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DOE OSTI2021

ARENA: Asynchronous Reconfigurable Accelerator Ring to Enable Data-Centric Parallel Computing

The next generation HPC and data centers are likely to be reconfigurable and data-centric due to the trend of hardware specialization and the emergence of data-driven applications. In this work, we propose ARENA – an asynchronous reconfigurable accelerator ring architecture as a potential scenario on how the future HPC and data centers will be like. Despite using the coarse-grained reconfigurable arrays (CGRAs) as the substrate platform, our key contribution is not only the CGRA-cluster design itself, but also the ensemble of a new architecture and programming model that enables asynchronous tasking across a cluster of reconfigurable nodes, so as to bring specialized computation to the data rather than the reverse. We presume distributed data storage without asserting any prior knowledge on the data distribution. Hardware specialization occurs at runtime when a task finds the majority of data it requires are available at the present node. In other words, we dynamically generate specialized CGRA accelerators where the data reside. The asynchronous tasking for bringing computation to data is achieved by circulating the task token, which describes the dataflow graphs to be executed for a task, among the CGRA cluster connected by a fast ring network. Evaluations on a set of HPC and data-driven applications across different domains show that ARENA can provide better parallel scalability with reduced data movement (53.9 percent). Compared with contemporary compute-centric parallel models, ARENA can bring on average 4.37× speedup. The synthesized CGRAs and their task-dispatchers only occupy 2.93mm 2 chip area under 45nm process technology and can run at 800MHz with on average 759.8mW power consumption. ARENA also supports the concurrent execution of multi-applications, offering ideal architectural support for future high-performance parallel computing and data analytics systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Beam Dynamics of the Muon $g\textrm{-}2$ Experiment

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of 0.20 ppm. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: \texttt{gm2ringsim} (an internal Geant4-based code), \textit{COSY INFINITY}, and \textit{BMAD}. The advantages of \texttt{gm2ringsim} include using CAD-based geometry and modelling the detector effects. \textit{COSY INFINITY} is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Opportunities in multiscale modeling of mosquito-borne flaviviruses

Mosquito-borne flaviviruses, such as Zika, dengue, West Nile, and yellow fever virus, represent a growing public health concern due to their widespread distribution and the severe diseases they cause. These viruses are difficult to control as climate change and urbanization help mosquitoes expand into new areas, increasing the risk of outbreaks. Mathematical models play a key role in understanding their spread, providing insights at every level—from how the virus multiplies inside cells to how it circulates through entire populations. This review examines various approaches used in modeling arboviruses, including microscale models that focus on cellular and molecular dynamics, mesoscale models that address within-host processes, and macroscale models that capture population-level transmission. We briefly summarize the methodology used for models at each scale, which primarily consists of sets of differential equations with parameters that represent physical rates of change for different subprocesses. We particularly highlight how temperature affects virus transmission, which is key to understanding the impact of climate change. We also show how multiscale models can connect viral replication, immune response, and the spread of infection at a larger scale. This is essential for developing better vaccines and treatments, evaluating disease control measures, predicting the impact of climate change, and improving public health responses to outbreaks.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Contributions of extreme and non-extreme precipitation to California precipitation seasonality changes under warming

Changes in seasonality of extreme precipitation have important implications for flood and fire hazards and water resources. Here we explore the contributions of extreme and non-extreme precipitation in the sharpened wet season in California under warming and the underlying mechanisms. Modeling evidence shows that increased extreme precipitation due to enhanced extreme intensity and more extreme days dominates the wetter winter, while decreased non-extreme precipitation due to fewer wet days induces the dryer spring and fall. Moisture budget analysis indicates that increased moisture dominates the extreme precipitation increase in winter, while weakened circulation offsets the moisture increase, resulting in no changes in spring and fall. The sharpened seasonal cycle of extreme precipitation via both dynamic and thermodynamic effects is consistent with the seasonality changes in atmospheric river days and is mainly attributed to the seasonality changes in the number of extreme days rather than the intensity during extreme days.

Dong, Lu↗

DOE OSTI2022

Assessment of Thermal Stratification in Versatile Test Reactor Transients

The Versatile Test Reactor (VTR) is a fast-spectrum test reactor currently being developed in the United States under the direction of the US Department of Energy. The conceptual design of the 300 MWth pool-type sodium-cooled fast reactor (SFR) has been led by the US National Laboratories in collaboration with General Electric-Hitachi and Bechtel National Inc. Safety performance analysis for the VTR conceptual design is being performed with the systems thermal-hydraulics (SYSTH) module of the SAS4A/SASSYS-1 liquid-metal reactor safety analysis code system. Since the current model of the VTR employs a simple perfect mixing model for large plena like the hot pool, it is not able to predict temperature variations that may develop during the transient. Prior work simulating the response of SFRs to postulated events like the Protected Station Blackout (PSBO) has shown that the phenomenon of thermal stratification, where stable thermal layers accumulate in the hot pool, may delay the transition to natural circulation and thus impact the predicted transient progression. Thus, an effort has begun to model this transient by integrating a Computational Fluid Dynamics (CFD) model of the hot pool into the SAS4A/SASSYS-1 model of the Primary Heat Transport System during the simulation of the PSBO event. A three-dimensional Volume-Of-Fluid CFD model of the VTR hot pool has been developed for the co-simulation of SAS4A/SASSYS-1 with CFD. In this work, the standalone SAS4A/SASSYS-1 calculation and the standalone CFD calculation based on the SAS4A/SASSYS-1 calculation result were produced on the Idaho National Laboratory High Performance Computing cluster, SAWTOOTH. At this time, only the standalone CFD and SAS4A/SASYS-1 simulation results are provided.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2020

Modifications to the Bubble experiment and preparation for additional irradiations

SHINE Medical Technologies is planning to use neutron-induced fission in a subcritical low-enriched-uranium uranyl sulfate target solution for production of 99 Mo. During this operation, the solution will undergo self-heating due to fissioning of the uranium, radiolytic decomposition of the water, and circulation due to thermal gradients generated in the solution, and will be cooled by cooling tubes running through the annulus and from cooling outside the annulus. Because the formation of the radiolysis-induced bubbles (H 2 and O 2 ) and their size and dynamics will impact the operational parameters of the liquid target, an understanding of bubble behavior is critical for the ability to predict the behavior of the target solution during this operation. It is also important to be able to predict the thermal gradients and the circulation in the vessel. Researchers at Argonne National Laboratory have designed an experimental setup to study radiolytic gas formation in uranyl sulfate under direct electron beam irradiation and have conducted initial experiments. Results of those experiments provided invaluable information on thermal hydraulic behavior of the solution and some information on bubble formation and behavior, but those initial experiments fell short in the measurements of the gas generation rates and bubble behavior. To address the shortcomings of the original experiment, the irradiation setup was modified to improve our abilities to measure gas generation rates and measure the temperature distribution in the solution with better precision. Modifications to the experimental setup and preparation for the irradiations are described below.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2025

Using a Large Language Model for Accurate Technical Language Generation in the Predictive Maintenance of Circulating Water Systems in Nuclear Power Plants

Machine learning (ML) methods for predictive maintenance (PdM) are emerging as effective proactive strategies for diagnosing equipment degradation and enabling effective decision-making. However, explainability and trustworthiness of artificial intelligence are two salient challenges that need to be addressed for wider deployment of these technologies in nuclear power plants (NPPs). Large language models (LLMs) offer a unique approach to tackle these challenges by explaining PdM, work orders, diagnosis results, and ML algorithms to users, who may not be familiar with ML and PdM in general. Moreover, by dynamically retrieving relevant information from technical documents and evaluating factuality of LLM generation, the accuracy and relevance of LLM generations can be improved. This work demonstrates using LLMs to explain the causes and consequences of circulating water system failures based on multiyear NPP work orders. This work tests the capability of multimodal LLM approaches in explaining the differences in the circulating water system from both the Salem and Hope Creek NPPs using both text and image resources. This work also demonstrates the use of multimodal LLMs in describing the diagnosis tab of a predictive maintenance software named VIsualization for PrEdictive maintenance Recommendation (VIPER) to users.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Why Do Oceanic Nonlinearities Contribute Only Weakly to Extreme El Niño Events?

Abstract Extreme El Niño events have outsized global impacts and control the El Niño Southern Oscillation (ENSO) warm/cold phases asymmetries. Yet, a consensus regarding the relative contributions of atmospheric and oceanic nonlinearities to their genesis remains elusive. Here, we isolate the contribution of oceanic nonlinearities by conducting paired experiments forced with opposite wind stress anomalies in an oceanic general circulation model, which realistically simulates extreme El Niño events and oceanic nonlinearities thought to contribute to ENSO skewness (Tropical Instability Waves (TIWs), Nonlinear Dynamical Heating (NDH)). Our findings indicate a weak contribution of oceanic nonlinearities to extreme El Niño events in the eastern Pacific, owing to compensatory effects between lateral (NDH and TIWs) and vertical processes. These results hold across different vertical mixing schemes and modifications of the upper‐ocean heat budget mixed layer criterion. Our study reinforces previous research underscoring the pivotal role of atmospheric nonlinearities in shaping extreme El Niño events.

Geology↗

DOE OSTI2023

Influence of Mild Chronic Stress and Social Isolation on Acute Ozone-Induced Alterations in Stress Biomarkers and Brain-Region-Specific Gene Expression in Male Wistar–Kyoto Rats

Individuals with psychosocial stress often experience an exaggerated response to air pollutants. Ozone (O 3 ) exposure has been associated with the activation of the neuroendocrine stress-response system. We hypothesized that preexistent mild chronic stress plus social isolation (CS), or social isolation (SI) alone, would exacerbate the acute effects of O 3 exposure on the circulating adrenal-derived stress hormones, and the expression of the genes regulating glucocorticoid stress signaling via an altered stress adaptation in a brain-region-specific manner. Male Wistar–Kyoto rats (5 weeks old) were socially isolated, plus were subjected to either CS (noise, confinement, fear, uncomfortable living, hectic activity, and single housing), SI (single housing only, restricted handling and no enrichment) or no stress (NS; double housing, frequent handling and enrichment provided) for 8 weeks. The rats were then exposed to either air or O 3 (0.8 ppm for 4 h), and the samples were collected immediately after. The indicators of sympathetic and hypothalamic–pituitary axis (HPA) activation (i.e., epinephrine, corticosterone, and lymphopenia) increased with O 3 exposure, but there were no effects from CS or SI, except for the depletion of serum BDNF. CS and SI revealed small changes in brain-region-specific glucocorticoid-signaling-associated markers of gene expression in the air-exposed rats (hypothalamic Nr3c1, Nr3c2 Hsp90aa1, Hspa4 and Cnr1 inhibition in SI; hippocampal HSP90aa1 increase in SI; and inhibition of the bed nucleus of the stria terminalis (BNST) Cnr1 in CS). Gene expression across all brain regions was altered by O 3 , reflective of glucocorticoid signaling effects, such as Fkbp5 in NS, CS and SI. The SI effects on Fkbp5 were greatest for SI in BNST. O 3 increased Cnr2 expression in the hypothalamus and olfactory bulbs of the NS and SI groups. O 3 , in all stress conditions, generally inhibited the expression of Nr3c1 in all brain regions, Nr3c2 in the hippocampus and hypothalamus and Bdnf in the hippocampus. SI, in general, showed slightly greater O 3 -induced changes when compared to NS and CS. Serum metabolomics revealed increased sphingomyelins in the air-exposed SI and O 3 -exposed NS, with underlying SI dampening some of the O 3 -induced changes. These results suggest a potential link between preexistent SI and acute O 3 -induced increases in the circulating adrenal-derived stress hormones and brain-region-specific gene expression changes in glucocorticoid signaling, which may partly underlie the stress dynamic in those with long-term SI.

gene expression↗

DOE OSTI2024

The Muon g-2 Experiment at Fermilab: Precision Measurements and Nonlinear Beam Dynamics

The Muon g-2 Experiment has achieved a significant milestone by measuring the positive muon anomalous magnetic moment to an unprecedented accuracy of 0.20 ppm, paving the way to a better understanding of particle physics, including beyond-the-Standard-Model possibilities. In the experiment, muons are circulated within a storage ring, and their anomalous precession frequency — the spin precession relative to momentum — is determined from decay positron time and energy data, captured using calorimeters. In support of accurate storage ring simulations, we performed high-order calculations of the field of the experiment's high-voltage quadrupoles. We also carried out accurate, transfer map–based calculations of the storage ring's chromaticity. These calculations are essential for understanding the beam dynamics effects in the Muon g-2 storage ring.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Evaluation of precipitation across the contiguous United States, Alaska, and Puerto Rico in multi-decadal convection-permitting simulations

Abstract This study is an early effort to generate a multi-decadal convection-permitting regional climate dataset that covers nearly the entire North American continent. We assessed a 20 year dynamically downscaled regional climate simulation at a 4 km spatial resolution with explicit convection across the contiguous United States (CONUS), Alaska, and Puerto Rico. Specifically, we evaluated the model’s performance in representing mean, 95th percentile, and extreme precipitation across regions. Our findings indicate that when compared with ERA5 reanalysis, the forcing data, convection-permitting simulation improves representations of seasonal, 95th percentile, and extreme precipitation over a large portion of the CONUS, Alaska, and Puerto Rico, particularly in areas where precipitation is heaviest. The simulation adds value over its forcing data (ERA5) in up to 53% of all grid cells in the CONUS, 68.8% in Alaska, and 84.0% in Puerto Rico. It is important to note that, however, despite improvements, model errors in Puerto Rico remain large. Similar improvements are observed in extreme indices, including consecutive dry days, maximum 5 days precipitation, and extreme precipitation. Analysis of the diurnal cycle of mean hourly precipitation suggests that representations of convective processes—including onset, dissipation, suppression, downstream propagation, and local circulation—improved overall.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Modulation of Tropical Convection-Circulation Interaction by Aerosol Indirect Effects in Convective Self-Aggregation Simulations of a Gray Zone Global Model

Disentangling the response of tropical convective updrafts to enhanced aerosol concentrations has been challenging. Leading theories for explaining the influence of aerosol concentrations on tropical convection are based on the dynamical response of convection to changes in cloud microphysics, neglecting possible changes in the environment. In recent years, global convection-permitting models (GCPM) have been developed to circumvent problems arising from imposing artificial scale separation on physical processes associated with deep convection. Here, we use a global model in the convective gray zone that partially simulates deep convection to investigate how enhanced concentrations of aerosols that act as cloud condensate nuclei (CCN) impact tropical convection features by modulating the convection-circulation interaction. Results from a pair of idealized non-rotating radiative-convective equilibrium simulations show that the enhanced CCN concentration leads to weaker large-scale circulation, the closeness of deep convective systems to the moist cluster edges, and more mid-level cloud water at an equilibrium state in which convective self-aggregation occurred. Correspondingly, the enhanced CCN concentration modulates how the physical processes that support or oppose convective aggregation maintain the aggregated state at equilibrium. Overall, the enhanced CCN concentration facilitates the development of deep convection in a drier environment but reduces mean precipitation. Our results emphasize the importance of allowing atmospheric phenomena to evolve continuously across spatial and temporal scales in simulations when investigating the response of tropical convection to changes in cloud microphysics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Global energy spectrum of the general oceanic circulation

Abstract Advent of satellite altimetry brought into focus the pervasiveness of mesoscale eddies $${{{{{{{\bf{{{{{{{{\mathcal{O}}}}}}}}}}}}}}}}({100})$$ O ( 100 ) km in size, which are the ocean’s analogue of weather systems and are often regarded as the spectral peak of kinetic energy (KE). Yet, understanding of the ocean’s spatial scales has been derived mostly from Fourier analysis in small "representative” regions that cannot capture the vast dynamic range at planetary scales. Here, we use a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three decades of length-scales reveal the Antarctic Circumpolar Current as the spectral peak of the global extra-tropical circulation, at ≈ 10 4 km, and a previously unobserved power-law scaling over scales larger than 10 3 km. A smaller spectral peak exists at ≈ 300 km associated with mesoscales, which, due to their wider spread in wavenumber space, account for more than 50% of resolved surface KE globally. Seasonal cycles of length-scales exhibit a characteristic lag-time of ≈ 40 days per octave of length-scales such that in both hemispheres, KE at 10 2 km peaks in spring while KE at 10 3 km peaks in late summer. These results provide a new window for understanding the multiscale oceanic circulation within Earth’s climate system, including the largest planetary scales.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Regional MJO Modulation of Northwest Pacific Tropical Cyclones Driven by Multiple Transient Controls

The Madden–Julian Oscillation (MJO) is widely acknowledged for its ability to modulate Northwest Pacific tropical cyclones (TCs), but a complete understanding of the underlying mechanisms remains uncertain. Beyond established effects of the MJO's relative humidity envelope, other dynamical factors have recently been invoked via new genesis potential indices and high-resolution modeling studies. Here we revisit the ability of the MJO to modulate West Pacific TCs through a quasi-explicit cyclone downscaling strategy driven by composited observations, paired later with a genesis index to investigate regional drivers of modulation. In this work, we reveal two distinct spatial modes of TC modulation in which the MJO's dynamic and thermodynamic effects act in tandem to increase TCs. In the South China Sea, for instance, shear reductions associated with the MJO's circulation lead to increasing potential intensity ahead of the arrival of a positive humidity anomaly, all of which combine for an extended period of cyclogenesis favorability.

58 GEOSCIENCES↗

DOE OSTI2022

An Assessment of Nonhydrostatic and Hydrostatic Dynamical Cores at Seasonal Time Scales in the Energy Exascale Earth System Model (E3SM)

Abstract In global atmospheric modeling, the differences between nonhydrostatic (NH) and hydrostatic (H) dynamical cores are negligible in dry simulations when grid spacing is larger than 10 km. However, recent studies suggest that those differences can be significant at far coarser resolution when moisture is included. To better understand how NH and H differences manifest in global fields, we perform and analyze an ensemble of 28 and 13 km seasonal simulations with the NH and H dynamical cores in the Energy Exascale Earth System Model global atmosphere model, where the differences between H and NH configurations are minimized. A set of idealized rising bubble experiments is also conducted to further investigate the differences. Although NH and H differences are not significant in global statistics and zonal averages, significant differences in precipitation amount and patterns are observed in parts of the tropics. The most prominent differences emerge near India and the Western Pacific in the boreal summer, and the central‐southern Indian Ocean and Pacific in the boreal winter. Tropical differences influence surrounding regions through modification of the regional circulation and can propagate to the extratropics, leading to significant temperature and geopotential differences over the middle to high latitudes. While the dry bubble experiments show negligible deviation between H and NH dynamics until grid spacing is below 6.25 km, precipitation amount and vertical velocity are different in the moist case even at 25 km resolution.

58 GEOSCIENCES↗

DOE OSTI2020

Loss circulation prevention in geothermal drilling by shape memory polymer

Geothermal formations are naturally fractured with large fracture openings and networks. This can often lead to frequent drilling fluid loss events which is a major contributor to the cost and non-productive time in geothermal drilling. Development of smarter technologies and methods to tackle problem lost circulation is vital for geothermal drilling cost reduction required for geothermal energy to be recognized as a competitive alternative energy source. Mitigation of this problem and other drilling problems such as stuck pipe can minimize overall project cost. In this report, a thermoset shape memory polymer that can be activated by formation natural heat was assessed to seal near wellbore fractures in geothermal wells. The performance of the shape memory polymer (SMP) was evaluated using artificial fractures created in aluminum discs and cylindrical granite cores. Rheology and particle size distribution were considered. A novel testing setup was built for this work, which allows testing of sealing efficiency under dynamic conditions at high temperature. Analysis showed that the SMP has efficiently succeeded in forming a strong plug inside the fractures and stopped fluid loss at high sealing pressure. This smart loss circulation material can expand within the fractures to reduces non-drilling time and strengthen the wellbore in high-temperature drilling operations.

58 GEOSCIENCES↗

DOE OSTI2025

East Antarctic Ice Sheet variability in the central Transantarctic Mountains since the mid Miocene

The response of the East Antarctic Ice Sheet to warmer-than-present climate conditions has direct implications for projections of future sea level, ocean circulation, and global radiative forcing. Nonetheless, it remains uncertain whether the ice sheet is likely to undergo net loss due to amplified melting coupled with dynamic instabilities or whether such losses will be balanced, or even offset, by enhanced accumulation under a higher-precipitation regime. The glacial depositional record from the central Transantarctic Mountains (TAM) provides a robust geologic means to reconstruct the past behaviour of the East Antarctic Ice Sheet, including during periods thought to have been warmer than today, such as the mid-Pliocene Warm Period (~3.3–3.0 Ma). This study describes a new surface-exposure-dated moraine record from Otway Massif in the central TAM spanning the last ~9 Myr and synthesises these data in the context of previously published moraine chronologies constrained with cosmogenic nuclides. The resulting record, although fragmentary, represents the majority of direct and unambiguous terrestrial evidence for the existence and size of the East Antarctic Ice Sheet during the last 14 Myr, and it thus provides new insight into the long-term relationship between the ice sheet and global climate. At face value, the existing TAM moraine record does not exhibit a clear signature of the mid-Pliocene Warm Period, thus precluding a definitive verdict on the East Antarctic Ice Sheet's response to this event. In contrast, an apparent hiatus in moraine deposition both at Otway Massif and the neighbouring Roberts Massif suggests that the ice sheet surface in the central TAM was potentially lower than present during the late Miocene and earliest Pliocene.

58 GEOSCIENCES↗

DOE OSTI2024

DCMIP2016: the tropical cyclone test case

This paper describes and analyzes the Reed–Jablonowski (RJ) tropical cyclone (TC) test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). This intermediate-complexity test case analyzes the evolution of a weak vortex into a TC in an idealized tropical environment. Reference solutions from nine general circulation models (GCMs) with identical simplified physics parameterization packages that participated in DCMIP2016 are analyzed in this study at 50 km horizontal grid spacing, with five of these models also providing solutions at 25 km grid spacing. Evolution of minimum surface pressure (MSP) and maximum 1 km azimuthally averaged wind speed (MWS), the wind–pressure relationship, radial profiles of wind speed and surface pressure, and wind composites are presented for all participating GCMs at both horizontal grid spacings. While all TCs undergo a similar evolution process, some reach significantly higher intensities than others, ultimately impacting their horizontal and vertical structures. TCs simulated at 25 km grid spacings retain these differences but reach higher intensities and are more compact than their 50 km counterparts. These results indicate that dynamical core choice is an essential factor in GCM development, and future work should be conducted to explore how specific differences within the dynamical core affect TC behavior in GCMs.

Willson, Justin L.↗