Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ordering transformation”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Resistive Switching of Spinel Li 4 Ti 5 O 12 Lithium-Ion Battery Material for Neuromorphic Computing

The rapid rise of AI has exposed significant limitations in conventional Von Neumann computing architecture, particularly in regard to speed and energy efficiency. To address these challenges, researchers are exploring a brain-inspired neuromorphic architecture that mimics biological neural networks, enabling massive parallel processing with reduced power consumption for complex AI computational demands. Recent interest has focused on utilizing battery electrodes and solid electrolyte materials for their resistive switching properties in developing a neuromorphic architecture. These properties are precisely tuned through local- and bulk-level chemical composition modifications via voltage bias stimuli. In this study, we demonstrate fabricating a three-terminal lithium-ion electrochemical transistor based on lithium titanium oxide (Li 4 Ti 5 O 12 ), a popular lithium-ion battery anode material. We deposited and characterized LTO thin films using RF sputtering, demonstrating a 6 orders of magnitude increase in electronic conductivity upon lithiation, with conductivity plateauing after 20% lithiation. Density functional theory calculations revealed transformation from the insulating to conducting state, supported by experimental characterization through X-Ray Photoelectron Spectroscopy (XPS) and Direct Current (DC) polarization analyses. The fabricated transistor consisted of LTO as the channel layer, gold as source/drain terminals, lithium phosphorus oxynitride (LiPON) as the lithium-ion conductor, and copper as the gate terminal. The device exhibited clear hysteresis in transfer characteristics due to lithium insertion/extraction processes. Long-term potentiation (LTP) and long-term depression (LTD) measurements showed an asymmetric ratio of 1.425 and maximum/minimum conductance ratio of 7.83. When implemented in a deep neural network (DNN) for MNIST handwritten digit recognition, the device achieved 92.03% accuracy over 20 training epochs. Detailed transport mechanism analysis revealed the crucial role of oxygen vacancies and interface effects in device operation. Our preliminary findings establish LTO-based lithium-ion electrochemical transistors as promising candidates for energy-efficient neuromorphic computing applications, offering potential solutions to traditional Von Neumann architecture limitations.

25 ENERGY STORAGE↗
DOE OSTI2022

Investigation of the photoluminescent properties, scintillation behaviour and toxicological profile of various magnesium tungstate nanoscale motifs

We have synthesized several morphologies and crystal structures of MgWO 4 using a one-pot hydrothermal method, producing not only monoclinic stars and large nanoparticles but also triclinic wool balls and sub-10 nm nanoparticles. Herein we describe the importance of reaction parameters in demonstrating morphology control of as-prepared MgWO 4 . Moreover, we correlate structure and composition with the resulting photoluminescence and radioluminescence properties. Specifically, triclinic-phase samples yielded a photoluminescence emission of 421 nm, whereas monoclinic-phase materials gave rise to an emission maximum of 515 nm. The corresponding radioluminescence data were characterized by a broad emission peak, located at 500 nm for all samples. Annealing the wool balls and sub-10 nm particles to transform the crystal structure from a triclinic to a monoclinic phase yielded a radioluminescence (RL) emission signal that was two orders of magnitude greater than that of their unannealed counterparts. Finally, to confirm the practical utility of these materials for biomedical applications, a series of sub-10 nm particles, including as-prepared and annealed samples, were functionalized with biocompatible PEG molecules, and subsequently were found to be readily taken up by various cell lines as well as primary cultured hippocampal neurons with low levels of toxicity, thereby highlighting for the first time the potential of this particular class of metal oxides as viable and readily generated platforms for a range of biomedical applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

High-pressure phase transitions and melt structure of Pb O 2 : An analog for silica

In situ x-ray diffraction measurements and inverse Monte Carlo simulations of pair distribution functions were used to study the structural response of PbO 2 under pressure and to characterize the local structure of liquid PbO 2 . Two phase transitions are observed upon room-temperature compression of crystalline PbO 2 up to ~65 GPa. Here, the starting mixture of rutile structured β– PbO 2 and orthorhombic α– PbO 2 undergoes a transition to a ZrO 2 -type orthorhombic phase with space group Pbca at ~21 GPa. Above 42 GPa, the Pbca phase transforms to a cotunnite-type phase with space group Pnam. In this paper, we also report short-range order in liquid PbO 2 , showing ~8–9-fold and 4–5-fold coordination around Pb and O atoms, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Fundamental mechanistic insights into the catalytic reactions of Li-S redox by Co single-atom electrocatalysts via operando methods

Lithium-sulfur batteries represent an attractive option for energy storage applications. A deeper understanding of the multistep lithium-sulfur reactions and the electrocatalytic mechanisms are required to develop advanced, high-performance batteries. We have systematically investigated the lithium-sulfur redox processes catalyzed by a cobalt single-atom electrocatalyst (Co-SAs/NC) via operando confocal Raman microscopy and x-ray absorption spectroscopy (XAS). The real-time observations, based on potentiostatic measurements, indicate that Co-SAs/NC efficiently accelerates the lithium-sulfur reduction/oxidation reactions, which display zero-order kinetics. Under galvanostatic discharge conditions, the typical stepwise mechanism of long-chain and intermediate-chain polysulfides is transformed to a concurrent pathway under electrocatalysis. In addition, operando cobalt K-edge XAS studies elucidate the potential-dependent evolution of cobalt’s oxidation state and the formation of cobalt-sulfur bonds. Our work provides fundamental insights into the mechanisms of catalyzed lithium-sulfur reactions via operando methods, enabling a deeper understanding of electrocatalysis and interfacial dynamics in electrical energy storage systems.

36 MATERIALS SCIENCE↗
DOE OSTI2026

WHONDRS 2016 Sediment Organic Matter Characterization Data from Streams across HJ Andrews Experimental Forest, Oregon

This dataset supports a broader synoptic effort to map morphological, hydrological, chemical, and biological conditions across a fifth-order mountain stream network. Samples were generated through a collaborative synoptic sampling effort in 2016. The dataset provides sediment Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FTICR-MS) from 60 sites across the HJ Andrews Experimental Forest, Oregon (https://andrewsforest.oregonstate.edu). Related data were collected as part of the event and were published separately in collaboration with other team members. The data are available at http://www.hydroshare.org/resource/ea6c0832885a46c3939e7bb22e48e754 and are described within https://doi.org/10.5194/essd-11-1567-2019 (Ward et al., 2019). The hydroshare data package contains processed FTICR-MS data from the samples included in this data package. The data were processed via Formultitude (previously called Formularity; https://github.com/PNNL-Comp-Mass-Spec/Formultitude). However, we have re-processed the data using Core-MS and included it in this data package. Additional related data collected in 2025 from a similar effort can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3023310 and http://www.hydroshare.org/resource/b274c4a234bf4b12b7cb8a54a696c629. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) a folder of sample data; (2) data dictionary; (3) file-level metadata; (4); (5) coordinates; and (6) readme. The sample data subfolder contains 12 Tesla (12T) FTICR-MS data. This folder contains the processed data and three subfolders, one containing the .xml files, one containing the CoreMS output files, and the other containing instructions and scripts for processing the files in CoreMS (https://github.com/EMSL-Computing/CoreMS). All files are .csv, .pdf, .R, .xml, .Rmd, .py, .cal, or .json.

Biogeochemistry↗
DOE OSTI2021

Modeling and Simulation of Inrush Currents in Harmonic Domain

Modeling and simulation capabilities are critical to the stability analysis and evaluation of power distribution systems, with respect to the emphasis on resiliency, microgrids, and distributed energy resources. In this paper, a computational method in the harmonic domain is proposed for the periodic steady-state analysis of the nonlinear inrush current phenomenon. The efficient inrush calculation facilitates the predictions of current amplitudes for the power system operation and control. To demonstrate the accuracy and efficiency, simulation results in the harmonic domain are compared with results from PSCAD in an electromagnetic timescale, as well as the authors’ previous works in the frequency-domain. Impacts of the settings of both offset flux and interested harmonic order are discussed. In addition, within the proposed harmonic-domain method, a general approach that utilizes the discrete Fourier transform to obtain the response of a nonlinear device from a stimulus represented in the frequency-domain is utilized. This method can also be extended to perform the transient analysis in future, using trapezoidal rule for the integration.

Xie, Jing↗
DOE OSTI2025

Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from the NRHybSur3dq8 surrogate, which provides spherical-harmonic modes up to $\ell$ ≤ 4 (excluding (4, 0) and (4,±1), and including (5, 5)) for mass ratios q ≤ 8, dimensionless spin components s$^{z}_{1,2}$ ϵ[–0.8, 0.8], and inclination angles θ ϵ [0, π]. Waveforms are supplied on the interval t ϵ [–5000M, –100 M) and the model autoregressively generates the plus and cross polarizations (h + , h x ) on t ϵ [–100 M, 130M]. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required ~15 h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of 840,000 samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth.

black-hole merger↗
DOE OSTI2021

Architected mesoporous crystalline magnesium silicates with ordered pore structures

Novel approaches to harness earth abundant silicates as building blocks for carbon dioxide removal, capture, utilization, and storage are gaining increasing attention in the context of sustainable and low carbon energy and resource recovery. Advancing a calibrated understanding of these fluid-silicate interactions is essential for developing scalable processes. One of the challenges in developing predictive controls over these interactions is the compositional and morphological heterogeneity of naturally occurring, heterogeneous magnesium silicate minerals. To address this challenge, the synthesis of architected mesoporous crystalline magnesium silicate (Mg 2 SiO 4 ) is proposed. While synthesis routes for producing amorphous mesoporous magnesium silicates have been developed via sol-gel methods, approaches to synthesize crystalline magnesium silicates with well-controlled pore size distributions have not been explored. The conventional approaches of converting matter that is amorphous to crystalline states at elevated temperatures results in a heterogeneous pore size distribution. To develop controls on pore size distribution, amorphous mesoporous magnesium silicates are coated with carbon. This approach preserves the pore size distributions during the amorphous to crystalline transformations of Mg-silicates at elevated temperatures. The carbon coating is removed on heating. Magnesium silicate particles produced using this approach have highly ordered pores around 2.58 nm and a specific surface area of 124.25 m 2 /g. In this study, we report the chemical compositions, morphologies, phase transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. The transitions, and pore structures of the intermediate materials produced during the synthesis of crystalline mesoporous magnesium silicates. Furthermore, the synthesis routes discussed in this study can be applied translationally to produce metal silicates with ordered mesoporous structures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

D$e^+e^-$ffusion: Capturing the Beam-Beam Physics of $e^+e^-$ Collisions with Diffusion Models

Beam-induced backgrounds at high-luminosity $e^+e^-$ colliders, such as the FCC-ee, are dominated by incoherent pair creation (IPC), and require computationally expensive simulations with dedicated Monte Carlo (MC) event generators. Reliable detector and machine-detector interface studies necessitate event samples that are several orders of magnitude larger than what is practically attainable with existing MC. To alleviate this bottleneck, we present D$e^+e^-$ffusion, a denoising diffusion probabilistic model that operates as a permutation-equivariant, set-valued surrogate for fast IPC simulation. Trained on a small GuineaPig++ sample, D$e^+e^-$ffusion faithfully reproduces the marginal and joint kinematic, angular, and positional distributions of all three IPC production processes. In addition, we assess the fidelity at the detector level by propagating both Geant4 and D$e^+e^-$ffusion events through a Geant4 simulation of the CLD vertex detector and by training a transformer-based two-sample classifier; the classifier achieves an area under the ROC curve of $0.553 \pm 0.016$. The trained model generates events nearly four orders of magnitude faster than Geant4, paving the way for a fast-simulation surrogate for FCC-ee design studies.

Chahine, Antonio [Imperial Coll., London]↗
DOE OSTI2020

High‐order symmetric cubature rules for tetrahedra and pyramids

Abstract In this article, we present an algorithm to construct high‐order fully symmetric cubature rules for tetrahedral and pyramidal elements, with positive weights and integration points that are in the interior of the domain. Cubature rules are fully symmetric if they are invariant to affine transformations of the domain. We divide the integration points into symmetry orbits where each orbit contains all the points generated by the permutation stars. These relations are represented by equality constraints. The construction of symmetric cubature rules require the solution of nonlinear polynomial equations with both inequality and equality constraints. For higher orders, we use an algorithm that consists of five sequential phases to produce the cubature rules. In the literature, symmetric numerical integration rules are available for the tetrahedron for orders p = 1 – 10, 14 , and for the pyramid up to p = 10 . We have obtained fully symmetric cubature rules for both of these elements up to order p = 20 . Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, weakly singular, and trigonometric test functions over both elements with flat and curved faces. With increase in p , improvements in accuracy is realized, though nonmonotonic convergence is observed.

Jaśkowiec, Jan↗
DOE OSTI2023

Green Needle Coke Production from Pyrolysis Biocrude toward Bio-based Anode Material Manufacture: Biochar Fines Addition Effect as “Physical Template” on the Crystalline Order

Here, a new method for producing green needle coke (GNC) is developed by replacing the “heavy fraction” of petroleum pitch delayed coking with fast pyrolysis biocrude. A series of alternative biocrude distillation, carbonization, and calcination conditions were investigated to determine the influence of these processing parameters onto the crystalline structure of the resulting graphitized material. For the first time, the addition of biochar fines was found to serve as a “physical template” to increase the graphitic nature of the final product. During the initial biocrude carbonization (350–450 °C), volatile compounds are released, and aromatics in pyrolysis biocrude experience condensation, resulting in GNC solids with carbon contents above 95 wt % and some early lamellar structure. In the second stage of the thermal process (25–1500 °C), there are additional thermal decomposition reactions with an increase in the aromatic nature of the graphitized solid. It was found that systematic addition of biochar fines induces a nucleating effect during the GNC development. Thermogravimetric analysis suggests that biochar fines promote polycondensation reactions by modifying the biopitch structure and molecular weight, while elemental analysis (CHN) shows a reduction in both H/C and O/C ratios which are consistent with the increase in aromaticity and removal of oxygenated compounds as thermal treatment evolves. The effects of different bio-based pitch materials (after distillation) and GNC intermediates were evaluated by pyrolysis-gas chromatography mass spectrometry and Fourier transform infrared, displaying slight changes on product yields and quality. X-ray diffraction patterns taken after graphitization evidence an increase in the graphitic order with the addition of biochar fines. Transmittance electron microscopy depicts an improvement on graphitic morphology as biochar fine content increases. The use of biochar fines showed a significant increase in graphitic ordering at addition levels above 0.01 wt %. These results show that thermally treated biocrude/biochar fine systems can produce graphitic structures (hard carbon-like) that might be suitable for the manufacture of sodium-ion batteries.

09 BIOMASS FUELS↗
DOE OSTI2022

Solvent-Driven Transformation of Zn/Cd 2+ -Deoxycholate Assemblies

Deoxycholic acid (DOC) is a unique, biologically derived surfactant with facial amphiphilicity that has been exploited, albeit minimally, in supramolecular assembly of materials. Here, we present the synthesis and structural characterization of three hybrid metal (Zn 2+ and Cd 2+ )-DOC compounds. Analysis by single-crystal Xray diffraction reveals the many interactions that are possible between these facial surfactants and the influence of solvent molecules that drive the assembly of materials. These structures are the first metal- DOC complexes besides those obtained from alkali and alkaline earth metals. We isolated polymeric chains of both Cd and Zn (Zn poly -DOC and Cd poly -DOC) from water. Major interactions between DOC molecules in these phases are hydrophobic in nature. Cd poly -DOC exhibits unique P1 symmetry, with complete interdigitation of the amphiphiles between neighboring polymeric chains. Zn 4 -DOC, obtained from methanol dissolution of Zn poly -DOC, features the OZn 4 tetrahedron, widely known in basic zinc acetate and MOF-5 (metal organic framework). We document a solvent-driven, roomtemperature transition between Zn poly -DOC and Zn 4 -DOC (in both directions) by scanning and transmission electron microscopies in addition to small-angle X-ray scattering, powder X-ray diffraction, and infrared spectroscopy. These studies show the methanoldriven transition of Zn poly -DOC to Zn 4 -DOC occurs via an intermediate with no long-range order of the Zn 4 clusters, indicating the strongest interactions driving assembly are intramolecular. On the contrary, water-driven solid-to-solid transformation from Zn 4 -DOC to Zn poly -DOC exhibits crystal-to-crystal transformation. Zn poly -DOC is robust, easy to synthesize, and comprised of biologically benign components, so we demonstrate dye absorption as a proxy for water treatment applications. It favors absorption of positively charged dyes. These studies advance molecular level knowledge of the supramolecular assembly of facial surfactants that can be exploited in the design of organic-inorganic hybrid materials. This research also highlights the potential of solvent for tuning supramolecular assembly processes, leading to new hybrid materials featuring facial surfactants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the conformal symmetry of exceptional scalar theories

The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

A novel formulation is presented for the treatment of electrostatics in the periodic GFN1-xTB tight-binding model. Periodic GFN1-xTB is hindered by the functional form of the second-order electrostatics, which only recovers Coulombic behavior at large interatomic distances and lacks a closed-form solution for its Fourier transform. We address this by introducing a binomial expansion of the Klopman–Ohno function to partition short- and long-range interactions, enabling the use of a generalized Ewald summation for the solution of the electrostatic energy. This approach is general and is applicable to any damped potential of the form |R n + c| –m . Benchmarks on the X23 molecular crystal dataset and a range of prototypical bulk semiconductors demonstrate that this systematic treatment of the electrostatics eliminates unphysical behavior in the equation of state curves. In the bulk systems studied, we observe a mean absolute error in total energy of 35 meV/atom, comparable to the machine-learned universal force field, M3GNet, and sufficiently precise for structure relaxation. These results highlight the promising potential of GFN1-xTB as a universal tight-binding parametrization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Nanocrystal Geometry Governs Phase Transformation Pathways in Palladium Hydride

Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride (PdH x ) nanocrystals are an ideal model system for studying solute-induced phase transformations, where elastic energy from lattice mismatch between α-PdH x and β-PdH x phases is often considered a key to determining the transformation pathways. α/β-PdH x interfacial elastic energy is affected by the confined geometry of a nanocrystal. However, how nanocrystal geometry influences phase transformation pathways is largely unknown. Using in situ liquid phase transmission electron microscopy, we directly visualize hydrogenation in Pd nanocrystals with two geometries, a nanocube and a hexagonal nanoplate. Both follow similar sequences of an initially curved nucleus, interface flattening, and reverse-stage nucleation; however, their evolving α/β-PdH x interfaces exhibit geometry-dependent crystallographic alignments. In nanocubes, {100}-aligned configurations conform to static elastic energy ordering, representing a pathway that maintains a local mechanical equilibrium, whereas nanoplates display both {110}- and {211}-aligned interfaces. Theoretical simulations show that geometry determines the accessibility of alternative phase transformation pathways as the system is driven far from equilibrium during hydrogenation. In conclusion, these findings identify geometry as a fundamental parameter for directing phase transformation pathways, offering design principles for accessing atypical configurations and improving properties of intercalation-based devices.

Lee, Daewon [Lawrence Berkeley National Laboratory↗
DOE OSTI2024

Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system

We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group β function. The gradient flow β function exhibits a zero at g GF ⋆ 2 = 6.60 ( 62 ) , implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent γ g ⋆ = 0.199 ( 32 ) . Our prediction for γ g ⋆ is consistent with available literature at the 1 − 2 σ level. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗