cup, to isolate the beads from the container itself so that only grain-to-grain interactions occurred, and to assure neutrality of the beads before the experiment began. A discrete element method (DEM) modeling package already incorporating many granular mechanics interactions was augmented to include the electrostatic behaviors seen in experiments. The model can reproduce the experimental results above by tracking the number of contacts between pairs of individual grains and applying a charge transfer condition related to this contact parameter. The experimental results as well as their incorporation into the improved modeling suite will be discussed. Future work includes adding additional asymmetries into the experiments/model such as polydisperse populations of spherical particles and irregularly shaped grains.

granular↗

NASA NTRSDate not supplied

Monodisperse Single-Material Granular Tribocharging Modeling and Experimental Validation

Charge transfer between insulating grains has been a topic of interest for many years as this phenomenon is extremely important to many areas in industry. Of particular interest to NASA is the behavior of electrically insulative dust grains such as those found on the lunar surface. Whether poured from a scoop during sample collection activities, agitated inside a drum via mining robots, or fluidized by a gas plume, particle-particle interactions between similar granular materials will be widespread on the Moon. Designers hope to have a predictive model for how dust grains are charged, transported, and deposited on flight systems to better understand issues electrostatics may cause in future missions. While difference in work function is often seen as a driver for charge transfer between two materials, this is an incomplete representation for insulative particles. Other asymmetries in the system can also lead to charge being transferred: one such being the difference between static vs dynamic particles. Experiments performed under vacuum in the Electrostatics and Surface Physics Laboratory (ESPL) clearly show that particles having more contacts with other particles tend to charge positively and particles having fewer contacts tend to charge negatively, despite being made from the same material. During these experiments, monodisperse (population of single diameter) spherical particles were held in a reservoir which was then elevated at one end to slope into a Faraday cup used to measure bulk charge of the grains. Care was taken to limit the number of spheres bouncing out of the cup, to isolate the beads from the container itself so that only grain-to-grain interactions occurred, and to assure neutrality of the beads before the experiment began. A discrete element method (DEM) modeling package already incorporating many granular mechanics interactions was augmented to include the electrostatic behaviors seen in experiments. The model can reproduce the experimental results above by tracking the number of contacts between pairs of individual grains and applying a charge transfer condition related to this contact parameter. The experimental results as well as their incorporation into the improved modeling suite will be discussed. Future work includes adding additional asymmetries into the experiments/model such as polydisperse populations of spherical particles and irregularly shaped grains.

electrostatics↗

DOE OSTI2023

Corrosion Electrochemistry of Chromium in Molten FLiNaK Salt at 600 °C

The manuscript revisits the corrosion behavior of pure Cr in molten FLiNaK salt at 600 °C from the perspective of corrosion electrochemistry. In this work, the potential-dependent, rate-limiting charge-transfer, and salt film-mediated mass-transport controlled regimes of Cr corrosion in FLiNaK at 600 °C are investigated. The kinetic and thermodynamic parameters that limit electrodissolution and the consideration of grain orientation on these regimes are elucidated. At low Cr(III) concentrations, the corrosion process is governed by charge transfer control at low overpotentials and is crystal orientation dependent. However, when Cr(III) concentrations are high or when there is a high overpotential, the formation of a metal fluoride salt film on the Cr surface shifts the kinetic behavior to be governed by mass transport control at all anodic potentials with a surface morphology controlled by salt film deposition location and identity. Evan’s diagrams were developed to consolidate and elucidate these observations. These findings were supported by an examination of the post-corrosion microstructure, X-ray diffraction of solidified salts, and thermo-kinetics analysis in each corrosion regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A tensor density measure of topological charge in three dimensional nematic phases

A path independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A related measure, when integrated over either closed or open surfaces, reduces to known results for the charge associated with point defects (hedgehogs) or Skyrmions. We further define a tensor density, the disclination density tensor D, from which the location of a disclination line can be determined. This tensor density has a dyadic decomposition near the line into its tangent and its rotation vector, allowing a convenient determination of both. The tensor D may be nonzero in special configurations in which there are no defects (double-splay or double-twist configurations), and its behavior there is provided. The special cases of Skyrmions and hedgehog defects are also examined, including the computation of their topological charge from D.

36 MATERIALS SCIENCE↗

NASA NTRS2024

Storm-Time Variability of Terrestrial Hydrogen Exosphere: Kinetic Simulation Results

Recent studies of TWINS Lyman-α observations have reported an increase in geocoronal column brightness during geomagnetic storms, indicating enhanced exospheric hydrogen atom density (NH). This suggests a complex role of exospheric neutrals in determining storm-time magnetosphere dynamics and their energy release through charge-exchange processes. We developed a Model for Analyzing Terrestrial Exosphere (MATE) to investigate storm-time exospheric behaviors and their physical drivers. MATE traces test hydrogen atoms backward in time from locations in the exosphere to a nominal exobase altitude of 500 km, employing Newtonian mechanics with gravitational force. The model then calculates the phase-space densities (PSDs) of test hydrogen atoms at the exobase using the Maxwellian distribution with physics-based exobase conditions from the TIMEGCM upper atmosphere model. MATE maps PSDs at the exobase to the exosphere using Liouville’s Theorem under collisionless assumptions and derives NH by integrating the PSDs across velocity space. We conducted MATE simulation before, during, and after a minor geomagnetic storm from 12 to 18 June 2008, and compared the model results with NH estimates from the TWINS geocorona data. MATE reproduces storm-time density enhancements soon after the minimum Dst is reached, matching well with a general trend of TWINS NH estimates. The results suggest that upper atmospheric heating during a geomagnetic storm increases the number of ballistic and escaping hydrogen atoms entering the exosphere from the exobase, thereby boosting NH. However, the magnitude of modeled NH mismatches the TWINS NH estimates. The potential mechanisms of this density discrepancy include the physics excluded in the MATE model — such as neutralneutral collisions, neutral-plasma charge exchange, solar radiation pressure, and photoionization — as well as the higher exobase hydrogen density of TIMEGCM compared to typical empirical values, which will be addressed in future.

Hyunju K Connor↗

DOE OSTI2024

Self-assembled nanofiltration membranes with thermo- and pH-responsive behavior

We produce controlled nanostructured membranes from cross-linking of self-assembled diacrylated poloxamers. At sufficiently high concentrations, poloxamers form lyotropic liquid crystals (LLCs), such as lamellar (L α ), cubic packing of spherical micelles, and hexagonal packing of rod-like micelles in water (H 1 ). We use the H 1 phase as a template to produce orderly packed nanofibrous membranes. The obtained membrane has a continuous 3D transport pathway and can alter its nanofiltration (NF) properties in response to changes in temperature and pH. The formulation includes Pluronic P84-diacrylate (P84DA), a thermoresponsive component that acts as both macromer and structure-directing amphiphile. P84DA facilitates changes in membrane pore size with temperature due to its thermoresponsiveness when it is in contact with water. Furthermore, the precursor contains acrylic acid (AAc) as the charged component, which upon copolymerization with P84DA, not only enables ion separation through Donnan exclusion but also imparts pH-responsive behavior for the separation of ionic species. The membrane performance is studied and compared with a commercial NF membrane (NF270). We show that the synthesized NF membrane has separation properties adjustable with temperature and pH with exceptional resistance to fouling by various solutes due to its highly hydrophilic surface. Furthermore, the membrane shows an outstanding sulfate over chloride ion selectivity, which is a requirement for salt fractionation applications. Deducted from separate experiments, the ideal chloride/sulfate selectivity for magnesium cation is about 2.38 at low ionic strengths. This study is done on a model system to show the capability of incorporating pH-responsiveness in LLC templated membranes, in which the pH-responsive range can be designed by changing the charged groups of comonomer in the formulation.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Ionospheric plasma flow about a system of electrically biased flat plates

The steady state interaction of two electrically biased parallel plates immersed in a flowing plasma characteristic of low earth orbit is studied numerically. Fluid equations are developed to describe the motion of the cold positively charged plasma ions, and are solved using finite-differences in two dimensions on a Cartesian grid. The behavior of the plasma electrons is assumed to be described by the Maxwell-Boltzmann distribution. Results are compared to an analytical and a particle simulation technique for a simplified flow geometry consisting of a single semi-infinite negatively biased plate. Comparison of the extent of the electrical disturbance into the flowing plasma and the magnitude of the current collected by the plate is very good. The interaction of two equally biased parallel plates is studied as a function of applied potential. The separation distance at which the current collected by either plate decreases by five and twenty percent is determined as a function of applied potential. The percent decreases were based on a non-interacting case. The decrease in overall current is caused by a decrease in ionic density in the region between the plates. As the separation between the plates decreases, the plates collect the ions at a faster rate than they are supplied to the middle region by the oncoming plasma flow. The docking of spacecraft in orbit is simulated by moving two plates of unequal potential toward one another in a quasi-static manner. One plate is held at a large negative potential while the other floats electrically in the resulting potential field. It is found that the floating plate does not charge continuously negative as it approaches the other more negatively biased plate. Instead, it charges more and then less negative as ionic current decreases and then increases respectively upon approach. When the two plates come into contact, it is expected that the electrically floating plate will charge rapidly negative to a potential near that of the other plate.

Herr, Joel L.↗

DOE OSTI2023

Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids

The charge carriers in a material can, under special circumstances, behave as a viscous fluid. Here, in this work, we investigated such behavior by using scanning tunneling potentiometry to probe the nanometer-scale flow of electron fluids in graphene as they pass through channels defined by smooth and tunable in-plane p-n junction barriers. We observed that as the sample temperature and channel widths are increased, the electron fluid flow undergoes a Knudsen-to-Gurzhi transition from the ballistic to the viscous regime characterized by a channel conductance that exceeds the ballistic limit, as well as suppressed charge accumulation against the barriers. Our results are well modeled by finite element simulations of two-dimensional viscous current flow, and they illustrate how Fermi liquid flow evolves with carrier density, channel width, and temperature.

Science & Technology - Other Topics↗

DOE OSTI2021

A systematic solution to quantify economic values of vehicle grid integration

We report Vehicle-Grid-Integration (VGI) supplies one of the potential benefit extensions for electric vehicles (EVs) to make use of their parking time, which enables the EVs to provide grid services while still meeting consumer driving needs. However, the costs, benefits and risks of VGI still remain unclear, which limits the development of the VGI to promote the interaction between the EV and grid. In this study, we propose an integrated framework to quantify and utilize the aggregate flexibility of the EVs to supply the grid services in electricity markets. The integrated solution includes five sub-modules that cover end-to-end functionalities from individual EV energy consumption estimation to final monetary values calculation of providing grid services. Both wholesale market and local level charging management are formulated in the optimization module. A predictive control algorithm is proposed to allocate power to individual vehicles in real time, considering uncertainties from dispatch signal and travel behavior. Simulation results from 10,000 EVs indicate that the proposed optimization methods can significantly reduce the system cost in both wholesale market and retail market. Local tariff optimization reduces the electricity cost by 24.4% compared to uncontrolled charging. Wholesale market optimization results show that $\$$691 and $\$$255 revenues can be captured by each EV in ERCOT and CAISO markets per year, although with a conservative assumption on battery throughput cost at 0.16$\$$/kWh.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS2017

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Natural cloud-to-ground (CG) lightning and the charge structure of the associated clouds behave differently over land and ocean. Existing literature has raised questions over the years on the behavior of thunderstorms and lightning over oceans, and there are still open scientific questions. We expand on the observational datasets by obtaining identical electric field observations over coastal land, near-shore, and deep ocean regions during both clear air and thunderstorm periods. Oceanic observations were obtained using two 3-meter NOAA buoys that were instrumented with Campbell Scientific electric field mills to measure the static electric fields. These data were compared to selected electric field records from the existing on-shore electric field mill suite of 31 sensors at Kennedy Space Center (KSC). CG lightning occurrence times, locations and peak current values for both on-shore and ocean were provided by the U.S. National Lightning Detection Network. The buoy instruments were first evaluated on-shore at the Florida coast, to calibrate field enhancements and to confirm proper behavior of the system in elevated-field environments. The buoys were then moored 20NM and 120NM off the coast of KSC in February (20NM) and August (120NM) 2014. Statistically larger CG peak currents were reported over the deep ocean for first strokes and for subsequent strokes with new contacts points. Storm-related static fields were significantly larger at both oceanic sites, likely due to decreased screening by nearby space charge. Time-evolution of the static field during storm development and propagation indicated weak or missing lower positive charge regions in most storms that initiated over the deep ocean, supporting one mechanism for the observed high peak currents in negative first strokes over the deep ocean. This project also demonstrated the practicality of off-shore electric field measurements for safety-related decision making at KSC.

Lightning↗

NASA NTRS2017

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Natural cloud-to-ground (CG) lightning and the charge structure of the associated clouds behave differently over land and ocean. Existing literature has raised questions over the years on the behavior of thunderstorms and lightning over oceans, and there are still open scientific questions. We expand on the observational datasets by obtaining identical electric field observations over coastal land, near-shore, and deep ocean regions during both clear air and thunderstorm periods. Oceanic observations were obtained using two 3-meter NOAA buoys that were instrumented with Campbell Scientific electric field mills to measure the static electric fields. These data were compared to selected electric field records from the existing on-shore electric field mill suite of 31 sensors at Kennedy Space Center (KSC). CG lightning occurrence times, locations and peak current values for both on-shore and ocean were provided by the U.S. National Lightning Detection Network. The buoy instruments were first evaluated on-shore at the Florida coast, to calibrate field enhancements and to confirm proper behavior of the system in elevated-field environments. The buoys were then moored 20NM and 120NM off the coast of KSC in February (20NM) and August (120NM) 2014. Statistically larger CG peak currents were reported over the deep ocean for first strokes and for subsequent strokes with new contacts points. Storm-related static fields were significantly larger at both oceanic sites, likely due to decreased screening by nearby space charge. Time-evolution of the static field during storm development and propagation indicated weak or missing lower positive charge regions in most storms that initiated over the deep ocean, supporting one mechanism for the observed high peak currents in negative first strokes over the deep ocean. This project also demonstrated the practicality of off-shore electric field measurements for safety-related decision making at KSC.

Electric Fields↗

DOE OSTI2021

Dimensionality effects on multicomponent ionic transport and surface complexation in porous media

Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media. Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ~ 2.8, NaBr - 100 mM, HCl - pH ~ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H + (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup. Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na + , B – , and H + , and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.

58 GEOSCIENCES↗

DOE OSTI2023

Electrochemical Behavior of Low Loading Slurry Electrodes for Redox Flow Batteries

The scalability of all-iron redox flow batteries is limited by the plating reaction at the negative electrode on charge. Slurry electrodes have been proposed to allow the plated metal to remain dispersed in the electrolyte and alleviate this limitation. Greater understanding is needed in how faradaic current is distributed between the slurry and the stationary electrode/current collector, especially at relatively low slurry particle loadings. In this work, experiments were conducted using three carbon powders (Kuraray YP-50F, SGL Carbon GFG20HP, and Fisher Scientific GP14736) dispersed in aqueous acidic electrolyte to investigate the effects of slurry particle size, shape, composition, and loading on the behavior of the iron (II/III) reaction. The slurries of YP-50F carbon particles were shown to significantly enhance the faradaic reaction rate due to their high specific surface area but failed to pull the majority of the faradaic current away from the stationary electrode due to the low conductivity of the percolated network. The two graphitic carbons’ slurries did not accelerate the reaction in the same way, but their higher electrical conductivity did succeed in allowing the faradaic reaction to occur primarily on the mobile slurry instead of the stationary current collector.

25 ENERGY STORAGE↗

DOE OSTI2026

Modulating charge transport via 2 MeV He + irradiation in VO 2

Vanadium dioxide (VO 2 ) is of interest for adaptive electronic applications such as neuromorphic neuristor devices and variable emissivity or tunable thermal control materials, thanks to its key property—a metal–insulator transition (MIT) at 68 °C that is accompanied by a dramatic change in electrical and optical properties. To improve performance in these roles, it is critical to develop approaches to engineer transport properties and the MIT behavior. While many documented techniques exist to modulate the MIT and film resistivities via lattice strain and chemical doping, less is known about the effects of ion irradiation on the intrinsic properties of VO 2 , despite the ability to control the spatial distribution of irradiation beams and the prevalence of high energy ion implantation in the semiconductor industry. The impact of irradiation of different acceleration energies on the responses of VO 2 is of specific interest, as charged particle energy generally impacts both the resulting defect profile and corresponding transport behavior. Here, we demonstrate that 2 MeV He ions at equivalent calculated displacements per atom, in two different types of films, can create remarkable changes to the nature of charge transport in VO 2 , especially in the low-temperature insulating phase. Simulation of resulting changes in electrical conductivity reveals that He ion irradiation offers a strategy to increase both oscillation frequency and the signal transmission. These results provide insights into the intentional design of defect populations to modulate transport for neuromorphic VO 2 devices.

Gurrola, Rebeca M. [Texas A & M Univ., College Sta↗

DOE OSTI2025

New electric force and charge exchange modules in discrete element model enables particle dynamics simulation in electric field

Discrete element modeling (DEM) is an important technique for particle dynamics simulation. The field of metal additive manufacturing often utilizes DEM to simulate the rheological behaviors of powder. Standard contact and short-range interactions are sufficient in most cases but insufficient to describe the particle dynamics with the influence of an electric field. Modeling such a system requires additional physics to describe the particle–field interactions. The relevant physics has been experimentally understood but is not yet available in DEM. Here, we develop a charge exchange and an electric force module. The electric force module governs particle response to the electric field, while the charge exchange module enables particles to acquire proper charge during contact with charged geometries. We validate the modules against analytical calculations and high-speed videos of electrostatic powder deposition experiments. Notably, the model struggles to capture the initial particle levitation. We later deploy a modified electric field, as supported by static electric field simulation, to better approximate the electric field penetration into the powder layer. This modification improves the model’s capability of simulating realistic particle levitation. The results highlight the challenges of modeling particle behaviors in the electric field while demonstrating the feasibility of obtaining quantitative results, which are difficult to measure experimentally.

charge exchange↗

NASA NTRS2003

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.↗

DOE OSTI2025

Radiation Response of Ga 2 O 3 MOSFETs Probed via Focused Particle Beams

Gallium Oxide (Ga 2 O 3 ), particularly in its β-phase, is attracting lots of interest for high-power and high-voltage electronics due to its wide bandgap, high breakdown field, and thermal stability. This study investigates the radiation response of Ga 2 O 3 Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) under Total Ionizing Dose (TID) and Displacement Damage (DD) conditions, which are critical for applications in radiation environments. Utilizing a dual-beam Focused Ion Beam and Scanning Electron Microscope setup, microscale analysis of radiation effects on individual devices is performed. The findings reveal distinct behaviors under TID and DD + TID conditions, with TID leading to threshold voltage shifts due to trapped charges, while DD results in decreased drive current attributed to increased carrier scattering from lattice defects. Notably, it is demonstrated that the TID effect can be mitigated through dynamic threshold voltage adjustments and that the predicted TID from ions calculated by Monte Carlo simulations overestimates actual TID due to unaccounted charge yield effects. In conclusion, this research enhances the understanding of Ga2O3 MOSFETs' performance in harsh radiation environments, providing insights for the design of robust electronic devices for space and nuclear applications.

MOSFET↗