Search NASA⌕ Search

SEARCH · Search NASA

Results for “Path integrals”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Steady-State Microbunching using Optical Stochastic Cooling

Optical Stochastic Cooling (OSC) is a state-of-the-art beam cooling technology first demonstrated in 2021 at the IOTA storage ring at Fermilab's FAST facility. A second phase of the research program is planned to run in 2026 and will incorporate an optical amplifier to enable significantly increased cooling rates and greater operational flexibility. In addition to beam cooling, an OSC system can be configured to enable advanced control over the phase space of the beam. An example operational mode could enable crystallization, where the particles in a bunch are locked into a self-reinforcing, regular microstructure at the OSC fundamental wavelength; we refer to this as Optical Stochastic Crystallization (OSX). OSX represents a new path toward Steady-State Microbunching (SSMB), which may enable light sources combining the high brightness of a free-electron laser with the high repetition rate of a storage ring. Such a source has applications from the terahertz to the extreme ultraviolet (EUV), including high-power EUV generation for semiconductor lithography. This contribution will discuss the integration of OSX development as part of the OSC program at IOTA. The design of an accelerator lattice to enable the mechanism and associated high fidelity simulations demonstrating the beam dynamics will be shown, and a path to realizing an experimental demonstration will be discussed.

Wallbank, Michael James [Fermilab]↗

Knowledge-guided graph machine learning for spatially distributed prediction of daily discharge and nitrogen export dynamics

Spatially distributed prediction of streamflow and nitrogen export dynamics is essential for precision management of agricultural watersheds. While temporal deep learning models such as Long Short-Term Memory (LSTM) have shown strong performance at basin scales, their ability to generalize spatially is limited by insufficient representation of spatial dependencies and flow paths, particularly under data-scarce conditions. To address this gap, we propose HydroGraphNet, a knowledge-guided graph machine learning framework that integrates process-based knowledge and explicit spatial learning into temporal modeling. This framework incorporates directed graph topology to encode watershed connectivity and upstream inflows, with mass balance constraints to improve physical consistency. To enhance generalization in sparsely monitored regions, HydroGraphNet is pretrained on synthetic data generated by the SWAT+ (Soil and Water Assessment Tool Plus) model. We evaluated HydroGraphNet in the Upper Sangamon River Basin (44 HUC-12 subwatersheds, 2001–2020) against two LSTM baselines: a lumped basin-level model and a distributed variant. When benchmarked on SWAT+ simulations in pretraining, HydroGraphNet improved test NSEs by 8.9% (discharge) and 13.7% (NO₃–N load) in temporal extrapolation, and by 27.1% and 34.7% in spatial extrapolation, relative to the Lumped LSTM baseline. After fine-tuning with USGS monitoring data, the model achieved mean test NSE (KGE) scores of 0.768 (0.861) for discharge and 0.626 (0.664) for NO₃–N load, substantially outperforming baselines. Attribution analysis further highlighted the importance of upstream inflow representation and graph-based spatial learning in capturing cross-subwatershed dependencies. The model also reproduced seasonal hydrological and biogeochemical patterns consistent with known processes, demonstrating its robustness and process fidelity for spatially distributed prediction. Altogether, HydroGraphNet advances the integration of physical knowledge and spatially explicit learning in hydrological modeling, offering a generalizable framework for distributed modeling to support spatially targeted water quality management in data-scarce watersheds.

54 ENVIRONMENTAL SCIENCES↗

A Large Bore Conduction Cooled Superconducting Magnet for the Princeton Axion Search

Princeton University (PU) is designing and building a new experiment, called the Princeton Axion Search (PXS), that aims to discover (or exclude) Quantum Chromodynamics (QCD) axions in the 0.8–2 μeV mass range that are the cosmological dark matter. Core elements of the experiment are new, and in particular new to the search for axion dark matter. An essential component of the experiment is a 5 T superconducting magnet with a total bore volume of ~500 L. The Princeton Plasma Physics Laboratory (PPPL), a Department of Energy (DOE) Laboratory managed by Princeton University, has the unique expertise and experimental facilities to design and construct such a solenoid magnet assembled with the cavity resonator for PXS. To support this, PPPL utilizes legacy ITER-Nb3Sn conductors, along with its experimental facilities and expertises to design, build and test low-cost conduction-cooled superconducting solenoid magnets to be integrated into the axion detector. This paper discusses the various coil design and integration challenges in the large bore conduction cooled magnet in support of PXS. In conclusion, the proposed instrumental methods will help optimize the path to future and more ambitious axion searches at lower masses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A Privacy First Path Analysis using Clickstream Data

In the modern digital economy, data-driven decision making is crucial for effectively meeting the ever-evolving demands of consumer engagement and satisfaction. Clickstream data has become invaluable for understanding customer behavior, yet concerns over privacy and security persist, especially with some internet service providers profiting from its sale. This article introduces an innovative methodology that blends experiential learning with advanced cryptographic techniques, including differential privacy and graph analytics. The core objective of this methodology is to estimate Customer Lifetime Value (CLV) by analyzing clickstream data, achieving an average prediction accuracy of 92.4% in user engagement levels while ensuring user anonymity through Recency, Frequency, and Monetary (RFM) analysis. Our study introduces the concept of a “data depositor” and a privacy manager, employing the composition theorem to merge non-adaptive queries effectively. Privacy budgets (? = 1.0, d = 10-5), sensitivity-specific techniques, and data partitioning were applied. Randomization and noise addition protect data integrity, with special handling for categorical values. This approach, differing from prior studies, offers a 12.6% improvement in privacy-preserving targeting accuracy while maintaining strict confidentiality, presenting a novel path forward in data-driven decision-making.

Frequency and Monetary (RFM) analysis↗

M3SF-24LL010302052-Comprehensive Analysis of Radionuclide Interaction with Hydrothermally Altered Repository Materials

This progress report (Level 3 Milestone Number M3SF-24LL010302052) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Crystalline Work Package Number SF-24LL01030205. The research is focused on actinide and radionuclide sequestration in hydrothermally altered repository materials. In FY24, we completed a rigorous analysis of Se sorption to iron oxide phases using our L-SCIE sorption database. This effort explicitly accounts for surface titration behavior of oxide surfaces that was the subject of a recently published manuscript (Han et al., 2023). With this in mind, our Se sorption analysis now yields a more robust workflow for developing self-consistent surface complexation modeling approaches that can be adapted to specific SCM conceptual and numerical approaches (i.e. non-electrostatic, diffuse layer, triple layer models). In late FY24, we plan to publish the results of our comprehensive surface complexation modeling of Se(IV) and Se(VI) sorption to iron oxide mineral phases and provide a path forward to developing robust radionuclide sorption models for use in performance assessment. In FY24, we also submitted a manuscript summarizing our approach to integrating radionuclide sorption and coprecipitation phenomena and evaluation of radionuclide partitioning values across a range of radionuclides relevant to performance assessment. We demonstrated our approach in detail using Se sorption and coprecipitation with iron oxide minerals as a test case. This manuscript was recently accepted for publication in Applied Geochemistry (Balboni et al., Accepted). We also continued experiments to identify radionuclide interaction with hydrothermally altered crystalline repository and backfill materials. Recent research performed at Los Alamos National Laboratory (LANL) and Sandia National Laboratory (SNL) has provided key insights regarding the hydrothermal alteration behavior of bentonite backfill in the presence of repository materials (steel, concrete, etc.). We are now examining how mineral alteration affects retardation behavior of a suite of radionuclides of interest to repository performance assessment. These experiments also allow us to test the predictive ability of our component additivity approach to surface complexation and ion exchange. Our guiding hypothesis is that a robust surface complexation/ion exchange model and associated database, developed using our L-SCIE approach, can effectively predict changes in radionuclide sorption behavior resulting from the hydrothermal alteration of mineralogy in a repository near field. A short update of results to date is presented below.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Heliostat optical error inspection with polarimetric imaging drone

On a Concentrated Solar Power (CSP) field, optical errors have significant impacts on the collection efficiency of heliostats. Fast, cost-effective, labor-efficient, and non-intrusive autonomous field inspection remains a challenge. Approaches using imaging drone, i.e., Unmanned Aerial Vehicle (UAV) system integrated with high resolution visible imaging sensors, have been developed to address these challenges; however, these approaches are often limited by insufficient imaging contrast. Here, in this study, we report a polarimetry-based method with a polarization imaging system integrated on UAV to enhance imaging contrast for in-situ detection of heliostat mirrors without interrupting field operation. We developed an optical model for skylight polarization pattern to simulate the polarization images of heliostat mirrors and obtained optimized waypoints for polarimetric imaging drone flight path to capture images with enhanced contrast. The polarimetric imaging-based method improved the success rate of edge detections in scenarios which were challenging for mirror edge detection with conventional imaging sensors. We have performed field tests to achieve significantly enhanced heliostat edge detection success rate and investigate the feasibility of integrating polarimetric imaging method with existing imaging-based heliostat inspection methods, i.e., Polarimetric Imaging Heliostat Inspection Method (PIHIM). Our preliminary field test results suggest that the PIHIM hold the promise to enable sufficient imaging contrast for real-time autonomous imaging and detection of heliostat field, thus suitable for non-interruptive fast CSP field inspection during its operation.

CSP Field↗

Advanced Processing of Coal and Coal Waste to Produce Graphite for Fast-Charging Lithium-Ion Battery Anode

The University of North Dakota (UND) Energy & Environmental Research Center (EERC), in collaboration with the UND Center for Process Engineering Research (CPER), conducted a project to validate two technologies capable of converting North Dakota lignite and lignite coal waste to high-quality graphite for fast-charging lithium-ion battery (LIB) anode. The project was conducted over about 3 years from April 7, 2022, to July 6, 2025. The two technological paths pursued in this project include path A – direct conversion of coal or coal waste to graphite by the upgraded carbon ores to products (UCOP) process being developed at the EERC and path B – lignite-derived coal tar pitch (CTP) conversion to graphite (CTP2G) process being developed at CPER. The results from this project validate the two technological approaches and are expected to be an integral part of a portfolio of emerging technologies for making high-quality graphite not only from North Dakota lignite, but from all ranks of U.S. domestic coal and coal waste resources. The quality of the graphite produced by these technologies is high enough for various applications, including batteries for the fast-growing electric vehicle industry, energy storage applications, electric arc furnace electrodes for steel production, and graphene production, among others. Although the two technologies can produce high-quality graphite, they are fundamentally different in that the UCOP technology provides a direct path to transform coal to graphite, while the CTP2G technology needs to go through a CTP intermediate and a coking process for the intermediate, which requires a special facility to accomplish. For application in the industry, the UCOP process is designed to be more flexible, with feedstock to include potentially any carbonaceous material such as all coal ranks and biochar, while the CTP2G process is designed to utilize CTP as the starting precursor. The key project accomplishments include the following: • Successful preparation of high-quality synthetic graphite from North Dakota lignite coal/coal wastes and lignite-derived CTP. • Patent application has been filed for the UCOP process and an internal invention disclosure has been filed for the CTP2G process. • The produced graphite performs better than a commercial battery-grade sample in LIB coin cells, especially fast-charging capability, stability, and long-duration cycling. • Coin-type Li-ion half-cells with CTP2G graphite showed excellent performance, with >370 mAh/g capacity, >90% initial coulombic efficiency, and 93%/67% retention at 1C/2C rate, which outperforms commercial graphite in charging speed, stability, and cycling. • Results of fabricated 18650 cells were consistent with the observations in coin cells. • Preliminary techno-economic analysis (TEA) estimates for the UCOP technology indicate a manufacturing cost of about $\$$39/kg based on 50-metric ton/year capacity. • Preliminary TEA estimates for the CTP2G technology indicate a market price of about $\$$7107/ton ($\$$7/kg) based on 22,000-ton/year production capacity.

01 COAL, LIGNITE, AND PEAT↗

Comparative Study of Solvatomorphs of Stryker's Reagent Using MicroED and Quantum Mechanics

Abstract The atomic position of hydrogen atoms in metal hydrides has been a long‐standing structural question in inorganic chemistry given that hydride delivery is integral to diverse chemical reactions. Microcrystal electron diffraction (microED), with it's increased sensitivity toward hydrogen atoms relative to X‐ray diffraction, offers a potential path to addressing this challenge. Herein, the first microED study of Stryker's reagent is reported, resulting in the structure of a new benzene solvate. Improved accuracy for hydrogen atom positions was obtained via a quantum crystallography (QCr) approach, Hirshfeld atom refinement (HAR). Structural and topological analysis supports edge bridging hydrides in the microED structure of a THF solvate form, consistent with previous diffraction studies. Interestingly, analysis of a new benzene solvate, discovered in this study, is consistent with mixed edge‐ and face‐bridging hydrides.

Jha, Kunal K. [Division of Chemistry &amp, Chemica↗

Success Path Method: Conformance with Safety Management Systems

All industrial facilities deal with safety hazards such as equipment failures, chemical and toxic releases, and fires and explosions just to name a few. A disciplined framework for managing the integrity of operating systems and processes that handle hazardous substances by applying good design principles, engineering, and operating practices is called process safety. The goal of such framewoks is to prevent the release of energy or material that could cause harm to people or damage to equipment and/or environment. Process safety covers all aspects of facility operation also including design, maintenance, and human and organizational factors that could possibly have effect on process safety. As it will be seen from the discussion below, process safety is just one of the pieces of the much bigger matter, a safety culture. Many industries have long recognized the importance of safety culture in their day-to-day operation. Although the definition of safety culture can slightly differ from organization to organization, in general, a safety culture is how things are done to demonstrate a commitment to safety by everyone involved. An organization acquires safety culture over time as the product of individual and group values, actions, and behaviors toward overall safety. It is important to note that safety culture should not be viewed as some static state that an organization wants to reach. It is more like a constantly evolving level of “how things are done when nobody is watching.” Safety culture is an inherent characteristic of an organization, it is always present, but the level can range on a continuum from undesirable to desirable or more commonly used, from negative to positive. An example for an undesirable, negative safety culture would be a company in which accidents resulting in harm (physical and/or emotional) of its employees, equipment or surrounding environment and community occur frequently. At the other end of the spectrum would be a company in which such accidents are rare or do not occur at all (desired or positive safety culture). Every company/industry exists somewhere within this spectrum.

42 ENGINEERING↗

Diagnostic-free onboard battery health assessment

Diverse usage patterns induce complex and variable aging behaviors in lithiumion batteries, complicating accurate health diagnosis and prognosis. Separate diagnostic cycles are often used to untangle the battery’s current state of health from prior complex aging patterns. However, these same diagnostic cycles alter the battery’s degradation trajectory, are time-intensive, and cannot be practically performed in onboard applications. Here, in this work, we leverage portions of operational measurements in combination with an interpretable machine learning model to enable rapid, onboard battery health diagnostics and prognostics without offline diagnostic testing and the requirement of historical data. We integrate mechanistic constraints within an encoder-decoder architecture to extract electrode states in a physically interpretable latent space and enable improved reconstruction of the degradation path. The health diagnosis model framework can be flexibly applied across diverse application interests with slight fine-tuning.

battery aging reconstruction↗

Topological Green’s Function Zeros in an Exactly Solved Model and Beyond

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green’s function and show that in this model they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite “lifetime.” We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green’s function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross pollination between solid-state theory, high-energy physics, and quantum information science.

Bollmann, Steffen↗

Hot Springs and Geysers: Exploring Historical and Modern Impacts of Geothermal Energy Production on Associated Natural Surface Systems and Standardizing Management Practices

Surface thermal features, most notably hot springs and geysers are increasingly being recognized for their importance to ecosystems, indigenous cultures, and in some cases agriculture, recreation, and tourism. Geothermal project development poses a potential risk to these natural features but current regulatory requirements for assessing and managing these risks during exploration, permitting and monitoring are somewhat inconsistent and unpredictable across different geothermal fields. This has resulted in uncertainty and increases in exploration risk for geothermal energy developers that have led to costly project delays, cancellations, or hesitation to commit. Varying regulatory requirements may also influence public perception, fostering confusion, distrust and ultimately opposition to geothermal projects, further contributing to project delays or cancellations. At a time when there is an increasing urgency for reliable baseload clean energy, geothermal is a net-zero, renewable solution that additionally provides access to more equitable and environmentally just clean power. Continued integration of geothermal energy into the national energy roadmap can be facilitated through consistent and predictable permitting, providing regulators the framework they need, developers a clear path forward, and transparency that the public deserves. This project, currently in its beginning phases, seeks to address this important issue by providing a technical basis from which to build a preliminary protocol for assessing and managing potential impacts from new or existing geothermal energy projects to surface thermal features and their associated ecosystems. Development of this preliminary protocol will be informed by (1) a literature review of well-documented case studies in the western U.S. and New Zealand to understand the range of conditions that exemplify geothermal-surface thermal systems; (2) development of generic illustrative conceptual-numerical models to quantify, understand, and predict the first-order controls (e.g., pressure and permeability) on surface flows; and (3) additional independent and scientifically rigorous evaluations of geothermal-surface thermal system case studies from the Basin and Range Province that incorporate publicly available data as well as data provided by industry through data-sharing agreements. Learning from the successes of the process used to develop the Induced Seismicity Management Protocol (ISMP), we ultimately aim to use these initial efforts as a springboard for establishing a surface thermal feature management working group that will work collaboratively to finalize the protocol as well as co-create recommended best practices for implementation. We envision that the working group will primarily be composed of representatives from regulatory entities, government agencies, Tribes, academia, national laboratories, and industry, and will include early and regular engagement with community organizations and environmental groups. This will help ensure broad acceptance and implementation of the protocol, which will facilitate a more consistent, predictable, and standardized regulatory process, and help to ensure that geothermal energy continues to provide a reliable source of clean energy, and a pathway to achieving greater energy equity in the U.S.

Best Practices↗

Voices from Rural Electric Cooperatives: A Call for a DER Integration Playbook for Rural and Agricultural Income & Savings from Renewable Energy (RAISE)

Rural-serving electric utilities (RSEUs)—including electric cooperatives, municipal systems, and small investor-owned utilities—are essential players in the evolving energy landscape. These community-focused entities are increasingly being asked to consider distributed energy resources (DERs) such as rooftop and ground-mounted solar, wind, battery storage, smart water heaters, and demand response programs (NRECA 2025; Lenhart et al. 2020). Yet the path to DER adoption is far from straightforward in the rural context. This report is based on in-depth interviews with managers of rural electric cooperatives across the United States. These conversations offer a grounded, unvarnished look at how DERs are perceived, what barriers exist, and what conditions might enable integration and adoption. While the utilities interviewed vary in geography, size, and DER experience, several clear and common themes emerged across electric cooperatives such that the report recommends the development of a DER Integration Runbook to help utilities assess readiness, define local use cases, engage stakeholders, pilot projects, and iterate, expanding over time.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

SULI Report - Development of a Molten Salt Circulation Loop for in-situ Spectroscopy

This project supports the development of real time optical monitoring capabilities for molten salt reactor (MSR) environments by designing, testing, and refining a molten salt circulation loop suitable for combined laser induced breakdown spectroscopy (LIBS) and ultraviolet visible (UV Vis) absorption measurements. Online spectroscopic monitoring is increasingly important for nuclear safeguards, corrosion tracking, and material accountancy, yet MSR process fluids present substantial challenges due to their chemical complexity and hazards such as high temperatures and radiation. To address these needs, this work focuses on Phase I, the development of a room temperature aqueous circulation loop that serves as a surrogate platform for evaluating flow behavior, optical access, and component performance prior to high temperature salt operation. Initial testing identified several practical issues—including leaks, obstructions, and two-phase flow through the absorption cell—that were systematically resolved through hardware replacement, flow path redesign, and venturi pressure optimization. Relocating the flow cell upstream of the primary venturi enabled periods of stable single-phase flow, demonstrating the feasibility of integrating optical diagnostics into a circulation system. The results of Phase I provide essential design insight for Phase II, which will incorporate furnace compatible materials and LiCl KCl eutectic salt. Completion of the molten salt system will deliver a reusable testbed for evaluating multimodal spectroscopic techniques, advancing nondestructive, real time monitoring tools for future MSR and nuclear fuel cycle applications.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗

Computational methods in solution-based plastics purification

Plastic waste can be recycled into resins with near-virgin properties by solution-based purification processes that selectively dissolve polymers, remove contaminants, or detach printing residues. Here, in this review, we examine computational methods for predicting the behavior governing solution-based plastic purification, motivated by the vast polymer–solvent–contaminant compositional space. We discuss thermodynamic and machine learning methods for predicting polymer–solvent and polymer–contaminant interaction and review physics-based molecular dynamics simulations that resolve molecular-scale phenomena within polymer matrices inaccessible to screening methods. We highlight how these methods have informed experimental design for dissolution-based recycling and solvent-based contaminant removal. Finally, we discuss the prospective role of agentic AI in integrating these computational tools with real-time sorting data to adapt purification conditions to the compositional variability of real post-consumer feedstocks. This review charts a path toward computationally guided solution-based purification workflows that can respond to the complexity inherent in plastic waste streams.

Altamimi, Ali [Univ. of Wisconsin, Madison, WI (Un↗

Model Scripts for "Old-Aged Groundwater Contributes to Mountain Hillslope Hydrologic Dynamics"

The partitioning of water inputs between deep and shallow groundwater flow paths is a fundamental processes, yet is challenging to observe. Numerical models provide a valuable tool to further develop insights on these groundwater mixing processes. This repository contains scripts to run the ParFlow-CLM and EcoSLIM integrated hydrologic models along the Pumphouse Hillslope in the East River Watershed and associated python scripts to process model outputs. Files includes input decks for the associated models, python scripts, and text and css files to support the model runs and processing. The 2-D hillslope model simulates from 2000 to 2021 using transient forcing conditions from the publicly available NLDAS-2 dataset. We develop an ensemble of models with variable hydrogeologic and soil parameters. Model outputs from the ensemble of runs are compared to to water level observations at the PLM1 and PLM6 wells published at (https://data.ess-dive.lbl.gov/view/doi:10.15485/1866836) and groundwater mean ages published at (https://data.ess-dive.lbl.gov/datasets/doi:10.15485/1960042. The model results are used to evaluate hillslope water mass-balance transience and mixing dynamics between groundwater flow paths with young (<10 year) and old (>10 year) ages.

54 ENVIRONMENTAL SCIENCES↗

Model Diagnostics for Equation Oriented Models: Roadblocks and the Path Forward

Conference paper for FOCAPD24 describing efforts to develop a unified workflow and toolbox for diagnosing issues in equation-oriented models as part of the IDAES modeling framework. The paper presents the work currently underway within the IDAES project to develop and integrate cutting edge model analysis techniques into a common toolbox and workflow for model developers to use.

Lee, Andrew↗

Feedback, physics, and forecasts: The emerging paradigm of machine learning-driven battery research

Machine learning (ML) is reshaping how we understand, predict, and optimize electrochemical systems. In batteries, ML accelerates discovery across chemistry, design, and operation by transforming massive experimental and simulated datasets into predictive, interpretable models. This review consolidates a decade of progress in ML-driven battery innovation, from early-cycle feature extraction to operando image analysis and physics-informed modeling. We categorize approaches by data domain and physical fidelity, emphasizing interpretable ML for diagnostics, reinforcement learning for control, and multi-objective optimization for lifetime extension strategies. Additionally, we demonstrate how integrated models accelerate discovery, reduce testing time, and guide sustainable design. Economic analyses furthermore illustrate how these advances can lower cost per cycle and improve circularity. Together, these developments chart a path toward self-optimizing, sustainable battery technologies.

artificial intelligence↗