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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation

An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.

Park, Young-Keun↗
NASA NTRS1992

Mission and Safety Critical (MASC): An EVACS simulation with nested transactions

The Extra-Vehicular Activity Control System (EVACS) Simulation with Nested Transactions, a recent effort of the MISSION Kernel Team, is documented. The EVACS simulation is a simulation of some aspects of the Extra-Vehicular Activity Control System, in particular, just the selection of communication frequencies. The simulation is a tool to explore mission and safety critical (MASC) applications. For the purpose of this effort, its current definition is quite narrow serving only as a starting point for prototyping purposes. (Note that EVACS itself has been supplanted in a larger scenario of a lunar outpost with astronauts and a lunar rover). The frequency selection scenario was modified to embed its processing in nested transactions. Again as a first step, only two aspects of transaction support were implemented in this prototype: architecture and state recovery. Issues of concurrency and distribution are yet to be addressed.

Auty, David↗
NASA NTRS2010

Simulations of the Aerosol Index and the Absorption Aerosol Optical Depth and Comparisons with OMI Retrievals During ARCTAS-2008 Campaign

We have computed the Aerosol Index (AI) at 354 nm, useful for observing the presence of absorbing aerosols in the atmosphere, from aerosol simulations conducted with the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) module running online the GEOS-5 Atmospheric GCM. The model simulates five aerosol types: dust, sea salt, black carbon, organic carbon and sulfate aerosol and can be run in replay or data assimilation modes. In the assimilation mode, information's provided by the space-based MODIS and MISR sensors constrains the model aerosol state. Aerosol optical properties are then derived from the simulated mass concentration and the Al is determined at the OMI footprint using the radiative transfer code VLIDORT. In parallel, model derived Absorption Aerosol Optical Depth (AAOD) is compared with OMI retrievals. We have focused our study during ARCTAS (June - July 2008), a period with a good sampling of dust and biomass burning events. Our ultimate goal is to use OMI measurements as independent validation for our MODIS/MISR assimilation. Towards this goal we document the limitation of OMI aerosol absorption measurements on a global scale, in particular sensitivity to aerosol vertical profile and cloud contamination effects, deriving the appropriate averaging kernels. More specifically, model simulated (full) column integrated AAOD is compared with model derived Al, this way identifying those regions and conditions under which OMI cannot detect absorbing aerosols. Making use of ATrain cloud measurements from MODIS, C1oudSat and CALIPSO we also investigate the global impact on clouds on OMI derived Al, and the extent to which GEOS-5 clouds can offer a first order representation of these effects.

Source record↗
NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗
NASA NTRS1996

Simulation Software

Various NASA Small Business Innovation Research grants from Marshall Space Flight Center, Langley Research Center and Ames Research Center were used to develop the 'kernel' of COMCO's modeling and simulation software, the PHLEX finite element code. NASA needed it to model designs of flight vehicles; one of many customized commercial applications is UNISIM, a PHLEX-based code for analyzing underground flows in oil reservoirs for Texaco, Inc. COMCO's products simulate a computational mechanics problem, estimate the solution's error and produce the optimal hp-adapted mesh for the accuracy the user chooses. The system is also used as a research or training tool in universities and in mechanical design in industrial corporations.

Source record↗
NASA NTRS1992

An EVACS simulation with nested transactions

Documented here is the recent effort of the MISSION Kernel Team on an Extra-Vehicular Activity Control System (EVACS) simulation with nested transactions. The team has implemented the EVACS simulation along with a design for nested transactions. The EVACS simulation is a project wide aid to exploring Mission and Safety Critical (MASC) applications and their support software. For this effort it served as a trial scenario for demonstrating nested transactions and exercising the transaction support design. The EVACS simulation is a simulation of some aspects of the Extra-Vehicular Activity Control System, in particular, just the selection of communication frequencies. Its current definition is quite narrow, serving only as a starting point for prototyping purposes. (EVACS itself may be supplanted in a larger scenario of a lunar outpost with astronauts and a lunar rover.) Initially the simulation of frequency selection was written without consideration of nested transactions. This scenario was then modified to embed its processing in nested transactions. To simplify the prototyping effort, only two aspects of the general design for transaction support have been implemented: the basic architecture and state recovery. The simulation has been implemented in the programming language Smalltalk. It consists of three components: (1) a simulation support code which provides the framework for initiating, interacting and tracing the system; (2) the EVACS application code itself, including its calls upon nested transaction support; and (3) a transaction support code which implements the logic necessary for nested transactions. Each of these components deserves further description, but for now only the transaction support is discussed.

Auty, David↗
NASA NTRS1983

The water factor in harvest-sprouting of hard red spring wheat

Sprouting in unthreshed, ripe, hard red spring wheat (Triticum aestivum L.) is induced by rain, but sprouting does not necessarily occur because the crop is wetted. The spike and grain water conditions conducive to sprouting were determined in a series of laboratory experiments. Sprouting did not occur in field growing wheat wetted to 110% water concentration until the spike water concentration was reduced to 12% and maintained at this concentration for 2 days before wetting. When cut at growth stage 11.3, Feekes scale, Saratovskaya 20 (USSR) sprouted after 4 days drying, Olaf and Alex between 7 and 15 days drying and Columbus, recognized for its resistance to harvest time sprouting, after more than 15 days drying. Sprouting potential was enhanced after 4 wetting drying cycles in which any wetted interval was too brief to permit sufficient water imbibition to initiate sprouting. At harvest ripeness, grain water concentration exceeded spike water concentration by 0.7 percentage units. Following 6 months storage, 20% of the kernels in 300 spike bundles (simulating windrows) sprouted within 28 hrs after initiation of wetting to saturation (150% water concentration). Ninety percent sprouting occurred within 8 days in bundles maintained at 75% water concentration and higher, but less sprouting occurred in bundles dried to 50% water concentration before resaturation.

Bauer, A.↗
NASA NTRS2020

Attribution of Chemistry-Climate Model Initiative (CCMI) Ozone Radiative Flux Bias from Satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6-μm ozone band is a fundamental quantity for understanding chemistry-climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6-μm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Inter-comparison Project (ACCMIP) simulations. The principal culprits are tropical mid and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mWm-2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mWm-2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mWm-2). We found that AM3 and CMAM have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to difference processes. Overall, the multi-model ensemble mean bias is –133±98 mWm-2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation.

Aura Tropospheric Emission Spectrometer (TES) meas↗
DOE OSTI2025

Post-irradiation 1600°C Heating Test of AGR-1 UCO Fuel Kernels

Five bare kernels were selected from the U.S. Advanced Gas Reactor (AGR) 1 irradiation experiment Compact 5-3-1 to perform post-irradiation safety tests. The safety test involved heating the kernels in the Fuel Accident Condition Simulator (FACS) furnace in the inert atmosphere to a peak temperature of 1600°C and isothermally holding at this temperature for about 47 hours while collecting fission products released. This test was to assess the retention of fission products in bare kernels without the effects of the other TRISO layers (buffer, IPyC, SiC, and OPyC) or the graphitic matrix material. The bare kernels released nearly 100% of cesium and antimony, while they were able to maintain about 30% of europium, 50% of strontium, and the majority of cerium and ruthenium. In addition, about 48% of the calculated inventory of Kr-85 released during the test, indicating that kernels were capable of retaining a considerable fraction of fission gas K-85 during irradiation.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Physics and Components syntax to enable a systems-based approach to multiphysics

Simulations in MOOSE have traditionally used kernel and boundary condition classes to describe the equations. Downstream applications leveraged a system called Actions to define a pre-packaged discretization of the equations they solve. Unfortunately, the Action base class was very limited, and most applications implemented the same concepts in their Actions. This led to an increased maintenance burden and a reduction in coupling opportunities, save for the use of MultiApps which renders each input mostly independent. With the introduction of multi-system capabilities in MOOSE, there is growing interest in defining entire simulations of complex multiphysics systems in a single input file. By introducing a new Physics system, with its dedicated syntax and a new base class providing wide-ranging capabilities, we are now able to define multiple equations in a single input file in a compact and user-friendly way. With new interactions between Physics and the Component system, these equations can be defined on each component of a complex system. In this talk, we will present the capabilities of these new systems, their interactions, and how to define complex systems multiphysics simulations with Physics and Components.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗
NASA NTRS1991

Small convolution kernels for high-fidelity image restoration

An algorithm is developed for computing the mean-square-optimal values for small, image-restoration kernels. The algorithm is based on a comprehensive, end-to-end imaging system model that accounts for the important components of the imaging process: the statistics of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and display reconstruction. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernel values that restore the image with maximum fidelity, that is, the kernel minimizes the expected mean-square restoration error. The algorithm is consistent with the derivation of the spatially unconstrained Wiener filter, but leads to a small, spatially constrained kernel that, unlike the unconstrained filter, can be efficiently implemented by convolution. Simulation experiments demonstrate that for a wide range of imaging systems these small kernels can restore images with fidelity comparable to images restored with the unconstrained Wiener filter.

Reichenbach, Stephen E.↗
NASA NTRS2012

Helioseismology of a Realistic Magnetoconvective Sunspot Simulation

We compare helioseismic travel-time shifts measured from a realistic magnetoconvective sunspot simulation using both helioseismic holography and time-distance helioseismology, and measured from real sunspots observed with the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory and the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory. We find remarkable similarities in the travel-time shifts measured between the methodologies applied and between the simulated and real sunspots. Forward modeling of the travel-time shifts using either Born or ray approximation kernels and the sound-speed perturbations present in the simulation indicates major disagreements with the measured travel-time shifts. These findings do not substantially change with the application of a correction for the reduction of wave amplitudes in the simulated and real sunspots. Overall, our findings demonstrate the need for new methods for inferring the subsurface structure of sunspots through helioseismic inversions.

Sun-interior↗
NASA NTRS2018

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗
DOE OSTI2026

Inverse Mapping of the Collision Kernel and Wall Flux Scaling in a Tall Convection‐Cloud Chamber Using Local Sensors and Knowledge‐Informed Deep Learning

Droplet collision–coalescence is a crucial process in cloud physics, but accurately representing this process under different dynamical conditions remains challenging. A proposed future convective‐cloud chamber aims to investigate this key process, but the method for observing it remains unclear, even though it is theoretically established that collision‐coalescence will occur. This study serves as a proof‐of‐concept demonstration of how knowledge‐informed deep learning, combined with measurement data from local sensors in the chamber, can be used to estimate the collision kernels, which determine how the droplet size distribution evolves during collision‐coalescence. In addition to estimating the collision kernel, we also address wall fluxes, another uncertain but important process that acts as a source of heat and moisture in the chamber. Ensemble runs of large‐eddy simulations are conducted by scaling the wall fluxes and the collision kernel, while the measured flow and cloud properties are used as inputs for a neural network. Results indicate that this approach successfully maps the scaling of wall fluxes and the collision kernel with biases of approximately 1% or less relative to the range of the target data. This proof‐of‐concept lays the groundwork for future applications; when the real measurements are available, real sensor data combined with the trained model presented in this work will enable estimation of the actual wall fluxes and collision kernel.

cloud chamber↗
DOE OSTI2025

On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions

Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

"Source Term Modeling for Advanced Gas Micro-Reactors"

Maintaining the safety of the public, environment, and operating personnel is the most important factor in designing, operating, maintaining, and decommissioning nuclear reactors. In recent years, there has been a growing interest in the development of micro-reactors employing TRi-structural ISOtropic (TRISO)-coated particle fuel. In gas reactors, TRISO fuel plays an important role in the safety case for high temperature reactors because of the fission product retention properties of the fuel. This ability enables the use of a functional containment strategy for the reactor where multiple barriers are used to prevent fission product release to the environment. Part of the safety analysis of these advanced reactors is the assessment of radionuclide releases under normal and accident conditions through the multiple credited safety barriers. Using conservative assumptions, a mechanistic analysis can be performed to quantify these releases that combines the probabilistic assessment of failure with analytic solutions to radionuclide transport equations. Source term modeling for TRISO fuel has been performed for previous reactor designs; however, these models are outdated, in many cases proprietary, and need updates to be applied to the current state of TRISO fuel technology and alternative gas reactor core configurations [1]. Currently, the only publicly available source term assessment for gas reactors is an expert-based Monte Carlo simulation based on the effectiveness of the fuel kernel, coating layers, and graphite block in a modular high temperature gas reactor [2]. Thus, there is a need to develop a simple, versatile, and mechanistic model of fission product release and transport in gas reactor cores that could be applied to a variety of reactors through user inputs and reactor-specific radionuclide inventories. The release is calculated by the diffusion of the key safety important fission products through the kernel, silicon carbide (SiC), graphite for both intact and defective TRISO particles based on fuel and graphite temperatures in the reactor under normal operation. These releases from the fuel enter the coolant where they can plate-out on cooler surfaces. A clean-up model is included for designs with a coolant purification system to remove fission gases. This initial distribution of fission products in the reactor serves as an initial condition for potential releases under postulated accident conditions. The model then can calculate the fission product release for any transient temperature profile and fission product releases can then be used to assess radiological dose to the workers and the public using conventional dose tools. Data on the diffusion of fission products is based on historic German TRISO experiments and the more current Department of Energy (DOE) Advanced Gas Reactor (AGR) TRISO fuel development program. The model is coded in python with inputs and outputs in excel spreadsheets, as well as python plotting utilities to aid in the interpretation of the results. References: [1] INL, NGNP Mechanistic Source Term White Paper, INL-10-17997, July 2010. [2] David A. Petti, Richard R. Hobbins, Peter Lowry, Hans Gougar, “Representative Source Terms and The Influence of Reactor Attributes on Functional Containment in Modular High Temperature Gas-cooled Reactors,” Nuclear Technology, Vol. 184, p. 181-197, Nov. 2013.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1988

Convolution-controlled rotation and scale invariance in optical correlation

A method is presented for evoking a controlled, continuously-variable degree of rotation- and scale-invariance in optical correlation; the method is suitable for off-line computation of filters, though not for real-time computation. While a closed-form solution for the blur kernels has thus far evaded solution, a digital approximation method has been presented. A simulated correlation run with real, frame-grabbed imagery has indicated the method's desired performance. These Gaussian blur kernels can be replaced with box-car kernels or other blur kernels suitable for the given correlation-task.

Juday, Richard D.↗