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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Machine Learning Global Simulation of Nonlocal Gravity Wave Propagation

Global climate models typically operate at a grid resolution of hundreds of kilometers and fail to resolve atmospheric mesoscale processes, e.g., clouds, precipitation, and gravity waves (GWs).Model representation of these processes and their sources is essential to the global circulation and planetary energy budget, but subgrid scale contributions from these processes are often only approximately represented in models using parameterizations. These parameterizations are subject to approximations and idealizations, which limit their capability and accuracy. The most drastic of these approximations is the “single-column approximation” which completely neglects the horizontal evolution of these processes, resulting in key biases in current climate models. With a focus on atmospheric GWs, we present the first-ever global simulation of atmospheric GW fluxes using machine learning (ML) models trained on the WINDSET dataset to emulate global GW emulation in the atmosphere, as an alternative to traditional single-column parameterizations. Using an Attention U-Net-based architecture trained on globally resolved GW momentum fluxes, we illustrate the importance and effectiveness of global nonlocality, when simulating GWs using data-driven schemes.

Aman Gupta↗
NASA NTRS1978

Space qualification of optical instruments using the NASA Long-Duration Exposure Facility

The NASA Long-Duration Exposure Facility (LDEF), designed for the in situ testing of optical instrumentation in the space environment is described. The LDEF is basically a reusable structure which is three-axis gravity-gradient stabilized when flying free in space. The structure weighs about 8,000 lbs. and accommodates experiment trays weighing about 10,000 lbs. A vacuum exposure control canister is being designed for controlled exposure experiments. The LDEF will have an experiment power and data system and a shuttle bay environmental measurements system is being designed for measuring parameters such as acoustics, vibration, acceleration. The induced environment contamination monitor will evaluate the contamination levels of shuttle payloads. Experiments currently under development include the evaluation of active optical components and the study of fiber optic data transmission.

Clark, L. G.↗
NASA NTRS1985

Electric Field Containerless Processing Technology

The objective of this task is to develop the science and technology base required to design and construct a high temperature electric field positioning module that could be used by materials scientists to conduct containerless science experiments in a low gravity environment. Containerless science modules that employ electric fields to position and manipulate samples offer several advantages over acoustic or electromagnetic systems. The electric field system will operate not only at atmospheric pressures but also in a vacuum, in contrast to the acoustic modules which can only operate in atmosphere where the acoustic forces are sufficient. The electric field technique puts minimum energy into the sample, whereas the electromagnetic system can deposit energy into the sample through eddy current heat as well as physical mixing in the sample. Two types of electric field modules have been constructed and tested to date. One employs a charged sample and uses electrostatic forces to position and control the sample. The second type of module induces electrical polarization of the sample and electric field gradients to position and control the sample.

Elleman, D. D.↗
NASA NTRS1989

Graphical programming and the use of simulation for space-based manipulators

Robotic manipulators are difficult to program even without the special requirements of a zero-gravity environment. While attention should be paid to investigating the usefulness of industrial application programming methods to space manipulators, new methods with potential application to both environments need to be invented. These methods should allow various levels of autonomy and human-in-the-loop interaction and simple, rapid switching among them. For all methods simulation must be integrated to provide reliability and safety. Graphical programming of manipulators is a candidate for an effective robot programming method despite current limitations in input devices and displays. A research project in task-level robot programming has built an innovative interface to a state-of-the-art commercial simulation and robot programming platform. The prototype demonstrates simple augmented methods for graphical programming and simulation which may be of particular interest to those concerned with Space Station applications; its development has also raised important issues for the development of more sophisticated robot programming tools. Both aspects of the project are discussed.

Mcgrath, Debra S.↗
NASA NTRS1992

OSSA Space Station Freedom science utilization plans

Long duration exposure to an essentially zero-gravity environment is a phenomenon exclusive to the Space Station Freedom that cannot be duplicated on Earth. The Freedom Station will offer periods of time on orbit extending to weeks and months rather than hours or days, allowing for in-depth space based research and analysis to a degree never before achieved. OSSA remains committed to exploiting the unique capabilities provided by the Space Station as well as other space-based facilities to study the nature of physical, chemical, and biological processes in a low-gravity environment and to apply these studies to advance science and applications in such fields as biomedical research, plant and animal physiology, exobiology, biotechnology, materials science, fluid physics, and combustion science. The OSSA focus is on progressive science investigations, many requiring hands-on scientist involvement using sophisticated experiment hardware. OSSA science utilization planning for the Freedom Station is firmly established. For this presentation, this planning is discussed in three general areas: OSSA goals and overall approach, the current and on-going program, and plans for space station utilization. In the first area, OSSA addresses its overall approach to space science research, its commitment to transition to Space Station Freedom, and its top-level strategy for the utilization of Freedom. The current and on-going program is next discussed, focusing on the various Spacelab series of missions which are providing the stepping-stones to Space Station Freedom. Selected science results from SLS-1 and USML-1 are cited which underline the value of properly outfitted laboratories in space in which crew-intensive experiment interactions are possible. The presentation is concluded with a discussion of top-level goals and strategies for utilizing the Freedom Station by OSSA's Life Sciences Division and its Microgravity Science and Applications Division.

Cressy, Philip J.↗
NASA NTRS1998

NASA's Microgravity Fluid Physics Program: Tolerability to Residual Accelerations

An overview of the NASA microgravity fluid physics program is presented. The necessary quality of a reduced-gravity environment in terms of tolerable residual acceleration or g levels is a concern that is inevitably raised for each new microgravity experiment. Methodologies have been reported in the literature that provide guidance in obtaining reasonable estimates of residual acceleration sensitivity for a broad range of fluid physics phenomena. Furthermore, a relatively large and growing database of microgravity experiments that have successfully been performed in terrestrial reduced gravity facilities and orbiting platforms exists. Similarity of experimental conditions and hardware, in some cases, lead to new experiments adopting prior experiments g-requirements. Rationale applied to other experiments can, in principle, be a valuable guide to assist new Principal Investigators, PIs, in determining the residual acceleration tolerability of their flight experiments. The availability of g-requirements rationale from prior (mu)g experiments is discussed. An example of establishing g tolerability requirements is demonstrated, using a current microgravity fluid physics flight experiment. The Fluids and Combustion Facility (FCF) which is currently manifested on the US Laboratory of the International Space Station (ISS) will provide opportunities for fluid physics and combustion experiments throughout the life of the ISS. Although the FCF is not intended to accommodate all fluid physics experiments, it is expected to meet the science requirements of approximately 80% of the new PIs that enter the microgravity fluid physics program. The residual acceleration requirements for the FCF fluid physics experiments are based on a set of fourteen reference fluid physics experiments which are discussed.

Skarda, J. Raymond↗
NASA NTRS2006

Gravitational Focusing and the Computation of an Accurate Moon/Mars Cratering Ratio

There have been a number of attempts to use asteroid populations to simultaneously compute cratering rates on the Moon and bodies elsewhere in the Solar System to establish the cratering ratio (e.g., [1],[2]). These works use current asteroid orbit population databases combined with collision rate calculations based on orbit intersections alone. As recent work on meteoroid fluxes [3] have highlighted, however, collision rates alone are insufficient to describe the cratering rates on planetary surfaces - especially planets with stronger gravitational fields than the Moon, such as Earth and Mars. Such calculations also need to include the effects of gravitational focusing, whereby the spatial density of the slower-moving impactors is preferentially "focused" by the gravity of the body. This leads overall to higher fluxes and cratering rates, and is highly dependent on the detailed velocity distributions of the impactors. In this paper, a comprehensive gravitational focusing algorithm originally developed to describe fluxes of interplanetary meteoroids [3] is applied to the collision rates and cratering rates of populations of asteroids and long-period comets to compute better cratering ratios for terrestrial bodies in the Solar System. These results are compared to the calculations of other researchers.

Matney, Mark J.↗
NASA NTRSDate not supplied

Developing an Earth-Fixed Visual Reference to Aid Stability, Readaptation, and Egress After A Water Landing

Water landings present the worst possible sensory conditions for crews trying to orient and stabilize themselves immediately after long-duration spaceflight. Of the three sensory feedback systems involved in maintaining stability (i.e., proprioceptive, vestibular, and visual), none will provide reliable orientation information under the current water landing scenarios. The proprioceptive and vestibular systems are affected during spaceflight by disuse and adaptation to microgravity. Vision may not suffer the same degradation, but the visual environment within the enclosed space of a capsule, or interior room of a recovery ship, induces instability during wave motion. In addition to an increased fall risk, sensory readaptation is delayed until inputs from the three sensory systems can be synchronized with one another and aligned with Earth’s gravity. An Earth-fixed visual reference (EFVR) can be provided to increase crewmember stability and allow for earlier readaptation initiation.

B.T. Peters↗
NASA NTRS1976

Theoretical frameworks for testing relativistic gravity. V - Post-Newtonian limit of Rosen's theory

The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the post-Newtonian parameter alpha sub 2 (which is related to the difference in propagation speeds for gravitational and electromagnetic waves). Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific (but presumably special) form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity - and standard solar system experiments cannot distinguish between the two theories.

Lee, D. L.↗
NASA NTRS1984

Experiments on plants grown in space. Status and prospects

Space flight provides a unique capability to gravitational research by providing an environment in which gravity can be manipulated below the Earth norm of 1 to a state comparable to weightlessness. Although space experiments with seeds and plants have been conducted for almost 25 years, we are only now entering an era that promises the capability of routinely conducting controlled plant experiments in space. Results from experiments with higher plants and seeds flown thus far in both manned and unmanned spacecraft from both the USA and USSR are briefly summarized. An overview of the current status of space biology experimentation as it relates to plants is presented and present and future opportunities to conduct plant experiments under space flight conditions are discussed.

Flight Experiment↗
NASA NTRS2011

Influence of Sensory Dependence on Postural Control

The current project is part of an NSBRI funded project, "Development of Countermeasures to Aid Functional Egress from the Crew Exploration Vehicle Following Long-Duration Spaceflight." The development of this countermeasure is based on the use of imperceptible levels of electrical stimulation to the balance organs of the inner ear to assist and enhance the response of a person s sensorimotor function. These countermeasures could be used to increase an astronaut s re-adaptation rate to Earth s gravity following long-duration space flight. The focus of my project is to evaluate and examine the correlation of sensory preferences for vision and vestibular systems. Disruption of the sensorimotor functions following space flight affects posture, locomotion and spatial orientation tasks in astronauts. The Group Embedded Figures Test (GEFT), the Rod and Frame Test (RFT) and the Computerized Dynamic Posturography Test (CDP) are measurements used to examine subjects visual and vestibular sensory preferences. The analysis of data from these tasks will assist in relating the visual dependence measures recognized in the GEFT and RFT with vestibular dependence measures recognized in the stability measures obtained during CDP. Studying the impact of sensory dependence on the performance in varied tasks will help in the development of targeted countermeasures to help astronauts readapt to gravitational changes after long duration space flight.

Santana, Patricia A.↗
NASA NTRS2018

NASA GRC Compass Team Conceptual Point Design and Trades of a Hybrid Solar Electric Propulsion (SEP)/Chemical Propulsion Human Mars Deep Space Transport (DST) Vehicle

NASA has long been conducting studies which apply different in-space propulsion technology assumptions to the mission of sending humans to Mars. Two of the technologies under study that are considered to be the most near-term with respect to technology readiness level (TRL) are traditional chemical propulsion systems and high-power Solar Electric Propulsion (SEP) systems. The benefit of relatively low trip times inherent in using impulsive chemical propulsion systems to perform the full round-trip delta V is hampered by the large propellant mass required to perform these burns for human Mars missions. SEP systems offer the benefit of much lower propellant requirements to perform the same round-trip missions, at the cost of longer trip times. Traditionally, impulsive chemical systems are better suited than SEP when used in a gravity well, and SEP systems are more efficient than traditional impulsive systems when used in interplanetary space. A mission to Mars includes both of these scenarios, and thus several NASA architecture studies performed over the last few years have looked to combine the use of both SEP and chemical propulsion systems where they are the most beneficial to human Mars missions. This combined propulsion system concept has been referred to as a SEP/Chem hybrid Mars Transfer Vehicle and is currently shown as the concept Deep Space Transport (DST) in the March 2017 NASA presentation to the National Aerospace Council (NAC).

human exploration↗
NASA NTRSDate not supplied

A Notional Artemis Lunar Surface Exploration Package (ArLSEP) based on the Gandalf Staff Platform

Introduction: The Artemis program is planning to deliver crew and cargo to the lunar surface, but there is no current package for supporting lunar in-struments and experiments similar to the Apollo Lunar Surface Exploration Package (ALSEP). This abstract provides a possible concept for such a package using the Gandalf Staff Platform as a common core. Gandalf Staff: The Gandalf Staff is an early prototype system developed over FY’21/FY’22 using NASA Science Technology Mission Directorate (STMD) Center Information Fund (CIF) grants to de-sign, build and test “proof-of-concept” components. These components include a 24v battery powered monopole that powers a suite of subsystems, including a Graphical User Interface (GUI) for crew, surface voice and data communications, Lunar Search and Rescue (LunaSAR) navigation and communications, LiDAR, field site external lighting, 360-degree camera, and a geothermal instrument for measuring sub-surface temperature gradient. The staff can be carried independently by an Extra-Vehicular Activity (EVA) astronaut, or can be mounted into a tripod for “hands free” support at a surface site being investigated. The staff can be attached to an external solar array and power storage system for long-duration operations. [1,2] ALSEP: An ASLEP flew on each mission Apollo 12 to Apollo 17. For Apollo 11, a simplified packaged called the Early Apollo Scientific Experiments Pack-age (EASEP) was flown. Each package included a “Central Station” that provided the power and communications connected to a variety of instruments and sensors. The power was provided by a Radioisotope Thermoelectric Generator (RTG) fueled by Plutoni-um-238 generating 70 watts of power (initially, decayed over time) [3]. The communications system provide for direct to Earth data transfer from the lunar surface. Each pack-age was stowed externally in the Lunar Module (LM) Scientific Equipment (SEQ) bay with a mass up to 163 kg (Apollo 17). The crew unloaded the ALSEP from the LM and deployed the instruments on the lunar surface. Although designed to operate for only 1 year, many sites operated for up to 8 years successfully [4]. The Active Seismic Experiment (ASE) included 3 geophones for detecting seismic waves created by mortars and thumpers deployed by the crew. Other active experiments measured the lunar atmosphere, the heat flow in the subsurface, the lunar gravity and potential gravity waves, the lunar magnetic field, the solar wind and plasma interactions in cislunar space. Passive experiments included collectors for dust and cosmic rays, and retroreflectors for precise measurements of distance using a laser from Earth. The ALSEP program continues to generate insights into lunar formation and evolution. ArLSEP Concepts: The lunar surface science package for the Artemis program will hopefully exceed the capability of the ALSEP. There are multiple issues for discussion leading to the design of a new ArLSEP, needing requirements definition from the science community, NASA mission architecture, and NASA budget planners. 1. Delivery Mechanism Two possible projects currently provide capability to deliver scientific cargo to the lunar surface: 1) the Commercial Lunar Payload Services (CLPS) [5] and the Human Landing System (HLS) [6, 7]. Each project is controlled by a different organization within NASA and budgeted with different criteria although both support lunar exploration. The HLS system delivers crew (and potentially cargo) to human landing sites. If an ArLSEP is “predeployed” to such a site, the design must include power (either from the vehicle or independently) to keep the electronics functioning until deployed by the crew. If an ArLSEP is delivered on a vehicle after the crew is present on the lunar surface, safety protocols require adequate distance from the humans for impact from descent propelled sur-face regolith ejecta. This distance can not exceed the capability of the crew to walk (if no rover) to the vehicle for ArLSEP deployment. 2. Overall Guidelines The general design of ArLSEP will likely follow the ALSEP with a common system for communications and power; however, significant architecture differences between Apollo and Artemis exist. Power: The RTG will not be available for early Artemis missions nor likely follow-on Lunar Exploration Transportation Services (LETS) missions [8]. Thus, ArLSEP power must be supplied by solar arrays with sufficient battery capability to “keep alive” necessary electronics during any lunar surface eclipse period. Communication: The Artemis program is developing a series of communications satellites for lunar orbit to provide surface transmission of data and voice to Earth. Called “LunaNET”, this network is component useful for ArLSEP since south polar locations may not always have direct “line-of-sight” to Earth [9]. 3. Concept of Operations (ConOps) The general ConOps for ArLSEP is to deliver the package to lunar surface before the crew arrives, and then have the crew deploy the package after some period of time. This requires coordinated design (for power systems) and launch window (for schedule) on both the cargo and crew missions. Once the ArLSEP is deployed, it will operate autonomously for a number of years. It should be designed to be EVA compatible for crew maintenance and upgrade. 4. Notional Design (for discussion purpose only) The landing site near the South Pole is expected to have no eclipse cycle exceeding 5 days, so the “keep alive” power is 144 hours (6 days to include margin). A 12v ArLSEP will use rechargeable LiFePO4 cells, which are common in the Electric Vehicle (EV) industry. With a current of 5 amps and a 125 watt system, the mass is about 90kg. The comm. system and structure adds another 10kg, thus the “Central Station” is approximately 100kg. The solar power is collected on four arrays (each 2m above the surface), and the entire ArLSEP is designed to stow in a 2m x 1m x 1m volume. The experiment and instrument design will vary for each installation and add mass to the total (although they are expected to fit within the 2m3 volume). Seismic wave generation will likely not be provided with mortars, thus an electric “thumper” will be required. Active instruments such as imaging systems and sensing instruments will benefit from the additional power and communication capability provided by ArLSEP. Passive systems such as retroreflectors, witness plates, and cosmic dust collectors can be added to either the landing vehicle and/or the ArLSEP. With repeated HLS missions to the same human site, the ArLSEP can be expanded and easily maintained for long duration science collection on the lunar surface.

ALSEP↗
DOE OSTI2024

Anomalies in string-inspired nonlocal extensions of QED

We investigate anomalies in the class of nonlocal field theories that have been proposed as an ultraviolet completion of four-dimensional quantum field theory with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by the string field theory and ghost-free nonlocal approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired nonlocal extension of QED. We show that the vector anomaly vanishes as required by gauge invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in the scale of nonlocality. We also calculate the nonlocal vector and axial currents explicitly and present an illustrative example by applying our results to the decay of π 0 → γ γ . Published by the American Physical Society 2024

Abu-Ajamieh, Fayez↗
DOE OSTI2021

QCD thermalization: Ab initio approaches and interdisciplinary connections

Heavy-ion collisions at BNL's Relativistic Heavy Ion Collider and CERN's Large Hadron Collider provide strong evidence for the formation of a quark-gluon plasma, with temperatures extracted from relativistic viscous hydrodynamic simulations shown to be well above the transition temperature from hadron matter. Outstanding problems in QCD include how the strongly correlated quark gluon matter forms in a heavy-ion collision, its properties off-equilibrium, and the thermalization process in the plasma. In this work, we review the theoretical progress in this field in weak coupling QCD effective field theories and in strong coupling holographic approaches based on gauge-gravity duality. We outline the interdisciplinary connections of different stages of the thermalization process to non equilibrium dynamics in other systems across energy scales ranging from inflationary cosmology, to strong field QED, to ultracold atomic gases, with emphasis on the universal dynamics of non-thermal and hydrodynamic attractors. We survey measurements in heavy-ion collisions that are sensitive to the early non-equilibrium stages of the collision and discuss the potential for future measurements. We summarize the current state-of-the art in thermalization studies and identify promising avenues for further progress.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

Applications of SLR

Satellite Laser Ranging (SLR) has a rich history of development which began in the 1960s with 10 meter-level first generation systems. These systems evolved with order of magnitude improvements to the systems that now produce several millimeter single shot range precisions. What began, in part, as an interesting application of the new laser technology has become an essential component of modern, precision space geodesy, which in turn enables contributions to a variety of science areas. Modern space geodesy is the beneficiary of technological developments which have enabled precision geodetic measurements. Aside from SLR and its closely related technique, Lunar Laser Ranging (LLR), Very Long Baseline Interferometry (VLBI) has made prominent science contributions also. In recent years, the Global Positioning System (GPS) has demonstrated a rapidly growing popularity as the result of demonstrated low cost with high precision instrumentation. Other modern techniques such as DORIS have demonstrated the ability to make significant science contributions; furthermore, PRARE can be expected to contribute in its own right. An appropriate question is 'why should several techniques be financially supported'? While there are several answers, I offer the opinion that, in consideration of the broad science areas that are the benefactors of space geodesy, no single technique can meet all the requirements and/or expectations of the science areas in which space geodesy contributes or has the potential for contributing. The more well-known science areas include plate tectonics, earthquake processes, Earth rotation/orientation, gravity (static and temporal), ocean circulation, land, and ice topography, to name a few applications. It is unfortunate that the modern space geodesy techniques are often viewed as competitive, but this view is usually encouraged by funding competition, especially in an era of growing needs but diminishing budgets. The techniques are, for the most part, complementary and the ability to reduce the data to geodetic parameters from several techniques promotes confidence in the geophysical interpretations. In the following sections, the current SLR applications are reviewed in the context of the other techniques. The strengths and limitations of SLR are reviewed and speculation about the future prospects are offered.

Schutz, Bob E.↗
NASA NTRSDate not supplied

Global Ocean Mass Change Derived From Atmospheric Reanalyses

Barystatic sea level change is a significant climate variable and a gauge for water exchanges between land, atmosphere, and ocean, with consequential relevance to stakeholders. The monitoring and attribution of globally averaged sea level variations represents substantial challenges to the climate community. Atmospheric reanalyses provide a level of monitoring for elements of the climate system that are in communication with the ocean, including the atmosphere, terrestrial land, and the surfaces of glaciated land. Global atmospheric reanalyses comprise model output that is statistically adjusted to available observations. Potentially, reanalyses offer a climatic context to observed changes in water mass distribution. Improvement in the representation of the water cycle and in water mass conservation have been stated goals of reanalysis projects. Here, we assess the capability of atmospheric reanalyses to represent variations in the global water budget from the perspective of ocean mass balance. The purpose of this work is to provide a detailed evaluation of current atmospheric reanalyses and their ability to reproduce spatial and temporal variations in atmospheric and terrestrial water storage. A second goal is to identify and characterize recent apparent trends in the water balance. We examine the ERA5, MERRA-2, and JRA-3Q reanalyses with a focus on the radio-occultation observing period from 2007 to the present. For terrestrial water storage we also compare with ERA5-Land, a surface reanalysis. The primary validation is from the NASA/DLR Gravity Recovery and Climate Experiment (GRACE) and its follow-on, GRACE-FO. The Atmospheric Infrared Sounder (AIRS) onboard NASA's Aqua satellite is also used for evaluation of the atmospheric moisture budget. Comparisons reveal strengths and weaknesses in the reanalyses of each component of the climate system. Reanalyses agree closely on atmospheric moisture storage trends, although mean values differ. Reanalyses show significant differences in land water storage. They also apply large corrections to the land water budget. Finally, reanalyses have differing abilities in representing the surface mass balance over glaciated land. Using the observed gravimetry record, changes in the underlying glaciated land ice are examined as a residual.

Richard Cullather↗
NASA NTRS1976

The mesosphere

The mesosphere is an atmospheric region characterized by a negative gradient of solar energy absorption and temperature. Although the distribution of most minor constituents is dominated by photochemistry, vertical transport does have a pronounced effect on many of them. The basic dynamic principles are discussed along with their application to the important mesospheric motions: acoustic-gravity waves, tides, planetary-scale waves, and eddy motions. Oxides of nitrogen and hydrogen are also examined which strongly influence the balance of odd oxygen (O and O3). Brief discussions of the chemistry of carbon compounds and of excited species are also included. The chemistry of ionic species in the mesosphere is very important because it strongly influences the propagation and absorption of radio waves. Because of ion clustering and negative-ion formation, such chemistry is extremely complex. The current state of knowledge is discussed in some detail. The principles involved in constructing models for predicting the distribution of minor constituents, both neutral and ionic, are presented.

Poppoff, I. G.↗