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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Quantum Phases and Collective Excitations of a Spin-Orbit-Coupled Bose–Einstein Condensate in a One-Dimensional Optical Lattice

The ground state of a spin-orbit-coupled Bose gas in a one-dimensional optical lattice is known to exhibit a mixed regime, where the condensate wave function is given by a superposition of multiple Bloch-wave components, and an unmixed one, in which the atoms occupy a single Bloch state. The unmixed regime features two unpolarized Bloch-wave phases, having quasimomentum at the center or at the edge of the first Brillouin zone, and a polarized Bloch-wave phase at intermediate quasimomenta. By calculating the critical values of the Raman coupling and of the lattice strength at the transitions among the various phases, we show the existence of a tricritical point where the mixed, the polarized and the edge-quasimomentum phases meet, and whose appearance is a consequence of the spin-dependent interaction. Furthermore, we evaluate the excitation spectrum in the unmixed regime and we characterize the behavior of the phonon and the roton modes, pointing out the instabilities occurring when a phase transition is approached.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2025

MgO Nanostructures on Au(111) as Catalysts for Low-Temperature Methane Activation and C-C Coupling

The selective conversion of methane (CH4) under mild conditions remains challenging due to strong C-H bonds and catalyst coking. We systematically investigated sub-monolayer MgO nanostructures on Au(111), where two-dimensional (2D) MgO islands with stable Mg-O-Au interfaces catalyze low-temperature CH4 activation and C-C coupling. Upon CH4 exposure at 300 K, surface-bound CHx and C2Hx intermediates formed and persisted post-evacuation, indicating robust CHx-O-Mg linkages. Temperature-programmed studies revealed that C-H activation and C-C coupling intensify with heat: the CHx signal grew continuously while the C2Hx signal reached a plateau at 400-500 K. O 1s and Mg 2p attenuation confirmed adsorption of the hydrocarbons on MgO. Catalytic tests at 500 K yielded C2H6 (70%) and C2H4 (30%) without coking, underscoring MgO's role as an active catalyst. These results offer new design principles for developing coke-resistant and low-temperature methane upgrading catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Computational Investigation of the Chemical Bond between An(III) Ions and Soft-Donor Ligands

The chemical bonding of actinide ions with arene and borohydride ligands is explored via quantum chemical methods to understand how the transuranium elements interact with softdonor ligands. Specifically, the [An(C 6 Me 6 )(BH 4 ) 3 ] complexes (An = U, Np, and Pu) and their reduced congeners are studied. Density functional theory (DFT) shows that the metal–ligand interactions in the neutral complexes are governed by electrostatic interactions. Both DFT and complete active space (CASSCF) results show that as one moves from U to Pu, the 5f-orbitals are stabilized leading to a poorer energy match with the ligand orbitals. This contributes to progressively weaker metal-arene and metal-borohydride interactions across the series due to a decrease in energy-driven covalency. A reduction in orbital contributions to bonding is obtained for the transuranium-arene interactions as well. Upon reduction, the arene is reduced, forming a δ-bond. This causes the An–arene distances to contract by 0.1–0.2 Å compared to the neutral complexes. The ground state is assigned as the intermediate-spin state where the arene radical is antiferromagnetically coupled to the metal-centered f-electrons in Np and Pu. On the other hand, the ferromagnetically and antiferromagnetically coupled states are close in energy in the uranium complex, but do not mix when spin– orbit coupling is included using a state-interaction approach (SO-CASPT2). The population of the CASSCF δ*-antibonding natural orbital increases from U to Pu consistent with the increased An–arene distances, weaker interactions, and decreasing covalency across the series. Although the An–B distance increases by ca. 0.06 Å upon reduction, both the neutral and reduced species involve an An(III)–borohydride bond and as such are qualitatively similar. The Np complexes can be assigned to have slightly weaker bonding than the uranium analogs but are overall “uranium-like”. The Pu complexes are predicted to have less covalent contributions to bonding in both the Pu–arene and Pu–borohydride interactions; however, the Pu–arene interaction is predicted to be particularly weak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Tracking Site-specific C-C Coupling of Formaldehyde Molecules on Rutile TiO2(110)

Direct imaging of site-specific reactions of individual mole-cules as a function of temperature is a long-sought goal in molecular science. Here, we report the direct visualization of molecular coupling of formaldehyde on reduced rutile TiO2(110) surfaces as we track the same set of molecules when the temperature is increased from 75 to 170 K using scanning tunneling microscope (STM). Our recent study showed that formaldehyde preferably adsorbs on bridging-bonded oxygen (Ob) vacancy (VO) defect site. Herein, images from the same area as the temperature is increased show that VO-bound formaldehyde couples with Ti-bound formaldehyde forming a diolate intermediate. Exposure of formaldehyde at room temperature leads to diolate as the majority species on the surface and no VO-bound formaldehyde is observed. The diolate species are the key reaction intermediates in the formation of ethylene reported in previous ensemble-averaged studies.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2018

Biochemical and Structural Characterization of TtnD, a Prenylated FMN-Dependent Decarboxylase from the Tautomycetin Biosynthetic Pathway

Tautomycetin (TTN) is a polyketide natural product featuring a terminal alkene. Functional characterization of the genes within the ttn gene cluster from Streptomyces griseochromogenes established the biosynthesis of the TTN polyketide backbone, its dialkylmaleic anhydride moiety, the coupling of the two moieties to form the nascent intermediate TTN F-1, and the tailoring steps converting TTN F-1 to TTN. Here, we report biochemical and structural characterization of TtnD, a prenylated FMN (prFMN)-dependent decarboxylase belonging to the UbiD family that catalyzes the penultimate step of TTN biosynthesis. TtnD catalyzes decarboxylation of TTN D-1 to TTN I-1, utilizing prFMN as a cofactor generated by the TtnC flavin prenyltransferase; both TtnD and TtnC are encoded within the ttn biosynthetic gene cluster. TtnD exhibits substrate promiscuity but accepts only TTN D-1 congeners that feature an α,β-unsaturated acid, supporting the [3+2] cycloaddition mechanism during catalysis that requires the double bond of an α,β-unsaturated acid substrate. TtnD shares a similar overall structure with other members of the UbiD family but forms a homotetramer in solution. Each protomer is composed of three domains with the active site located between the middle and C-terminal domains; R169-E272-E277, constituting the catalytic triad, and E228, involved in Mn(II)-mediated binding of prFMN, were confirmed by site-directed mutagenesis. TtnD represents the first example of a prFMN-dependent decarboxylase involved in polyketide biosynthesis, expanding the substrate scope of the UbiD family of decarboxylases beyond simple aromatic and cinnamic acids. In conclusion, TtnD and its homologues are widespread in nature and could be exploited as biocatalysts for organic synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Inducing Kondo screening of vacancy magnetic moments in graphene with gating and local curvature

In normal metals the magnetic moment of impurity-spins disappears below a characteristic Kondo temperature which marks the formation of a cloud of conduction-band electrons that screen the local-moment. In contrast, moments embedded in insulators remain unscreened at all temperatures. What then is the fate of magnetic-moments in intermediate, pseudogap systems, such as graphene? Theory predicts that coupling to the conduction-band electrons will drive a quantum phase transition between a local-moment phase and a Kondo-screened phase. However, attempts to experimentally confirm this prediction and its intriguing consequences, such as electrostatically tunable magnetic-moments, have been elusive. Here we report the observation of Kondo-screening and the quantum phase-transition between screened and unscreened phases of vacancy magnetic moments in graphene. Using scanning tunneling spectroscopy and numerical renormalization-group calculations we show that this transition enables to control the screening of local moments by tuning the gate voltage and the local curvature of the graphene membrane.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A divergent route to core- and peripherally functionalized diazacoronenes that act as colorimetric and fluorescence proton sensors

Combining core annulation and peripheral group modification, we have demonstrated a divergent synthesis of a family of highly functionalized coronene derivatives from a readily accessible dichlorodiazaperylene intermediate. Various reactions, such as aromatic nucleophilic substitution, Kumada coupling and Suzuki coupling proceed effectively on α-positions of the pyridine sites, giving rise to alkoxy, thioalkyl, alkyl or aryl substituted polycyclic aromatic hydrocarbons. In addition to peripheral group modulation, the aromatic core structures can be altered by annulation with thiophene or benzene ring systems. Corresponding single crystal X-ray diffraction and optical studies indicate that the heteroatom linkages not only impact the solid state packing, but also significantly influence the optoelectronic properties. Furthermore, these azacoronene derivatives display significant acid-induced spectroscopic changes, suggesting their great potential as colorimetric and fluorescence proton sensors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Steering CO 2 electroreduction toward ethanol production by a surface-bound Ru polypyridyl carbene catalyst on N-doped porous carbon

Significance Electrochemical reduction of CO 2 can convert CO 2 emission back to value-added fuels and chemicals and store renewable electricity. Reducing CO 2 to multicarbon products has attracted great interest because of their higher energy densities and associated economic values. We report here a promising strategy for steering CO 2 electroreduction toward ethanol production by exploiting a surface-bound Ru polypyridyl carbene catalyst on an N-doped porous carbon electrode. We show the synergistic effects of Ru polypyridyl carbene for CO intermediate production with a porous carbon for C–C coupling that could boost ethanol production at relatively low overpotentials. The strategy provides insights on how to improve selectivity and efficiency for CO 2 reduction toward multicarbon products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Preheating after multifield inflation with nonminimal couplings. III. Dynamical spacetime results

This paper concludes our semianalytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of paper I in this series, we extend here the rigid-spacetime results of paper II by considering both the expansion of the Universe during preheating, as well as the effect of the coupled metric perturbations on particle production. The adiabatic and isocurvature perturbations are governed by different effective masses that scale differently with the nonminimal couplings and evolve differently in time. The effective mass for the adiabatic modes is dominated by contributions from the coupled metric perturbations immediately after inflation. The metric perturbations contribute an oscillating tachyonic term that enhances an early period of significant particle production for the adiabatic modes, which ceases on a time scale governed by the nonminimal couplings ${{\xi}}_{I}$. The effective mass of the isocurvature perturbations, on the other hand, is dominated by contributions from the fields' potential and from the curvature of the field-space manifold (in the Einstein frame), the balance between which shifts on a time scale governed by ${{\xi}}_{I}$. As in papers I and II, we identify distinct behavior depending on whether the nonminimal couplings are small [${{\xi}}_{I}{\lesssim}\mathcal{O}(1)$], intermediate [${{\xi}}_{I}{\sim}\mathcal{O}(1{-}10)$], or large (${{\xi}}_{I}{\ge}100$).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Dark Matter in the Heavens and at Colliders: Models and Constraints

In this dissertation, we investigate various aspects of dark matter detection and model building. Motivated by the cosmic ray positron excess observed by PAMELA, we construct models of decaying dark matter to explain the excess. Specifically we present an explicit, TeV-scale model of decaying dark matter in which the approximate stability of the dark matter candidate is a consequence of a global symmetry that is broken only by instanton-induced operators generated by a non-Abelian dark gauge group. Alternatively, the decaying operator can arise as a Planck suppressed correction in a model with an Abelian discrete symmetry and vector-like states at an intermediate scale that are responsible for generating lepton Yukawa couplings. A flavor-nonconserving dark matter decay is also considered in the case of fermionic dark matter. Assuming a general Dirac structure for the four-fermion contact interactions of interest, the cosmic-ray electron and positron spectra were studied. We show that good fits to the current data can be obtained for both charged-leptonflavor- conserving and flavor-violating decay channels. Motivated by a possible excess of gamma rays in the galactic center, we constructed a supersymmetric leptophilic higgs model to explain the excess. Finally, we consider an improvement on dark matter collider searches using the Razor analysis, which was originally utilized for supersymmetry searches by the CMS collaboration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Probing the Sustainable Reduction of CO 2 , N 2 and NO 3 to Fuels and Chemicals using Non-Traditional Porphyrinoid Catalysts

For the last several decades, numerous strategies have been proposed to be able to interconvert electricity and commodity fuels for transportation and other applications. Even as solar and wind energy become more widely available, these renewable energy sources are not always available where the population is most dense or during peak times of energy demand. One plausible solution to the issue of electricity storage and transport is to use electricity to drive the formation of high-energy compounds and chemical fuels. As a result, the electrochemical conversion of CO 2 into chemical fuels has received major attention as a multi-pronged approach for electricity coversion, storage, and transport. Similar strategies are also attractive for conversion of N 2 and NO x into value added compounds such as ammonia. Metalloporphyrin and metallocorrole complexes are comprised of aromatic tetrapyrrole scaffolds and have been extensively studied as homogeneous catalysts for critical catalytic processes like the electrochemical CO 2 reduction reaction (eCO 2 RR) to generate CO as feedstock for the Fischer–Tropsch process to generate a variety of hydrocarbons as chemical fuels. Despite their significance and impact, efficiently driving such catalytic reduction processes is challenging for multiple reasons. Such processes require multiple-electron transfer events, as opposed to single-electron redox chemistry that forms high-energy singly-reduced intermediates. In addition, these electron transfer events must be coupled to proton-transfer steps and avoid application of high overpotentials where proton (H + ) reduction to generate H 2 (as well as other side-reactions) can lower the selectivity and energy efficiency of the eCO 2 RR process. Certain Fe(III) aromatic tetrapyrroles (e.g., porphyrins and corroles) have been reported to overcome these challenges, but are often difficult to synthesize and modify, and have a tendency to support single-electron redox chemistry at the metal as opposed to multielectron redox involving the ligand and metal in concert. Other families of tetrapyrroles in which all four meso-carbons are reduced (i.e., sp 3 -hybridized) are also known in the literature. These non-aromatic tetrapyrroles are known as porphyrinogens and support multi-electron redox chemistry which has been elaborated by several groups, prompting researchers to consider whether these scaffolds may improve the kinetics and efficiencies of multi-electron steps attendant to activation of thermodynamically stable small-molecule substrates such as CO 2 , N 2 , NO 3 − , and NO 2 − . Although porphyrinogens support multi-electron redox properties, the four sp 3 -hybridized meso-carbons inherent to the tetrapyrrole core completely disrupt π-conjugation between pyrrolic units, which compromises the photochemical properties of porphyrinogens in comparison to that of traditional porphyrinoids. Moreover, the highly reducing nature of porphyrinogens predisposes these platforms to extreme air and water sensitivity. Accordingly, such metalated porphyrinogens are often pyrophoric and/or incompatible with many common organic solvents (CH 2 Cl 2 , CHCl 3 , CH 3 CN, EtOAc, etc.). Hence, reports of efficient small-molecule activation or catalysis supported by porphyrinogens have been limited. To overcome the instability of porphyrinogens while retaining the scaffold’s attractive multi-electron redox properties, we have directed attention to establishing less-well studied groups of non-aromatic tetrapyrroles (i.e., phlorins, biladienes, and isocorroles). These non-traditional tetrapyrroles each contain just a single sp 3 -hybridized meso-carbon, which ablates the platforms aromaticity but still provides an extended π-framework. In addition to developing innovative platforms that may be used to sustainably generate value-added chemicals, fuels, and ammonia via either photo- or electrocatalytic approaches our work also has significantly broadened our understanding of how to prepare and modulate the properties of non-aromatic tetrapyrroles for other applications. Our efforts entailed a synergistic partnership and active collaborations with Drs. David C. Grills and Mehmed Z. Ertem (both of Brookhaven National Lab) to better characterize isocorroles (and related non-aromatic tetrapyrroles) using a variety of advanced spectroscopic and theoretical methods. Our combined efforts have shown that the combination of properties that isocorroles (and related tetrapyrroles) provide results in good chemical stability paired with unique redox and photochemical characteristics that are not typically supported by simple and/or unadorned aromatic tetrapyrroles. Beside redox chemistry, the photochemistry of isocorroles and other non-aromatic tetrapyrroles containing one sp 3 -hybridized meso-carbon is also appealing due to their absorption in the long-visible to near-IR regions, which are essential for photocatalysis and related applications that benefit from direct excitation at these wavelengths. The results reported vastly improve our understanding of non-aromatic tetrapyrrole synthesis, properties and utility for activation of small molecule substrates such as O 2 and CO 2 in the presence of weak cationic organic acids.

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

Tunable Geometries in Sparse Clifford Circuits

We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Subphotospheric Emission from Short Gamma-Ray Bursts: Protons Mold the Multimessenger Signals

Abstract The origin of the observed Band-like photon spectrum in short gamma-ray bursts (sGRBs) is a long-standing mystery. We carry out the first general relativistic magnetohydrodynamic simulation of an sGRB jet with initial magnetizationσ 0 = 150 in dynamical ejecta from a binary merger. From this simulation, we identify regions along the jet of efficient energy dissipation due to magnetic reconnection and collisionless subshocks. Taking into account electron and proton acceleration processes, we solve for the first time the coupled transport equations for photons, electrons, protons, neutrinos, and intermediate particle species up to close to the photosphere (i.e., up to 1 × 10 12 cm), accounting for all relevant radiative and cooling processes. We find that the subphotospheric multimessenger signals carry strong signatures of the hadronic interactions and their resulting particle cascades. Importantly, the spectral energy distribution of photons is significantly distorted with respect to the Wien one, commonly assumed below the photosphere. Our findings suggest that the bulk of the nonthermal photon spectrum observed in sGRBs can stem from hadronic processes occurring below the photosphere and previously neglected, with an accompanying energy flux of neutrinos peaking in the GeV energy range.

Astronomy & Astrophysics↗
NASA NTRS1974

Device for recording the 20 Hz - 200 KHz sound frequency spectrum using teletransmission

The device described consists of two distinct parts: (1) The sound pickup system consisting of the wide-frequency band condenser microphone which contains in the same assembly the frequency-modulated oscillator and the output stage. Being transistorized and small, this system can be easily moved, so that sounds can be picked up even in places that are difficult to reach with larger devices. (2) The receiving and recording part is separate and can be at a great distance from the sound pickup system. This part contains a 72 MHz input stage, a frequency changer that gives an intermediate frequency of 30 MHz and a multichannel analyzer coupled to an oscilloscope and a recorder.

Baciu, I.↗
DOE OSTI2021

Tandem In 2 O 3 -Pt/Al 2 O 3 catalyst for coupling of propane dehydrogenation to selective H 2 combustion

Tandem catalysis couples multiple reactions and promises to improve chemical processing, but precise spatiotemporal control over reactive intermediates remains elusive. We used atomic layer deposition to grow In 2 O 3 over Pt/Al 2 O 3 , and this nanostructure kinetically couples the domains through surface hydrogen atom transfer, resulting in propane dehydrogenation (PDH) to propylene by platinum, then selective hydrogen combustion by In 2 O 3 , without excessive hydrocarbon combustion. Other nanostructures, including platinum on In 2 O 3 or platinum mixed with In 2 O 3 , favor propane combustion because they cannot organize the reactions sequentially. The net effect is rapid and stable oxidative dehydrogenation of propane at high per-pass yields exceeding the PDH equilibrium. Tandem catalysis using this nanoscale overcoating geometry is validated as an opportunity for highly selective catalytic performance in a grand challenge reaction.

Yan, Huan↗
DOE OSTI2015

On uniform plasma generation for the large area plasma processing in intermediate pressures

Radial plasma discharge characteristics in the range of 450 mm were studied in a dual inductively coupled plasma (ICP) source, which consisted of a helical ICP and the side type ferrite ICPs. Since the energy relaxation length is shorter than the distance between each of the ferrite ICPs in an intermediate pressure (600 mTorr), local difference in the plasma ignition along the antenna position were observed. In addition, large voltage drop in the discharge of the ferrite ICPs causes an increase in the displacement current to the plasma, and separate discharge mode (E and H mode) according to the antenna position was observed. This results in non-uniform plasma distribution. For the improvement in the discharge of the ferrite ICPs, a capacitor which is placed between the ends of antenna and the ground is adjusted to minimize the displacement current to the plasma. As a result, coincident transitions from E to H mode were observed along the antenna position, and radially concave density profile (edge focused) was measured. For the uniform density distribution, a helical ICP, which located at the center of the discharge chamber, was simultaneously discharged with the ferrite ICPs. Due to the plasma potential variation through the simultaneous discharge of helical ICP and ferrite ICPs, uniform radial distribution in both plasma density and electron temperature are achieved.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Controlled calculation of the thermal conductivity for a spinon Fermi surface coupled to a U(1) gauge field

Motivated by recent transport measurements on the candidate spin-liquid phase of the organic triangular lattice insulator EtMe{sub 3}Sb[Pd(dmit){sub 2}]{sub 2}, we perform a controlled calculation of the thermal conductivity at intermediate temperatures in a spin liquid system where a spinon Fermi surface is coupled to a U(1) gauge field. The present computation builds upon the double expansion approach developed by Mross et al. (2010) for small ϵ=z{sub b}−2 (where z{sub b} is the dynamical critical exponent of the gauge field) and large number of fermionic species N. Using the so-called memory matrix formalism that most crucially does not assume the existence of well-defined quasiparticles at low energies in the system, we calculate the temperature dependence of the thermal conductivity κ of this model due to non-critical Umklapp scattering of the spinons for a finite N and small ϵ. Then we discuss the physical implications of such theoretical result in connection with the experimental data available in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗