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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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Improved Gamma-Ray Point Source Quantification in Three Dimensions by Modeling Attenuation in the Scene

We discuss using a series of detector measurements taken at different locations to localize a source of radiation as a well-studied problem. The source of radiation is sometimes constrained to a single point-like source, in which case the location of the point source can be found using techniques such as maximum likelihood. Recent advancements have shown the ability to locate point sources in 2D and even 3D, but few have studied the effect of intervening material on the problem. In this work we examine gamma-ray data taken from a freely moving system and develop voxelized 3-D models of the scene using data from the onboard LiDAR. Ray casting is used to compute the distance each gamma ray travels through the scene material, which is then used to calculate attenuation assuming a single attenuation coefficient for solids within the geometry. Parameter estimation using maximum likelihood is performed to simultaneously find the attenuation coefficient, source activity, and source position that best match the data. Using a simulation, we validate the ability of this method to reconstruct the true location and activity of a source, along with the true attenuation coefficient of the structure it is inside, and then we apply the method to measured data with sources and find good agreement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Dataset of Simulated Intracardiac Transmembrane Voltage Recordings and ECG Signals

The dataset consists of pairs of computationally simulated intracardiac transmembrane voltage recordings and ECG signals. In total, 16140 organ-level simulations were conducted to create this dataset, using a range of cardiac geometries and physiological parameters. Simulations were performed at LLNL's Lassen supercomputer, concurrently utilizing 4 GPUs and 40 CPU cores. Each simulation produced pairs of 500ms-by-10 ECG signals and 500ms-by-75 transmembrane voltage signals. For convenience, the signals are concatenated and saved as matrices. Each of these matrices is then stored as a numpy array. See the documentation for further details.

Landajuela, Mikel↗
DOE OSTI2021

Thermal Effects on Far-Field Distributed Acoustic Strain-Rate Sensors

Summary Fiber-optic cables cemented outside of the casing of an unconventional well measure crosswell strain changes during fracturing of neighboring wells with low-frequency distributed acoustic sensing (LF-DAS). As a hydraulic fracture intersects an observation well instrumented with fiber-optic cables, the fracture fluid injected at ambient temperatures can cool a section of the sensing fiber. Often, LF-DAS and distributed temperature sensing (DTS) cables are run in tandem, enabling the detection of such cooling events. The increasing use of LF-DAS for characterizing unconventional hydraulic fracture completions demands an investigation of the effects of temperature on the measured strain response by LF-DAS. Researchers have demonstrated that LF-DAS can be used to extract the temporal derivative of temperature for use as a differential-temperature-gradient sensor. However, differential-temperature-gradient sensing is predicated on the ability to filter strain components out of the optical signal. In this work, beginning with an equation for optical phase shift of LF-DAS signals, a model relating strain, temperature, and optical phase shift is explicitly developed. The formula provides insights into the relative strength of strain and temperature effects on the phase shift. The uncertainty in the strain-rate measurements due to thermal effects is estimated. The relationship can also be used to quantify uncertainties in differential-temperature-gradient sensors due to strain perturbations. Additionally, a workflow is presented to simulate the LF-DAS response accounting for both strain and temperature effects. Hydraulic fracture geometries are generated with a 3D fracture simulator for a multistage unconventional completion. The fracture width distributions are imported by a displacement discontinuity method (DDM) program to compute the strain rates along an observation well. An analytic model is used to approximate the temperature in the fracture. Using the derived formulae for optical phase shift, the model outputs are then used to compute the LF-DAS response at a fiber-optic cable, enabling the generation of waterfall plots including both strain and thermal effects. The model results suggest that before, during, and immediately following a fracture intersecting a well instrumented with fiber, the strain on the fiber drives the LF-DAS signal. However, at later times, as completion fluid cools the observation well, the temperature component of the LF-DAS signal can be equal to or exceed the strain component. The modeled results are compared to a published field case in an attempt to enhance the interpretation of LF-DAS waterfall plots. Finally, we propose a sensing configuration to identify the events when “wet fractures” (fractures with fluids) intersect the observation well.

Engineering↗
DOE OSTI2020

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the polynomial order used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Effective Permeability of a Nuclear Fuel Assembly

This report aids in the development of models to perform characterization studies of aerosol dispersal and deposition within a spent fuel cask system. Due to the complex geometry in a spent-fuel canister, direct simulation of buoyancy-driven flow through the fuel assemblies to model aerosol deposition within the fuel canister is computationally expensive. Identification of an effective permeability as given in this work for a nuclear fuel assembly greatly simplifies the requirements for thermal hydraulic computations. The results of computations performed using OpenFOAM® to solve the Navier-Stokes Equations for laminar flow are used to determine an effective permeability by applying Darcy's Law. The computations are validated against an analytical solution for the special case of an infinite array of pins for which the numerical and analytical solutions have excellent agreement. The effective permeability of a 1717 PWR nuclear fuel assembly in a basket without spacer grids is numerically determined to be 1.85010 -6 m 2 for the range of fluid viscosities and pressure drops expected in a spent fuel storage canister. However, the flow is not uniform on the scale of multiple pins. Instead, significantly higher velocities are attained in the space between the assembly and the basket walls compared to the flow between the fuel pins within the assembly. Comparison with an analytical solution for fully developed flow through an infinite array of pins shows that the larger spacing near the basket walls results in about a 20% larger permeability compared to the analytical solution which does not include the enhanced flow in the space between the assembly and basket wall, or entrance and exit effects. A preliminary assessment of turbulence effects shows that with a k-epsilon model, significantly higher flow velocities are attained between the fuel pins within the assembly compared to the flow velocity in the space between the assembly and the basket walls. This is the opposite of what is determined for laminar flow.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Advanced Compact Generation Module with Fish Safe Runner Technology

Hydropower is an important contributor of stable, load-leveling renewable energy to our national grid. Increasingly, the development of new hydropower facilities or the retrofit of existing ones hinges not only on minimizing costs but also environmental impact. In this report, the analysis and testing of a modular and scalable low-head hydropower generation design using Natel Energy’s Restoration Hydro Turbine is described. This design leverages many established industry approaches for compactness and efficiency while simultaneously allowing for safe downstream fish passage through the turbines themselves. This unique approach reduces overall hydropower facility costs and enables a simpler inclusive method of project design and operation. To assess this design, mechanical and fluid computational analyses were used to study and optimize key parameters. Passage tests of important migratory species (salmonids, American eel) were conducted through representative turbines. The unique propeller geometry of the fish-safe Restoration Hydro Turbine was subjected to detailed design and testing using advanced manufacturing composite techniques. Comprehensive module cost models were developed and assessed alongside hydraulic efficiency. The results of this project show promising and economical applications for downstream passage offish through Restoration Hydro Turbine modules.

13 HYDRO ENERGY↗
DOE OSTI2025

Radiation GRMHD Models of Accretion onto Stellar-mass Black Holes. I. Survey of Eddington Ratios

We summarize results from a survey of radiation-dominated black hole accretion flows across a wide range of mass accretion rates, as well as two values of black hole spin and initial magnetic field geometry. These models apply an algorithm targeting direct solutions to the radiation transport equation in full general relativity and have been enabled by access to modern exascale computing systems. Super-Eddington accretion flows form geometrically thick radiation-pressure-supported disks that drive powerful equatorial outflows. A narrow funnel-shaped photosphere in the inner region results in very low radiative efficiencies in this regime. The structure of near- and sub-Eddington accretion depends on whether there is net vertical magnetic flux at the midplane of the disk. With net flux, the disk forms a thin, dense layer at the midplane surrounded by a magnetically dominated corona, whereas without net flux, the disk remains magnetically dominated everywhere. Although none of our models achieve the magnetically arrested disk regime, those with net vertical flux and a rapidly spinning black hole still produce powerful relativistic jets. Our calculations adopt simple opacity models (with scalings appropriate to stellar-mass black hole accretion). We discuss the application of our results to observations of X-ray binaries and ultraluminous X-ray sources such as Cyg X-3 and SS433. We also speculate on the application of our super-Eddington models to the interpretation of little red dots recently discovered by JWST.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Optimization of the deep neural network parameters for generating homogenized fuel assembly data for nodal codes

Homogenized fuel assembly (FA) data is a typical input data for nodal codes. Generating that data, however, could be time-consuming. One of promising ways to mitigate the computational burden of generating macroscopic cross-sections is to use trained artificial neural network (ANN) models for predicting nuclear data. However, there is a challenge to make the model support variable FA geometry. In this work, two most common types of FA were combined in one ANN model. Since there could be multiple ways of converting 2-dimensional FA data into 1-dimensional input vector for ANN, three different approaches of data flattening were evaluated. The input parameters included each fuel pin enrichment, fuel temperature, moderator temperature and boron concentration. The output parameters were 2-group macroscopic cross-sections (XS) and pin power distribution (HFF). A fully connected deep neural network (DNN) model was trained and tested using pre-generated data obtained with lattice physics code STREAM. The results of this study showed no statistically significant difference in the accuracy of XS and HFF generation for all 3 tested input vector orders. This means that fully connected DNN for XS generation demonstrated input sequence invariance. Results of comparing predicted XS data with reference solutions were found sufficiently close considering the reduction of computation time offered by ANN. Mean relative difference (MRD) for all output XS parameters was found below 0.7%, while HFF MRD was found higher compared to XS values, in some cases slightly exceeding 1%, mostly near guide tube locations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Design of a novel carbon/carbon composite microvascular solar receiver

Solar thermal power tower systems are the primary technology being proposed for solar electricity from thermal energy. Operational limits on these towers are often driven by mechanical properties under significant thermal loads, particularly at the receiver where incoming flux is converted to thermal energy. While the solar receiver’s efficiency is largely driven by its optical properties, thermomechanical stresses on the receiver limits the operational envelope. One pathway to higher efficiency is greater allowable solar fluxes on the receiver but novel materials are required. The present study uses computational fluid dynamics to describe a parametric design space for a microvascular carbon/carbon composite solar receiver as a new material option for high flux solar receivers. Simulations are conducted for different microvascular geometries considering the role of material properties and heat transfer fluids, for the impact on thermal efficiency, and allowable strain. Results show that microscale receiver modules made of the proposed carbon/carbon composite could achieve thermal efficiencies over 90% and full-scale receivers can achieve up to 85% thermal efficiency for the design explored considering realistic strain limits, flux levels, and material properties. These values are highly dependent on the heat transfer fluid pairing, the through plane thermal conductivity of the carbon/carbon composite, the path architecture of the microscale receiver, and the incident solar flux profiles.

14 SOLAR ENERGY↗
DOE OSTI2021

Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD [Sovinec et al., “Nonlinear magnetohydrodynamics with high-order finite elements,” J. Comput. Phys. 195, 355 (2004)] including a Chapman–Enskog-like (CEL) formulation and a more conventional df approach. Ion kinetic closure schemes are employed to describe the neoclassical flow properties in axisymmetric toroidal geometry. In particular, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided using both the df formulation and two different solution techniques for the CEL approach. These results are benchmarked against analytic theory predictions as well as results from the drift kinetic code DK4D. The continuum kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Computing virtual dark-field X-ray microscopy images of complex discrete dislocation structures from large-scale molecular dynamics simulations

Dark-field X-ray microscopy (DFXM) is a novel diffraction-based imaging technique that non-destructively maps the local deformation from crystalline defects in bulk materials. While studies have demonstrated that DFXM can spatially map 3D defect geometries, it is still challenging to interpret DFXM images of the high-dislocation-density systems relevant to macroscopic crystal plasticity. This work develops a scalable forward model to calculate virtual DFXM images for complex discrete dislocation structure(s) (DDS) obtained from atomistic simulations. Our new DDS-DFXM model integrates a non-singular formulation for calculating the local strain from the DDS and an efficient geometrical optics algorithm for computing the DFXM image from the strain field. We apply the model to complex DDS obtained from a large-scale mol­ecular dynamics simulation of compressive loading on single-crystal silicon. Simulated DFXM images exhibit prominent contrast for dislocation features between the multiple slip systems, demonstrating the potential of DFXM to resolve features from dislocation multiplication. In conclusion, the integrated DDS-DFXM model provides a toolbox for DFXM experimental design and image interpretation in the context of bulk crystal plasticity for a range of measurements across shock plasticity and the broader materials science community.

X-ray imaging↗
DOE OSTI2025

Window convolution of the galaxy clustering bispectrum

In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin 0.4 ≤ z ≤ 0.6. We first perform convergence checks on the measurement of the window function from discrete random catalogues, and then investigate the convergence of the window convolution series expansion truncated at a finite of number of terms as well as the performance of the window matrix. This work highlights the differences in window convolution between the power spectrum and bispectrum, and provides a streamlined pipeline for the latter for current surveys such as DESI and the Euclid mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Emulation of radiation transport in 3D stochastic media using 1D planar Monte Carlo stochastic media radiation transport algorithms

A subset of stochastic media radiation transport problems involves those in which radiation is incident on a thin slab of stochastic material. Particle tracking in 3D for such problems is expensive, and 1D planar models lack accuracy because they only allow the material to change in one dimension. Therefore, we propose dimensional emulation, which through a slight modification allows existing 1D planar geometry stochastic media radiation transport models to reproduce results from the equivalent 3D models by allowing the material to change in all three dimensions, reproducing the fidelity of the 3D model for the low computational cost of the 1D planar model. In this work, we apply dimensional emulation to three Monte Carlo stochastic media radiation transport models: Chord Length Sampling (CLS), the Local Realization Preserving method (LRP), and a variant of Conditional Point Sampling (CoPS). For a common Markovian benchmark set, the 3D emulation variants of these algorithms are numerically verified to reproduce the results of the 3D variants within statistics while running 1.3 to 2 times faster in the implementation within Sandia National Laboratories open-source research code PlaybookMC. The 3D emulation variants are also shown to yield a 72%–92% reduction in error for the thin slab problems in comparison to the 1D benchmark. As a result, the 3D emulation variant of CLS and CoPS-1 are shown to reproduce 3D CLS results that were used to approximate results for a 3D spherical inclusion geometry benchmark set.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A multi-dimensional parametric study of variability in multi-phase flow dynamics during geologic CO 2 sequestration accelerated with machine learning

Successful geologic CO 2 storage projects depend on numerical simulations to predict reservoir performance during site selection, injection verification, and post-injection monitoring phases of the project. These numerical simulations solve non-linear sets of coupled partial differential equations, while accounting for multi-phase fluid dynamics on the basis of constitutive equations that are embedded into the solution scheme. As a consequence, individual simulations often require tens to hundreds of hours to complete on high-performance computing clusters. Moreover, laboratory experiments reveal that parametric functions for capillary pressure and relative permeability exhibit substantial variability, even within the same rock type. This combination of computational expense and wide-ranging parametric variability means that there remains substantial uncertainty in the behavior of multi-phase CO 2 -water systems, particularly in the context of feedbacks between relative permeability and capillary pressure. To bridge this knowledge gap, here we develop a novel workflow that utilizes physics-based numerical simulation to train an artificial neural network (ANN) emulator for interrogating the multivariate parameter space that governs both capillary pressure and relative permeability. With this approach, the ANN is trained to emulate both fluid pressure distribution and CO 2 saturation, which are then interrogated quantitatively to generate parametric response surface mappings with high-fidelity resolution. Results from this study initially show that capillary entry pressure is the dominant control on both CO 2 plume geometry and fluid pressure propagation when considering the combined effects of capillary pressure and relative permeability, particularly when phase interference is low and residual CO 2 saturation is high. Moreover, the ANN emulator provides tremendous computational speed-up by computing 2691 individual simulations in several minutes; whereas, the same simulation ensemble would have required ~3 years of simulation time using only physics-based simulation methods (25,000 times speed up).

58 GEOSCIENCES↗
DOE OSTI2022

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

42 ENGINEERING↗
DOE OSTI2020

Interface capturing simulations of bubble population effects in PWR subchannels

As the computational power of high-performance computing (HPC) facilities grows, so too does the feasibility of using first principle based simulation to study turbulent two-phase flows within complex pressurized water reactor (PWR) geometries. Direct numerical simulation (DNS), integrated with an interface capturing method, allows for the collection of high-fidelity numerical data using advanced analysis techniques. The research presented here employs the massively parallel, finite-element based, unstructured mesh code, PHASTA, to simulate a set of two-phase bubbly flows through PWR subchannel geometries including auxiliary structures (spacer grids and mixing vanes). The main objective of the presented work is to analyze bubble dynamics and turbulence interactions at varying bubble concentrations to support the development of advanced two-phase flow closure models. Turbulent two-phase flows in PWR subchannels were simulated at hydraulic Reynolds numbers of 81,000 with bubble concentrations of 3%–15% by gas volume fraction (768–3928 resolved bubbles, respectively) and compared against a 1% void fraction case (262 bubbles) that had been previously simulated. The finite element mesh utilized for the study at higher bubble concentrations was composed of 1.55 billion elements, compared to the previous study which employed 1.11 billion elements, ensuring all turbulence scales and individual bubbles within the flow are fully resolved. For each case, the resolved initial bubble size was 0.65 mm in diameter (resolved with 25 grid points across the diameter). The simulations were analyzed to find flow features such as the mean velocity profile, bubble relative velocity and the effect of the bubbles on the turbulent conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

High fidelity multiphysics tightly coupled model for a lead cooled fast reactor concept and application to statistical calculation of hot channel factors

A tightly coupled multiphysics code system is established using the MOOSE framework for hot channel factor (HCF) evaluation on a Lead Fast Reactor (LFR) concept. The coupled system is driven by the Griffin multiphysics coupling capability under which the MOOSE Heat Transfer module and NekRS computational fluid dynamics solver are coupled for conjugate heat transfer using the Cardinal application. The coupled capability is demonstrated on an LFR assembly model based on materials and geometry of a prototypical lead-cooled fast reactor design by Westinghouse Electric Company, LLC. Moreover, the work integrates the Multiphysics Object Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM) to perform calculations for statistical analysis of HCF. Furthermore, the coupling strategy and workflow demonstrated in this paper is not only useful for predicting accurate hot channel factors for different kinds of advanced reactors but also for other engineering applications such as control rod worth assessment, generation of high-fidelity database for Artificial intelligence (AI)/machine learning (ML) training, design optimization and multi-resolution modeling.

Cardinal↗
DOE OSTI2024

Full Simulation of CMS for Run-3 and Phase-2

In this contribution we report the status of the CMS Geant4 simulation and the prospects for Run-3 and Phase-2. Firstly, we report about our experience during the start of Run-3 with Geant4 10.7.2, the common software package DD4hep for geometry description, and VecGeom runtime geometry library. In addition, FTFP_BERT_EMM Physics List and CMS configuration for tracking in magnetic field have been utilized. For the first time, for the Grid mass production of Monte-Carlo, this combination of components is used. Further simulation improvements are under development targeting Run-3 such as the switch to the new Geant4 11.1 in production, that provides several features important for the optimization of simulation, for example the new transportation process with built-in multiple scattering, neutron general process, custom tracking manager, G4HepEm sub-library, and others. We will present evaluation of various options, validation results, and the final choice of simulation configuration for 2023 production and beyond. The performance of the CMS full simulation for Run-2 and Run-3 will also be discussed. CMS development plan for the Phase-2 Geant4 based simulation is very ambitious, and it includes a new geometry description, physics, and simulation configurations. The progress on new detector descriptions and full simulation will be presented as well as the R&D in progress to reduce compute capacity needs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗