Search NASA⌕ Search

SEARCH · Search NASA

Results for “dynamic profiling”

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 415 records · Page 23

First Results of the LHC Longitudinal Density Monitor

The Large Hadron Collider (LHC) at CERN is the world's largest particle accelerator. It is designed to accelerate and collide protons or heavy ions up to the center-of-mass energies of 14 TeV. Knowledge of the longitudinal distribution of particles is important for various aspects of accelerator operation, in particular to check the injection quality and to measure the proportion of charge outside the nominally filled bunches during the physics periods. In order to study this so-called ghost charge at levels very much smaller than the main bunches, a longitudinal profile measurement with a very high dynamic range is needed. A new detector, the LHC Longitudinal Density Monitor (LDM) is a single-photon counting system measuring synchrotron light by means of an avalanche photodiode detector. The unprecedented energies reached in the LHC allow synchrotron light diagnostics to be used with both protons and heavy ions. A prototype was installed during the 2010 LHC run and was able to longitudinally profile the whole ring with a resolution close to the target of 50 ps. On-line correction for the effects of the detector deadtime, pile-up and afterpulsing allow a dynamic range of 105 to be achieved. First measurements with the LDM are presented here along with an analysis of its performance and an outlook for future upgrades.

43 PARTICLE ACCELERATORS↗

Estimating Beam-Target Heating

At Los Alamos National Laboratory, two high-current linear induction accelerators (LIAs) are used to produce bremsstrahlung source spots for flash radiography of high-explosive driven hydrodynamic experiments at the Dual Axis Radiographic Hydrodynamic Test (DARHT) facility. Measurements of the electron-beam current density profile are valuable for understanding the beam dynamics in order to improve the quality of the radiography source spot. A technique commonly used at DARHT is to image the profile in Cerenkov or Optical Transition Radiation (OTR) light created by the beam striking a thin target inserted into the beam line. Target materials include aluminized dielectrics and titanium foils for OTR, and fused silica wafers for Cerenkov radiation. A practical complication with this technique is heating of the target by the electron beam. If the beam density is too great, the target can be destroyed. Moreover, even if the beam density is kept low enough to be nondestructive, the beam can heat the target to a high enough temperature to desorb gas from the surface. In that case, direct impact ionization of the gas by beam electrons can partially neutralize the beam, causing it to over-focus, thereby spoiling the data, if not destroying the target. The purpose of this note is to review some of the fundamental physics of electron beam heating in order to provide some elementary guidance for design of these imaging experiments to avoid overheating the target. Some specific examples for materials that we often use for imaging targets and beam-target experiments are provided.

43 PARTICLE ACCELERATORS↗

STARLESS CLOUD CORE L1517B IN ENVELOPE EXPANSION WITH CORE COLLAPSE

Various spectral emission lines from the star-forming molecular cloud core L1517B manifest red asymmetric double-peaked profiles with stronger red peaks and weaker blue peaks, in contrast to the oft-observed blue-skewed molecular spectral line profiles with blue peaks stronger than red peaks. Invoking a spherically symmetric general polytropic hydrodynamic shock model for the envelope expansion with a core collapse (EECC) phase, we show the radial flow velocity, mass density, and temperature structures of a self-similar evolution for L1517B in a dynamically consistent manner. By prescribing simple radial profiles of abundance distribution for pertinent molecules, we perform molecular excitation and radiative transfer calculations using the publicly available RATRAN code set for the spherically symmetric case. Emphatically, the spectral profiles of line emissions from the same molecules but for different line transitions as well as spectra of closely pertinent isotopologues strongly constrain the self-similar hydrodynamics of a cloud core with prescribed abundances. Our computational results show that the EECC model reproduces molecular spectral line profiles in sensible agreement with the observational data of the Institut de Radioastronomie Millimetrique (IRAM), Five College Radio Astronomical Observatory, and Effelsberg 100 m telescopes for L1517B. We also report the spatially resolved observations of the optically thick line HCO{sup +}(1 - 0) using the Purple Mountain Observatory 13.7 m telescope at Delingha in China and the relevant fitting results. Hyperfine line structures of NH{sub 3} and N{sub 2}H{sup +} transitions are also fitted to consistently reveal the dynamics of the central core collapse. As a consistent model check, radial profiles of 1.2 mm and 850 {mu}m dust continua observed by the IRAM 30 m telescope and the Submillimeter Common-User Bolometer Array, respectively, are also fitted numerically using the same EECC model that produces the molecular line profiles. L1517B is likely undergoing an EECC shock phase. For future observational tests, we also predict several molecular line profiles with spatial distributions, the radial profile of the sub-millimeter continuum at wavelength 450 {mu}m, as well as the radial profiles of the column density and visual extinction for L1517B.

79 ASTRONOMY AND ASTROPHYSICS↗

Decadal carbon decomposition dynamics in three peatlands in Northern Minnesota

The uppermost portion of the peat profile, an area of active diagenetic processes, is exceedingly important for understanding peatland dynamics and the diagenesis and geochemistry of atmospherically-deposited materials. In this study, we investigated high resolution carbon (C) accrual and peat decomposition rates at two Sphagnum-rich ombrotrophic bogs and one fen in northern Minnesota, USA by analyzing 1 cm increments from 30 cm thick intact frozen blocks of peat soil. We conducted radiocarbon analysis of Sphagnum cellulose to determine peat age and net C accumulation at each depth interval. Calibrated peat ages were determined using CALIBomb and a compilation of calibration datasets for the pre-bomb period. We fit data with a negative exponential accumulation model and used model-derived parameters to estimate net primary productivity (NPP) and a peat decomposition rate constant k. FTIR spectroscopy and C:N were used to derive humification indices and to chemically characterize the peat. NPP ranged from 180 to 266 g C m -2 year -1 , k ranged from 0.015 to 0.019 year -1 . Net C accumulation rates ranged from 112 to 174 g C m -2 year -1 at 25 years and 70 to 113 g C m -2 year-1 at 50 years. Mass loss was up to 55% during the first 50 years of peat accumulation. Decomposition is greater at depth in the bogs—where 25 cm of peat correspond to 55 years of peat accumulation—than in the fen, where peat age is approximately 25 years at 25 cm depth. Lastly, information on fine-scale variations in peat mass decomposition and loss across ombrotrophic bogs and a fen help interpret other diagenetic processes in peatlands.

54 ENVIRONMENTAL SCIENCES↗

Open-source MFIX-DEM software for gas-solids flows: Part II — Validation studies

With rapid advancements in computer hardware and numerical algorithms, computational fluid dynamics (CFD) has been increasingly employed as a useful tool for investigating the complex hydrodynamics inherent in multiphase flows. An important step during the development of a CFD model and prior to its application is conducting careful and comprehensive verification and validation studies. Accordingly, efforts to verify and validate the open-source MFIX-DEM software, which can be used for simulating the gas–solids flow using an Eulerian reference frame for the continuum fluid and a Lagrangian discrete framework (Discrete Element Method) for the particles, have been made at the National Energy Technology Laboratory (NETL). In part I of this paper, extensive verification studies were presented and in this part, detailed validation studies of MFIX-DEM are presented. A series of test cases covering a range of gas–solids flow applications were conducted. In particular the numerical results for the random packing of a binary particle mixture, the repose angle of a sandpile formed during a side charge process, velocity, granular temperature, and voidage profiles from a bounded granular shear flow, lateral voidage and velocity profiles from a monodisperse bubbling fluidized bed, lateral velocity profiles from a spouted bed, and the dynamics of segregation of a binary mixture in a bubbling bed were compared with available experimental data, and in some instances with empirical correlations. In addition, sensitivity studies were conducted for various parameters to quantify the error in the numerical simulation.

42 ENGINEERING↗

Mixing and the dynamics of the deep chlorophyll maximum in Lake Tahoe

Chlorophyll-temperature profiles were measured across Lake Tahoe about every 10 days from April through July 1980. Analysis of the 123 profiles and associated productivity and nutrient data identified three important processes in the formation and dynamics of the deep chlorophyll maximum (DCM): turbulent diffusion, nutrient supply rate, and light availability. Seasonal variation in these three processes resulted in three regimes: a diffusion-dominated regime with a weak DCM, a variable-mixing regime with a pronounced, nutrient supply-dominated DCM, and a stable regime with a deep, moderate light availability-dominated DCM. The transition between the first two regimes occurred in about 10 days, the transition between the last two more gradually over about 3 weeks. The degree of spatial variability of the DCM was highest in the second regime and lowest in the third. These data indicate that the DCM in Lake Tahoe is constant in neither time nor space.

Abbott, M. R.↗

Progressing Analysis of Variable Electric Rates (PAVER) Study

The Progressing Analysis of Variable Electric Rates (PAVER) study analyzed the impact of a range of time-varying electric rates on the performance of a regional electric grid and the resulting costs for participating and non-participating customers. This analysis leveraged and extended the work of PNNL’s Distribution System Operator with Transactive (DSO+T) study. Five different rate designs were included: a flat volumetric energy charge, a typical Time of Use (TOU) rate, a dynamic energy (DE) rate (based on wholesale locational marginal prices), a dynamic energy and capacity (DE+C) rate, and, finally, a Block and Swing (B&S) rate that billed customers based on their average load profile at constant pricing, but used the DE+C dynamic price for load deviations from their average profile. These rates were analyzed in a large-scale co-simulation of an entire regional grid with a customer population representative of the current state. A large fraction (80%) of residential and commercial customers were assumed to participate in these time-varying rates with automatically controlled HVAC, water heaters, electric vehicles, and batteries. This study assumed no industrial sector participation. The DE and DE+C rates saw system peak loads reduced by 6-7%, while the large participation in the TOU rate case saw a significant rebound effect and a resulting peak load increase of >5%. The impacts to the annual and peak system demand impacted system wholesale prices and the overall grid operating costs. This cost structure determined the revenue needed to be collected from customers by each rate design. Participating customers on the DE and DE+C rates (located in one of the modeled DSOs) saw reductions in average annual electricity bills of 11-17% with average increases in monthly bill variation of no more than 13%. At such high participation levels, TOU customers saw 10% higher average annual bills (due to system-wide rebound effects) and average increased monthly bill variation of 16%. Residential owners of large flexible loads (such as electric vehicles) saw larger bill savings (17-20%) when on a fully dynamic rate. The presence of on-site generation (such as rooftop solar) did not appear to appreciably change customer outcomes. Customers on the Block and Swing rate did see 6% lower monthly bill variation (as intended) than the flat rate case, but at the expense of appreciable bill savings, which were only 3%, comparable to the savings seen by non-participants. Given this finding we recommend that additional research be conducted into how best various bill protection mechanisms can balance minimizing customer bill variation with providing financial incentives commensurate with the flexibility customers provide. We also recommend that customer outcomes be explored across a range of regions using current actual customer and system cost data.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Hardware Platform for Studying Naval Power Electronic Power Distribution Systems

Abstract – Future intelligent ship system designs will likely include electric propulsion, numerous highpower sensors, and directed energy weapons. Supply and control of these large nonlinear loads will require a networked, multi-converter power electronic power distribution system. This work presents a hardware platform to emulate a microgrid power system with multiple power converters and a power data communication network. The platform is reconfigurable and can include both AC and DC power distribution zones, representative of shipboard power systems. It also allows for the study of both power control actuation and power data communication delays. Since the platform is based on electric power hardware, spatial and temporal uncertainties are inherently embedded in the system. Specifically, this work examines the control actuation of multiple pulsed power loads in a single microgrid. Several pulse load levels and operating scenarios have been implemented and measured. A framework for control parameter quantification is presented, and various metrics are explored to capture pulse signal characteristics. The sensitivity of pulse load metric parameters is analyzed. Dynamic shipboard, mission-specific load profiles coupled with pulse loads can also be emulated in the hardware platform.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Cross-beam energy transfer in direct-drive ICF. I. Nonlinear and kinetic effects

Results are presented from a series of simulations examining the susceptibility of the cross-beam energy transfer (CBET) instability to nonlinear processes in the context of direct-drive inertial confinement fusion experiments on the OMEGA laser facility. These form the basis for the second paper of this series [A. G. Seaton, L. Yin, R. Follett, B. J. Albright, and A. Le, “Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth,” Phys. Plasmas 29, 042707 (2022)], where we examine the efficacy of increases in laser bandwidth at suppressing CBET. We choose laser and plasma conditions for the simulations that are favorable to CBET and promote nonlinearity. Through a comparison of outputs from the particle-in-cell code vector particle in cell (VPIC) and the linearized fluid code laser-plasma simulation environment (LPSE), a series of nonlinear effects have been identified in the kinetic simulations that include particle trapping, the two-ion wave decay, and ion-acoustic wave self-focusing. These effects produce time-dependent energy transfer, in contrast to the linearized fluid simulations in which a steady state is reached after an initial transient. Ion trapping is shown to allow for increased energy transfer relative to fluid simulations, with the remaining nonlinear processes acting to reduce the energy transfer. Nonlinear dynamics is contrasted for low- and high-intensity beams as well as between speckled and planar beams. For the parameters under consideration, beam profile has a significant effect on nonlinear dynamics, though the greatest sensitivity is to beam intensity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Enhanced simulation software for rocket turbopump, turbulent, annular liquid seals

One of the main objectives of this work is to develop a new dynamic analysis for liquid annular seals with arbitrary profile and to analyze a general distorted interstage seal of the space shuttle main engine high pressure oxygen turbopump (SSME-ATD-HPOTP). The dynamic analysis developed is based on a method originally proposed by Nelson and Nguyen. A simpler scheme based on cubic splines is found to be computationally more efficient and has better convergence properties at higher eccentricities. The first order solution of the original analysis is modified by including a more exact solution that takes into account the variation of perturbed variables along the circumference. A new set of equations for dynamic analysis are derived based on this more general model. A unified solution procedure that is valid for both Moody's and Hirs' friction models is presented. Dynamic analysis is developed for three different models: constant properties, variable properties, and thermal effects with variable properties. Arbitrarily varying seal profiles in both axial and circumferential directions are considered. An example case of an elliptical seal with varying degrees of axial curvature is analyzed in detail. A case study based on predicted clearances of an interstage seal of the SSME-ATD-HPOTP is presented. Dynamic coefficients based on external specified load are introduced to analyze seals that support a preload. The other objective of this work is to study the effect of large rotor displacements of SSME-ATD-HPOTP on the dynamics of the annular seal and the resulting transient motion. One task is to identify the magnitude of motion of the rotor about the centered position and establish limits of effectiveness of using current linear models. This task is accomplished by solving the bulk flow model seal governing equations directly for transient seal forces for any given type of motion, including motion with large eccentricities. Based on the above study, an equivalence is established between linearized coefficients based transient motion and the same motion as predicted by the original governing equations. An innovative method is developed to model nonlinearities in an annular seal based on dynamic coefficients computed at various static eccentricities. This method is thoroughly tested for various types of transient motion using bulk flow model results as a benchmark.

Padavala, Satya↗

A multichannel, real-time MRI RF power monitor for independent SAR determination

Purpose: Accurate measurements of the RF power delivered during clinical MRI are essential for safety and regulatory compliance, avoiding inappropriate restrictions on clinical MRI sequences, and for testing the MRI safety of peripheral and interventional devices at known RF exposure levels. The goal is to make independent RF power measurements to test the accuracy of scanner-reported specific absorption rate (SAR) over the extraordinary range of operating conditions routinely encountered in MRI. Methods: A six channel, high dynamic range, real-time power profiling system was designed and built for monitoring power delivery during MRI up to 440 MHz. The system was calibrated and used in two 3 T scanners to measure power applied to human subjects during MRI scans. The results were compared with the scanner-reported SAR. Results: The new power measurement system has highly linear performance over a 90 dB dynamic range and a wide range of MRI duty cycles. It has about 0.1 dB insertion loss that does not interfere with scanner operation. The measurements of whole-body SAR in volunteers showed that scanner-reported SAR was significantly overestimated by up to about 2.2 fold. Conclusions: The new power monitor system can accurately and independently measure RF power deposition over the wide range of conditions routinely encountered during MRI. Scanner-reported SAR values are not appropriate for setting exposure limits during device or pulse sequence testing.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A Dynamic Pricing Method to Manage the Impact of EV Charging on the Grid Using RL

This work addresses the challenge of managing electrical vehicle (EV) charging loads on distribution feeders with the increase in deployment of fast charging stations. To mitigate the adverse impacts on feeder health, a novel dynamic grid-informed pricing approach is proposed. This approach leverages reinforcement learning (RL) to determine hourly charging prices based on real-time grid conditions. A synthetic environment was developed to train the reinforcement learning agent. A model of an IEEE 34-bus distribution feeder with EV charging stations has been developed in OpenDSS utilizing Caldera for realistic EV charging profiles. Test cases demonstrate that the dynamic pricing strategy achieves higher energy delivery to the EV end user at a lower cost compared to constant pricing methods, while lowering voltage deviations and congestion. This approach offers more granular price adjustments, responding dynamically to feeder conditions and potentially improving grid stability and efficiency. The communication architecture to implement this dynamic pricing method is described. This research contributes to the development of smart grid-informed charging solutions that can reduce the cost of charging to the end user while also helping the grid.

EV charging, dynamic pricing, grid-informed chargi↗

A dynamic pricing method to manage the impact of EV charging on the grid using RL

This work addresses the challenge of managing electrical vehicle (EV) charging loads on distribution feeders with the increase in deployment of fast charging stations. To mitigate the adverse impacts on feeder health, a novel dynamic grid-informed pricing approach is proposed. This approach leverages reinforcement learning (RL) to determine hourly charging prices based on real-time grid conditions. A synthetic environment was developed to train the reinforcement learning agent. A model of an IEEE 34-bus distribution feeder with EV charging stations has been developed in OpenDSS utilizing Caldera for realistic EV charging profiles. Test cases demonstrate that the dynamic pricing strategy achieves higher energy delivery to the EV end user at a lower cost compared to constant pricing methods, while lowering voltage deviations and congestion. This approach offers more granular price adjustments, responding dynamically to feeder conditions and potentially improving grid stability and efficiency. The communication architecture to implement this dynamic pricing method is described. This research contributes to the development of smart grid-informed charging solutions that can reduce the cost of charging to the end user while also helping the grid.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

STRUCTURAL PARAMETERS FOR GLOBULAR CLUSTERS IN M31

In this paper, we present surface brightness profiles for 79 globular clusters in M31, using images observed with the Hubble Space Telescope, some of which are from new observations. The structural and dynamical parameters are derived from fitting the profiles to several different models for the first time. The results show that in the majority of cases, King models fit the M31 clusters just as well as Wilson models and better than Sersic models. However, there are 11 clusters best fitted by Sersic models with the Sersic index n > 2, meaning that they have cuspy central density profiles. These clusters may be the well-known core-collapsed candidates. There is a bimodality in the size distribution of M31 clusters at large radii, which is different from their Galactic counterparts. In general, the properties of clusters in M31 and the Milky Way fall in the same regions of parameter spaces. The tight correlations of cluster properties indicate a ''fundamental plane'' for clusters, which reflects some universal physical conditions and processes operating at the epoch of cluster formation.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermodynamic versus Dynamic Controls on Extreme Precipitation in a Warming Climate from the Community Earth System Model Large Ensemble

The moisture budget is evaluated as a function of the probability distribution of precipitation for the end of the twentieth century and projected end of the twenty-first century in the Community Earth System Model Large Ensemble. For a given precipitation percentile, a conditional moisture budget equation relates precipitation minus evaporation ( P − E) to vertical moisture transport, horizontal moisture advection, and moisture storage. At high percentiles, moisture advection and moisture storage cancel and evaporation is negligible, so that precipitation is approximately equal to vertical moisture transport, and likewise for projected changes. Therefore, projected changes to extreme precipitation are approximately equal to the sum of thermodynamic and dynamic tendencies, representing changes to the vertical profiles of moisture content and mass convergence, respectively. The thermodynamic tendency is uniform across percentiles and regions as an intensification of the hydrological cycle, but the dynamic tendency is more complex. For extreme events, per degree of warming, in the mid-to-high latitudes the dynamic tendency is small, so that precipitation approximately scales by the Clausius–Clapeyron 7% K −1 increase. In the subtropics, a drying tendency originating from dynamics offsets the thermodynamic wetting tendency, with the net effect on precipitation varying among regions. The effect of this dynamic drying decreases with increasing percentile. In the deep tropics, a positive dynamic tendency occurs with magnitude similar to or greater than the positive thermodynamic tendency, resulting in generally a 10%–15% K −1 precipitation increase, and with a >25% K −1 increase over the tropical east Pacific. This reinforcing dynamical tendency increases rapidly for high percentiles.

54 ENVIRONMENTAL SCIENCES↗

The Propulsive Small Expendable Deployer System (ProSEDS)

This Final Report covers the following main topics: 1) Brief Description of ProSEDS; 2) Mission Analysis; 3) Dynamics Reference Mission; 4) Dynamics Stability; 5) Deployment Control; 6) Updated System Performance; 7) Updated Mission Analysis; 8) Updated Dynamics Reference Mission; 9) Updated Deployment Control Profiles and Simulations; 10) Updated Reference Mission; 11) Evaluation of Power Delivered by the Tether; 12) Deployment Control Profile Ref. #78 and Simulations; 13) Kalman Filters for Mission Estimation; 14) Analysis/Estimation of Deployment Flight Data; 15) Comparison of ED Tethers and Electrical Thrusters; 16) Dynamics Analysis for Mission Starting at a Lower Altitude; 17) Deployment Performance at a Lower Altitude; 18) Satellite Orbit after a Tether Cut; 19) Deployment with Shorter Dyneema Tether Length; 20) Interactive Software for ED Tethers.

Lorenzini, Enrico C.↗

Flow field characteristics of a 127-pin rod bundle with hexagonal spacer grids

A determination of nominal flow phenomena in liquid metal fast reactor (LMFR) fuel assemblies is critical toward generation-IV reactor development. Axially positioned spacer grids are used to maintain the geometry of hexagonal rod bundles and simultaneously introduce perturbations in the flow. Three-dimensional (3D) printed asymmetric honeycomb spacer grids were installed in a prototypical 127-pin LMFR fuel assembly model to study complex fluid dynamics interactions induced by the spacer grid and rods. To characterize flow dynamics in this intricate geometry, time-resolved particle image velocimetry (TR-PIV) using the matched-index-of-refraction method was employed to obtain non-intrusive velocity measurements for three axial planes (one near-wall and two interior planes) at a Reynolds number of 6000. The statistical TR-PIV results compared sub-channel-dependent normalized time-averaged velocity, velocity fluctuations, Reynolds stress, vorticity, and turbulence kinetic energy distributions. TR-PIV line profiles characterized downstream spacer grid flow dynamics. Two-point spatial and spatial–temporal cross-correlation fields revealed local coherent structures and quantified convection velocities of traveling vortices. Spatial–temporal decomposition using dynamic mode decomposition (DMD) applied to the near-wall vorticity fields extracted turbulent structures and flow instabilities in the wake region of the spacer grid, along with their decay and frequency rates. Reduced-order velocity fields from DMD reconstructions identified the most energy-containing coherent structures persistent in the near-wall region. This research provides experimental data sets and analyses of flow behavior in rod bundles with hexagonal spacer grids. In conclusion, the results are critical toward LMFR design and geometry optimization, crucial for the validation of computational fluid dynamics and reduced-order flow models.

42 ENGINEERING↗

Mathematical modeling of a moving bed reactor for post-combustion CO 2 capture

A mathematical model for a moving bed reactor with embedded heat exchanger has been developed for application to solid sorbent-based capture of carbon dioxide from flue gas emitted by coal-fired power plants. The reactor model is one-dimensional, non-isothermal, and pressure-driven. The two-phase (gas and solids) model includes rigorous kinetics and heat and mass transfer between the two phases. Flow characteristics of the gas and solids in the moving bed are obtained by analogy with correlations for fixed and fluidized bed systems. From the steady-state perspective, this work presents the impact of key design variables that can be used for optimization. From the dynamic perspective, the article shows transient profiles of key outputs that should be taken into account while designing an effective control system. Additionally, the article also presents performance of a model predictive controller for the moving bed regenerator under process constraints.

42 ENGINEERING↗