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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Effect of Shear Displacement and Stress Changes on Fracture Hydraulic Aperture and Flow Anisotropy

Fluid flow in fractures has the potential to drastically change the economic, environmental, and safety risks associated with a subsurface operation. This work focuses on the analysis of experimental shear fracturing and subsequent shear displacement of a shale specimen that contains multiple pre-existing natural fractures. A triaxial direct shear apparatus with concurrent µCT imaging allowed continuous monitoring of sample permeability and changes in fracture geometry during fracture creation, displacement, and changes in stress. Steady-state, low Reynolds number fluid flow simulations were used to determine the changes of each individual fracture’s hydraulic aperture due to displacement and effective stress. The development of anisotropy in the hydraulic aperture of a generated shear fracture was determined for shear displacements of 0.38, 0.74, and 2.04 mm. At high confining stress (30 MPa), shear displacement significantly reduced the hydraulic aperture of the shear fracture to below flow detectable limits and X-ray imaging resolution (23 × 23 × 23 µm 3 ). The shear generated fracture was found to be more sensitive to changes in effective stress compared to the pre-existing natural fractures. Existing models derived from fluid flow equations accounting for stochastic fracture roughness were able to partially fit the simulated flow properties of the pre-existing fractures, but no model was found to fit the flow properties of the newly formed shear fracture. These results are the first report of simultaneous changes in the geometry and flow properties of surrounding, parallel natural fractures as a shear fracture is generated with varying stress and shear displacement conditions.

58 GEOSCIENCES↗
DOE OSTI2026

Velocity Extraction Using Complete Time-Domain Waveform Data and Audio Machine Learning

We developed a new machine learning-based tool for extracting information from interferometry measurements: MIDWAZE (Modular Interferometry Direct Waveform AnalyZEr). This paper showcases MIDWAZE’s ability to extract an object’s velocity information from Photonic Doppler Velocimetry (PDV) data at near-human accuracy with little to no human intervention. MIDWAZE can extract velocities roughly 350 times as fast as a human analyst "rushing" to complete their extractions, with similar extraction accuracy. MIDWAZE’s most outstanding feature is that it operates directly in waveform/temporal space, freeing analysis from certain limitations imposed by traditional spectrogram-based approaches and opening the way to "phase aware" PDV analysis. MIDWAZE also has limited ability to discriminate between different solid objects, which we develop as a first step towards automated discrimination of different kinds of objects such as ejecta clouds.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A two-phase three-field modeling framework for heat pipe application in nuclear reactors

Heat pipes and two-phase thermosyphons are highly efficient heat transfer devices utilizing continuous evaporation and condensation of working fluid for two-phase heat transport in closed systems. Because of the nearly isothermal and fully passive phase-change heat transfer mechanism, heat pipes and thermosyphons have found many applications in nuclear engineering, space technologies, and other energy systems. High-temperature heat pipes are used in nuclear microreactors to remove fission power from the primary system and are coupled with power conversion systems or process heat applications. Modeling of the two-phase flow phenomena inside a heat pipe is essential to its design and safety analysis. In this study, a comprehensive one-dimensional two-phase three-field flow model has been developed for the analysis of heat pipes in normal operation conditions and transients. The conservation or field equations of mass, momentum, and energy were developed for the liquid film, vapor, and droplet. In addition, constitutive models or correlations were reviewed thoroughly and provided for the closure of the three-field equations. Specific constitutive equations regarding interfacial mass and heat transfer at two interfaces, namely film-gas interface and gas-droplet interface, were reviewed for droplet entrainment and deposition rates as well as film and droplet evaporation rates. Furthermore, mechanistic correlations of annular flow film thickness were recommended for the modeling of the thermosyphons without a wick as a critical constitutive correlation. Furthermore, experimental data needs from new experiments using a prototype working fluid or surrogate fluids for the model validation of high-temperature heat pipes in microreactors were recommended for future research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

The onset of alloying in Cu-Ni powders under high-shear consolidation

Friction consolidation (FC) is a solid phase processing methodology that densifies a material through high-shear deformation and pressure at elevated temperature. The method has garnered interest in the scientific community because of its ability to produce extremely refined and homogeneous microstructures, off-axis texture development, and improved material properties. This manuscript presents an investigation of Cu and Ni material mixing via evaluation of morphological evolution, grain boundary characterization, and compositional analysis to provide insights on the operational alloying mechanisms occurring under high shear and elevated temperature. Using correlative microscopy techniques, we show alloying progresses via a combination of grain boundary diffusion and interfacial roughening at heterophane boundaries. Evidence supporting Cu infiltration along Ni-Ni grain boundaries along with asymmetric diffusion of Cu into Ni grains is highlighted. The resultant, consolidated microstructure was produced directly from a powder compact in ~30 s and exhibited a submicron, equiaxed grain size.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Performance and transport in the ARC tokamak

The ARC TM tokamak, a high-field (𝐵 𝑇 = 11.4 T) fusion power plant, under development by Commonwealth Fusion Systems, is studied using a suite of integrated modelling tools to predict its fusion power generation (𝑃𝑓⁡𝑢⁢𝑠), transport and confinement properties. Analysis is based off an ARC operational point scoped first with zero-dimensional (0-D) plasma operational contour (POPCON) modelling to produce 1.13 GW of fusion power. A suite of integrated modelling tools (TRANSP, ASTRA and TORAX) were applied to predict the performance and kinetic profiles of the ARC design point, yielding a range of predicted performance spanning from ∼900 to 1300 MW in rough quantitative agreement with POPCON predictions. The sensitivity of these results to uncertain modelling inputs was probed using scans of pedestal boundary conditions around EPED-predicted values (total pressure and temperature ratios), tungsten concentration and seperatrix density around their nominal assumptions. Pedestal pressure and pedestal top (𝑇 𝑖 /𝑇 𝑒 ) play a large role in 1.5-dimensional performance predictions, able to modify the predicted 𝑃 𝑓⁡𝑢⁢𝑠 by a factor of 2 within reasonable assumptions. High-fidelity core nonlinear gyrokinetic profile predictions, performed using CGYRO (Candy et al. 2016 J. Comput. Phys., vol. 324, pp. 73–93) coupled with the PORTALS (Rodriguez-Fernandez et al. 2024 Nucl. Fusion, vol. 64, 076034; Phys. Plasmas, vol. 31, 2024, 062501) framework, yield substantially lower performance (𝑃 𝑓⁡𝑢⁢𝑠 =677 MW) compared with 0-D and medium-fidelity modelling for nominal assumptions, showing that there is non-negligible uncertainty between models and that future work on SPARC may help resolve discrepancies. Lower overall performance results from significantly reduced volume-averaged densities and temperatures, along with reduced levels of density and temperature peaking. Turbulence and transport are largely dominated by ion temperature gradient across the profile, confirmed by both linear stability and the response of the nonlinear fluxes to changes in gradients, with some impact of kinetic ballooning modes in the deep core. This work represents one of the most complete scoping of potential fusion power plant conditions performed to date. The extensive integrated modelling provides confidence in ARC performance approaching 1 GW, while nonlinear gyrokinetic modelling results in open questions into the physics of density and temperature peaking in fusion-power-plant-relevant operational space. A discussion of results and the role that the SPARC tokamak (Creely et al. 2020 J. Plasma Phys., vol. 86, 865860502) will play in informing ARC design, performance and operation is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Operando XPS for Plasma Process Monitoring: A Case Study on the Hydrogenation of Copper Oxide Confined under h-BN

Here, we demonstrate that ambient pressure x-ray photoelectron spectroscopy (APXPS) can be used for in situ studies of dynamic changes in surface chemistry in a plasma environment. This opens a new and vast application space for XPS and greatly complements modern spectroscopy techniques to probe plasma-solid/liquid interactions relevant to process monitoring in the semiconductor industry, bio-medical plasma applications and plasma remediation technologies. Hexagonal boron nitride (h-BN) grown on Cu was used in this study as a well-defined model system for plasma process monitoring and because of its unique chemical, optical and electrical properties that make it a prospective material for advanced electronics. To better understand the stability and surface chemistry of h-BN during plasma assisted processing, we track in real time the plasma-induced chemical state changes of B, N and the underlying Cu substrate using APXPS equipped with an AC discharge plasma source operating at 13 Pa. Residual gas analysis (RGA) mass-spectra were concurrently collected during plasma-XPS to track reaction products formed during plasma exposure. A clear reduction of Cu x O is seen, while an h-BN layer remains intact, suggesting hydrogen radical (H • ) species can attack the exposed and h-BN covered Cu oxide patches and partially reduce the underlying substrate without significantly damaging the overlaying h-BN, which is of practical importance for development of h-BN encapsulated devices and interfaces. In addition to demonstration of plasma-XPS capabilities we discuss the observed challenges (e.g., parasitic plasma-chamber walls reactions and charging effects) and propose potential solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Source-Resolved Inversion of Elemental Carbon Emissions in California Using Log-Space Bayesian Inference

Elemental carbon (EC), operationally quantified by thermal-optical analysis, is widely used as a proxy for black carbon (BC) relevant to short-term climate forcing and public health. Current EC emission inventories remain highly uncertain, with persistent discrepancies between bottom-up and top-down estimates. In this study, we develop a source-resolved, log-space Bayesian inversion framework applied to estimate California’s statewide EC emissions in 2019. By integrating surface EC measurements from the EPA’s Air Quality System network with high-resolution source contributions simulated by a chemical transport model, we identify a one-third underestimation in the existing statewide EC inventory, requiring an increase of the total from a prior of 8.58 [5.49–13.75] Gg year–1 to a posterior estimate of 12.78 [10.71–15.37] Gg year–1. This discrepancy is primarily driven by substantial underestimations in the power and industrial and off-road mobile sectors. Furthermore, population-weighted exposure analysis reveals a marked sectoral divergence between emission mass and health burden: off-road mobile sources dominate both emissions and exposure, accounting for 31% of statewide exposure, while residential wood combustion contributes 26% of total exposure despite comprising only 19% of total emissions, due to its source proximity to population. These findings underscore the need to update sector-specific EC speciation profiles and demonstrate that mitigation strategies targeting off-road mobile sources and residential wood combustion are critical for reducing EC-related health impacts in California.

Zhang, Jie↗
DOE OSTI2024

Mild pH-decoupling aqueous flow battery with practical pH recovery

Establishing a pH difference between the two electrolytes (pH decoupling) of an aqueous redox flow battery (ARFB) enables cell voltages exceeding the 1.23 V thermodynamic water-splitting window, but acid–base crossover penalizes efficiency and lifetime. Here we employ mildly acidic and mildly alkaline electrolytes to mitigate crossover, achieving high round-trip energy efficiency with open circuit voltage >1.7 V. We implemented an acid–base regeneration system to periodically restore electrolytes to their initial pH values. The combined system exhibited capacity fade rate <0.07% per day, round-trip energy efficiency >85% and approximately 99% Coulombic efficiency during stable operation for over a week. Cost analysis shows that the tolerance of acid–base crossover could be increased if the pH-decoupling ARFB achieved a higher voltage output and lower resistance. Finally, this work demonstrates principles for improving lifespan, rate capability and energy efficiency in high-voltage pH-decoupling ARFBs and pH recovery concepts applicable for pH-decoupling systems.

25 ENERGY STORAGE↗
DOE OSTI2025

Spacetime pq theory for AC and DC electric power systems

The 50/60 Hz alternating current (AC) electric power has been the standard and most flexible energy source powering our modern societies for one and a half centuries since the war of the currents: AC versus direct current (DC). A reactive power concept that was introduced at the beginning of the AC power was very useful for circuit/system analysis, design, control, optimization, and ultimately for more efficient and stable generation, transmission, distribution, and consumption. The initial reactive power theory was based on single-phase sinusoidal AC power to capture inductive and capacitive power that yields to net-zero average power over one fundamental cycle. Soon it was expanded to non-sinusoidal AC power and finally to instantaneous three-phase AC power. However, these reactive power theories remain separate and limited to special cases and have never been consolidated and made valid to all cases. Today, more widespread adoption of power electronics and renewable energy is bringing back DC power into the electric grids. The reactive power concept has never been applied to DC power systems. There is no reactive power in DC power systems according to the existing reactive power theories. Do DC power systems really have no reactive power? Capacitors and inductors are widely used in DC just like in AC power systems. Are they not reactive power components? Why are they different from their AC counterparts? Furthermore, are batteries active or reactive power components? What about active devices like power converters (or inverters) with AC (or DC) on one side and DC (or AC) on the other? Do they generate or consume reactive power? Finally, what about AC and DC hybrid power systems? How to define reactive power in such a complex power system that has a multitude of loads, buses, and sources? Is there reactive power between any two loads, any two buses, or any two sources in a power system and what is the total reactive power in such a complex power system as a whole? As the motivation and goal of this paper to answer the above basic questions, to unify the existing AC reactive power theories and to ultimately provide theoretical and insightful guidance for system analysis, design, control, efficiency, optimization, and operation of complex power systems, a concept of spacetime (both spatial and temporal) active and reactive power (pq) theory—the spatiotemporal aspect of active and reactive power—is developed for both AC and DC power systems. The theoretical definitions and physical meanings of the spacetime reactive power will be developed, and real applications and thought experiments/cases/exercises will be explored and discussed. The developed mathematics to define the active (or real) and reactive (or imaginary) power— p and q respectively by dot (scalar) and cross (vector) products of multi-dimension spacetime vectors and time-space mapping principle/law can have some fundamental implications as well.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

More land is needed for solar and wind infrastructure under a high renewables scenario in the Western US by 2050

Expanding United States electricity infrastructure to meet growing demand could require extensive power plant development footprints and land use conversion, depending on the mix of generation types chosen. Understanding where future power plant sitings are likely to take place and identifying potential conflicts and land-use tradeoffs will be key to identifying feasible and affordable investments and evaluating regional planning coordination needs. Here we use an integrated modeling framework that combines capacity expansion planning, hourly grid operations, and geospatial techno-economic analysis to develop projections (2025-2050) of power plant sitings in the Western United States (US) at a 1 km 2 resolution for a business-as-usual scenario and a high renewables penetration scenario. We find that 30% more land will be needed in the high renewables scenario as compared to business-as-usual, and that 75% of that development is projected to be located within 10 km of natural areas.

Mongird, Kendall [Pacific Northwest National Labor↗
DOE OSTI2020

Evaluating aqueous flow battery electrolytes: a coordinated approach

Here, we outline some basic pitfalls in the electrochemical investigation of aqueous metal complexes and advocate for the use of bulk electrolysis in redox flow cells for electrolyte analysis. We demonstrate the methods of operation and performance of a lab scale redox flow battery (RFB), which is assembled from unmodified, commercially available material and cycled with a vanadium electrolyte in order to provide a comparative baseline of expected performance. Common misconceptions about the thermodynamic window for water splitting are addressed and further express the need to develop next-generation aqueous redox flow battery electrolytes. Although non-aqueous electrolytes are a popular approach, they suffer from distinct challenges that limit energy and power density in comparison with aqueous electrolytes. Expanding the scope of aqueous electrolytes to include metal–chelate complexes allows electrolytes to be as tailorable as organic species, while maintaining robust metal-based redox processes. A flow battery assembly and operation guide is provided to help facilitate the use of flow battery testing in the evaluation of next-generation electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

ExoMars Mars Organic Molecule Analyzer (MOMA) Laser Desorption/Ionization Mass Spectrometry (LDI-MS) Analysis of Phototrophic Communities from a Silica-Depositing Hot Spring in Yellowstone National Park, USA

The Mars Organic Molecule Analyzer (MOMA) is a key scientific instrument on the ExoMars Rover mission. MOMA is designed to detect and characterize organic compounds, over a wide range of volatility and molecular weight, in samples obtained from up to two meters below the martian surface. Thorough analog sample studies are required to best prepare to interpret MOMA data collected on Mars. We present here the MOMA characterization of Mars analog samples collected from an alkaline silica depositing hot spring in Yellowstone National Park, WY, USA. These samples contain microbial streamer communities composed primarily of oxygenic and anoxygenic phototrophs. Additionally, in a study focused on detection of key classes of nonvolatile organics, samples of microbial streamers and their total lipid extract (TLE) have been measured on a MOMA Engineering Test Unit (ETU) instrument using its laser desorption/ionization mass spectrometry (LDI-MS) mode. MOMA LDI-MS detected a variety of lipids and pigments in the TLE sample. Species such as chlorophyll a were also detected from the streamer sample with the help of mass isolation. The results add to the LDI-MS sample characterization database, as well as demonstrate the benefit of using mass isolation on the MOMA instrument to reveal the presence of complex organics, and potential biomarkers, preserved in a natural sample, providing guidance to the in situ analysis of surface samples during Mars operations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Quantum algorithm to simulate Lindblad master equations

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest. Published by the American Physical Society 2025

Borras, Evan (ORCID:000900017709037X)↗
DOE OSTI2024

Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to Z d qudits, including instances where d is a nonprime number. This capability allows the identification of topological orders that differ from the Z d toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for Z p qudits (with p being a prime) are equivalent to finite copies of Z p toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Nonlinear Photovoltaic Degradation Rates: Modeling and Comparison Against Conventional Methods

Although common practice for estimating photovoltaic (PV) degradation rate (RD) assumes a linear behavior, field data have shown that degradation rates are frequently nonlinear. This article presents a new methodology to detect and calculate nonlinear RD based on PV performance time-series from nine different systems over an eight-year period. Prior to performing the analysis and in order to adjust model parameters to reflect actual PV operation, synthetic datasets were utilized for calibration purposes. A change-point analysis is then applied to detect changes in the slopes of PV trends, which are extracted from constructed performance ratio (PR) time-series. Once the number and location of change points is found, the ordinary least squares method is applied to the different segments to compute the corresponding rates. The obtained results verified that the extracted trends from the PR time-series may not always be linear and therefore, “nonconventional” models need to be applied. All thin-film technologies demonstrated nonlinear behavior whereas nonlinearity detected in the crystalline silicon systems is thought to be due to a maintenance event. A comparative analysis between the new methodology and other conventional methods demonstrated levelized cost of energy differences of up to 6.14%, highlighting the importance of considering nonlinear degradation behavior

14 SOLAR ENERGY↗
DOE OSTI2024

Enhancing Distribution System Resilience: A First-Order Meta-RL Algorithm for Critical Load Restoration

The increasing frequency of extreme events and the integration of distributed energy resources (DERs) into modern grids have elevated the need for resilient and efficient critical load restoration strategies in distribution systems. However, the stochastic nature of renewable DERs, limited energy resource availability and the intricate nonlinearities inherent in complex grid control problem make the problem challenging. Although reinforcement learning (RL) and warm-start RL methods have shown promising results, their performance often falls short in rapidly adapting to new, unseen situations and typically requires exhaustive problem-specific tuning. To address these gaps, we propose a First-Order Meta-based RL (FOM-RL) algorithm within an online framework for adaptive and robust critical load restoration. By harnessing local DERs as the enabling technology, FOM-RL allows the RL agent to swiftly adapt to new unseen scenarios by leveraging previously acquired knowledge of different tasks. Experimental results provide evidence that proposed algorithm learns more efficiently and showcases generalization capabilities across diverse set of operational scenarios. Moreover, a rigorous theoretical analysis yields a tight sublinear regret bound, sensitive to temporal variability, with a task-averaged optimality gap bounded by O(VM+D*/(Tsquare root(M))). These results suggest that optimality improves with task similarity and an increased number of tasks M, reaffirming the efficacy and scalability of the proposed approach in addressing the complexities of critical load restoration in distribution systems.

complexity theory↗
DOE OSTI2026

Electromagnetic Analysis of ITER Electron Cyclotron Emission Model

The ITER electron cyclotron emission (ECE) diagnostic system is located at diagnostics shielding module 2 (DSM2), equatorial port 9 (EP9), to measure electron temperature profile and electron temperature fluctuations, and also assess nonthermal electron distributions via the oblique view. Therefore, ECE has both radial and oblique views with two hot sources for calibration and two couples of mirrors for two different optical views. It shall receive that the large electromagnetic (EM) loads up to 100-MN/m3 force density due to the eddy currents on the copper mirrors generated by the short transient plasma disruption. The simplified EM analysis model using magnetic field ( B ) data and flux variations (dB/dt) method based on the worst case of plasma disruption, MD_DW_EXP16MS_CATIII, has been developed to calculate the force and moments for each ECE component and support structure for EP9 DSM2 Bay2 and Bay3. The B and dB/dt methods use the constant B and dB/dt assumed for each local bay space, but the real B and dB/dt are basically varied along the radial direction of each bay. The complex global model with the local ECE components and support structure using Maxwell transient has been developed to do EM analysis to compare the results of the B and dB/dt models. The volumetric EM force density of the whole ECE components and support structure can be used for the subsequent structural analysis. In conclusion, combined with the thermal and nuclear loads and seismic and initial loads, the ECE integration analysis can be finalized for the operation case.

Fang, J. [Princeton Plasma Physics Laboratory (PPP↗
DOE OSTI2022

Training data selection for event classification in a highly variable environment

A problem of interest for nuclear nonproliferation is monitoring activities at nuclear facilities, where proliferation events may only take place a few times and often under variable conditions. Machine learning has revolutionized data analytics by enabling the use of measurable signatures to generate predictive models of facility operations. However, traditional methods for training these models require large, reliable data sets with labeled observations, a challenge for nonproliferation. Highly variable conditions further complicate this as events from training data may have occurred in conditions quite different from the event of interest. Our hypothesis is that when events occur in a highly variable environment, careful training data selection for each test event could outperform the standard approach of using all available training data. We developed a method to optimize training data selection for the given test event and applied it to predicting the power level of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. In this study, the reactor startup exhibits variability between occurrences due to natural variability in environmental conditions and operational procedures. Using a combination of analysis techniques, a similitude assessment was performed on data collected from HFIR to isolate clusters that were optimal for training a predictive model. Concepts such as dynamic time warping and Jaccard similarity were used in conjunction with clustering analysis. In order to validate this approach, the model was trained on every combination of unique training events and the predictive performance was compared to the performance using a subset of the training data selected by isolated clusters found through the similitude assessment.

Iyer, A↗