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At least 937 records · Page 52

BETO 2021 Peer Review - FCIC Task 6: High Temperature Conversion

The impacts of feedstock variability on pyrolysis processes are significant but poorly defined. Current engineering designs are based on empirical guidelines, useful only over a narrow range of feedstock properties. The objectives of this project are to (1) Develop science-based knowledge of how feedstock attributes and operational parameters impact pyrolysis process reliability and product quality; and (2) Build an experimental and computational toolset that predicts these outcomes, enabling processes to optimize reliability and product quality. Biomass is a complex feedstock. Controlling for and testing the effects of individual attributes is very challenging. This project couples multiscale experimentation and modeling to accurately capture the fundamental physics and chemistry of biomass flow and conversion behavior in feeding and pyrolysis reactor operations. Our focus is on pine residue attributes – anatomical fraction (bark, needles, wood), particle morphology (size/shape distribution, density, porosity), and chemical composition (extractives, biopolymers, alkali metals) – that impact product quality for downstream catalytic upgrading. Because detailed pyrolysis product characterization is limited, cutting-edge analytical techniques are being developed to reveal impactful product attributes. The tools and knowledge developed here will enable integrated pyrolysis-based processes that are more robust, flexible, and market-responsive with respect to feedstock variability.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Geospatial Data Platform for All

Spatiotemporal data has evolved in scale due to augmented use in cross-domain applications. Simultaneously, there is substantial growth in the availability of Geographic Information Systems (GIS) data provided by the United States Geological Survey (USGS) along with other federal, state, county, or local agencies through open-data portals and public access APIs. However, data availability does not equate with accessibility. Large-scale analyses and applications require robust, performant data management with co-location of data storage and computing. The insufficiency of data management infrastructure compels researchers to adopt ad hoc project- specific GIS data storage solutions (e.g., copying data to High-Performance computer file systems). As an ad hoc storage strategy does not scale, it hampers cross-domain analyses causing difficulty in data reuse and utilizing existing code bases. Furthermore, GIS data is complex and requires expertise to analyze and manipulate due to its intricate data structures and data-specific projection transformations. Despite the challenges, we recognize that derived GIS data products, e.g., satellite or LIDAR-based images, can be used in downstream applications such as AI by domain, but non-GIS experts. To address the data needs and overcome the challenges, we are working towards a GIS Data Platform focused on efficient data storage, data discovery and access, and an API to enable common workflows. We propose a knowledge-graph (KG) approach for data discovery, whereby datasets are semantically linked to higher- level constructs such as projects and research areas. The semantic data links enable researchers to explore datasets in a top-down approach by specifying relevant and meaningful terms (assists in finding hidden data). An advantage is that the nodes and edges in a knowledge graph create built-in semantic documentation. Deeper spatiotemporal connections between data sources can be encoded via Graph Neural Networks (GNN) (Zhang et al., 2021). The KG approach can be extended to integrate the data itself in a Virtual KG (VKG). Our work will derive inspiration from large-scale VKG efforts that have been undertaken or are currently underway as part of the OpenStreetMap project (Ding et al., 2021). For DOE Data Days, we share the proposed geospatial data platform hybrid (cloud/on-prem) architecture, our work-to-date on storing, retrieving, and transforming LiDAR and raster data relevant to two important NREL use-cases, including the Renewable Energy Potential (reV) Model, and present our proposal for a KG based data discovery engine.

data platform↗

Integrating computation and experiment to investigate photoelectrodes for solar water splitting at the microscopic scale.

CONSPECTUS: Photoelectrochemical water-splitting is a promising and sustainable way to store the energy of the sun in chemical bonds and use it to produce hydrogen gas, a clean fuel. The key components in photoelectrochemical cells (PECs) are photoelectrodes, including a photocathode that reduces water to hydrogen gas and a photoanode that oxidizes water to oxygen gas. Materials used in photoelectrodes for PECs must effectively absorb sunlight, yield photogenerated carriers, and exhibit electronic properties that enable the efficient shuttling of carriers to the surface to participate in relevant water-splitting reactions. Discovering and understanding the key characteristics of optimal photoelectrode materials is paramount to the realization of PEC technologies. Oxide-based photoelectrodes can satisfy many of these materials requirements, including stability in aqueous environments, band edges with reasonable alignment with the redox potentials for water splitting, and ease of synthesis. However, oxide photoelectrodes generally suffer from poor charge transport properties and considerable bulk electron-hole separation, and they have relatively large band gaps. Numerous strategies have been proposed to improve these aspects and understand how these improvements are reflected in the photoelectrochemical performance. Unfortunately, the structural and compositional complexity of multinary oxides accompanied by the inherent complexity of photoelectrochemical processes makes it challenging to understand the individual effects of composition, structure, and defects in the bulk and on the surface on a material's photoelectrochemical properties. The integration of experiment and theory has great potential to increase our atomic-level understanding of structure-composition-property relationships in oxide photoelectrodes. In this Account, we describe how integrating experiment and theory is beneficial for achieving scientific insights at the microscopic scale. We highlight studies focused on understanding the role of (i) bulk composition via solid-state solutions, intercalation, and comparison with isoelectronic compounds, (ii) dopants for both the anion and cation and their interactions with oxygen vacancies, and (iii) surface/interface structure in the photocurrent generation and photoelectrochemical performance in oxide photoelectrodes. In each instance, we outline strategies and considerations for integrating experiment and theory and describe how this integration led to valuable insights and new directions in uncovering structure-composition-property relationships. Our aim is to demonstrate the unique value of combining experiment and theory in studying photoelectrodes and to encourage the continued effort to bring experiment and theory in closer step with each other.

Wang, Wennie↗

A gated graph transformer for protein complex structure quality assessment and its performance in CASP15

Abstract Motivation Proteins interact to form complexes to carry out essential biological functions. Computational methods such as AlphaFold-multimer have been developed to predict the quaternary structures of protein complexes. An important yet largely unsolved challenge in protein complex structure prediction is to accurately estimate the quality of predicted protein complex structures without any knowledge of the corresponding native structures. Such estimations can then be used to select high-quality predicted complex structures to facilitate biomedical research such as protein function analysis and drug discovery. Results In this work, we introduce a new gated neighborhood-modulating graph transformer to predict the quality of 3D protein complex structures. It incorporates node and edge gates within a graph transformer framework to control information flow during graph message passing. We trained, evaluated and tested the method (called DProQA) on newly-curated protein complex datasets before the 15th Critical Assessment of Techniques for Protein Structure Prediction (CASP15) and then blindly tested it in the 2022 CASP15 experiment. The method was ranked 3rd among the single-model quality assessment methods in CASP15 in terms of the ranking loss of TM-score on 36 complex targets. The rigorous internal and external experiments demonstrate that DProQA is effective in ranking protein complex structures. Availability and implementation The source code, data, and pre-trained models are available at https://github.com/jianlin-cheng/DProQA.

59 BASIC BIOLOGICAL SCIENCES↗

Mapping structural heterogeneity at the nanoscale with scanning nano-structure electron microscopy (SNEM)

Here, in this work, we explore the use of scanning electron diffraction (also known as 4D-STEM) coupled with electron atomic pair distribution function analysis (ePDF) to understand the local order (structure and chemistry) as a function of position in a complex multicomponent system, a hot rolled, Ni-encapsulated, Zr 65 Cu 17.5 Ni 10 Al 7.5 bulk metallic glass (BMG), with a spatial resolution of 3 nm. We show that it is possible to gain insight into the chemistry and chemical clustering/ordering tendency in different regions of the sample, including in the vicinity of nano-scale crystallites that are identified from virtual dark field images and in heavily deformed regions at the edge of the BMG. In addition to simpler analysis, unsupervised machine learning was used to extract partial PDFs from the material, modeled as a quasi-binary alloy, and map them in space. These maps allowed key insights not only into the local average composition, as validated by EELS, but also a unique insight into chemical short-range ordering tendencies in different regions of the sample during formation. The experiments are straightforward and rapid and, unlike spectroscopic measurements, don’t require energy filters on the instrument. We spatially map different quantities of interest (QoI’s), defined as scalars that can be computed directly from positions and widths of ePDF peaks or parameters refined from fits to the patterns. We developed a flexible and rapid data reduction and analysis software framework that allows experimenters to rapidly explore images of the sample on the basis of different QoI’s. The power and flexibility of this approach are explored and described in detail. Because of the fact that we are getting spatially resolved images of the nanoscale structure obtained from ePDFs we call this approach scanning nano-structure electron microscopy (SNEM), and we believe that it will be powerful and useful extension of current 4D-STEM methods.

36 MATERIALS SCIENCE↗

Radiative Heat Transport and Optical Characterization of High Temperature Molten Salts

The goal of this project was to advance the field of molten fluoride radiative heat transfer (RHT), through optical property measurements, heat transfer loop construction and operation, and computational fluid dynamics simulations. The following outcomes have been accomplished. A comprehensive review has been conducted to compile all available RHT-relevant optical absorption data for molten fluorides. The various measurement methods have also been compiled and critiqued. Thermal emission measurement methods have been refined and documented. A unique thermal emissivity measurement facility has been constructed and used to measure the emissivity of flowing FLiBe-exposed SS316 samples. A slight increase has been observed in the emissivity compared to unexposed SS316. A dual reflectance-emission setup was partially demonstrated for the purpose of molten fluoride absorption measurement. Preliminary infrared edge data for FLiNaK was obtained. A visible near-infrared (NIR) measurement setup has been constructed and will be used to measure absorption of corrosion products in FLiBe. A new multi-band thermal radiation method using blackbody-weighted spectral bands for the absorption-coefficient was deployed to investigate the thermal performance of the UW Natural Circulation FLiBe Loop under various power levels and operating conditions. The results showed an increasing and decreasing trend in the overall heat transfer with optical thickness with a maximum at optical thickness τ D ≈Ο(1). A forced convection FLiBe loop was constructed for the purpose of studying corrosion and thermal hydraulic phenomena. A vertical cantilever pump is used to achieve up to 5 gpm and 5 m/s flow velocity in hot and cold test sections. A methodology has been established for modeling radiative heat transfer (RHT) in molten salt coolants for the purpose of quantifying the contribution of thermal radiation in conditions relevant to FHR or MSR systems. The comparison between the results obtained for forced and mixed convection showed that in the studied ranges of optical thickness, the maximum effect of RHT on overall heat transfer was 60% improvement observed at z/D = 250 for forced convection; whereas for mixed convection, that value was higher at 170% observed at z/D = 30. The highest effect of RHT on the overall energy distribution was observed at τ D ≈3.4. Negligible effect (<20%) was observed above τ D =18 and below τ D ≈0.002. A CFD code-to-code comparison was conducted using COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT, for a forced and mixed convection laminar flow for a grey medium in a vertical heated using both COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT. The relative error was the largest at τ D =40 for the radiative heat flux, bulk temperature, and Nusselt number. On the other hand, the relative error was the least at τ D =0.002 for the conductive heat flux, bulk temperature, and Nusselt number.

Anderson, Mark↗

Advanced surrogate model for electron-scale turbulence in tokamak pedestals

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor q, electron beta β e and normalized electron Debye length λ D , in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport.

fusion plasma↗

Probing entanglement in a 2D hard-core Bose–Hubbard lattice

Entanglement and its propagation are central to understanding many physical properties of quantum systems. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose–Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Mountaintop View Requires Minimal Sorting: A Faster Contour Tree Algorithm

Consider a scalar field f : M → R, where M is a triangulated simplicial mesh in R d . A level set, or contour, at value v is a connected component of f –1 (v). As v is changed, these contours change topology, merge into each other, or split. Contour trees are concise representations of f that track this contour behavior. The vertices of these trees are the critical points of f, where the gradient is zero. The edges represent changes in the topology of contours. It is a fundamental data structure in data analysis and visualization, and there is significant previous work (both theoretical and practical) on algorithms for constructing contour trees. Suppose M has n vertices, N facets, and t critical points. A classic result of Carr, Snoeyink, and Axen (2000) gives an algorithm that takes O(n log n+Nα(N)) time (where α(·) is the inverse Ackermann function). A further improvement to O(t log t + N) time was given by Chiang et al. All these algorithms involve a global sort of the critical points, a significant computational bottleneck. Unfortunately, lower bounds of Ω(t log t) also exist. We present the first algorithm that can avoid the global sort and has a refined time complexity that depends on the contour tree structure. Intuitively, if the tree is short and fat, we get significant improvements in running time. For a partition of the contour tree into a set of descending paths, P, our algorithm runs in O($\Sigma$ pϵP |p| log |p| + tα(t) + N). This is at most O(t log D + N), where D is the diameter of the contour tree. Moreover, it is O(tα(t) + N) for balanced trees, a significant improvement over the previous complexity. Our algorithm requires numerous ideas: partitioning the contour tree into join and split trees, a local growing procedure to iteratively build contour trees, and the use of heavy path decompositions for the time complexity analysis. There is a crucial use of a family of binomial heaps to maintain priorities, ensuring that any comparison made is between comparable nodes of the contour tree. We also prove lower bounds showing that the $\Sigma$ pϵP |p| log |p| complexity is inherent to computing contour trees.

97 MATHEMATICS AND COMPUTING↗

Efficient Scalable Contact Network Generation from Population Data

Modeling the contacts among a population is critical to understanding the dynamics of a disease outbreak. Contact networks, where nodes are individuals and edges are contacts among them, are used to represent these complex individual-level interactions. In this work, we are given the daily activity schedules of an urban population that represent the activity location and time of individuals in a population during a single twenty four hour period over multiple days. Using collocation to determine contact between individuals, our goal is to extract hourly contact networks from large-scale activity data. We improve upon the existing adjacency matrix-based method by implementing our custom sparse matrix multiplication algorithm. Starting with a Python implementation, we achieve a 1600x speed up in the computation with a fast custom designed sparse matrix multiplier algorithm implemented in the C++ language. This work is central to future parallel designs of the problem.

97 MATHEMATICS AND COMPUTING↗

Ultra-Low Disorder Graphene Quantum Dot-Based Spin Qubits for Cyber Secure Fossil Energy Infrastructure (Final Technical Report)

The overarching goal of the proposed project is to demonstrate the feasibility of creating ultralow local disorder graphene quantum dots (GQDs)-based high-speed, high-fidelity spin quantum bits (qubits) for extremely cyber-secure coal energy plants of the future. Despite their inherent benefits, the coherence times in the state-of-the-art GQD qubits are still low primarily due to the local disorder in GQD devices generated during lithographic fabrication of GQDs. Hence, the focus of this research is to prepare ultralow disorder GQDs (e.g., edge roughness ~0.5nm) and evaluate the low temperature (~mK) charge/spin transport characteristics of the engineered GQD qubit platform. To achieve minimal disorder in GQD qubits, we employ a novel approach that combines nanotomy (novel GQD fabrication technique developed by the PI) and scanning probe microscopy-atomic oxidation lithography (SPM-AOL).

20 FOSSIL-FUELED POWER PLANTS↗

Self‐Strain Suppression of the Metal‐to‐Insulator Transition in Phase‐Change Oxide Devices

Strongly correlated materials exhibiting phase transitions which can be controlled through external stimuli, such as electric fields, are promising for future computing technologies beyond conventional semiconductor transistors. Devices that take advantage of structural phase transitions have inherent built‐in memory, reminiscent of synapses and neurons, and are thus natural candidates for neuromorphic computing. Of particular interest are phase‐change oxides, which allow for control over the metal‐to‐insulator transition. Here, X‐ray nano‐diffraction structural imaging of micro‐devices fabricated with the archetypal phase‐change material vanadium sesquioxide (V 2 O 3 ) is reported. The devices contain a Ga ion‐irradiated region where the metal‐to‐insulator transition critical temperature is lowered, a useful feature for controlling neuron‐like spiking behavior. Results show that strain, induced by crystal lattice mismatch between the pristine and irradiated material, leads to a suppression of the metal‐to‐insulator‐transition. Suppression occurs within the irradiated region or along its edges, depending on the defect‐distribution and the size of the region. The observed self‐straining effect can extend to other phase‐change oxides and dominate as device dimensions are reduced and become too small to dissipate strain within the irradiated region. The findings are important for phase engineering in phase‐change devices and highlight the necessity to study phase transitions at the nanoscale.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Near L-edge Single and Multiple Photoionization of Doubly Charged Iron Ions

Using the photon-ion merged-beams technique at a synchrotron light source, we have measured relative cross sections for single and up to five-fold photoionization of Fe 2+ ions in the energy range of 690-920 eV. This range contains thresholds and resonances associated with ionization and excitation of 2p and 2s electrons. Calculations were performed to simulate the total absorption spectra. The theoretical results show very good agreement with the experimental data, if overall energy shifts of up to 2.5 eV are applied to the calculated resonance positions and assumptions are made about the initial experimental population of the various levels of the Fe 2+ ([Ar]3d 6 ) ground configuration. Furthermore, we performed extensive calculations of the Auger cascades that result when an electron is removed from the 2p subshell of Fe 2+ . These computations lead to a better agreement with the measured product-charge-state distributions as compared to earlier work. We conclude that the L-shell absorption features of low-charged iron ions are useful for identifying gas-phase iron in the interstellar medium and for discriminating against the various forms of condensed-phase iron bound to composite interstellar dust grains.

79 ASTRONOMY AND ASTROPHYSICS↗

Local structure graph models with higher-order dependence

Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies.

97 MATHEMATICS AND COMPUTING↗

Adsorbate-induced adatom formation on Au-Cu bimetallic alloys and its possible consequences for CO 2 electroreduction

The adsorbate-induced formation of sub-nanometer clusters on transition-metal single crystals observed in previous high-pressure microscopic studies hinted at the in-situ formation of unique active sites even on large nanoparticle catalysts. We propose that the adatom formation energy can be used as an energetic descriptor for the initial step toward the adsorbate-induced metal-cluster formation process. This descriptor can be efficiently computed using density functional theory (DFT) calculations and applied for screening and identification of metal catalysts where this phenomenon may play an important role in generating active sites in-situ. As a proof of concept, here, we construct an adatom formation energy database for three Au x Cu y alloys (x:y = 3:1, 1:1, or 1:3) and eighteen adsorbates (H, C, N, O, F, S, Cl, Br, I, CH x , NH x (x = 1 – 3), CO, NO, and OH) commonly involved in catalytic reactions. The energetics of adatom formation were examined in all cases where the (111) terrace, (211) step-edge, and (874) kink were the sources of the adatom. We demonstrate that the presence of an adsorbate could alter not only the energetics for adatom formation but also the elemental nature of the preferred adatom being formed. Using our database, we identified promising systems which favor adsorbate-induced adatom formation under near-ambient conditions. Specifically, CO-induced adatom formation on all three Au-Cu alloy surfaces could occur under CO 2 electroreduction (CO 2 RR) conditions. This phenomenon offers a qualitative explanation for the experimentally observed CO 2 RR activity on Au-Cu alloy catalysts. As a result, our methodology offers an easily expandable and efficient approach for large-scale catalyst screening with regards to adatom/cluster formation under reaction conditions and provides insight into the possible nature of active sites on alloy catalysts from a novel perspective.

Active site↗

Unsupervised atomic data mining via multi-kernel graph autoencoders for machine learning force fields

Constructing a chemically diverse dataset while avoiding sampling bias is critical to training efficient and generalizable force fields. However, in computational chemistry and materials science, many common dataset generation techniques are prone to oversampling regions of the potential energy surface. Furthermore, these regions can be difficult to identify and isolate from each other or may not align well with human intuition, making it challenging to systematically remove bias in the dataset. While traditional clustering and pruning (down-sampling) approaches can be useful for this, they can often lead to information loss or a failure to properly identify distinct regions of the potential energy surface due to difficulties associated with the high dimensionality of atomic descriptors. In this work, we introduce the Multi-kernel Edge Attention-based Graph Autoencoder (MEAGraph) model, an unsupervised approach for analyzing atomic datasets. MEAGraph combines multiple linear kernel transformations with attention-based message passing to capture geometric sensitivity and enable effective dataset pruning without relying on labels or extensive training. Demonstrated applications on niobium, tantalum, and iron datasets show that MEAGraph efficiently groups similar atomic environments, allowing for the use of basic pruning techniques for removing sampling bias. This approach provides an effective method for representation learning and clustering that can be used for data analysis, outlier detection, and dataset optimization.

Materials science↗

Leading Energy Analysis: Data-Driven Insights That Power Our Energy Future

Energy analysts at the National Renewable Energy Laboratory (NREL) use a broad set of expertise and cutting-edge tools to capture the complexities of our interconnected energy system. Decision-makers rely on these insights to drive cost savings, enhance grid reliability, support long-term innovation, and bolster America's energy workforce and global competitiveness. This fact sheet highlights some of NREL's high-impact analyses, data, and tools, largely focusing on power grid analysis.

data↗

Resolving atomistic structure and oxygen evolution activity in nickel antimonates

The oxygen evolution reaction (OER) requires electrodes that are not only catalytically active, but also stable under harsh electrochemical environments to enable efficient, durable technologies. Our recent report of a stable amorphous Ni 0.5 Sb 0.5 O z OER photoanode established Ni–Sb–O as an important system for computational understanding of both the structural and catalytic behavior of these complex oxides. In the present work we show that Ni x Sb 1-x O z with x > 0.33 crystallizes into a previously unknown phase. Guided by experimental X-ray diffraction, here, we use density functional theory calculations to perform a prototype phase search to identify a broad family of stable and metastable mixed rutile and hexagonal-like phases for x = 0.33, 0.50, and 0.66 compositions. For the identified phases, we predict favorable oxygen vacancy formation energies for Ni-rich compositions under the reducing synthesis conditions which match measured Ni K-edge X-ray absorption spectra. The calculated overpotential for the most active site decreases with increasing Ni content, from 0.91 V (x = 0.33) to 0.49 V (x = 0.66), which captures the experimentally observed trend. We find the active site changes from the Ni–O–Sb bridge to a Ni–O–Ni bridge at increasing Ni concentrations, rather than the commonly studied singly under-coordinated sites. Finally, detailed Pourbaix analysis of the identified phases show excellent electrochemical stability, consistent with experimentally measured low metal ion concentrations in the electrolyte of photoelectrochemical cells. Collectively, our consideration of an ensemble of structures enables identification of the most catalytically prolific structural motifs, aiding the understanding of crystalline and amorphous catalysts and elucidating the co-optimization of activity and durability in nickel antimonates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗