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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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DOE OSTI2024

Probabilistic Seismic Hazard Assessment for Azerbaijan

Probabilistic Seismic Hazard Assessments (PSHA) underpin the determination of seismic loads in most contemporary seismic provisions of building codes around the world. Modern building codes are migrating towards using the entire uniform hazard spectrum at a range of vibration periods (typically up to 4 s or 10 s) rather than a single peak value such as peak ground acceleration (PGA), thus requiring a larger range of PSHA outputs. The hazard maps in the current version of the building code of Azerbaijan (2011) are in terms of intensity and peak ground acceleration. Recognizing the need for an up-to-date seismic hazard assessment in the country, Seismic Cooperation Program (SCP) under the Lawrence Livermore National Laboratory (LLNL) undertook, in coordination with the Republican Seismic Survey Center of the Azerbaijan National Academy of Sciences and the Azerbaijan Scientific Research Institute of Construction and Architecture, a PSHA study that reflects new seismic data recorded locally and recent research conducted nationally and regionally since the last update to the building code. The PSHA framework for this project was designed to help develop a new earthquake catalogue, to incorporate a novel characterization of ground motions that specifically reflects the attenuation characteristics in the eastern Caucasus, and to generate hazard information in a form that is useful for an update of the current building code or the development of a new building code for Azerbaijan. The project also aimed to provide training and support for the local seismologists and engineers related to the seismic hazard models, probabilistic seismic hazard results and their use towards changes in the building code.

58 GEOSCIENCES↗
DOE OSTI2019

Use of Neutron Flux Calculated by Shift in a Grizzly Reactor Pressure Vessel Fracture Simulation

The reactor pressure vessel (RPV) plays the critical role of containing the reactor and coolant in a light water reactor nuclear power plant, and must be able to safely perform this function under a variety of normal and off-normal transient loading conditions. The RPV is subjected to harsh environmental conditions (elevated temperature and high neutron flux) whenever the plant is operating, which leads to embrittlement of the steel over time. RPVs contain populations of flaws introduced during the manufacturing process, and the primary safety concern is that during a transient event, a fracture could initiate at the site of one of these flaws and lead to rupture of the RPV. RPVs are very rugged structures, and the probability of this occurring is very low, but as the RPV's steel becomes embrittled over time, its resistance to fracture decreases and this becomes more likely. Assessing the likelihood of RPV fracture during a transient event involves performing a probabilistic fracture mechanics analysis, in which random sampling procedures are used to assess the probability of fracture of a population of flaws. Grizzly offers unique capabilities for modeling the RPV using 1D, 2D, or 3D representations, taking advantage of parallel computing for this type of analysis. One of the important inputs to Grizzly is the spatial distribution of the neutron fluence, which has a large impact on the material embrittlement, and should thus be characterized as accurately as possible. The VERA core simulator developed by the CASL program takes advantage of high performance computing resources to perform high-fidelity multiphysics simulations of reactor physics, including the effects of neutron transport, fuel performance, and thermal hydraulics. Recently a capability was developed to also evaluate neutron fluxes away from the reactor core through the Shift code. This allows for a detailed 3D map of the spatial variation of the fluence in components such as the RPV to be computed, which is ideal for use with Grizzly. This report documents a procedure developed to use the fluences computed in Shift in a Grizzly simulation, which allows for improved realisim in the prediction of the effects of environmental exposure on propensity for reactor pressure vessel fracture. This capability demonstrated on RPVs with multiple types of configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Generation and evaluation of synthetic patient data

Background: Machine learning (ML) has made a significant impact in medicine and cancer research; however, its impact in these areas has been undeniably slower and more limited than in other application domains. A major reason for this has been the lack of availability of patient data to the broader ML research community, in large part due to patient privacy protection concerns. High-quality, realistic, synthetic datasets can be leveraged to accelerate methodological developments in medicine. By and large, medical data is high dimensional and often categorical. These characteristics pose multiple modeling challenges. Methods: In this paper, we evaluate three classes of synthetic data generation approaches; probabilistic models, classification-based imputation models, and generative adversarial neural networks. Metrics for evaluating the quality of the generated synthetic datasets are presented and discussed. Results: While the results and discussions are broadly applicable to medical data, for demonstration purposes we generate synthetic datasets for cancer based on the publicly available cancer registry data from the Surveillance Epidemiology and End Results (SEER) program. Specifically, our cohort consists of breast, respiratory, and non-solid cancer cases diagnosed between 2010 and 2015, which includes over 360,000 individual cases. Conclusions: We discuss the trade-offs of the different methods and metrics, providing guidance on considerations for the generation and usage of medical synthetic data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Solar, Wind, and Load Forecasting Dataset for MISO, NYISO, and SPP Balancing Areas

The Performance-based Energy Resource Feedback, Optimization, and Risk Management (PERFORM) program is an initiative intended to foster "a fundamental shift in grid management rooted in an understanding of asset risk and system risk" (ARPA-E 2020). Launched by the Advanced Research Projects Agency-Energy (ARPA-E), the program supports efforts to incorporate uncertainty in electric power decision making. In support of PERFORM, the National Renewable Energy Laboratory (NREL) has produced a set of time-coincident forecasts of solar, wind, and load profiles. As part of Phase I of the PERFORM effort, NREL created a dataset that consists of one year of time-coincident load, wind, and solar actuals and probabilistic forecasts based on data from the Electric Reliability Council of Texas (ERCOT) (Bryce et al. 2023). In Phase II, NREL developed similar datasets for three other U.S. Independent System Operators (ISO): the Midcontinent Independent System Operator (MISO), the New York Independent System Operator (NYISO), and the Southwest Power Pool (SPP).

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

A Decentralized Bi-Level Fuzzy Two-Stage Decision Model for Flood Management

Flood, as a serious worldwide environment problem, can lead to detrimental economic losses and fatalities. Effective flood control is desired to mitigate the adverse impacts of flooding and the associated flood risk through development of cost-effective and efficient flood management decisions and policies. A bi-level fuzzy two-stage stochastic programming model, named BIFS model is developed in this study to provide decision support for economic analysis of flood management. The BIFS model is capable of not only addressing the sequential decision making issue involving the two-level decision makers, but also correcting the pre-regulated flood management decisions before the occurrence of a flood event in the two-stage environment. The probabilistic and non-probabilistic uncertainties expressed as probability density functions and fuzzy sets are quantitatively analyzed. The overall satisfaction solution is obtained for meeting the goals of the two-level decision makers by compromising, reflecting the tradeoffs among various decision makers in the two decision-making levels. The results of application of the BIFS model to a representative case study indicate informed decision strategies for flood management. Tradeoffs between economic objectives and uncertainty-averse attitudes of decision makers are quantified.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

An Approach to Dynamic Human Reliability Analysis and Its Data Collection Framework

Human reliability analysis (HRA) is a method for evaluating human errors in a variety of complex systems such as nuclear power plants, military systems, aircraft, and chemical plants. Most HRA methods currently used by regulatory institutes or utilities are called static HRA and are carried out by simple worksheets or simple calculators. To date, there are many unsolved or intrinsic challenges in static HRA. For example, existing static HRA does not realistically model and evaluate human actions as they would be performed at actual systems. There is no method with HRA to objectively estimate the time required for human actions despite being essential to HRA processes. In addition, many HRA methods still rely on a dataset generated prior to the 1980s, from unrelated industry experience or simply from expert judgment. Accordingly, this study attempted to research how to overcome the challenges of existing HRA via dynamic risk assessment (a.k.a., simulation-based or computation-based risk assessment) techniques. First, this study developed a dynamic HRA method, named as PRocedure-based Investigation Method of EMRALD Risk Assessment – HRA (PRIMERA-HRA). The PRIMERA-HRA mainly concentrates on providing HRA analysts with specific guidelines on how to reasonably model human actions, assign human reliability data and evaluate output of simulation within a dynamic probabilistic risk assessment tool, called as Event Modeling Risk Assessment using Linked Diagrams (EMRALD). Second, this study also developed a module for performance shaping factors (i.e., the key concept in HRA quantification) applicable to dynamic HRA, then implemented it based on PRIMERA-HRA within the EMRALD tool. Third, this study developed an HRA data collection framework to support dynamic HRA, called as Simplified Human Error Experimental Program (SHEEP). Originally, the SHEEP study aimed to support static HRA and its data collection, but recently extended the scope to the new technologies such as dynamic HRA or HRA for advanced reactors. SHEEP focuses on the use of data collected from simplified simulators to complement—but not replace—data collection studies using full-scope simulators and actual operators. To date, many experiments were conducted under the SHEEP framework. Multiple analyses, such as human performance analysis, human error analysis, task complexity analysis, learning effect analysis and time distribution analysis, were also carried out using the collected data. Then, based on the major insights, an approach to inferring full-scope data based on simplified simulator data was proposed. The PRIMERA-HRA and SHEEP research are expected to evaluate human actions more realistically than existing static HRA, provide an opportunity to collect more HRA data with reasonable cost and labor, then contribute to enhance the quality of HRA.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

An Approach to Dynamic Human Reliability Analysis and Its Data Collection Framework

Human reliability analysis (HRA) is a method for evaluating human errors in a variety of complex systems such as nuclear power plants, military systems, aircraft, and chemical plants. Most HRA methods currently used by regulatory institutes or utilities are called static HRA and are carried out by simple worksheets or simple calculators. To date, there are many unsolved or intrinsic challenges in static HRA. For example, existing static HRA does not realistically model and evaluate human actions as they would be performed at actual systems. There is no method with HRA to objectively estimate the time required for human actions despite being essential to HRA processes. In addition, many HRA methods still rely on a dataset generated prior to the 1980s, from unrelated industry experience or simply from expert judgment. Accordingly, this study attempted to research how to overcome the challenges of existing HRA via dynamic risk assessment (a.k.a., simulation-based or computation-based risk assessment) techniques. First, this study developed a dynamic HRA method, named as PRocedure-based Investigation Method of EMRALD Risk Assessment – HRA (PRIMERA-HRA). The PRIMERA-HRA mainly concentrates on providing HRA analysts with specific guidelines on how to reasonably model human actions, assign human reliability data and evaluate output of simulation within a dynamic probabilistic risk assessment tool, called as Event Modeling Risk Assessment using Linked Diagrams (EMRALD). Second, this study also developed a module for performance shaping factors (i.e., the key concept in HRA quantification) applicable to dynamic HRA, then implemented it based on PRIMERA-HRA within the EMRALD tool. Third, this study developed an HRA data collection framework to support dynamic HRA, called as Simplified Human Error Experimental Program (SHEEP). Originally, the SHEEP study aimed to support static HRA and its data collection, but recently extended the scope to the new technologies such as dynamic HRA or HRA for advanced reactors. SHEEP focuses on the use of data collected from simplified simulators to complement—but not replace—data collection studies using full-scope simulators and actual operators. To date, many experiments were conducted under the SHEEP framework. Multiple analyses, such as human performance analysis, human error analysis, task complexity analysis, learning effect analysis and time distribution analysis, were also carried out using the collected data. Then, based on the major insights, an approach to inferring full-scope data based on simplified simulator data was proposed. The PRIMERA-HRA and SHEEP research are expected to evaluate human actions more realistically than existing static HRA, provide an opportunity to collect more HRA data with reasonable cost and labor, then contribute to enhance the quality of HRA.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2018

Probabilistic N - k failure-identification for power systems

This work considers a probabilistic generalization of the N - k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N - k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Progress on Grizzly Development for Reactor Pressure Vessels and Reinforced Concrete Structures

The Grizzly code has been under development for the U.S. Department of Energy’s Light Water Reactor Sustainability program to provide predictive tools for the evolution of material degradation in critical light water reactor structural components due to long-term exposure to the environmental conditions of normal reactor operation, and for the effects of this degradation on the safety of these components. This development has primarily targeted reactor pressure vessels and reinforced concrete structures. Work performed during Fiscal Year 2019 added important features for both of these types of structures. For probabilistic fracture mechanics analysis of reactor pressure vessels, capabilities were added to account for the effects of warm prestressing and residual stresses, as well as to model crack initiation, growth, and arrest. For modeling microstructure evolution in reactor pressure vessels, a cluster dynamics model for evolution of Mn-Ni-Si phases has been implemented. For modeling degraded reinforced concrete structures, capabilities to consider the combined effects of damage and creep in the concrete constitutive model and model nonlinear behavior of reinforcing bars has been added. These newly-developed features fill important gaps in Grizzly’s feature set for engineering-scale analysis of degraded reactor pressure vessels and reinforced concrete structures. Grizzly development in both of these areas has reached a point where it is ready for extensive testing on relevant engineering problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Optimal Transport as a Tool for Scientific Discovery in Radiation Biology

This report summarizes findings from research conducted for the “Exploration of the Poten tial for Artificial Intelligence and Machine Learning to Advance Low-Dose Radiation Biology Re search” (RadBio-AI) program, supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, under Awards KP1601011/FWP CC121 and KP1601017/FWP CC121. The research reported here was undertaken in an effort to assess the potential of optimal measure transport methods as components within the larger scope of a com putational framework envisioned to support research in the radiation biology domain. Within this effort, our interest centered on enabling a unified generic framework where probabilistic modeling, inference, and statistical learning can be carried out for a wide range of data distributions. As described next in Section 1 (and in more detail in our original publication), optimal measure transport offers the possibility of such unified approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Sizing battery energy storage and PV system in an extreme fast charging station considering uncertainties and battery degradation

In this paper, we present mixed integer linear programming (MILP) formulations to obtain optimal sizing for a battery energy storage system (BESS) and solar generation system in an extreme fast charging station (XFCS) to reduce the annualized total cost. The proposed model characterizes a typical year with eight representative scenarios and obtains the optimal energy management for the station and BESS operation to exploit the energy arbitrage for each scenario. Contrasting extant literature, this paper proposes a constant power constant voltage (CPCV) based improved probabilistic approach to model the XFCS charging demand for weekdays and weekends. This paper also accounts for the monthly and annual demand charges based on realistic utility tariffs. Furthermore, BESS life degradation is considered in the model to ensure no replacement is needed during the considered planning horizon. Different from the literature, this paper offers pragmatic MILP formulations to tally BESS charge/discharge cycles using the cumulative charge/discharge energy concept. McCormick relaxations and the Big-M method are utilized to relax the bi-linear terms in the BESS operational constraints. Finally, a robust optimization-based MILP model is proposed and leveraged to account for uncertainties in electricity price, solar generation, and XFCS demand. Case studies were performed to signify the efficacy of the proposed formulations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Probabilistic Cloud Optimized Day-Ahead Forecasting System Based on WRF-Solar (Final Report)

The most persistent challenge in both intraday and day-ahead solar forecasting is to get numerical weather prediction models to produce the right type of clouds with the right frequency at the right time and place. Another challenge is to understand and communicate the forecast uncertainty. The objective of this project was to develop an optimized ensemble-based solar irradiance forecasting system that will (1) demonstrably improve the current state-of-the-art solar forecasts from the deterministic Weather Research and Forecasting-Solar (WRF-Solar) model and (2) provide probabilistic forecasts for grid operations. This probabilistic solar forecasting system, referred to as the WRF-Solar Ensemble Prediction System (WRF-Solar EPS), aims to significantly enhance both the intraday and the day-ahead solar forecasting capability for grid operations. This technical report summarizes the work performed in the past 3 years through a collaboration between the National Renewable Energy Laboratory and the National Center for Atmospheric Research as part of the U.S. Department of Energy's Solar Forecasting 2 program that aims to improve the accuracy of solar energy forecasts and enable increased deployment of solar energy on the electric grid.

14 SOLAR ENERGY↗
DOE OSTI2018

An Ensemble Optimization Framework for Coupled Design of Hydropower Contracts and Real-Time Reservoir Operating Rules

Often, revenues from hydropower generation depend on the operator's ability to provide firm power in the presence of uncertain inflows. The primary options available for optimizing revenue are negotiation of a firm power contract before operations begin and adjustment of the reservoir release during operations. Contract and release strategy optimization are closely coupled and most appropriately analyzed with stochastic real-time control methods. Here we use an ensemble-based approach to stochastic optimization that provides a convenient way to construct nonparametric revenue probability distributions to explore the implications of uncertainty. The firm power contract is a simplified bilateral fixed price agreement that partially insulates operator and buyer from price fluctuations. The release control laws and firm energy target are jointly optimized to maximize the operator's expected revenue. Revenue probability distributions and related spill performance statistics indicate that predictive operating strategies such as stochastic dynamic programming and model predictive control can give significantly better performance than standard deterministic operating rules. The performance obtained from batch optimization with perfect inflow information establishes a convenient upper bound on potential revenue and provides a baseline for assessing the significance of differences between real-time operating strategies. Sensitivity analysis indicates that the benefits of predictive operational strategies are greatest for reservoirs with medium nondimensional residence times and less important for reservoirs with large residence times. Overall, probabilistic analysis of the coupled hydropower contract-operations problem provides a realistic way to assess revenue and risk for reservoirs that must provide firm power when inflows are uncertain.

13 HYDRO ENERGY↗
DOE OSTI2020

Risk-Informed Safety Analysis for Accident Tolerant Fuels

Accident Tolerant Fuels (ATF) are being tested by different nuclear vendors and research organizations and their introduction in the US light water reactors fleet is planned for the second half of the 2020`s. In the framework of the US-DOE Light-Water Reactor Sustainability program, Risk-Informed Systems Analysis pathway, researches are being conducted at the Idaho National Laboratory for developing tools and methods that can help the industry quantifying the benefits from the adoption of ATF technology. In this paper we describe the developed risk-informed methodology including the safety analysis codes improvements, and we present some results for selected accident scenarios. The developed methodology combines INL state-of-the-art deterministic Best Estimate code RELAP5-3D, and Probabilistic Risk Analysis tools RAVEN and SAPHIRE. The analyses are performed on a three-loops pressurized water reactor, simulating Station Blackout and LB-LOCA accidents and considering near-term ATFs, or FeCrAl and Chromium-coated clads. Finally, we show how, applying our methodology, the new Core Damage Frequency can be assessed. The results indicated that the main benefits in introducing near-term ATFs concern a significant reduction in the hydrogen production during accident conditions. No significant Core Damage Frequency reduction was found.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Risk-Informed Safety Analysis for Accident Tolerant Fuels

Accident Tolerant Fuels (ATF) are being tested by different nuclear vendors and research organization and their introduction in light water reactors fleet is planned for the second half of the 2020`s. In the framework of the US-DOE Light-Water Reactor Sustainability program, Risk-Informed Safety Analysis pathway (LWRS-RISA), research activities are being conducted at the Idaho National Laboratory (INL) for developing tools and methods that can help the industry in quantifying the ATF introduction benefits. In this paper we describe the developed risk-informed methodology, the codes improvements and we present some results for selected accidental conditions. The developed methodology combines INL state-of-the-art deterministic Best Estimate tools like RELAP5-3D code, and Probabilistic Risk Analysis tools like RAVEN and SAPHIRE codes. The analyses are performed on a three-loops pressurized water reactor (PWR) simulating accidental conditions like Station Blackout and LB-LOCA and considering near-term ATF (FeCrAl and Chromium-coated clads). Finally, we show, through our methodologies, how the delta-Core Damage Frequency can be assessed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

West Valley Demonstration Project (WVDP) Annual Site Environmental Report (ASER) for Calendar Year 2018

The report, prepared for the U.S. Department of Energy West Valley Demonstration Project office (DOE-WVDP), summarizes the environmental protection program at the WVDP for calendar year (CY) 2018. Monitoring and surveillance of the facilities used by the DOE are conducted to verify protection of public health and safety and the environment. The report is a key component of DOE’s effort to keep the public informed of environmental conditions at the WVDP. The quality assurance protocols applied to the environmental monitoring program ensure the validity and accuracy of the monitoring data. In addition to demonstrating compliance with environmental laws, regulations, and directives, evaluation of data collected in 2018 continued to indicate that WVDP activities pose no threat to public health or safety, or to the environment.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Industry Fire Modeling Enhancement Tools and Methods. Light Water Reactor Sustainability Program report

Modeling and implementing fire safety for nuclear power plants is a costly activity. Because of the complexity of fire phenomenon and multiple operational procedures, it is difficult to computationally provide assurance that the mitigation methods are adequate for critical areas using current analysis methods. An economical method to provide more accurate modeling and optimize mitigation methods is needed to improve nuclear power viability. This report describes the background of current fire model strategy; the first stage of a tool to help reduce resources needed in fire analysis and the plan for the next step in advancing fire. The report lays out the path decided upon by Idaho National Laboratory and Industry representatives to best help reduce costs and improve realism in Fire Probabilistic Risk Analysis.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Hazard and risk analysis framework for nuclear power plant–based integrated energy systems

Employing integrated energy systems (IESs) with nuclear power plants (NPPs) can improve NPP utilization by leveraging dedicated thermal and electric power delivery, but it may also increase operational safety risks. This paper presents a framework to identify and quantify hazards and risks for such IESs. The framework combines accidentology to review past industrial accidents with failure modes and effects analysis (FMEA) to identify potential future incidents. Hydrogen explosion and toxic chemical release hazards are of particular concern. Explosion consequences are quantified using the Bauwens-Dorofeev (Bauwens) and trinitrotoluene equivalent mass (TNT-EM) methods, while chemical release consequences are computed using the Gaussian atmospheric dispersion method. Operational disturbances from direct electrical and thermal integration that may affect NPP safety are modeled using probabilistic risk analysis (PRA). Hazards and risks are then evaluated for regulatory compliance. The framework is applied to IESs comprising pressurized or boiling water reactors supplying three levels of thermal and electrical power to industrial customers. Case studies include high-temperature steam electrolysis hydrogen plants of varying capacities and a synthetic fuel production plant. Sensitivity analysis examines piping component failures in the PRA model as a precursor to cost estimation for thermal extraction line design. Additionally, Fussel-Vessely (FV) and risk increase importance (RII) measures identify risk-informed design improvements for the thermal extraction system. FMEA highlights hazards such as loss of offsite power, prompt loss of electrical load, loss of thermal output, and immediate steam diversion, in addition to hydrogen explosions and toxic chemical releases. Both Bauwens and TNT-EM methods suggest maintaining several hundred meters of separation between the NPP and hydrogen facility to mitigate explosion risks. PRA results show a maximum initiating event frequency increase of 1.15% and an overall risk increase of 0.28%. Importance measure analysis identifies upstream pipe leak isolation components as critical. Evaluating the results against safety regulations, it is concluded that hazards and risks can be managed to comply with regulations through risk-informed thermal and electrical connection designs, component selection, maintenance programs, and safe separation distances between NPPs and integrated industrial facilities.

08 - HYDROGEN↗