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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗
DOE OSTI2022

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors

Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers ($\mathscr{M}$ son ≲ 10 –2 ). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant–Friedrichs–Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume SEVEN-LEAGUE HYDRO (SLH) code, and it makes use of a low-Mach version of the five-wave Harten–Lax–van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit–explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at $\mathscr{M}$ son ~ 10 –3 . We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Quantum kinetic modeling of KEEN waves in a warm-dense regime

We report the first fully kinetic, quantum study of kinetic electrostatic electron nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrows harmonic locking to the fundamental, and hastens post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner–Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. We focus on collisionless dynamics in a weakly coupled regime, providing a controlled baseline before collisional extensions. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of non-equilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electric charge and strangeness-dependent directed flow splitting of produced quarks in Au+Au collisions

We report directed flow (v 1 ) of multistrange baryons (Ξ and Ω) and improved v1 data for $K¯$, $\bar{p}$, $\bar{Λ}$ and φ in Au+Au collisions at $\sqrt{s_{NN}} =27$ and 200 GeV from the STAR at the Relativistic Heavy Ion Collider (RHIC). We focus on particles whose constituent quarks are not transported from beam rapidity rather produced in the collisions. In midcentral collisions, we observe a coalescence sum rule for hadron combinations with identical quark content and a difference (“splitting”) in the slope of v 1 vs. rapidity for combinations having nonidentical quark content. The splitting strength appears to increase with the electric charge difference and strangeness content difference of the constituent quarks in the combinations, consistent with an electromagnetic effect. The peripheral collision statistics are insufficient to draw firm conclusions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks

Reacting astrophysical flows can be challenging to model, because of the difficulty in accurately coupling hydrodynamics and reactions. This can be particularly acute during explosive burning or at high temperatures where nuclear statistical equilibrium is established. We develop a new approach, based on the ideas of spectral deferred corrections (SDC) coupling of explicit hydrodynamics and stiff reaction sources as an alternative to operator splitting, that is simpler than the more comprehensive SDC approach we demonstrated previously. We apply the new method to a double-detonation problem with a moderately sized astrophysical nuclear reaction network and explore the time step size and reaction network tolerances, to show that the simplified-SDC approach provides improved coupling with decreased computational expense compared to traditional Strang operator splitting. This is all done in the framework of the Castro hydrodynamics code, and all algorithm implementations are freely available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

First benchmarked electron cooling simulations from first principles

We present the first microscopic electron cooling simulations from first principles with accurate prediction of cooling time. These simulations were performed using our previously developed numerical method, PHAD, which is the first efficient large-scale collisional numerical method in beam physics. The simulation results are benchmarked with the experimental data of the low energy bunched electron cooling of ion beams at the storage ring CSRm at the IMP facility in China. Here, we have accurately considered the nonlinear dynamics in the whole accelerator system in addition to the electron cooling section. As a result, our simulations correctly reproduced cooling times of the experiments from first principles and without any tuning or fitting parameters in the code.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Initializing BSQ with Open-Source ICCING

While it is well known that there is a significant amount of conserved charges in the initial state of nuclear collisions, the production of these due to gluon splitting has yet to be thoroughly investigated. The ICCING (Initial Conserved Charges in Nuclear Geometry) algorithm reconstructs these quark distributions, providing conserved strange, baryon, and electric charges, by sampling a given model for the g → qq¯ splitting function over the initial energy density, which is valid at top collider energies, even when µB = 0. The ICCING algorithm includes fluctuations in the gluon longitudinal momenta, a structure that supports the implementation of dynamical processes, and the c++ version is now open-source. A full analysis of parameter choices on the model has been done to quantify the effect these have on the underlying physics. We find there is a sustained difference across the different charges that indicates sensitivity to hot spot geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Formation of 6H-Ba 3 Ce 0.75 Mn 2.25 O 9 during Thermochemical Reduction of 12R-Ba 4 CeMn 3 O 12 : Identification of a Polytype in the Ba(Ce,Mn)O 3 Family

The resurgence of interest in a hydrogen economy and the development of hydrogen-related technologies has initiated numerous research and development efforts aimed at making the generation, storage, and transportation of hydrogen more efficient and affordable. Solar thermochemical hydrogen production (STCH) is a process that potentially exhibits numerous benefits such as high reaction efficiencies, tunable thermodynamics, and continued performance over extended cycling. Although CeO 2 has been the de facto standard STCH material for many years, more recently 12R-Ba 4 CeMn 3 O 12 (BCM) has demonstrated enhanced hydrogen production at intermediate H 2 /H 2 O conditions compared to CeO 2 , making it a contender for large-scale hydrogen production. However, the thermo-reduction stability of 12R-BCM dictates the oxygen partial pressure (pO 2 ) and temperature conditions optimal for cycling. In this study, we identify the formation of a 6H-BCM polytype at high temperature and reducing conditions, experimentally and computationally, as a mechanism and pathway for 12R-BCM decomposition. 12R-BCM was synthesized with high purity and then controllably reduced using thermogravimetric analysis (TGA). Synchrotron X-ray diffraction (XRD) data is used to identify the formation of a 6H-Ba 3 Ce 0.75 Mn 2.25 O 9 (6H-BCM) polytype that is formed at 1350 degrees C under strongly reducing pO 2 . Density functional theory (DFT) total energy and defect calculations show a window of thermodynamic stability for the 6H-polytype consistent with the XRD results. These data provide the first evidence of the 6H-BCM polytype and could provide a mechanistic explanation for the superior water-splitting behaviors of 12R-BCM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Monte Carlo event generator for initial conditions of conserved charges in nuclear geometry

At top collider energies where baryon stopping is negligible, the initial state of heavy-ion collisions is overall charge neutral and predominantly composed of gluons. Nevertheless, there can also be significant local fluctuations of the baryon number, strangeness, and electric charge densities about zero, perturbatively corresponding to the production of quark/antiquark pairs. These previously ignored local charge fluctuations can permit the study of charge diffusion in the quark-gluon plasma (QGP), even at top collider energies. In this paper we present a new model denoted ICCING (initial conserved charges in nuclear geometry) which can reconstruct the initial conditions of conserved charges in the QGP by sampling a (g→q¯q) splitting probability over the initial energy density. We find that the new charge distributions generally differ from the bulk energy density; in particular, the strangeness distribution is significantly more eccentric than standard bulk observables and appears to be associated with the geometry of hot spots in the initial state. The new information provided by these conserved charges opens the door to studying a wealth of new charge- and flavor-dependent correlations in the initial state and ultimately the charge transport parameters of the QGP.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Observation of a critical charge mode in a strange metal

Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation–based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB 4 as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. Here, we interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Investigating the Electronic Structure of Prospective Water-Splitting Oxide BaCe 0.25 Mn 0.75 O 3-δ before and after Thermal Reduction

BaCe 0.25 Mn 0.75 O 3-δ (BCM), a non-stoichiometric oxide with a layered perovskite-like crystal structure, has recently emerged as a prospective contender for application in renewable energy harvesting by solar thermochemical hydrogen generation. Using solar-thermal energy and a reducing environment, oxygen vacancies can be created in high-temperature BCM, and the reduced crystal so obtained can, in turn, produce H 2 by stripping oxygen from H 2 O. Therefore, a first step toward understanding the working mechanism and optimizing the performance of BCM is a thorough and comparative analysis of the electronic structure of the pristine and the reduced material. In this paper, we probe the electronic structure of BCM using the combined effort of first-principles calculations and experimental O K-edge X-ray absorption spectroscopy (XAS). The computed projected density of states (PDOS) and orbital plots are used to propose a simplified model for orbital mixing between the oxygen and metal atoms. With the help of state-of-the-art simulations, we are able to find the origins of the XAS peaks and categorize them on the basis of contribution from Ce and Mn. For the reduced crystal, the calculations show that the change in electron density resulting from the reduction is strongly localized around the oxygen vacancy. Experimental measurements reveal a marked lowering of the first O K-edge peak in the reduced crystal. Using theoretical analysis, this is shown to result from lifting of spin degeneracy in the absorption peaks as well as from a diminished O 2p contribution to the frontier unoccupied orbitals, in accordance with the tight binding scheme. The simulated results serve as a reference for the extent of spectral change as a function of the percentage of oxygen vacancies in the reduced crystal. Here, our study paves the way for the investigation of the working mechanism of BCM and for computational and experimental efforts aimed at design and discovery of efficient water-splitting oxides.

08 HYDROGEN↗
DOE OSTI2022

Synthesis and structure of high-purity BaCe 0.25 Mn 0.75 O 3 : an improved material for thermochemical water splitting

Solar thermochemical hydrogen production (STCH) via redox-active metal oxides is an approach for direct solar-driven hydrogen generation typically using a high-temperature redox cycle involving refractory oxides and steam. Typical cycles involve high-temperature reduction of oxides to form oxygen vacancies, followed by lower temperature reaction between oxygen vacancies and steam where the oxide is re-oxidized and the steam is reduced to hydrogen. Only a few materials have demonstrated reversible cycling under the typically harsh STCH conditions (e.g. 1500°C reduction, 900°C re-oxidation) and critical questions remain on the true reversibility of non-stoichiometric multi-cation oxide systems, significantly hampered by the lack of single-phase samples for these material systems. To date, most STCH processes have relied on CeO 2 as a benchmark active material, but more recently, the 12R phase of BaCe 0.25 Mn 0.75 O 3 (BCM) has demonstrated greater hydrogen-generation potential at lower peak temperatures. However, previous reports of 12R-BCM have included large fractions, > 10 wt%, of secondary phases, which complicate analysis of the stability and performance. A comprehensive understanding of the redox mechanism and reversibility of the process in BCM can only be achieved with nearly single-phase samples which, to date, have been difficult to produce. Here two approaches to BCM synthesis are reported: solid state and sol–gel-based routes. It is demonstrated that both routes can be tuned to produce the 12R structure with > 97 wt% yield when annealed ≥1450°C. Herein synchrotron-based diffraction measurements of rhombohedral 12R-BCM enabled characterization of the anisotropy between thermal expansion along the c-axis and within the ab plane. The impact of high-temperature redox cycling on the stability and phase fraction of the 12R-BCM polytype was also investigated. Our results offer two viable routes for synthesis of high-purity 12R-BCM critically needed for evaluating the efficacy of BCM as a STCH material and validate its ability to split water at lower temperatures over extended numbers of redox cycles.

08 HYDROGEN↗
DOE OSTI2022

Synchrotron-based techniques for characterizing STCH water-splitting materials

Understanding the role of oxygen vacancy–induced atomic and electronic structural changes to complex metal oxides during water-splitting processes is paramount to advancing the field of solar thermochemical hydrogen production (STCH). The formulation and confirmation of a mechanism for these types of chemical reactions necessitate a multifaceted experimental approach, featuring advanced structural characterization methods. Synchrotron X-ray techniques are essential to the rapidly advancing field of STCH in part due to properties such as high brilliance, high coherence, and variable energy that provide sensitivity, resolution, and rapid data acquisition times required for the characterization of complex metal oxides during water-splitting cycles. X-ray diffraction (XRD) is commonly used for determining the structures and phase purity of new materials synthesized by solid-state techniques and monitoring the structural integrity of oxides during water-splitting processes (e.g., oxygen vacancy–induced lattice expansion). X-ray absorption spectroscopy (XAS) is an element-specific technique and is sensitive to local atomic and electronic changes encountered around metal coordination centers during redox. While in operando measurements are desirable, the experimental conditions required for such measurements (high temperatures, controlled oxygen partial pressures, and H 2 O) practically necessitate in situ measurements that do not meet all operating conditions or ex situ measurements. Here, we highlight the application of synchrotron X-ray scattering and spectroscopic techniques using both in situ and ex situ measurements, emphasizing the advantages and limitations of each method as they relate to water-splitting processes. The best practices are discussed for preparing quenched states of reduction and performing synchrotron measurements, which focus on XRD and XAS at soft (e.g., oxygen K-edge, transition metal L-edges, and lanthanide M-edges) and hard (e.g., transition metal K-edges and lanthanide L-edges) X-ray energies. The X-ray absorption spectra of these complex oxides are a convolution of multiple contributions with accurate interpretation being contingent on computational methods. The state-of-the-art methods are discussed that enable peak positions and intensities to be related to material electronic and structural properties. Through careful experimental design, these studies can elucidate complex structure–property relationships as they pertain to nonstoichiometric water splitting. A survey of modern approaches for the evaluation of water-splitting materials at synchrotron sources under various experimental conditions is provided, and available software for data analysis is discussed.

08 HYDROGEN↗
DOE OSTI2023

Chapter 14: Surface plasmon resonance enhanced artificial photosynthesis of chemical fuels for energy storage

Nanostructured noble metals such as Au, Ag, and Cu have interesting optical properties because of the oscillation motions of their surface electrons upon strong coupling with light under resonance conditions. This resonant oscillation motion of conduction electrons refers to surface plasmon resonance (SPR) and localized SPR (LSPR) when localized near the surface of a nanoparticle. The extinction spectrum of a solution of plasmonic nanoparticles has tunable wavelength responses from UV to NIR due to strong light scattering and absorption which are highly sensitive to the permittivity of the nanoparticles, their sizes and shapes, and chemical environment. Strong light scattering due to the LSPR of plasmonic nanoparticles creates a strong localized and far-field intensity capable of enhancing light absorption characteristics of a chromophore near a plasmonic surface. Engineering the chromophores’ radiative decay dynamics can be done by 1) increasing its radiative decay rate to increase its photoluminescence intensity and 2) increasing its nonradiative decay rates associated to direct charge transfer to the metal surface. Such interesting photophysical properties of a chromophore can be extended to other light-absorbing materials such as semiconductor thin films and nanostructures. This plasmonic effect on the photophysics of a light-absorbing material can be theoretically and experimentally validated. The phenomenon has also been applied to advanced optoelectronic devices such as organic light-emitting diodes (OLED)1 and organic photovoltaics (OPV).2-4 The local field created by the SPR can provide an intense EM field to enhance photoluminescence emission of an organic chromophore5-8 and Raman scattering of an organic molecule, and single-molecule Raman9-10 can be detected on specially designed LSPR substrate. (Figure 1 on SPR for energy) Recent studies suggest that LSPR can be incorporated in light-harvesting and conversion systems to increase energy conversion in a solar cell and photoelectrochemical cell and chemical transformations of CO2 to chemical fuels.11-12 Plasmonic active metals naturally exhibit catalytic activities for electrochemical fuel conversion that can be enhanced by engineering their structures to form unique catalytic structures such as symmetry-broken Au-Cu Janus nanocrystals.13 These studies are critical to addressing the global challenges of energy14-15 and CO2 emission from nonrenewable sources such as coal, petroleum, and natural gas.16-17 Electrochemical systems comprised of unique photonic structures and functions that enable efficient and affordable energy harvesting/conversion/storage are highly desired for providing safe and environment-friendly energy sources. This chapter reviews our recent work of LSPR enabled photoelectrochemical water splitting and recent advances in LSPR-enabled CO2 reduction and photochemical reactions reported in the literature. Scientific and technical challenges of applying LSPR to enhance these energy conversion and storage systems are discussed at the conclusion of this chapter.

Pan, Shanlin↗
DOE OSTI2023

Formation of Ba 3 Nb 0.75 Mn 2.25 O 9 -6H during thermochemical reduction of Ba 4 NbMn 3 O 12 -12R

The resurgence of interest in hydrogen-related technologies has stimulated new studies aimed at advancing lesser-developed water-splitting processes, such as solar thermochemical hydrogen production (STCH). Progress in STCH has been largely hindered by a lack of new materials able to efficiently split water at a rate comparable to ceria under identical experimental conditions. BaCe 0.25 Mn 0.75 O 3 (BCM) recently demonstrated enhanced hydrogen production over ceria and has the potential to further our understanding of two-step thermochemical cycles. A significant feature of the 12R hexagonal perovskite structure of BCM is the tendency to, in part, form a 6H polytype at high temperatures and reducing environments ( i.e. , during the first step of the thermochemical cycle), which may serve to mitigate degradation of the complex oxide. An analogous compound, namely BaNb 0.25 Mn 0.75 O 3 (BNM) with a 12R structure was synthesized and displays nearly complete conversion to the 6H structure under identical reaction conditions as BCM. The structure of the BNM-6H polytype was determined from Rietveld refinement of synchrotron powder X-ray diffraction data and is presented within the context of the previously established BCM-6H structure.

08 HYDROGEN↗
DOE OSTI2025

Large-scale experimental validation of thermochemical water-splitting oxides discovered by defect graph neural networks

Thermochemical water-splitting (TCH) based on 2-step thermal redox cycles in metal oxides is a promising approach to generating H 2 , but state-of-the-art (SOTA) CeO 2 has several practical limitations, which has motivated continued materials discovery efforts in this field. Here, in this study, we improve upon a SOTA defect graph neural network (dGNN) surrogate model's oxygen vacancy predictions and combine them with materials project phase diagrams to down-select and discover structurally diverse, experimentally known metal oxides whose TCH performance was previously unknown. Amongst twelve candidates selected based on our high-throughput screening and down-selection criteria, we achieved ∼80% accuracy in identifying materials with stable redox cycling and hydrogen production in stagnation flow reactor water-splitting experiments. Closer to 100% accuracy can be achieved if higher-accuracy, hybrid DFT-predicted vacancy formation energies were computed and used in lieu of the most uncertain dGNN-based screening predictions, as they correct false positives to true negatives. Notably, two discovered candidates, Sr 3 PrMn 2 O 8 and Ba 2 Fe 2 O 5 , display hydrogen yields greater than CeO 2 under specific redox conditions. In conclusion, these results demonstrate our ability to computationally predict and experimentally validate promising candidate TCH materials that have the potential to compete with CeO 2 .

08 HYDROGEN↗