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At least 55 records · Page 3

Photochemical and Photophysical Dynamics of the Aqueous Ferrate(VI) Ion

Ferrate(VI) has the potential to play a key role in future water supplies. Furthermore, its salts have been suggested as “green” alternatives to current advanced oxidation and disinfection methods in water treatment, especially when combined with ultraviolet light to stimulate generation of highly oxidizing Fe(V) and Fe(IV) species. However, the nature of these intermediates, the mechanisms by which they form, and their roles in downstream oxidation reactions remain unclear. Here, we use a combination of optical and X-ray transient absorption spectroscopies to study the formation, interconversion, and relaxation of several excited-state and metastable high-valent iron species following excitation of aqueous potassium ferrate(VI) by ultraviolet and visible light. Branching from the initially populated ligand-to-metal charge transfer state into independent photophysical and photochemical pathways occurs within tens of picoseconds, with the quantum yield for the generation of reactive Fe(V) species determined by relative rates of the competing intersystem crossing and reverse electron transfer processes. Relaxation of the metal-centered states then occurs within 4 ns, while the formation of metastable Fe(V) species occurs in several steps with time constants of 250 ps and 300 ns. Results here improve the mechanistic understanding of the formation and fate of Fe(V) and Fe(IV), which will accelerate the development of novel advanced oxidation processes for water treatment applications.

54 ENVIRONMENTAL SCIENCES↗

Frequency Recovery in Power Grids Using High-Performance Computing

Maintaining electric power system stability is paramount, especially in extreme contingencies involving unexpected outages of multiple generators or transmission lines that are typical during severe weather events. Such outages often lead to large supply-demand mismatches followed by subsequent system frequency deviations from their nominal value. The extent of frequency deviations is an important metric of system resilience, and its timely mitigation is a central goal of power system operation and control. This paper develops a novel nonlinear model predictive control (NMPC) method to minimize frequency deviations when the grid is affected by an unforeseen loss of multiple components. Our method is based on a novel multi-period alternating current optimal power flow (ACOPF) formulation that accurately models both nonlinear electric power flow physics and the primary and secondary frequency response of generator control mechanisms. We develop a distributed parallel Julia package for solving the large-scale nonlinear optimization problems that result from our NMPC method and thereby address realistic test instances on existing high-performance computing architectures. Our method demonstrates superior performance in terms of frequency recovery over existing industry practices, where generator levels are set based on the solution of single-period classical ACOPF models.

nonlinear model predictive control↗

A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in turn provides us with information about the nature of dark energy. Conventional methods generate shear maps from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser–Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations—an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly scaling shear map construction alternative using a scalable Gaussian process prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest neighbors and fits hyperparameters using batched leave-one-out cross-validation. This work is the first step toward a full, scalable mass mapping method. We work in a simplified regime where we validate our method by interpolating and analyzing maps given noisy point-estimate data from all three shear fields, taken from a suite of N -body ray-tracing simulations. We also show that we can perform these operations at the scale of billions of galaxies on high-performance computing platforms.

79 ASTRONOMY AND ASTROPHYSICS↗

Revisiting Gauge Ambiguities for DUNE Precision

The de Forest prescription for handling off-shell initial states in the impulse approximation for lepton-nucleus scattering breaks gauge invariance. We discuss existing methods to address this problem and handle the form factor scale ambiguity. We demonstrate that the irreducible differences between the prescriptions are significant compared to the precision expected of next-generation accelerator neutrino experiments. A novel approach directly using the off-shell currents is proposed as a systematically improvable alternative.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Engineering a modular 44 Ti/ 44 Sc generator: eluate evaluation in preclinical models and estimation of human radiation dosimetry

Background: 44 Sc/ 47 Sc is an attractive theranostic pair for targeted in vivo positron emission tomographic (PET) imaging and beta-particle treatment of cancer. The 44 Ti/ 44 Sc generator allows daily onsite production of this diagnostic isotope, which may provide an attractive alternative for PET facilities that lack in-house irradiation capabilities. Early animal and patient studies have demonstrated the utility of 44 Sc. In our current study, we built and evaluated a novel clinical-scale 44 Ti/ 44 Sc generator, explored the pharmacokinetic profiles of 44 ScCl 3 , [ 44 Sc]-citrate and [ 44 Sc]-NODAGA (1,4,7-triazacyclononane,1-glutaric acid-4,7-acetic acid) in naïve mice, and estimated the radiation burden of 44 ScCl 3 in humans. Methods: 44 Ti/ 44 Sc (101.2 MBq) in 6 M HCl solution was utilized to assemble a modular ZR resin containing generator. After assembly, 44 Sc was eluted with 0.05 M HCl for further PET imaging and biodistribution studies in female Swiss Webster mice. Based on the biodistribution data, absorbed doses of 44 / 47 ScCl 3 in human adults were calculated for 18 organs and tissues using the IDAC-Dose software. Results: 44 Ti in 6 M HCl was loaded onto the organic resin generator with a yield of 99.97%. After loading and initial stabilization, 44 ScCl 3 was eluted with 0.05 M HCl in typical yields of 82.9 ± 5.3% (N = 16), which was normalized to the estimated generator capacity. Estimated generator capacity was computed based on elution time interval and the total amount of 44 Ti loaded on the generator. Run in forward and reverse directions, the 44 Sc/ 44 Ti ratio from a primary column was significantly improved from 1038 ± 440 to 3557 ± 680 (Bq/Bq) when a secondary, replaceable, ZR resin cartridge was employed at the flow outlet. In vivo imaging and ex vivo distribution studies of the reversible modular generator for 44 ScCl 3 , [ 44 Sc]-citrate and [ 44 Sc]-NODAGA show that free 44 Sc remained in the circulation significantly longer than the chelated 44 Sc. The dose estimation of 44 ScCl 3 reveals that the radiation burden is 0.146 mSv/MBq for a 70 kg adult male and 0.179 mSv/MBq for a 57 kg adult female. Liver, spleen and heart wall will receive the highest absorbed dose: 0.524, 0.502, and 0.303 mGy/MBq, respectively, for the adult male. Conclusions: A clinical-scale 44 Ti/ 44 Sc generator system with a modular design was developed to supply 44 ScCl 3 in 0.05 M HCl, which is suitable for further radiolabeling and in vivo use. Our data demonstrated that free 44 ScCl 3 remained in the circulation for extended periods, which resulted in approximately 10 times greater radiation burden than stably chelated 44 Sc. Stable 44 Sc/ 47 Sc-complexation will be more favorable for in vivo use and for clinical utility.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Floquet Spin Splitting and Spin Generation in Antiferromagnets

In antiferromagnetic spintronics, accessing the spin degrees of freedom is essential for generating spin currents and manipulating magnetic order, which generally requires lifting spin degeneracy. This is typically achieved through relativistic spin-orbit coupling or nonrelativistic spin splitting in altermagnets. Here, we propose an alternative approach: a dynamical spin splitting induced by an optical field in antiferromagnets. By coupling the driven system to a thermal bath, we demonstrate the emergence of steady-state pure spin currents as well as linear-response longitudinal and transverse spin currents. Crucially, thermal bath engineering enables a nonrelativistic Edelstein effect—the generation of a net spin accumulation—without relying on spin-orbit coupling. Furthermore, our results provide a broadly applicable and experimentally tunable route to control spins in antiferromagnets, offering new opportunities for spin generation and manipulation in antiferromagnetic spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

MarK, a Novosphingobium aromaticivorans kinase required for catabolism of multiple aromatic monomers

The aromatic compounds used in a variety of industrial products are currently obtained from nonrenewable petroleum sources. Alternatively, the plant polymer lignin is an abundant renewable source of aromatics, and its depolymerization generates a variety of products that can include acetovanillone, a vanillin derivative containing an acetyl side chain. The Alphaproteobacterium Novosphingobium aromaticivorans DSM12444 can metabolize several chemically modified aromatics in deconstructed lignin, but not acetovanillone. In this work, adaptive laboratory evolution identified a single amino acid change in the previously uncharacterized gene product Saro_1862 that is necessary and sufficient for N. aromaticivorans growth with acetovanillone as a sole growth substrate, as well as other aromatic monomers not metabolized by wild-type cells. We show that a glutamate (E) to lysine (K) substitution at amino acid residue 16 of Saro_1862 results in a ~1600-fold increase in the rate of ATP-dependent acetovanillone phosphorylation. We also find that recombinant Saro_1862 E16K phosphorylates several other aromatic compounds in vitro , defining the first reported catalytic activity for the widespread UPF0261 protein domain contained in Saro_1862. Thus, we propose naming Saro_1862 MarK, for multiple aromatic kinase. A 1.57 Å crystal structure of MarK E16K predicts that the E16K substitution lies in a potential ATP binding site, suggesting how this amino acid change increased catalytic activity. A search for homologs of MarK and other proteins required for acetovanillone degradation predicts that this pathway for aromatic metabolism exists throughout the bacterial phylogeny.

Novosphingobium↗

Microwave-Assisted Production of Polycarbonate Diols using Carbon Dioxide

Carbon dioxide (CO2) is a cheap and readily available resource that can be converted to value-added chemicals including fuels, polymers, and other products. One lucrative option is polycarbonate diols, which are the precursor to polyurethanes that find wide applications in automotive and aerospace industries. The traditional process for the synthesis of polycarbonate diols involves using hazardous phosgene and alcohols in a strongly basic medium that generates significant amounts of salt. Alternately, CO2 can be reacted with alkanediols over CeO2 catalysts to produce polycarbonate diols. For the current work, a microwave-assisted atmospheric flow system was investigated for converting CO2 into polycarbonate diols and was compared against a thermal system. Various parameters such as type and ratio of solvents, and the addition of dehydrating agents for the microwave system was tested. The different CeO2 catalysts used were characterized using Brunauer–Emmett–Teller (BET) surface area analysis, Raman spectroscopy, X-ray diffraction, and temperature programmed desorption (NH3-TPD and CO2-TPD).

CO2 utilization↗

Prototype Modeling for a Light-Trapping Planar-Cavity Enclosed Particle Solar Receiver

Concentrating solar thermal (CST) systems present a promising avenue for affordable and reliable energy production. Solar receivers are key components that determine the efficiency and longevity of these systems. Particle-based solar receivers have emerged as a compelling alternative to traditional technologies, offering several advantages that address limitations in current CST systems. This is especially true as next-generation CST technologies target applications including electricity generation, thermochemical processes, and industrial process heat, many of which necessitate higher operating temperatures than current commercial molten salt systems. Molten-salt thermal energy storage (TES) systems, commonly used in CSP, face challenges related to freezing and corrosion. Particle-based TES systems, in contrast, do not experience these issues, as particles are stable at high temperatures, exceeding 1000 degrees Celsius. This capability allows for a wider range of applications, including those requiring higher temperatures for industrial processes and efficient electricity generation. A novel innovation in particle-based solar receiver technology is the light-trapping planar cavity receiver (LTPCR) configuration developed by NREL. The LTPCR design consists of small cavity-like structures using opaque planar surfaces, enabling efficient capture and absorption of solar energy. A high incident flux concentration at the cavity aperture is absorbed on the receiver walls, and subsequently transferred to particles on the inside of cavities. The particles flow through the system, forming a fluidized bed inside of the receiver panels, effectively capturing the absorbed solar heat. Air is used as a fluidizing medium in this process to enhance particle heat transfer and mixing. The effectiveness of this design lies in its ability to manage solar flux conditions and ensure high solar-to-thermal receiver efficiency. A 100-kW prototype is currently being tested at the King Saud University in Saudi Arabia to assess the receiver performance. A range of modeling analyses for the optical, thermal, and mechanical effects were conducted to assess the performance of the receiver under on-sun conditions. The solar flux resulting from the KSU heliostat field was modeled using NREL SolTrace software and produced up to 600 kW/m2 at the receiver aperture. The solar flux absorbed on the receiver walls was then used within a computational fluid dynamics (CFD) model to predict wall temperature distributions along with radiation and convection loss. A two-phase CFD model was developed for the fluidized bed of silica sand inside the receiver panels to predict local wall-to-particle heat transfer coefficients, particle temperature distributions, and outlet temperature of the particles. We have also conducted analyses to understand the thermomechanical behavior of these innovative enclosed light-trapping solar receivers optimized for particle heating. We used finite element analysis (FEA) to predict the receiver's performance using temperature distributions obtained from CFD and based on the resulting stress profiles, evaluated creep-fatigue damage with a goal of achieving a 30-year service life. Analysis showed a significant impact of the particle-to-wall heat transfer coefficients (HTCs) on receiver performance, with higher HTCs resulting in reduced stress and increased lifespan. For instance, when using Inconel 740H, increasing the HTC from 800 W/m2 K to 1400 W/m2 K increased the creep life from 4,000 hours to over 100,000 hours. This highlights the importance of understanding and optimizing heat transfer in the design of high-efficiency receivers.

14 SOLAR ENERGY↗

Lower-Hybrid-Drift Vortices in the Electron-Scale Magnetic Reconnection Layer

Lower-hybrid-drift waves driving vortical flows have recently been discovered in the electron current layer during magnetic reconnection in the terrestrial magnetotail. Yet, spacecraft measurements cannot address how pervasive the waves are. In this work, we perform three-dimensional particle-in-cell simulations of guide field reconnection to demonstrate that electron vortices driven by the lower-hybrid-drift instability (LHDI) are excited immediately downstream from the electron jet reversal in 3-D channels of enhanced electron outflow. The resulting fluctuations generate a series of alternating vortices, producing magnetic field perturbations opposing and enhancing the local guide field and causing kinking of the enhanced electron outflow and patches of increased current. Our results demonstrate for the first time that LHDI exists in the electron current layer and enhanced outflow channels, providing a conceptual breakthrough on the LHDI in reconnection.

58 GEOSCIENCES↗

Experimental Validation of a Modular All-Electric Power Take-Off Topology for Wave Energy Converter Enabling Marine Renewable Energy Interconnection

Power electronic converters are an enabling technology for the emerging marine energy applications, such as using ocean waves to produce electricity. This paper outlines the power take-off system and its key components used in a wave energy converter offering modularity and scalability to generate power efficiently. The proposed power take-off system was implemented based on a modular multilevel converter and could be deployed to convert any alternating current electrical energy to a different alternating current for interconnection to grid or non-grid applications. Examples of widespread deployment are supplying electricity to coastal communities or producing clean drinking water. The analysis using both the simulation tests and laboratory experiments verified the design objectives and basic functionality of the developed power take-off system. An acceptable response using a field programmable gate array-based controlled laboratory testbench was achieved, complying with guidelines specified in the prevalent industry standards. Seamless operation during steady-state and transients for the studied wave energy converter was achieved as supported by the obtained results. The key findings of this work were experimentally examined under different load conditions, direct current bus voltage fluctuations, and generator speed–torque regulation. The ability of the power take-off system to generate high-power quality of the waveforms, e.g., against adhering to the IEEE 519-2022 standard for total harmonic distortion limits, is also confirmed.

Engineering↗

Multi-Fidelity Scheme for Accelerating 4D Finite Element Analysis for Mircoreactors

Next-generation microreactors are currently being designed to be operated terrestrial and extraterrestrial for remote surface power production. These systems will provide an alternative source of carbon-free energy that is versatile and can be utilized for various applications. These applications of microreactors have prompted the usage of high-fidelity unstructured finite element (FE) based approaches to provide time-dependent solutions for multiple physics fields. Computing these high-fidelity (4-D) solutions for multiple design iterations, physics fields, and transient events requires an immense computational cost. These high-fidelity solutions are computational expensive and the cost can be reduced through the implementation of less accurate low-fidelity solutions. Unlike the current fleet of commercial nuclear reactors, these next-gen systems present challenges due to the material and physical limitations required. Due to these constraints, the brute force technique of parameterizing important system characteristics determines whether a design meets the project objective. A system such as a nuclear reactor could have thousands of design parameters that affect system performance. In order to analyze the entire parameter space of such a complex system would require millions of CPU hours and countless design iterations. This costly approach is not practical due to regulatory and budget limitations. In this proposal, an approach that utilizes hybrid high-fidelity and low-fidelity FE models to reduce the computational cost of evaluating these applications in 4-D will be presented. The accuracy of the high-fidelity model and the computational efficiency of the low-fidelity model are taken advantage of to produce a solution that closely resembles the full order high-fidelity solution. By utilizing an unconverged coarse FE mesh, operation limits such as temperature, structural loading, etc., can be evaluated in an accelerated fashion and then can be spatially interpolated onto a finer mesh. The resulting error arising from the coarse mesh can be mitigated with a discrepancy function that actively quantifies and corrects the error in the coarse solution. This discrepancy function can be periodically updated with high-fidelity calculations across the temporal domain thus requiring less iterations on the fine mesh. As a result, the computational cost can be reduced for the evaluation and design iteration of microreactors. The proposal for this research contains three sections: Section 2 provides a literature review, Section 3 outlines the methodology for the proposed multi-fidelity scheme, and Section 4 displays preliminary results of the proposed research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Implementing the LSST Software Stack for DESGW processing and the Integration of Convolutional Neural Networks into the DESGW Pipeline

The Dark Energy Survey Gravitational Wave (DESGW) group strives to understand thelargescale structure of the universe and galaxies by looking for electromagnetic signatures intelescope images following gravitational wave detections. The DESGW group uses a processing pipeline to perform difference imaging to look for potential candidates. In order to perform these searches more effectively, we first explored using an alternative processing pipeline, the LSST Software Stack to analyze the telescope images. Because the LSST software stack is currently transitioning between its generation 2 and generation 3 system, we decided that while the software will be usable in the future once generation 3 is complete, at the moment its incompleteness makes it impractical to use. We then decided to work on improving the current pipeline by developing a module that integrates a Convolutional Neural Network (CNN) to test difference imaging products for bad subtractions due to misalignment.

Navarro, Alexander↗

Advanced Microstructured BaTiO 3 -Embedded PVDF–HFP/PEO Film for Enhanced Triboelectric Interface in Self-Sufficient Energy Generation and Sensing

The global reliance on fossil fuels and natural gas has largely dominated the energy production field, but due to finite resource depletion and escalating greenhouse gas emissions, the immediate exploration of sustainable energy alternatives to mitigate climate change and ensure resource security has been a major concern. There has been extensive research into other more renewable methods of energy production, such as wind and hydropower. Of these current energy generation types, there are many areas of untapped potential from the mechanical movements generated ambiently not only in the large scale of power generation but also on a smaller scale. The piezoelectric and triboelectric effects are phenomena where these ambient mechanical movements can generate electrical energy. Developing a hybrid system that leverages both mechanical stress and surface charges presents an ideal opportunity to exploit these untapped energy sources. Producing a hybrid PVDF–HFP/PEO film with perovskite BaTiO 3 (BTO) enables ambient power harvesting from both mechanical movement and surface charge. The optimized cell produced a potential of up to 15 V and a current of 200 nA with a 68 kΩ resistor, a substantial increase from a base system with an average of 2.1 V and 40 nA. These hybrid TENGs offer significant potential for energy harvesting in small-scale applications, such as health monitoring devices and indicators in electric circuits.

Ybarra, Rigobert [University of Texas Rio Grande V↗

Development of a phonon-based sampling method for thermal neutron scattering data

Simulations of reactor systems require access to accurate nuclear data. For many systems, thermal neutron scattering data can have large effects on the eigenvalue and neutron flux distributions. Inelastic thermal neutron scattering can excite or de-excite vibrational, rotational, and translational modes in a material, so thermal scattering evaluations are often obtained by summing over the number of phonons created/destroyed by a scattering event. In recent years, the thermal scattering cross sections and angular distributions have greatly improved in accuracy, but the format in which this data is delivered to simulation codes has remained virtually unchanged. Thermal scattering data is typically either compiled into large tables and sorted by incoming neutron energy, outgoing neutron energy, scattering angle, and material temperature, or represented as cumulative distribution functions of momentum exchange or energy exchange. Either method can be quite memory intensive when fine bins are used. In an effort to decrease the amount of space that processed thermal scattering data requires, an alternate format is proposed. The phonon-based sampling method introduced here can sample the number of phonons excited for each collision, the change in neutron energy, and the scattering angle while avoiding pre-computed angular bins and limiting the amount of data that is dependent on incoming energy. Through this method, the generation and storage of large interpolation tables is avoided, which could have benefits in both memory storage and accuracy. While the initial implementation of this method is slower than current alternatives, it is significantly more resistant to grid coarseness errors and has good potential for improvement. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Capacity contributions of Southern Oregon offshore wind to the Pacific Northwest and California

Variable renewable energy generation poses unique capacity challenges, which increasingly depend on weather events at varying timescales. Facilitated by transmission planning, geographic and technological diversity of the generation fleet may provide a mitigation to capacity shortfalls. In this work, offshore wind (OSW) energy is sited in the areas off the West Coast between Coos Bay, Oregon, and Crescent City, California. Three generation and transmission scenarios are modeled within the Western Interconnection: (i) 3.4 gigawatts (GW) of installed OSW capacity connected to Southern Oregon through a High Voltage Alternating Current (HVAC) Radial Topology in 2030; (ii) 12.9 GW of installed OSW capacity connected to Washington, Oregon, and California through a High Voltage Direct Current (HVDC) Radial Topology post-2030, and (iii) the same 12.9 GW connected to the same locations through a Multi-terminal DC (MTDC) Backbone Topology post-2030. Zonal dispatch simulations assuming coincident wind, solar, and hydropower production and loads over 18 meteorological years, accounting for temperature-dependent equipment derating and forced outages, serve as inputs to the Associated System Capacity Contribution (ASCC) methodology. The capacity credit is 33%, 25% and 34% for the 2030 HVAC Radial Topology, 2030+ HVDC Radial Topology, and 2030+ MTDC Backbone Topology, respectively. Transmission design is shown to mitigate the typical erosion of marginal capacity contribution as more OSW is developed, underscoring the opportunity for grid modernization while decarbonizing the generation mix.

17 WIND ENERGY↗

Apparatus and methods of detecting transient discharge modes and/or closed loop control of pulsed systems and method employing same

A system and method for differentiating between different modes of pulsed electrical discharges via of an amplitude to time (ATC) conversion circuit is described. A bipolar ATC circuit is used to add together the positive and negative portions of an attenuated and filtered signal derived either from the voltage or current of a pulse. Alternatively, a unipolar ATC circuit may be employed. The resulting processed signal is compared against a reference voltage to generate an output signal that is active for the amount of time that the processed signal exceeds the reference voltage. Discharge mode is determined based on three factors: did a pulse occur, if a pulse occurred when did the pulse start relative to the original pulse event, and what is the duty cycle of the pulse. Subsequent pulse generated may be controlled accordingly.

Fitzpatrick, Joseph F.↗

Enabling the Electrification of Offshore Activities – Co-Demonstration of Next-Generation Autonomous Offshore Power System and Resident, Uncrewed Mobile and Static Assets at PacWave Wave Energy Test Site

Oceans cover two-thirds of the earth's surface and form the world's biggest and best – yet largely untapped – battery. Ocean waves have more energy density than other renewables, including wind, solar, and biomass, and have the potential to supply 4x the world's annual energy consumption (Masterson, 2022; Zic, 2020). In addition to the impact wave energy can have on decarbonizing and diversifying the electric grid, it offers a significant value proposition in the emerging blue economy sector (LiVecchi et al, 2019). The blue economy consists of industries operating offshore, including shipping, oil and gas, defense and security, aquaculture, and research. These industries require bringing people and energy on site to perform daily work, but current energy costs in the blue economy are extremely high. Here, the prevailing processes are complex, including shore dependencies and fuel transportation logistics. Few alternatives for reliable power generation exist, with the most prominent being high cost and high carbon emissions diesel generation. Because of this lack of affordable, reliable power, the trends of electrification, digitization, and automation that have led to substantial innovation and improvements in the terrestrial economy over the last two decades are slow to come to the blue economy.

16 TIDAL AND WAVE POWER↗