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At least 469 records · Page 26

Coherence Analysis of the Space Launch System using Unsteady Pressure Sensitive Paint

Transonic buffet forces are a major source of unsteady loading on launch vehicles, thus requiring accurate estimation for efficient vehicle design. The state of the art in modeling these unsteady loads utilizes wind-tunnel tests where the fluctuating pressures are measured by pressure transducers (PTs) at discrete locations on a rigid buffet model. These pressures are then integrated over the surface of the vehicle to yield a series of orthogonal centerline loads called buffet forcing functions (BFFs). Typically, the PT layout aims at resolving the pressure correlation along the longitudinal axis of the vehicle. As a result, the distribution of azimuthal correlation and its impact on the estimated BFFs are not well known. To fill these gaps, extremely high-spatial-resolution uPSP data were collected for three different configurations of the Space Launch System in the NASA Ames Research Center 11-Foot Transonic Unitary Plan Wind Tunnel. The spatio-temporal behavior of the pressure correlation on these vehicles is analyzed and flow features of interest are investigated. It is shown that terminal shocks interacting with turbulence are a source of increased azimuthal coherence, especially when the shock develops at a junction. Vortex shedding off the forward attachment hardware that connects the core stage to the solid rocket boosters (SRBs) is the most severe buffet environment on the vehicle. The associated fluctuating pressures are shown to be highly coherent as far as the vehicle tail and up to 40 degrees away from the boosters. For selected areas of the vehicle, factoring the azimuthal coherence into the attenuation of discrete-measurements-based BFFs results in under prediction relative to the BFFs obtained from full integration of the uPSP data.

buffet↗

Comparing Two Weather-Robust Microphone Configurations for Outdoor Measurements

This paper discusses comparisons made between two ground-based outdoor microphone configurations. The first is known as the Compact Outdoor Unit for Ground-based Acoustical Recordings (COUGAR) and consists of an inverted microphone placed above a convex circular plate and covered by a large dome windscreen. The second configuration is the COUGARxt, where the “xt” simultaneously refers to an extra thick windscreen and an extra thin ground plate. COUGAR and COUGARxt were subjected to laboratory testing where their responses to sound were recorded at several different elevation and azimuthal angles. At almost all shown elevation angles, both configurations recorded levels that were within ±3 dB of a baseline measurement between 50 Hz – 20 kHz. At all shown azimuthal angles and over the same frequency range, both recorded levels within ±2 dB of the levels reported at an azimuthal angle of 0°, with COUGARxt having less variation than COUGAR. The configurations were also subjected to wind noise testing, where COUGARxt demonstrated superior wind noise rejection at low frequencies. The conclusion is that both configurations are suitable for outdoor acoustical measurements and that COUGARxt is the superior configuration, especially when measuring low-frequency noise.

sonic boom↗

Pretest Simulations of a Supersonic Mixing and Combustion Validation Experiment to Assess Sensitivities

The reliance on CFD simulations to develop, design, and optimize scramjet systems (or components) has become commonplace. This reliance inevitably hinges on the ability of the computational analyst to quantify the level of confidence in their computational results. Unfortunately, nearly all the measured data available for this assessment comes from antiquated experimental datasets, or from tests that focused on the extraction of scramjet system (or component) performance. The objective of a CFD validation experiment is to quantify the predictive accuracy of one or more of the CFD physics submodels, implying that other uncertainties related to replicating the facility flow environment (e.g., knowledge of boundary conditions) must be minimized to the extent possible. This inevitably places stringent requirements on the quality and quantity of measurements taken to accurately specify inflow, outflow, and surface conditions for the CFD simulations; in addition to the measurements taken for the validation of physics submodels. This places additional demands on the experimental process above and beyond those for test article performance assessment. A recent high speed code credibility workshop series sponsored by AFRL identified a gap in existing validation data for fundamental assessments of turbulent mixing and combustion CFD closure models at scramjet engine relevant conditions. To address this gap, engineers at AFRL have designed a coaxial jet flame configuration that will be tested at two facilities (Research Cell 19 at the Air Force Research Lab, and at Purdue University). The effort described here documents pretest simulations of this validation experiment with the goal of fleshing out the extent of the facility flowpath that must be included to adequately reproduce the facility test section flow environment. The findings indicate that the flow around the support structure for the fuel injection centerbody upstream of the facility nozzle generates disturbances that persist throughout the nozzle expansion process; corrupting the azimuthal symmetry that was desired in the fuel/air mixing region of the test section. Simulations without this support structure maintained a high degree of azimuthal symmetry up until the fuel injection plane. However, even in this scenario the azimuthal symmetry was not maintained once the centerbody boundary layer transitioned to a wake flow downstream of the fuel injection plane.

CFD↗

Pretest Simulations of a Supersonic Mixing and Combustion Validation Experiment to Assess Sensitivities

The reliance on CFD simulations to develop, design, and optimize scramjet systems (or components) has become commonplace. This reliance inevitably hinges on the ability of the computational analyst to quantify the level of confidence in their computational results. Unfortunately, nearly all the measured data available for this assessment comes from antiquated experimental datasets, or from tests that focused on the extraction of scramjet system (or component) performance. The objective of a CFD validation experiment is to quantify the predictive accuracy of one or more of the CFD physics submodels, implying that other uncertainties related to replicating the facility flow environment (e.g., knowledge of boundary conditions) must be minimized to the extent possible. This inevitably places stringent requirements on the quality and quantity of measurements taken to accurately specify inflow, outflow, and surface conditions for the CFD simulations; in addition to the measurements taken for the validation of physics submodels. This places additional demands on the experimental process above and beyond those for test article performance assessment. A recent high speed code credibility workshop series sponsored by AFRL identified a gap in existing validation data for fundamental assessments of turbulent mixing and combustion CFD closure models at scramjet engine relevant conditions. To address this gap, engineers at AFRL have designed a coaxial jet flame configuration that will be tested at two facilities (Research Cell 19 at the Air Force Research Lab, and at Purdue University). The effort described here documents pretest simulations of this validation experiment with the goal of fleshing out the extent of the facility flowpath that must be included to adequately reproduce the facility test section flow environment. The findings indicate that the flow around the support structure for the fuel injection centerbody upstream of the facility nozzle generates disturbances that persist throughout the nozzle expansion process; corrupting the azimuthal symmetry that was desired in the fuel/air mixing region of the test section. Simulations without this support structure maintained a high degree of azimuthal symmetry up until the fuel injection plane. However, even in this scenario the azimuthal symmetry was not maintained once the centerbody boundary layer transitioned to a wake flow downstream of the fuel injection plane.

CFD↗

FLORA Equilibrium and Stability Code Archive

FLORA solves, in a 2-D domain (radial and axial dimensions) with a specified azimuthal Fourier mode, for the linearized stability of a long, thin, axisymmetric plasma equilibrium in an applied magnetic field. Before the stability equation is solved, FLORA solves a set of simple equations for pressure balance that specify the equilibrium magnetic field and plasma pressure in the long-thin limit given a simplified description of the magnetic coils. It uses an initial-value method for the linear stability problem in which an equilibrium is given an initial perturbation to its magnetic field, and the temporal behavior of the perturbation is followed. The perturbation has been Fourier expanded in the azimuthal coordinate; each azimuthal mode must be examined separately. The complex partial differential equation of motion for the perturbed radial displacement of the field lines is solved as a coupled system of two real p.d.e.'s and the solution consists of two parts, the real part and the imaginary part. The system is solved by bringing the coupling terms in each equation to the right side and using an iterative technique.

Cohen, Bruce [Lawrence Livermore National Laborato↗

Collins function for pion-in-jet production in polarized pp collisions: a test of universality and factorization

We present an updated study of the Collins azimuthal asymmetries for pion-in-jet production in polarized pp collisions. To this aim, we employ a recent extraction of the transversity and Collins fragmentation functions from semi-inclusive deep inelastic scattering and e + e - annihilation into hadron pairs processes, obtained within a simplified transverse momentum dependent (TMD) approach at leading order in the strong coupling constant α s . In the present case we adopt a collinear configuration for the initial state, keeping transverse momentum effects only in the fragmentation mechanism. Our theoretical estimates, when compared against 200 GeV and 510 GeV data from the STAR Collaboration, show a generally good agreement for the distributions in the transverse momentum of the jet, the pion longitudinal momentum fraction and its transverse momentum with respect to the jet direction. While not being a proof, due the assumptions and limitations behind the entire approach, these findings corroborate the hypothesis of TMD factorization for such processes as well as of the universality of the Collins function and, once again, of a reduced impact of the proper TMD evolution on azimuthal asymmetries. We will also present predictions based on an extraction of the Collins and transversity distributions where information from data on single spin asymmetry for inclusive pion production in p ↑ p collisions is included through a Bayesian reweighting procedure.

Azimuthal asymmetries↗

Collins asymmetries for pion-in-jet production in polarized ℓp collisions at the EIC

We study Collins azimuthal asymmetries for pion-in-jet production in polarized lepton-proton collisions, extending previous analyses of polarized pp scattering to a complementary and theoretically simpler process. We keep adopting a simplified transverse momentum dependent (TMD) approach, with a collinear configuration for the initial state, and employ the transversity and Collins fragmentation functions as extracted from semi-inclusive deep inelastic scattering and $e^{+}e^{-}$ annihilation processes. We then compute azimuthal asymmetries for the Electron-Ion Collider (EIC) kinematics, both within a leading order (LO) approach and by including quasireal photon exchange in the Weizsäcker-Williams approximation. Although this contribution is relevant in the whole kinematical range explored, it does not spoil the dominance of quark-initiated channels, leaving only a marginal role to their gluon counterparts. In this respect, Collins asymmetries in lepton-proton processes allow for a much clearer access to the transversity distribution, including its sea-quark component. As we will argue, a comparison with future EIC data could represent a further step in testing the hypothesis of the universality of the Collins function as well as of the TMD factorization for this class of processes.

Azimuthal asymmetries↗

A New Modeling Approach for a Priori Uncertainties of Laser Tracker Angle Measurements

Methods for modeling the uncertainty in laser tracker angle measurements vary within the metrology industry, leading to confusion and questionable stochastic modeling for survey network adjustments and error propagation analysis. Interpreting the published laser tracker manufacturer performance specifications to determine an a priori sigma value for weighting azimuth and zenith angle measurements can be confusing and has led to differing implementations. Furthermore, this paper proposes a unique way to model survey network a priori laser tracker angular uncertainties based on laser tracker manufacturers’ published maximum permissible error (MPE) values referenced to current standards for weighting survey network measurements. This paper’s proposed model takes into account the disparate effects that pointing errors, target centering errors, and leveling errors have on azimuth and zenith angular uncertainties for measurements with steep sightings and at near ranges.

42 ENGINEERING↗

Measurement of elliptic flow of 𝐽/𝜓 in $\sqrt{s_{NN}}$ = 200 GeV ⁢Au + Au collisions at forward rapidity

Here, we report the first measurement of the azimuthal anisotropy of 𝐽/𝜓 at forward rapidity (1.2 < |𝜂| < 2.2) in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at the BNL Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5 nb −1 . The second Fourier coefficient (𝑣 2 ) of the azimuthal distribution of 𝐽/𝜓 is determined as a function of the transverse momentum (𝑝𝑇) using the event-plane method. The measurements were performed for several selections of collision centrality: 0%–50%, 10%–60%, and 10%–40%. We find that in all cases the values of 𝑣 2 ⁡(𝑝 𝑇 ), which quantify the elliptic flow of 𝐽/𝜓, are consistent with zero. Within uncertainties, the results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the 𝐽/𝜓 within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{NN}}$ = 200 GeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Production of b b ¯ at forward rapidity in p + p collisions at s = 510 GeV

The cross section of bottom quark-antiquark ( b b ¯ ) production in p + p collisions at s = 510 GeV is measured with the PHENIX detector at the Relativistic Heavy Ion Collider. The results are based on the yield of high mass, like-sign muon pairs measured within the PHENIX muon arm acceptance ( 1.2 < | y | < 2.2 ). The b b ¯ signal is extracted from like-sign dimuons by utilizing the unique properties of neutral B meson oscillation. We report a differential cross section of d σ b b ¯ → μ ± μ ± / d y = 0.16 ± 0.01 ( stat ) ± 0.02 ( syst ) ± 0.02 ( global ) nb for like-sign muons in the rapidity and p T ranges 1.2 < | y | < 2.2 and p T > 1 GeV / c , and dimuon mass of 5 – 10 GeV / c 2 . The extrapolated total cross section at this energy for b b ¯ production is 13.1 ± 0.6 ( stat ) ± 1.5 ( syst ) ± 2.7 ( global ) μ b . The total cross section is compared to a perturbative quantum chromodynamics calculation and is consistent within uncertainties. The azimuthal opening angle between muon pairs from b b ¯ decays and their p T distributions are compared to distributions generated using ps pythia 6, which includes next-to-leading order processes. The azimuthal correlations and pair p T distribution are not very well described by pythia calculations, but are still consistent within uncertainties. Flavor creation and flavor excitation subprocesses are favored over gluon splitting.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Full-length Quench Antenna for MQXFA Production Series Quadrupole Magnet Testing

The MQXFA production series quadrupoles being built for the Hi-Lumi (HL) LHC upgrade by the US Accelerator Upgrade Project (US-HL-LHC AUP) will have very limited instrumentation for characterizing quench events that occur during magnet training and performance validation testing. In order to understand the origin of the quenches, and whether they have some implication for ongoing magnet fabrication, it was decided to build a full-length Quench Antenna (QA) with axial resolution of 50mm to be employed during cold testing in the anticryostat used for magnetic measurements. The goal is to have fineresolution, full-length coverage detection of quench events axially, as well as to have azimuthal resolution on the order of the cable width (about 1 degree for the cross-section), in a device that can be used both for vertical and horizontal testing. To achieve this, a 5m long QA with 128 channels of high-speed data acquisition has been designed and fabricated. The cylindrical antenna features an array of 12 full-length, dipole- and quadrupole-bucked coils positioned radially in the QA interior for azimuthal localization, and over 100 individual channels of short, high-sensitivity, antennas etched as flexible PCB circuits (which also buck dipole and quadrupole fields) wrapped circumferentially on the cylinder exterior in steps of 50mm along the magnet length for axial detection. This report discusses the design, construction and analysis of the MQXFA QA, and first results from using the antenna during quench testing in the production magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CROCUS Urban Canyons - Space Science and Engineering Center (SPARC) Doppler lidar data

This is the netCDF format output from the Halo Photonics Streamline XR Doppler lidar that was deployed next to the Space Science and Engineering Center (SPARC) trailer at the University of Illnois-Chicago greenhouse parking lot during CROCUS Urban Canyons. The purpose of collecting this dataset is to provide vertical and horizontal wind profiles for studying the characteristics of turbulence over the urban canyon of Chicago. This data contains the radial velocity, intensity, and backscatter from the vertical profile, range height indicator, and sector scans that were performed over both Intensive Operating Period 1 and 2 of CROCUS Urban Canyons. There are four different types of files: * The Range Height Indicator (RHI) files contain scans that are along a constant azimuth, spanning the entire hemisphere of elevation values above the surface. * The Velocity Azimuth Display (VAD) files contain the raw radial velocity data from the 6-beam, 60 degree scans. * The User1 files contain stacked Plan Position Indicator scans over a 45 degree quadrant over downtown Chicago. * The Stare files contain vertically pointing scans. These are standard netCDF files that can be opened using xarray. The VAD scans can be processed from their raw radial velocities to horizontal wind speeds with the Atmospheric data Community Toolkit (https://arm-doe.github.io/ACT/).

EARTH SCIENCE > ATMOSPHERE > ATMOSPHERIC WINDS↗

Inclusive prompt photon-jet correlations as a probe of gluon saturation in electron-nucleus scattering at small x

We compute the differential cross-section for inclusive prompt photon+quark production in deeply inelastic scattering of electrons off nuclei at small x (e + A DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling α s ) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale Q s,A (x). We perform a numerical study of this process for the kinematics of the Electron-Ion Collider (EIC), exploring in particular the azimuthal angle correlations between the final state photon and quark. We observe a systematic suppression and broadening pattern of the back-to-back peak in the relative azimuthal angle distribution, as the saturation scale is increased by replacing proton targets with gold nuclei. Our results suggest that photon+jet final states in inclusive e + A DIS at high energies are in general a promising channel for exploring gluon saturation that is complementary to inclusive and diffractive dijet production. They also provide a sensitive empirical test of the universality of dipole matrix elements when compared to identical measurements in proton-nucleus collisions. However because photon+jet correlations at small x in EIC kinematics require jet reconstruction at small k ⊥ , it will be important to study their feasibility relative to photon-hadron correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC

Measurements of charged-particle production in pp, p–Pb, and Pb–Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum $(p^{trig}_T)$ in the range 8 < $p^{trig}_T$< 15 GeV/c. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, $R_T = N^T_{ch}/\langle N^T_{ch}\rangle$, is used to group events according to their UE activity, where $N^T_{ch}$ is the charged-particle multiplicity per event in the transverse region and $\langle N^T_{ch}\rangle$ is the mean value over the whole analysed sample. The energy dependence of the R T distributions in pp collisions at $\sqrt{s_{NN}}$ = 2.76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle p T spectra as a function of R T in the three azimuthal regions in pp, p–Pb, and Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p–Pb).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probing the top Yukawa coupling at the LHC via associated production of single top and Higgs

We study Higgs boson production associated with single top or anti-top via t-channel weak boson exchange at the LHC. The process is an ideal probe of the top quark Yukawa coupling, because we can measure the relative phase of htt and hWW couplings, thanks to the significant interference between the two amplitudes. By choosing the emitted W momentum along the polar axis in the th ($\bar{t}h$) rest frame, we obtain the helicity amplitudes for all the contributing subprocesses analytically, with possible CP phase of the Yukawa coupling. We study the azimuthal asymmetry between the W emission and the Wb ($\bar{b}$) → t($\bar{t}$) h scattering planes, as well as several t and $\bar{t}$ polarization asymmetries as a signal of CP violating phase in the htt coupling. Both the azimuthal asymmetry and the polarization perpendicular to the scattering plane are found to have the opposite sign between the top and anti-top events. We identify the origin of the sign of asymmetries, and propose the possibility of direct CP violation test in pp collisions by comparing the top and anti-top polarization at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Investigating strangeness enhancement with multiplicity in pp collisions using angular correlations

A study of strange hadron production associated with hard scattering processes and with the underlying event is conducted to investigate the origin of the enhanced production of strange hadrons in small collision systems characterised by large charged-particle multiplicities. For this purpose, the production of the single-strange meson ${\textrm{K}}_{\textrm{S}}^0$ and the double-strange baryon Ξ ± is measured, in each event, in the azimuthal direction of the highest-p T particle (“trigger” particle), related to hard scattering processes, and in the direction transverse to it in azimuth, associated with the underlying event, in pp collisions at $\sqrt{s}$ = 5.02 TeV and $\sqrt{s}$ = 13 TeV using the ALICE detector at the LHC. The per-trigger yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± are dominated by the transverse-to-leading production (i.e., in the direction transverse to the trigger particle), whose contribution relative to the toward-leading production is observed to increase with the event charged-particle multiplicity. The transverse-to-leading and the toward-leading Ξ ± /${\textrm{K}}_{\textrm{S}}^0$ yield ratios increase with the multiplicity of charged particles, suggesting that strangeness enhancement with multiplicity is associated with both hard scattering processes and the underlying event. The relative production of Ξ ± with respect to ${\textrm{K}}_{\textrm{S}}^0$ is higher in transverse-to-leading processes over the whole multiplicity interval covered by the measurement. The ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± per-trigger yields and yield ratios are compared with predictions of three different phenomenological models, namely Pythia8.2 with the Monash tune, Pythia8.2 with ropes and EPOS LHC. The comparison shows that none of them can quantitatively describe either the transverse-to-leading or the toward-leading yields of ${\textrm{K}}_{\textrm{S}}^0$ and Ξ ± .

hadron-hadron scattering↗

Comparison of improved TMD and CGC frameworks in forward quark dijet production

For studying small- x gluon saturation in forward dijet production in high-energy dilute-dense collisions, the improved TMD (ITMD) factorization formula was recently proposed. In the Color Glass Condensate (CGC) framework, it represents the leading term of an expansion in inverse powers of the hard scale. It contains the leading-twist TMD factorization formula relevant for small gluon’s transverse momentum k t , but also incorporates an all-order resummation of kinematical twists, resulting in a proper matching to high-energy factorization at large k t . In this paper, we evaluate the accuracy of the ITMD formula quantitatively, for the case of quark dijet production in high-energy proton-proton( p + p ) and proton-nucleus ( p + A ) collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal angle Δ ϕ distribution to that obtained with the CGC formula. For a dijet with each quark momentum p t much larger than the target saturation scale, Q s , the ITMD formula is a good approximation to the CGC formula in a wide range of azimuthal angle. It becomes less accurate as the jet p t ’s are lowered, as expected, due to the presence of genuine higher-twists contributions in the CGC framework, which represent multi-body scattering effects absent in the ITMD formula. We find that, as the hard jet momenta are lowered, the accuracy of ITMD start by deteriorating at small angles, in the high-energy-factorization regime, while in the TMD regime near Δ ϕ = π , very low values of p t are needed to see differences between the CGC and the ITMD formula. In addition, the genuine twists corrections to ITMD become visible for higher values of p t in p + A collisions, compared to p + p collisions, signaling that they are enhanced by the target saturation scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

GPU-accelerated kinetic Hall thruster simulations in WarpX

Abstract Two-dimensional (axial-azimuthal) simulations of a Hall thruster are performed using the open-source particle-in-cell code WarpX. The simulation conditions are chosen to match those of the axial-azimuthal benchmark first reported by Charoy et al. in 2019. A range of numerical and solver parameters is investigated in order to find those which yield the best performance. It is found that WarpX completes the benchmark case in 3.8 days on an Nvidia V100 GPU, and in as low as 1.5 days on a more recent Nvidia H100 GPU. Of the numerical parameters investigated, it is determined that the field-solve tolerance and particle resampling thresholds have the largest effect on the simulation wall time and that particle resampling may artificially widen electron velocity distribution functions, leading to unphysical heating. A semi-implicit scheme for the electrostatic field solve is tested and is found to produce results consistent to within 10% of the benchmark in less than twelve hours. The scaling properties of the electrostatic solver to multiple GPUs are also assessed on a uniform plasma test problem. The results of this work are discussed in the context of advancements in GPU hardware and the suitability of kinetic Hall thruster simulations for engineering applications.

Marks, Thomas A.↗